1.sarwar_2982_phd_thesis.pdf

THE MECHANICS OF POWER HACKSA14ING AND THE CUTTING

ACTION

OF BLUNT TOOLS

by

MOHAMMEDSARWAR, BSc(Eng),

A Thesis Academic

Submitted

Awards

in

to

Partial

the

MIMechE,

for

Council

for

and Production

Sheffield

City

National the

Degree

Engineering

Polytechnic 1982

April

Collaborating

Neill Napier

AMIST

Philosophy

of

of Mechanical

James

CEng,

FulfilmenIC

Doctor

Department

MSc,

Establishment

(Services) Street

Sheffield

Ltd

of

THE

MECHANICS

AND THE

CUTTING

OF POWER IIACKSAWING ACTION

OF BLUNT

TOOLS

by MOHAMMED SARWAR SUMMARY

is part of and continuation in this thesis The work presented by the author the on the Mechanics out of carried work of Power Hacksawing, on behalf of a hacksaw blade manufacturer. Process parameters which influence have been during power hacksawing detailed explanation of the basic Power hacksaw machine characteristics investigated.

the metal. removal rate identified and thus a sawing mechanism-suggested. have also been

for is discussed., The problem of blade testing method -A -. the blade performance is proposed which is based assessing rate but is independent on metal removal of the machine index for This could be 'used as a quality characteristics. , blades. hacksaw is found to index This power performance breadth A theoretical vary with workpiece pitch. and tooth variation. of this model is used to give some explanation is evidence there that the gullet iiowever, size and goemetry influencing factors in the variation arc, more significant blade performance oL the workwith changes in the breadth blade the teeth. of pitch piece and blade teeth have revealed have that they Examinations saw of to the layer large compared of metal edge radii cutting blades that blunt indicating saw are basically removed, large of tools The cutting tools. action with cutting edge investigated been tests has and extensive simulation radii From the observations have been undertaken. of the chip formation and measurements of the relative mechanism during and machined surface cutting, of the tool position is thrown the light upon ploughing process. new some

field is proposed represents A slip-line which qualitatively the assumed chip state mechanism under steady 'formation The application of an empirical cutting conditions. between the chip tool length and relationship contact the the undeformed in conjunction chip thickness with field, with provides slipline quantitative correlation the test tool results of a single and qualitative point correlation with a hacksaw blade.

DECLARATION

has not been The candidate the CNAA or of a University

for another registered award of during the research programme.

Work on the Mechanics has been underof Power Hacksawing taken continuously City Polytechnic at Sheffield since 1970. The Candidate Technical was employed as a full-time to work under the direction officer PJ Thompson. of Professor from September 1971 to of Power Hacksawing on the Mechanics The Candidate August 1973. was then appointed as a in September City 1973. Lecturer Polytechnic at Sheffield Since the date of this has the Candidate appointment, on the Mechanics worked part-time of Power Sawing and A project associated work. on the Mechanics of Sawing was devised to register for the Candidate and an application degree was approved the award of a Doctor of Philosophy by, the Council. Since the date of registration the has been supervised jointly by Professor Candidate p j'Thompson DS Dugdale. title The present and Professor of the 'The Mechanics thesis: of Power Hacksawing and the Cutting Action Tools' of Blunt was defined and based on the work to the submission for undertaken prior of the thesis in 1982. examination had not been underA scientific study of Power Hacksawing to the work initiated Polytechnic taken prior at Sheffield*City in 1970. The work reported 2: in Chapter Characteristics 3: of Power Hacksaw Machines and Blades and in Chapter during Testing Performance of Hacksaw Blades was undertaken 1971 to the date of the Candidate's September the period The Candidate, therefore, registration. made significant to the work reported in these chapters contributions prior to his registration. The work on the Cutting Action of Tools arose from the earlier Blunt work on Power Hacksawing that the cutting and from the fact edges of saw blades the work on the cutting All of blunt action are blunt. the cutting tools relationships and its with characteristics 4,5 in Chapters contained and 6 has been of saw blades by the Candidate since registration. undertaken , by the Candidate The work presented for any other academic award.

has not

been

submitted

CONTENTS

ACKNOWLEDGEMENTS

(i)

SUMMARY

(ii)

NOMENCLATURE

(iv)

PAGE CHAPTER I-

INTRODUCTION

1

1.1

Sawing

1.1.1

Power

1.1.2

Hacksawing

1.1.2.1

Gravity

1.1.2.2

Hydraulic

1.1.2.3

Positive

1.1.3

Bandsawing

1.1.4

Circular

1.1.5

Relative sawing

1.1.6

for consideration Factors selecting cut-off method

1.2

Alternative

1.2.1

Friction

sawing

17

1.2.2

Abrasive

cut-off

18

1.2.3

Single

point

1.3

Survey

of

4 Hacksawing

5

Machines

6

Feed Machines

7

Machines

8

Dis. placement

Machines

9 9

Sawing

11

merits and requirements operations

cut-off

cut-off

previous

viften

methods

and shearing work

of

13

16

17

20 21

1.3.1

Sawing

1.3.2

The cutting

CHAPTER 2-

21 action

of blunt

tools

24

CHARACTERISTICS OF POWER HACKSAWMACHINES 30 , AND BLADES

2.1

Power Hacksaw Machines

30

2.1.1

Instrumentation

32

2.1.2

Observations

2.1.3

Load developed

2.1.4

Results

2.1.5

Stroke

2.1.5.1

The equivalent

2.1.5.2

Requirements

2.2

Power Hacksaw Blades

46

2.2.1

Hacksaw Blade Material

47

2.2.2

Hacksaw blade

48

2.2.3

Cutting

2.2.4

Slot

CHAPTER 3-

of the

load

characteristics

by hydraulic

from the machine of the

machines survey

35 38 39

saw number of te eth of the

33

40 44

saw stroke

specifications

50

edge geometry

52

width

PERFORMANCETESTING OF HACKSAW BLADES

53

55

3.1

Introduction

3.2

Formulation assess'the

3.2.1

A method for performance

3.2.2

Determination of the average of cut per-tooth

of a cutting performance assessing

test to of a blade the blade

depth

57

58

58

3.2.3

Determination of load per tooth

3.2.4

'The establishment of parameter efficiency

the

mean thrust

62

a cutting

64

and Testing blades

Procedures

65

3.3

Instrumentation for Hacksaw

3.4

Processing test of-cutting results depth of the average to determine force and the mean thrust cut, per blade thickness tooth per unit

66

3.5

Experimental testing of

Results hacksaw

Performance blades

68

3.5.1

The cutting

action

new blades

68

3.5.2

Comparison different

of blade pitches

3.5.3

Comparison different

of the performance of blades manufacturers

3.6

influencing Some factors of power performance hacksaw blades

3.6.1

Teeth

3.6.2

Cutting

3.6.3

Slot

3.6.4

Effect

3.6.5

Effect

3.6.6

Blade

3.7

3.7.1

of

performance

the

cutting

71

.

74

74

spacing

75

edge geometry

77

width

of blade of performance of

69

of

blade

width power

on the cutting hacksaw blades

78

82

tension on blade

85

Variation blades

with of blade performance different and pitch of 'of different breadth workpieces

93

Introduction

93

wear and its performance

effects

96

3.7.2

Theory

3.7.3

Explanation of the variation constant cutting

3.8

Economics

3.8.1

Process

3.8.2

Estimating and cost

CHAPTER4-

of the

of hacksawing

104 104

and the machine

costs

blade

102

life,

cutting

rate

CUTTING ACTION OF BLUNT TOOLS

106

110

4.1

Introduction

4.1.1

Material point

4.2

Experimental

approach

113

4.2.1

Experimental

apparatus

115

4.2.2

Preparation geometry

4.2.3

Workpiece material specifications conditions and cutting

120

4.2.4

Measurement of nominal depths of cut

120

4.2.5

between the base of the Relationship tool and the machined surface

4.3

Procedure

4.3.1

Analysis of overcutting undercutting

4.3.2

Chip-tool ments

4.3.3

Nature zone

4.3.4

Photomicrographs

110 behaviour

near

of tools

and cutting

forcutting

contact

of the chip

the tool

tool

and true

tests

length

and

measure-

and the dead metal

117

124

126 128

134

135

137

of Results

139

Results

139

4.4

Discussion

4.4.1'

Cutting

4.4.2

dead metal Ploughing, chip mechanics

Test

Steady

4.4.3 CHAPTER55.1

state

148

FIELD MODEL

SLIP-LINE

152

field cutting

theory 152

Development of the slip-line for cutting with a'blunt Stress

5.2.2

Calculation of cutting the model Discussion

5.2.3 CHAPTER6-

field tool

162

fields

5.2.1

167 forces

from 169 171

of results

PREDICTING THE PERFORMANCE OF SAW BLADES DERIVED FROMTHE SIMULATION TESTS AND THE SLIP-LINE FIELD MODEL forces and specific sawing

6.1

Predicting in energy

6.2

Comparison of a Single Blade Performance

6.3

Examination

6.4

Gullet

6.5

Discussion

CHAPTER7-

144 forces

cutting

Review of slip-line to metal applied

5.2

zone and the

Point

of the Pitch

cutting Tool

and 179

Effect

Size and Geometry of Results

GENERALCONCLUSIONS

180 181 183 187

SUGGESTIONSFOR FUTURE WORK

191

APPENDIX

193

REFERENCES LIST OF FIGURES FIGURES

ACKNOWLEDGEMENTS

The author

to his

supervisors

CEng, FIMechE, Professor

Thanks

I

DS

express

his

most

Professor

PJ

Thompson, BSc, MSc, DTech,

to

wishes

FIProdE,

Production

Engineering,

Sheffield

DSc of

due to Mr 0 Bardsley,

are

City

and

Sheffield

University.

Head of Mechanical

and the

Polytechnic

gratitude

Polytechnic,

of Trent PhD,

Dugdale,

sincere

for

authorities

and

of to undertake

permission

the work. is

The author Director (Services)

support Particular

extremely

Research

of

and the for

Limited,

in the earlier thanks

authorities

in the

their

latter

part

Mr R Roddis

for

their

Last, support

help

but

least,

on sawing.

Dr B Worthington discussions

and

of the project.

Mr J Taylor, and all

and co-operation

not

and

co-operation

valuable

Thanks are due to Mr S Leigh, Mr R Wilkinson,

James Neill

of the project

parts

for

of

their'interest,

go to my colleagues,

and Dr D Gillibrahd

encouragement ,ý

to Mr D Taylor,

grateful

thanks

and patience.

(1)

other

in the

technician

experimental

to my wife

for

her

staff work.

moral

SUMMARY

The work of

the

in

presented

work

carried

Process

on behalf

during

hacksawing

power

detailed

Power hacksaw

been

Mechanics

blade

metal

sawing

of

manufacturer.

removal

identified

rate

and thus mechanism

have

characteristics

machine

and continuation

on the

the

basic

the

of

explanation

of

a hacksaw

of

have

part

author

influence

which

parameters

is

thesis

by the

out

Hacksawing,

Power

this

a

suggested.

been

also

investigated. The

the

assessing

blade

of

problem

blade

on metal

power vary

used

of

the

cutting

removed, tools.

of

some

The cutting

used

as

that

the

in

the

index

is

gullet

found

to

variation. and

size

the

geometry in

variation of

for

A theoretical this

of

breadth

based

a quality

pitch.

the

is

machine

index

tooth

for

the

of

explanation

changes

blade

workpiece

and

teeth.

saw blade

indicating

be

influencing

edge

which

proposed

independent

factors

blade

is

and

evidence

with

Examinations large

is

A method

performance

breadth give

significant

performance pitch

to

there

However, more

This

workpiece

is

model

is

could

blades.

hacksaw with

but

This

characteristics.

discussed.

performance

rate

removal

is

testing

radii that action

(ii)

teeth

have

compared

to

revealed the

layer

saw blades

are

basically

tools

with

large

of

that

they

of

metal

have

blunt cutting

edge

are

radii

.1 been -has

investigated

tests

have

undertaken.

been

formation

chip position

of

some new

light

mechanism the

is

A slip-line

field

the

chip

assumed

cutting

conditions.

between

the

chip

of

a single

a hacksaw

and

and

thrown

is

extensive

observations

of

measurements

of

the

relative

upon

the

in

point

length

contact

conjunction

with

correlation

quantitative tool

under of.

and

qualitative

the with

steady

an empirical and

cutting,

represents

qualitatively

mechanism

the

process.

ploughing

which

proposed

during

surface

The'application tool

simulation

F-rom the

machined

formation

chip

thickness

provides

tool

and

the

rel4tiohship

undeforined

slipline the

state

test

correlation

field, results with

blade.

0

(iii)

Nomenclature

Symbol

Definition

a

material

constant

for

a particular

blade

type

b..

material

constant

for

a particular

blade

type

blade

type

ý

breadth

of a rectangular

material depth

Fc

constant

instantaneous

F

mean total

tM

stroke

fc

thrust

force

component

acting

force

component

(3.7)

(3.16)

(5.4)

force

thrust

force

mean total

force

component

cutting

instantaneous

thrust

workpiece

cutting

force

cutting

Ft

a particular

of a rectangular

Fc

cm

for

workpiece

during

component

the

cutting

(3.16)

(5.5)

acting

during

the cutting

(3.12)

instantaneous

cutting

force

per unit

thickness

per

I

tooth (iv)

instantaneous

ft

ta

average

per unit

thickness

(3.8.1)

per tooth f

force

thrust

instantaneous

force

thrust

per unit

thickness

(3.8.9)

per tooth

I

f

tm

force

mean thrust the cutting tooth its

during

from

taken

the

tooth

just

beginning

cut

K

cutting

k

Specific

k

per tooth

(3.12)

stroke

number,

thickness

per unit

constant

cutting

shear

yield

length

of

effective

energy

Y -73

stress

blade

length

m

constant

cutting

n

number of teeth

in

(3.18)

(5.4)

contact

with

the

workpiece

blade the of for

a fully

per unit

(v)

established

distance

(section

chip 2.1.5.1)

Symbol

Definition

force

n

cutting

nc

number of B. p.

nt

for

ation N

P p

S

teeth

having

a paitly

strokes

a rectangular

number of

formed

teeth

required

deform-

which

number of

of

hydrostatic

make contact

teeth

the blade

teeth

stress

(5.2)

cutting

edge radius

stroke

of the saw

(0vi

to saw

workpiece

stroke

equivalent

pitch

the workpiece

workpieces

number of cuýPing

cutting Ne

with

(3.8.6) zone

through Ne

in contact

teeth broad

number of

(3.8.1)

index

(3.5)

during

the

Symbol

Definition

t

blade

width

w W

width

y

length

thickness

of

the slot

produced

of

the tool

(5.4)

by made cut a tooth of length

critical

Yc

N

zone

ratio depth

instantaneous

6s

to fully

the material

of

stress

thickness

Z

of cut

made by a tooth

a deformation

establish flow

(3.6)

in

increase

slot

of cut per

depth

produced

tooth

per cutting

stroke

6'a

average

depth

of cut

per

tooth

one stroke

A

PQ

undeformed

chip-tool

chip

contact

(vii)

thickness

length

(5.8)

(5.4)

measured over

Symbol

R

UP

.

Definition

contact

workpiece-tool

at

the flank

(5.4)

rake angle

UA

friction

angle

apparent

coefficient

shear plane angle chip S B

stroke

angle

n

(3.8.3)

= tan-'*UA

of

friction

angle ion

of rotat

of the slip

lines

(5.2)

(3.8.11)

factor

efficiency

of

the

fan

field

in

the

slip

(5.4)

Brand

')e

Refers

to

Brand

'Z'

Refers

to the 3 TPI blades

the

4,6

(Viii)

and 10 TPI

blades

line

field

CHAPTER 1

... INTRODUCTION

The problem

of cutting-off

practically

every

operation

carried

surprising

that

is

for

a routine

cut-off

stock.

lack

of

and that

there

and difficult

foreman

are frequently areas to

foul

to

of the cost

per piece(3). the present

work is

the part

of manufacturers

that

and economics

of power hacksawing

-1-

which

a significantý

the growing

both of

control

are complex.

increased

of the remains

for

the factors

away

stores

can account

out

has been receiving

Furthermore,,

The fact

carrying

it

that

and the operation

and machines,

it

assign

will

up.

housed in

be simple.

part

have

is. no need to

on the principle

cutting-off

hacksawing

such as that

task,

operations

realisation)on

interest,

to a sawing

appears

is

Many reasons

common operation.

that

for

it

Therefore,

the

machines

The reason

the first

Often

machines

common to

work has been done to understand

from the main production sawing

is

sawing

methods.

learn

to

easy

out on bar

operation

a new trainee is.

this

better

consider

Often,

of this

the problems been given

industry.

so little

is

to size

material

blades

the mechanics Alsopower

competition

from

off

processes,

the British

Standard

cutting

other

band as and circular such

sawing. Whilst

the

etc, for

hacksaw blades regarding

for

specifications

and does not

have experienced

and users establishing

standard

consistency

in test

revealed not

that

contribute in

requirement normal

mechanics affecting

metal

machine

one of

the

the

test

data.

conditions

removal

been primarily

and in

obtaining

have were

methods

which

characteristics, reasons

for

the has been

Hence, there

the machine

sawing process

Most of the early

author

testing

to

working

of the

has

blade

in

power hacksaw machines.

by the

to identify

difficulty

procedures

data using

the

of

inconsistency

under

testing

existing

independent

could

of hacksaw blades

considerable

investigations

Preliminary

power hacksaw

include

Thus, both manufacturers

testing.

dimensions

of hacksaw blades

to tes. ting

relates

standard

hand use only

blade

BS 1919: 1974 gives

characteristics

and to investigate and the variables

work on cutting-off

concerned with

circular

and band

between comparisons cost altbrnative and sawing processes.

Whilst

the

rate.

published

these alternative

-

a

processes

are

frequently,

than

quicker

higher.

in many applications

on the

processes

alternative

power

Whilst

impact

unchallenged(4, i-Z)Afactor

remain

is

manufacturers

machine,

potential

field

fifty

years

of

of prime

these

of

power

hack-

field

is

likely

to to

interest

of power hacksawing

the blade of

(3,4)

costs

a significant

which

the. costs

by developing

be reduced can the

if

that,

the

remains

power hacksawing

for

of application

their

application

be deniedthere

sawing cannot

hacksawing

and the

saw be

will

application

widened. the

During been

past

devoted

to

the

blade

or

blade

material,

developing

machine,

process,

work critically

both

The factors

with

the

methods

metal

improvements some and

in both

are proposed,

which

hacksawing. of power

-

the

hacksaw in

of applying

the

the

have been achieved. the metal

and machine

controlling

lead can

of

some improvements

examines

saw blade

has

attention

geometry

handling, work

load and mechanised The present

the

although,

together

little

very

removal

characteristics.

rate

the blade

removal

are outlined,

and saw machine

to a reduction

in the cost

are

blade the of

Examinations large

cutting

Thus

extensive

1.1

SAWING

over

to the the

perform

the

stock

and shapes; company it

is

necessary

has

simpler

cutting-to-size

to

requires

this to

the

the mechanics

tools

of the

however pay

and more

sawing

could

in

merely

workpiece,

fact

is

buy-in

introduces and, in

the

Such a

the majority

that

to to

prepared

a service

the

of

to

out

carry

this lengths the

which

majority

economical

the

cases, b asic

in house.

operation

is the narrowness of cut,

and cutting-out

operations.

-

go

and

some way prior

to

in

machines

The alternative

sawing

for

for

operations.

be cut

shapes

ready-to-machine

suitable

schedule. of

of machining

cutting-off

blunt

point

One of the major advantages of sawing over all kinds

thickness.

chip

single

due to the

exists,

operation

primary

uncut

operators

finishing

a machining

starting

Machine

select

stock,

in

be no need

would

shop.

rarely

situation of

was delivered

there

working

a metal

with

to investigate

out

raw stock

and sizes,

with

a

process.

removal

all

tests

simulation

metal

If

compared

edge radii

have been carried

have shown them to-have

teeth

other in both

Most sawing

stock

the cut-off

perform

machines

is cut

where large

out operations, removed, vertical

contouring

for

one of

tlýe price other coupled

the

the

of

types

of

with

types

in

industry.

blade

is

tensioned

the

the blade

return giving

a discontinuous the

than

cheaper

popular

initial

cost) has

second half lifted

cutting

I

-

of

the

in the bow,

half

The

of the cycle

of the cycle,

clear

action,

enabled

the workpiece.

during

only

is

drawbacks

over

designed

has kept

motion

and adaptability,

achieved

During

blade

made the

machines

The low

back and forth is

sawing

relatively

flexibility

strokep

to be one of

the

machines.

a single

and reciprocated

of operation.

out on

blade

the

of of

in

saw machine

sawing

the

In hacksawing,

cutting

are

are carried

motion

first

the hacksaw to remain

action

Cutting-

saws.

bandsaws and holesaws.

The simplicity

power.

job

this

accomplish

of material

pieces chips,

back-and-forth

The simple

that

Hacksawing

Power

hacksaw

tiny

than

rather

1.1.1

Machines

of

to subsequent

prior

bandsaws and circular

hacksaws,

include

length

to a workable

operations.

machining

where a piece

operation,

the

of the workpiece, which

operation7.

is

considered

Despite

this

disadvantage, action

bandsaw,

the

of

is

less

dependent

bar

is

for

minimum

solely

likely

can be left

skill.

rate

available according

between

the

feed machines corrmon)machine

large

diameter

Blade

replacement

blade

is

material

removal

fed machines

and gravity

loads

controlled,

rates

are

developed.

to be a process

force

There-

in which

unlike

the

most

processes. be divided can

into

two broad

to the method used to develop and the

and hydraulic is

the

by the thrust

removal

material

The machines

load

and less

tension

when cutting

may be said

removal

categories,

method,

and easy to repair,

hacksaws

and workpiece

by hydraulic

hacksawing

material other

blade

a given

fore,

many other

and tested

quick

operator

even

Machines

Hacksawing

controlled

a tried

or

cheap and simple.

relatively

achieved

periods

equally

As with

blade

on correct

long

and require

For

is

Furthermore)power

to run-out. unattended

remain

accurate,

consistently

reliable,

continuous-cutting

machines.

hacksawing

processes,

the

hacksaws

alternative

more popular basic

to

as compared

the positive

-

workpiece,

machines.

the

namely)gravity

A third,

displacement

but not

machine.

Power hacksaw machines

for

are used mainly

cutting-off

operations.

In this ion

for

gravity

type

duty,

the

load adjustment.

load

of light

load

developed

is

In many of these is

fixed,

adjustable

masses

The thrust,

load

(Figure

stroke

is usually

thrust

saw bow.

thrust

with

provided

cutting

the

feed of the of

which

of machine,

general

magnitude are

Feed Machines

Gravity

1.1.2.1

although on the

device

the

stroke.

capacity is

ideal

is

only

cut

of

at the beginning

acts

type

of machine

occasional from mild

sections

diameter

where the cutting

and

requirement

of workpieces

to be

flat

shaped sections

and

steel

up to 6 inches

are

displace-

and the configuration

and gravity

machine

the

has a workpiece

generally

small

workshop

thrust

and the end of

for

the

for

of the cam operated

150 - 200 mm (6 and 8 inches)

construction type

This

over-arm

between

ranges

tubular

which

the

some machines

2G), due to the reciprocating

ment of the over arm mass and the action lift-off

by the

machines

throughout

varies

construct-

feed

limited.

-

complex diameter.

the applications

Due to the for

this

light

1.1.2.2

Hydraulic

The thrust this

force

type

Pressure

between

developed

may be developed back-flow from

performance heavy duty

from the

of

fully

automatic

feeding

of

and unloading

bar

form, stock, etc.

incorporated bow saw

combined with

saw blade.

with

in

to

The feature

of

power

machines

machines

are the most common and develop

loads for

than machines

sawing without

of other problems

skill.

-

type

better typesof wide or

automatic sizes

down-feed

the

to

makes the machine

suitable

the tougher

a univers-

predetermined

for

cutting

by

semi-automatic

for

provisions

these

machines,

have a very

available

cutting-off

in

allows

The advanced

hacksaws

and are

operation

range

may be

these

some of

system which

electro-hydraulic

by either

cylinder

has been introduced

action

hydraulic

controlled

ally

In

pump.

of control

means of an arc cutting

load

device.

or the pressure

system,

in

and the workpiece by a hydraulic

in the

a separate

flexibility

greater

the blade

is

of machine

a restricted supplied

Machines

steels

and alloys., greater

These

thrust

and have a reputation

and requiring

minimum operator

1.1-2.3

Positive

Whilst feed

these

Displacement

Machines

not

as popular

or hydraulic

removal

rate

device,

giving

during

machines

prone

stroke-since

the

rate

hacksawing,

screw

of machine

Positive

is worn.

in thrust

to variation

directly

loads

thrust

can

blade

premature

of penetration

between two shrouded,

Pf-the

The band travels

workpiece.

the teeth

earlier

fed against

metal

and were used strictly introduced

out

about

is

wheels,

blade

for

the cutting

of the of the

operation

in a continuous

motion,

the workpiece.

cut

off'methods,

agolbrought.

due to the

-

tensioned

and part

sawing bands were wide

50 years

Furthermore,

band,

small

(over

25 mm),

narrow

blades,

contouring throat

capabil-

clearance

loads arise

cutting

a continuous

the

rotating

exposed to carry

band is

is

blade,

An endless

operation.

ities.

type

giving

are not

of the constant

Bandsawingjunlike

Whilst

available

Bandsawing

1.1.3

with

This

when the blade

the cutting

as a result

feed.

of the blade

particularly

displacement

are

by a mechanical

controlled

a positive

to overloading

failureq

gravity

hence; blade; the metal the and,; of

directly

is

as the

a few machines

machines,

feed the rate where

lead

are

machines

of

teeth.

bandsaws,, they were limited

the early design, long

the length

thus

as the

been modifiedýto intentionally is

give

the machine

with

a gravity

fed

systemjcontrolled

25 mm (I

inch)

deep blade,

and accurate

work

ation

is

of machine

for

high

necessary

for

incorporate

allow

to

the toothed

face

into

bandsawhavino,

by a dash-pot

and using

the most popular

machine

cutting

of

for

general

solid

bars.

175 mm (7

about

0 a

fabriC7 This

type

diameter

inches)

grades

and reliability,

accuracy

the bandsaw machine in the design

capacities innovations

the cutting

of

not

only

of difficult

heavy duty

0

-

to construction

diameterst

down-feed., to power

alloys., such as nimonics

and titanium. 10

and to

has been

manufacturers

(18 450 inches) to up mm in the hydraulic

steel

it

high

for

day requirements all

cutting

production,

introduce

also

purpose

suitable

to meet the present

In order

having

limited

have

steel.

mild

volume

machine

machines

throat.

is is

be a's

clearance, ýby

so that

A general

categories.

available.

only

bandsaws can be divided

two broad

This

could

modern

throat

the blade

hacksaw machines,

As with

However

adequate

twisting

line

in

of the workpiece

throat.

machine

in use by the basic

-

but

Sawing

Circular

saws have a continuous

Circular having This

operation

hand-loaded

to a milling

operation.

the

and the

vertical

feed,

straight

line

horizontal

from the back. motion

as a vertical The benchjor installed in a small

devices

for

The

loaded

type

and

semi and then

saws are built

circular

type

application

power

feed mechanisms

basic

suitable

speeds.

inexpensive,,

large,

very

head and variations

rocking

pivot

of rotational

operations.

automatic

alternate

range

handling

material

Modern production

for

to

use blades

action,

from the earliei;,

range

models

incorporate fully

similar

available

machines

most

and a large

many teeth, is

cutting

size

engage

feed

together

on the

of the

particular

With

the blade

is

basic

On machines

fed

into

feeding system,

system and is

a general

workshop, provides

-

11

a rugged

a comýlete

-

is

this

duty

designed

the workpiece

arrangement

mountedmanual-feed with

downwards in a

travels

workpiece.

or rocking-head

floor

The choice

depends

blade

the

A third

feed

vertical,

and shape of component.

the rotating to

several

ie horizontal,

of these.

of machine

with

is

a

as efficient

arrangement.

circular

saw.,when

bandsaw or hacksaw cutting

facility

for

the

features

having

widely

present

choice

the cut

bandsaw will

not

require

and will

Compared with

the blade

in excess

types

for

width

requires

(15 inches) 400 mm up to removal

rate,

hacksaw is is

often

lower

similar

circular

capital

loss

12 -

mainly more power Although for

economically

cost

work

metal

bandsaw the and of If

however

account

,, due to the thickness

sawing becomes amore

of cutting.

capacity,

capacity.

factor. (loss

circular

high have a and

diameter

a dominant

kerf the of

taken

blade),

the

in material

sawsjthe

considerably

be used reasonably can saws

circular

of the component.

quickly(i5).

similar

bandsaw hacksaw of or than a

and

required

and bandsawing.

savings

of cut-off

machine

are

etc,

150 mm (6 inches)pthe

of

very

reloading

in-

a difficult

with

length

the

show any significant

other

heavier is a saw because

is

is

sawing

circular

is usually

length

magazines,

engineer

saws,,

length,

production

production

factor

circular

component

quality

to make between

The deciding If

high

the

automatic

loading

of

choice

where

used

Fully as dial-in

such

gauging,

process.

often

fabricator.

small

expensive

of the

method

Relative

1.1.5

merits

and requirements

design of

and operation,

sawing

of

operations

The simplicity

due to its are

limitations

cutting

half on

only

fact the and utilised. achieve (i)

that

Some of the improved

the

of

not

the

features

A range of cutting

Means to regulate

slow

speed,

cutting

blade the of

is

in a modern hacksaw which

are: speeds,

stroke,

the

length

the

all

ie

mode of operation,

stroke,

performance

the cutting (ii)

with

hacksaw hasin the grow made popularity. cost,

low initial Its

coupled

uniform

and a fast and monitor

over

return

stroke.

the cutting

pressure.

Adjustable

(iii)

(iv)

Automatic return

(V)

stroke.

of the blade

relief

on the

stroke.

Some means of indicating

blade

and correcting

tension. (vi)

Automatic

stopping

device

complete.

13 -

when the cut

is

Power hacksawing

is

low cutting

operation.

rate

forms

the metal

and machines,

I

the., 6utting

far

blade

the kerf

1.0

mm; andbandsaws

a need

the

the required

finish

blade

accuracy,

obtained.

is bandsaw a this

rigidity

size

Some of

the

per cut

with

differences

in

are; for

at

At times

mm.

increased higher

loss

with

limited

to about guides

thickness,

lo'ss.

kerf the of

bandsawingpa

wide

and the desired

of section

cut

750 mm (30 inches),

are so far

apart

at

rates

production

the cost

may be

there

blade

The maximum diameter

the blade

lacks

in a circular

factor

and shapes can be cut

of materials

variety

2.5

for

to low kerf

In addition

to

between

compromise,,

to provide

loss

3.5 to 10 or even 20 mm; hacksaws 2.0 to

saws

to

saw may be

circular

essential

losses

Although

saws.

the kerf

the

tooth

in bandsawing

rates

a critical

Due to

thicknesses,

circular

is

which

greater, materials.

expensive

efficiency

a bandsaw,

than

30-40% greater is saw

of a high

rate

removal

cost,

materials,

modern circular

with

are more comparable

4.0

of bandsaw blade

the developments

With

as a low

thoughtof

generally.

that

on

above the

rigidity. features

to

be considered

14 -

when selecting

a

bandsawing

A range

band

of

different

(ii)

are: -

machine

speeds

newer types

of blades

The machine

should

power available (iij)

(V)

Rigid

and wear resistant

vices

necessary

for

rate,

loss

method. (i)

sawing

force

when sawing

designed material.

cost for

blade

guides.

rates.

fixtures

sawing

limited

of work.,, it

of blade

with

types

however,

size

etc.

effective,

Some of the reasons Initial

removal

application.

angle

can be cost

and variety

adequate

metal

and clamping

range of sections;

small kerf

feed

Adequate

and have

devices.

tensioning

Circular removal

high

Blade

Controlled

(vi)

available.

be rigid

for

cutting

to use the

and able

materials

for

suitable

a high

of metals

when taking

metal in

account

a

of

may be a more expensive

are: is high. and must be

of work and workpiece

Sharpening,

15 -

re-tensioning

(bý

peening)

and

add to the cost.

rebalancing Blade

is

time

change

than

greater

hacksawing

in

or bandsawing.

damage from hard

Blade

frequent,

is cheaper

to use a hacksaw or bandsaw.

of

the

of

teeth

saw blade

circular

spaces

by

and by the

is

then

limited

highest

feed

per

it

by

limiting

an important

swarf,

can be

etc,

and if

practical'factor, is

damage is

scale

a problem,

The performance clogging

spots,

tooth

which

usable(19).

1.1.6

for

Factors

Consideration

when Selecting

cut-off

Method

(i)

(ii)

Machinability

Dimensions

of the workpiece

material.

of the workpiece. 0

(iii)

Accuracy

Kerf

Metal

of

cut

- run

out.

loss.

removal

rate.

16 -

(vi)

Cost

(Vii)

of

Transmission

(ix)

of importance.

may be inter-related,

parameters

blade the of

strength

is

neither

Furthermorefthe eg increasing

introduces

in blade

increase or

an increase

above the beam in kerf

both.

costor

ALTERNATIVE CUT-OFF METHODS

1.2

Sawing is

one of a number of methods

only There

material.

are

not

generally

alternative

classed

cut-off

cutting-off

methods

which

these

below: -

Sawing

friction

The work expended between a stationary

for

Some of

as sawing.

methods are outlined

alternative 1.2.1

load.

of thrust

is by no means comprehensive,

in order

the list

are

pitch.

Cost of machine.

The above list

loss

blade. saw or

band teeth or

Blade

(Viii)

band

workpiece

is

a fast

moving

sufficient

to create

heat to soften

the workpiece

material

blade. the, of

Under certain

conditions

17 -

blade

band and or enough

near to the edge this

may be used

to

remove

metal

some conditions

than

blades

need not have teeth)but

A comprehensive

hardened

range

is

is

The method

the

breakdown

of

softening

of the material;

since

order

for

the

the

process

to

speed.

If

an attempt

ness. )the blade

of

limited

the

the the high

being

material

to approximately a workpiece

outj

carried

to maintain

which. in

overheats,

without

state

40-80 m/secand

is made to cut

blade

materials,

cut

12 to 25 mm. thick-

of greater

turn, leads

in

to excessive

wear.

Abrasive

1.2.2

Abrasive thin

be successfully

be sufficient

is

to

prior

occurs

softened

the

blade.

The thickness

bandsawing

materials.

due to

non-ferrous

a suitably

to

machine power should

friction

or for

cutting

similar

irons,,

which

speed must be high,

the blade

blade

cast

structure

reach

and adhering

melting

In

grain

do not

they

for

suitable

not

and other

steel

for

useful

particularly

stainless

steel's

can be an

they

can be cut by friction

of steels

and the process

sawing,

Under

sawing.

away the softened metal.

to carry

advantage

by conventional

faster

cut-off

Cut-off

machines use a grinding

bonded abrasive

wheels

-

action. and when

are used a wide

18 -

range

of

can be cutrespecially

materials

and hardness. are

wheels

The peripheral

extremely

is

for 2 seconds and

capital

of

low compared to a sawing machine power required

of the abrasive

costs the

downstroke,

simple

similar

systems

are used.

heads which

machine

capacity,

is

the

annual

to the cost

for

sections,

machines

of

There

are also

use on plates

100 mm diameter..

large

with

-

action,

machines

-

handling

have oscillating-

and lead

horizontal-traversing

and slabs.

19

the

up to about

and complex materials

a sawing

are

and may be

production

Some of the machines

simulate

rates.

abrasive

volume

or tubes

systems

special

machines

sections,

pipe.

can be equal

head

high

more massive coolant

cutting

for

bars

cutting

To cut-off

solid

and)furthermorethe

wheels

pivoted

used

commonly

for used

higher

times

cutting

an abrasive

of

the

itself.

machine

most

far

is

abrasive

when grinding.

brass

cost

strength

requires

HSS round

40 mm diameter

initial

the

of

and achieves

25 mm diameter

for 5 secs of

the

fast

high

with

operator

as are taken

precautions

The process

speeds

and; hence, the

high

very

same safety

Whilst

those

to improved

Single

1.2.3

lathes

Since

are the primary

on a lathe

cut-off

Traditionally, take

favourable

tip

approaches

conditions

a tendency towards

the

off

centre,

cut-off

methods. flat,

are narrow, is near

The loss

butlas

the

of

cutting

speed is

and there

its

cut

Furthermoreythe

occur

over,

cutting

wandering,

can all

cutting

progresses

workpiece.

flexing,

and

the outside

conditions

to jam as it

point

during

this

cut-

operation.

Shearing

relatively it

under

cutting

tool

single

of the workpiece,

cutting

the

sheariný.

are obtained,

favourabld.

of

the

of

tools

the centre

the tool

centre

possibility or

less

for

tools,

results

unfavourable

can produce

machine

When the cut

cut.

get

and

lathe

cut-off

a plunge

machines

basic the one of

is

diametert tool

cut-off

pOint

is

a typical

metal

seldom used in general

is probably

in bar rolling process

sheet

which

process

workshops.

the most common cut-off mills. involves

Incidentally, hardly

20 -

and it

is

Howeverj

method employed shearing

any loss

is

the only

of material.

SURVEY OF PREVIOUS WORK

1.3

Sawing

Although

the popular

cutting-off

frequent

in practically

all

has been given

attention

the behaviour have taken media,

place

Most of the earlier

descriptions,

cost

emphasis

particular the

between

comparisons

processes

work

previous

cases.

these

general hacksawing,

of

merits

methods,

cut-off

of each operation.

on applications been

(1,2,4,5,

with

and alternative

to

extended

alternative

have been outlined conditions

for

together per cut

a hacksawing

by Nelson

bandsawing

with for

the choice

affecting

either

when selecting

cost

of

work on sawing

has

edge has

of the cutting

include

cut-off

(3,8,10).

Some of the variables

A),

the cutting

been concerned

sawing

circular

or

developments some

and relative

principles

bandsawing,

Some of

published

the process

used for

majority

has mainly

6,7,9,12,14)

with

the

little

relatively

Whilst

the geometry in

sawing is

of

to understanding

on the materials

unaltered

remained

industries,

of the machine.

the blade,

ie

process

are given

comparative both

this

(4).

cutting

to be made

or bandsawing Some suggested in Table times

operation cutting

19 (Appendix and blade

and the hacksaw operation

21 -

figure bandsaw cut-off square

1 (Appendix will

A). faster

cut

than

minute)

per inch

The results

show thatyalthough

(on

of

a basis

a hacksaw,

may be greater

cut

the

band.

high

Nelson by out

(4)

have shown that

to an area of cut square applied

inches

of the apart

the lower'the larger

feed

More recently Metalworking

the bandsaw;

several Production

and circular

2, Appendix

appropriate

the

the workpiece,

furthermore.

hence, and Thus for

articles

1for

essential.

(13,15,18,19)

qualitative sawing,

for

22 -

has become

operation.

These

assessments

of hacksawing,

with

A) as to the Proper

sawing machine

in

the

stressing

method which

production

and

harder-to-cut

on sawing have appeared

'cutting-off'

make general

bandsawing

by the beam

may be applied.

hacksaw becomes almost

integrated an of

articles

can be

týat

must be placed,

which

limited

the power hacksaw is more practical

of this

importance

force

is

force

limited

The larger

the band guides

than

materials/the

(Table

The feed

sawband.

workpieces,

economical

a part

hacksawing. machine

carried

as compared to 140

inches

is

per

operation

Tests

bandsawing

50 square of

by a bandsawing

strength further

for

of

cost

bandsaw

the

the

cost

total

for

to

due mainly

inches

square

1the

a

some guidelines selection

a particular

of the

application.

indicate

They

solutions

possible (Table

3,

better

Appendix

performance

Production

Average

of

width

the

cut,

Furthermore,

teeth.

force

thrust

does not

take

teeth

setting,

or

do not

life,

hard

to all

the life

= Service

rate,

was accurately

longer

assessing

ie Capacity

the results

of

He has shown

giving

used for

(20),

in

in Metalworking

(18).

difference,,

price

the criteria

removal

metal

value,

for

requirements

of the performance

are better

of the blades,

performance

basic

the

has been discussed

minimal

However,

blades.

the

Some of

and made by Soderberg

a relatively

the

A).

blades

bimetal

for

the power hacksaw machines

comparisons

(20)

and their

encountered

with

hacksaw blades

different

problems

of bandsaws has been discussed

and some relative

that

the

some of

x

into

account

geometry

of

indicate

whether'

the

the

throughout

controlled

tests. It

from this

is apparent in

sawing

removal

rate

both of

the machine

bandsawing teeth

the metal

of the blade

the blade penetration

and the

information is

dependent

and blade. removal into

load

on several

In both is

andphence)cutting

23 -

by forcing

during

to achieve rate

of the variables

hacksawing

achieved

the workpiece required

the material

that

and the

the motion adequate

is based on the

of

0

of the metal

machinability either

being

a hacksaw or bandsaw to make a cut

efficiently

depends on how well

the applied

load

The literature

applications ences, taking

into

of the machine the

characteristicsp

differ-

cost

of the machine

that

a detailed

the blade

geometry

the

controlling

extensive

metal

study

and

removal

Circular

21-31.

dimensions

This

Sarwar,

rate

The cutting

on examination

et

al,

and see

machine controlling

metal

of blade geometry and

the effects using

parameters

out at

Bandsawing

Taylor

work investigated

the process

characteristics,

removalY -

on Hacksawing,

by Thompson,

sawing

references

work has been carried

Polytechnic

City

Sheffield

it

particular

been undertaken.

More recently

1.3.2

for

the costs

indicated

survey

parameters

process

had not

the

has

some effort

some relative

consideration

blades,

distortion.

without

a code of practice

and to highlight

and

or band transmits

showed that, whilst

survey

of

accurately

the blade

to the workpiece

been made to produce

and the

The ability

cut.

a more scientific

action

of

approach.

blunt

tools

of the geometry of hacksaw blade teeth

was found that

their

cutting 24 -

edges consisted

of large

large

which were extremely

radii

sharp,, single

nominally

conventionalp The hacksaw

tools.

cutting

a consequence,, been classified

hasyas

blade

point

compared with

as a blunt

tool. In conventional turning,

is

at

In

the

an advanced

blunt

single

icance

point

flank

the is

the

connecting

or crater

to

the

wear

large

(32) flank

tool

is

to be blunt.

considered

refer

as

of a tool

sharpness

have been defined

of

a tool

edge

force

conventional

diagram

have developed

(34,35)

to be the and tool

separates

the edge radius displaced

of the

or ploughed

edge.

Rubenstein

occurs

when the rake

shear plane

et al

angle.

received

(33),

from

In addition (32)

to the

and others

force

diagram

which

the forces

induced

by

and have shown that

around

material

and under

such a cutting F have shown that ploughing

(36)

angle

considerable

Albrecht

a more complete

tool

on conventional

workers.

force

the chip-rake

radius

has

tools

cutting

from many research

attention

the

tools

such operations

surfaces.

The signif

is

tool

surfaces

cylindrical face

stagepthe

which

edge radii

cutting

ie if

study

present

of

wear,

tool

with

associated

lack

the

etc,

milling

during

cutting,

metal

is negative

Connolly

25 -

and coincides

and Rubenstein

(35)

with

a theory

proposed

ness by considering

this

angle,

around front

material

During

ploughing

deformed

from

bulk,

the

have

40,41) istics

the

of

carried

out

metal

flow

the relevance

The results

to exist large

to exhibit

the

tool

is

and part

separating

without

(38,39,

researchers

investigations

into

the

character-

near

the

tool

point

using

with

the

implications

of

establish-

sharp

tools.

zone existed even with

of nominally

(42).

Heginbotham on abrasive

wear, considered

that near

materials

built-up

and Gogia

different

in

flank

the

under

and other

(37). impýlied

active

ploughed

a two-dimensional

not

to the action

reported

unstablejdead-metal appeared

tools

to,,

equal

of the material

part

sideways

is

(37) Yeo and

blunt

artificially

spread this

-so that

Palmer

process.

to

angle.

rake

was always

behind

of a

rake angle,

compressed

recovers

and elastically

plastically

is

tool

the-cutting

of

face

the workpiece

the tool.

negative

thanpor

greater

angle

at any rake

such that

sharp-

edge radius

a critical

existed

finite

of

cutting

a large

face with

there

They showed that

ing

the extreme

to form a rake

tool

to tools

related

which

a small, active) the tool that

edges,

Kregelski the

modes of deformation

26 -

tip,

and

did not

tend

as described (43), in his

transition of a surface

by work

between loaded

by a

sliding

spherical

Kregelski

concluded

discussed more

'piling

involving

a process

virtually

Previous

work

has

established

of

the

cutting

region

cutting

metal

conclusion

that

under

nominally

sharp

tools.,

far

force

is

is valid

or more appropriate thickness

the undeformed to the cutting

edge radius. tools

nominally the order

of 7pm

influence

and has

cutting

such that

the undeformed

conventto the

led

with

chip

thickness

the

ploughing

radius,

the concept

to cutting. relatively

and cutting

chip

thickness

edge

radius.

27 -

of

conditions'

edge

is

in

some of the

The cutting

(0.0003 inch)

cutting

behaviour

in previous

(33),

to

surface.

material

has been estimated

sharp

the

the

existed

However,

insignificant.

than

tearing

cutting

chip

greater

of a spherical

where the undeformed

the

than

greater

He further-

in front

to clarify

normal

plastic

loads.

edge and the

theories

and

indentation

the

phenomena which

unexplained

is

or

edge configuration

cutting

ional

cutting

on was ,

from plastic up'

indentor

the

light

under

transition

the

indentor

surfaces,

most

established

were

conditions

for

that

of indentati

of the

the radius

compared with

small

The depth

indentor.

of ploughing where

conditions small

compared

edge radius (32)

of

to be in

conditions is many times

are

In

Fig

23 presented the

shown that

here,

depth

of

with

also

achieved

the

cutting

compared

the blade

was new and the

20

The cuýting

blades

depth

various

was

to be in the range teethwhilst

pitch

wa*s found

achieved load

thrust

sawing

even when

to the blade

applied

on the

during

edge radius

Of Cut per tooth

30 um, depending

be 2-

of

has been

it

tooth

per

were found

edge radii

for 76 jim Pm -

the average

load

(21)

paper

cut

was small

high.

in

to

to the

applied

blade.

Preliminary

(23) Thompson

showed that the

where

conditions

formation

stages

of the cut,

orthogopal

the

than

cutting

of modes of chip

Furthermore,

which

cutting

was less

cut

combination

a transient

exhibited

the induced

behaviour

during

the

the geometry

reflected

cutting initial

of the

produced.

Previous with

of

were produced.

forces

chip

under

depth

a complex

edge radius,

out by Sarwar and

work carried

experimental

the

interest

where the depth

situation

the cutting cutting

work on metal

experimental

edge radius;

process

df

as is

hacksawing.

in the cutting

action

23 -

has not

cutting of cut

is

known to exist This

has

of blunt

led

tools.

far

dealt

less

than

in the metal to

a further

Whereas

most previous edge radii of

studies

relating

An experimental

in the present with

blunt

reported

tools

have been concerned to sharp

nature,

or

work extensive

have been related

led

to

tests

to this

29 -

the cutting

and have been either

tools

and the various

with

empirical

models I

have been carried

phenomena previously mode of cutting.

out

CHAPTER 2

2.0

CHARACTERISTICS OF POWER HACKSAWMACHINES AND BLADES

2.1

POWERHACKSAWMACHINES

discussedý)the

As previously

is basically

hacksawing

develop during

the

load

this

and the types

all

be removed on the return

should

hacksaw as

In

strokes.

cutting

blades

are

not

and the

controlled

blades

the

in power

rate

to the methods used to

according

between

loads

the

removal

force

thrust

are classified

machines

metal

designed

to

cut

workpieces

of machines

or idle on the

stroke, return

stroke.

The performance

were

machines

used

for

were: -

this

(i)

Wear tests blade

-rhe

was suggested

possibly

that for

characteristics

apparently

30 -

test

be accounted

machine

under

blades,

similar It

by different

when operating

hacksaw

have shown wide variation

when using

could

reasons

principat

by out various

carried

and machines.

variation partly

investigated,

manufacturers

in results bars

of the power hacksaw

characteristics

identical

this

and conditions.

settings

(ii)

Traditionally, power

saw,

force

the thrust

the

particularly

has been measured when the stroke

mid-cutting point

of

This

ment has been taken machine

(iii)

the

A more appropriate could

of

performance

to

of the

undertaking With

needed

tests carried

on a selection out,

those available testing

it the

at Sheffield

below,

in the

31 -

Limited

the

performance were

survey

City*Polytechnic,

of James Neill

effects

hacksaw blades. on

of power sawing machines covered

was

when

characteristics

described

The machines

laboratory

be defined.

to

whether

tests

which

work on the

in mind and by using

the above objectives

portable

examination.

completely

performance

instrumentation

This

load parameter

saw blades

sawing machine

measure-

stroke.

research

eliminate

its

by the

applied

cutting

There was a need to verify possible

type,

force

single

thrust

be used during

by a

and at the mid-

detailed

required

assumption

saw was in

as that

throughout

fed

gravity

position

blade.

the

developed

were

at the and those

by Wickstead

supplied

Limited.

Instrumentation

1 The basic

the

enable

load

between

developed

and the other

workpiece

instrumentation

of the

requirement

and to be easily

stroke

the blade

and the force,

of the cutting

components

to be measured continuously,

was to

in the

the position

against

hack-

to the various

adaptable

sawing machines. The components

of the cutting

the

by a Kistler

workpiece,

component

dynamometer,

workpiece

vice

blade

of

the

The output at

transducer, displayed loads

via

against

charge blade

camera. hacksaw

displacement. signals

oscilloscope Figure

1 gives

and associated

and the results a schematic instrumentation.

saw, were to record

plotter

At high reciprocating

were displayed

32 -

and the

speeds. of the on to an x-y

the

trans-

from the dynamometer

amplifiers

in the

of

displacement

slow reciprocating

speeds the output channel

signals

base

The position

a linear

force

three

on a special

machine.

via

were measured,

piezoelectric,

clamped

was measured using

ducer.

force

on a multi-

recorded diagram

with

a

of the power

The list

below

some details

gives

of

the

power

hacksaws

tested. Saw Machines

Type

Kasto

or Number

Principle Operation

of

UBS 240R

Hydraulic

feed

Kasto

VBS 221

Hydraulic

Wickstead

Hydromatic

Hydraulic

Wickstead

ACME

Hydraulic

Wickstead

Hydromatic

Hydraulic

Marvel

No 9

Positive

load characteristics

to show the thrust a thrust

machines, produced

for

force

M

These

each machine.

diagrams

for

has been the

using

above

the

load characteristics

of the

All

developed

thrust

33 -

loads

cam

of these

diagram

2 and obtained 1.

Observations

machines

angle

- crank

in Figure are shown machines in Figure shown arrangement. 2.1.2

fed,

Gravity lift

Rapidor

In order

feed

which under-

went considerable The position

cycle.

'loop'

load

angle

load

setting,

(ii)

Most

or idle

tested.

the most constant

stroke

load

some thrust

which

by the adjustment

eliminate

and

characteristics.

developed

machines

return

on the

was impossible

to

available.

The Kast o UBS 240R saw developed

a reduction

thrust

51 degrees.

force

at

for

The reason found but

it

this

No 2 with The load

andjin

was not

develops

with the

was seen on setting Hydromatic

when provided

saw.

was not

the case of the Wickstead progressive.

34 -

in

has not been

must be connected

effect

adjustment

of

characteristic

the Wickstead

linear

Hydromatic,

angle

mechanism which

A similar

thrust.

always

a crank

obviously

the hydraulic

(iv)

force

thrust

of

the

adjustment

on most of the machines No 9 saw developed

The Marvel

thrust to

relative

by dashpot

position

the cutting

developed

the

of

can be changed

crank

form

during

variation

2.1.3

The force

the blade

between

type

by a restricted

back-flow

be supplied may

from

the most common, and develop machines

of other

types.

' The thrust

hydraulic

machine

varies

considerably

ting

hydraulic the of

istic

5,

Figure

mechanical hydraulic flow

(21)

hydraulic and

housed in about

shown.

and, the fixing

assembly,

bow, are arranged the cutting _The

effect

so that

cutting

stroke,

rotate

clockwise

developed

taper

is

are

than by any

the

throughout

on the

cut-

character-

for

a small

is

principal

back-

restricted in

This

The slideway points

the

of

of a typical

carried

assembly.

edge of the blade of this

load

arrangements

operating

the swing-arm

the pivot

loads

diagram

The saw bow is

principle.

machines

system used.

shows a 'simplified

machine,

cylinder

thrust

4, and the variation

Figure

stroke,

These

pump.

greater

loading

3, or the pressure

Figure

system,

a separate

in the

the thrust by a hydraulic

of machine

may be developed

Pressure

device.

Machines

and the workpiece,

in this

developed

is

force,

by Hydraulic

Developed

Load

a slideway,

assembly

in the

swing-am

the blade taper

and the

exists swing-arm

such that,

durin'g

rotates

on the

between slideway. the inward

the blade and the swing-arm assembly about the pivot 35 -

point.

saw

This motion

causes

displaces flow

the flow

through

oil

develops

in

pressure

the pivot

about

in the hydraulic

the piston

is

swing-arm. load between

control

this

torque

and a torque

the motion develops

which

of the the thrustý

and the blade.

the workpiece

An analysis

(21) has the above mechanism of shown

the

shape

of

the

no load

is

developed

general that

such

it

makes

loading

for

loaded

to

easy

suddenly that

part

this

part

that

the

of

engage and disengage

the

the

small.

developed

is

7, high material

in the effective

loads

typical

The effect

lightly

The analysis

loaded

lightly, blade

see deflection

large cause

throughout

36 -

predicted

of those measured is

of blade

shows

also

at the mid-stroke

rates., which

wedge angle

does mean

during removed

cause considerable

removal

only

without

shape of the curve

when the blade

experimentally

6.

is

is

is

this

it

teeth,

the material

the general

by the above analysis

Figure a

is

stroke

Whilst

high and

stroke

a -onsequence,

maximum load

position.

the blade

Whilst

the blade

the blade

5, the

at

machine

stroke.

that

Figure

curve,

by the

or unloading

of

andyas

Figure

load

thrust

or the end of the cutting

begimitig

and

The back-

valve.

cylinder

-which opposes

point

It

the

to rise,

cylinder

deflection

variation

the cutting and material

stroke#

I

is

rate

removal

the mid-stroke

blade the of

istics

the magnitude

in particular

interaction

between action,

for

flow

a given

from

the end of the

and the cutting

by the machine

developed

maximum load

of

towards

These effects

to strong

mechanism prone

point

7, and to affect

Figure

developed.

loads

the

the

usually

position,

stroke,

cutting

displace

to

of

make this the character-

and the control

load

valve

setting. way in

The only

for

by the operator

of the

adjustment method

which

large

the

an attempt

control

and it

in

setting

difference

load

This

the cutting the parameter

'Assessing

cannot

the

stroke

a crude

doubles

that

the mean

characteristics,

load

a thrust

parameter to be

of the machine of the blade.

has been defined

enables

to be taken

does ignore

is

be assumed

machine

the performance

parameter

is by

and the workpiece. in

parameter

which

the machine

the blade

can be controlled

of conditions valve,

from the performance

the section

(3.2.3).

set

the characteristics

a mean thrust in

developed

has been made to devise

enables

eliminated

flow

between

acting

Despite

a given

adjustment

load

the

doubling load

load

for

load

the

which

the

37 -

any load into

effects

ofa

To do this and is blade'

variation

account. of thrust

given

during

However, load

applied

f

on the be seen

in

The

stroke.

return

success

of

this

parameter

may

9.

Figure

0

This

shows the number of

graph

through

force.

thrust different,

can be seen that

It

machines

trend.

This

curve

Brand'X'

6TPI

blade,

with

the machine

agree

used

results

reasonably

well

the mean

throughout

the general

with

characteristics

the

on the

obtained

the performance

represents

to cut

required

bar against

test

steel

mild

a-standard

strokes

of the survey,

machine

as far

eliminated

as

possible. 2.1.4

(i)

from

-Results

Slaw machines

the

the

and return

not

different

some apply idle

or

during

designed

normal to cut

use.

thrust,

force

thrust

load

partial

latter

This

stroke.

must have some effect

characteristic induced

Survey

do have widely

characteristics during

Machine

on the wear

Since normal

on the return

stroke,

probable

that

material

removed would occur on the return

This

could

observed

considerable

go some way to

by various

wear in relation

explain

hacksaw blade

- 38 -

the

blades it

is to the

stroke.

variations

testers.

are

(ii)

The results

and at

stroke

position

is not

an accurate

thrust

load,

If

characteristics.

for

performance

of blades,

9troke

A feature

effective to over-

considerable

a much improved

estimate a method

and provides

the order then

of accuracy

any production

the

assessing

providing

in saw

removal

material

the mean thrust

is measured. of the Saw

which was common between

that was many others and saw important

the

blade,

to another.

load

acceptable,

may be used

load

2.1.5

9 is

the

much of the machind's individual

of eliminating

Figure

and give

gives

thrust

effective

along

The method tends

load

load

The mean thrust the

4.

Figure

from one machine

variation

of

mid-point

saw is at mid-

way of measuring

the thrust

estimate

the method of

load when the

the thrust

measuring

(iii)

show that

clearly

between

relationships of the

piece,

stroke

length

are derived

the

saw machine

below.

39 -

the Wickstead

stroke

was fixed.

the breadth

Hydraulic Some

of the work-

and the effective

blade

If

'Ll

length

of the blade 10 it

From Figure

the workpiece;

with

makes contact

can be seen that,

P- =S+B

or

and

1=

(L) L max

(1) L

The final

expression

workpiece

to

for

length

Note the

limiting

the

enables

be determined

saw stroke. is

'B Of)

+

breadth

of blade

length

blade

a given

the

of

in contact

and

at any time

always The equivalent

of determining

For the purpose

the

a fraction

only

traverses

same fraction

tooth

which

contributes

number

one half

of a tooth

number,

To calculate the breadth

the

to the

equivalent

during removed

a stroke

of the

the workpiece

number of teeth

by each tooth is

determinedv

which

which

contributes

ie a

breadth number. of the

equivalent

made by all

edge of the blade

equivalent

traversed

breadth

of the workpiece

from a knowledge

of the cutting

any tooth

number of teeth,

the common depth of penetration

the width

e)

workpiece

equivalent

half one

determined be can

with

the

traversed

Thus the volume of metal

teeth,

this

of

to the

of

(N

teeth

saw

number of

teeth

and

teeth.

the

fraction

makes contact

the variation

of

in

tooth

this

is

number of teeth

in shown

is

factor

sum of these

the

all

stroke

teeth

during

the

by the pitch

the breadth

normal

(-1-2B+ (S - B) + -1-2B)n

is

the

teeth

of

number

chip

slot

some time

at

and debris

clearance

Sn

distance.

unit

per

geometric

efficient

most

for

situation

hack-

sawing. When S
When the piece

10 (b))

Figure

is

stroke

enclosed

section

clearance efficiency

than

smaller

some of the teeth

completely

centre

(See

at

the breadth

the centre

blade the of

the workpiece

within

of the work-

slot.

remain

Over this

the normal process of chip and debris

cannot

take

of

of the workpiece

place.

when n=

This

than

so that

stroke

or the area

of the workpiece

are clear

can take

N e

larger

is

fractions

10 (a))

When S >, B (See Figure

When the

The equivalent

10 divided

in Figure shown

under the graphs the teeth.

10.

Figure

place

is most likely

and some reduction to occur.

41 -

in cutting

S -1-2

Sn {S, +1-S Ei

Sn

or N e

It

is

this

seen that

they

may be more appropriate

it

in the centre

section

to since

'clog'. and

to become filled

likely are

as in the previous

same result

of the teeth

the effect

ignore

the

However,

case.

geometric

is

Hencep + '2S (-a) In B

or

Ne

-2

Sn {s

B

Hence Ne=S.

All

these

geometric

in the graphs workpiece

length

n=

efficiency

of the

(S,. L

42 -

B

11, in which

to the effective

the ratio

-S

have been incorporated

relationships

shown in Figure

breadth

shown against blade

n. n where

blade

saw stroke

the ratios

length

(B) L

of is

to the effective

Use of

11

Figure

The following machines

in

data use

Make

Kasto

(A)

Wickstead (B)

to

relate Sheffield

at

Effective Blade Length (in)

5.25

9.50

16.56

5.50

8.00

15.22

breadth

quoted

manufacturer.

on the

graphs

in -the

Figure graphs

are

points

B max L

. .

has been taken These

11,

hacksawing

Polytechnic.

Maximum Workpiece Breadth (in) max

by the

obtained

City

two power

Stroke S (in)

The maximum workpiece

from

the

575

.

525

.

318 361

to be that

two machines A and B.

s

are

shown data

Other

as follows:

Kasto

Wickstead

88%

87%

Percentage of blade length enclosed by the workpiece

26%

16%

3

Stroke

57%

68%

4

Reduced equivalent number of teeth (assuming 10 TPI)

30

38

Equivalent (assuming 10 TPI)

52

55

Percentage of blade which makes contact workpiece 2

5

length with the

efficiency

number of teeth 100% efficiency and

43 -

a.

11 clearly

Figure

half one

of the

the

blade

effective

and Wickstead

the Kasto

a fixed

efficiency

of the machine,

capacity

both

for

shows that

and maximum cutting

machine full

Saw Stroke

of the

Requirements

2.1.5.2

stroke the

over

be

should

stroke

length,

s

(1)

ie

0.5, =

are below

machines

this

limit.

b.

Another

11, is

Figure is the

general

conclusion

to be obtained capacity

the

of

have a greatly

stroke

sizes

with

a facility

metal ,,

be used that

blade

length

be

should

stroke

such

overall

within

of workpiece

machineýthe

should

the effective

breadth,

all

improved

of the blade

utilisation

For optimum efficiency,

efficiency.

with

for

A machine

adjustable.

possible

full

that)if

from

may be drawn.

which

would.

removal the

largest

is

consistent

and'workpiece

eg

max ce

The data

obtained

the Wickstead ie requires of workpiece

from Figure

machine fewer for

is

strokes a given

44 -

likely

11, indicate

to be more efficient,

per cut, thrust

that

with

load

larger

than

sizes

the Kasto

machine. From the analysis for

that

NF

tm

3, it

is

shown

workpiece

a given S=

in Chapter

given

constant

where N=

through

needed to cut

number of strokes

the workpiece

stroke

cut

through

either of the

of the the

shows that

This

the

increasing

for

additional

cost

thrust load

in providing

as load

be adjusted

be reduced,

be more uniformly

only but

45 -

be varied

on

was fixed.

stroke

because

this

is

If

the

would

also,

distributed

stroke

of the

such adjustment.

adjustment.

then not

or the

could

is presumably

this

by

may be reduced

load

to

required

strokes

but the

the above shows that

important

strokes

the

saws tested

The reason

of

workpiece

The thrust

hydraulic

However,

saw number

a given

saw.

developed

force

Ftm = mean thrust

just

as

stroke

could

the number of

the blade along

wear would

the blade.

This

would

influence

The major

this

reduce costs.

time,

is,

therefore,

sawing machine

out

in

any changes

12b thrust show and at

two different

It

was seen

load

speeds

that,

at

high

at

variations under

high

speeds7the

load

variations

of a cyclic

nature

to dynamic

instability

in the machine.

limiting

and its is worthy 2.2

of

effect

some further

which

on speed, is

a the

to

look

at 12a

F igures

speeds.

otherwise

labour

with

machine

for

would

have been carried

tests sawing

speed

in operating

speed compatible

Hydraulic.

performance

the

the direct

much benefit

Some preliminary

Wickstead

on the

in

therefore,

and,

at the highest

done.

work being

speed of the saw is

An increase

time.

cutting

There

sawing machine

of the rotational

cutting

required

life.

blade

improved

to

speed of the

Rotational

2.1.6

the

lead

the above machine identical

conditions.

developed

exhibited

was most probably

due

The instability

another

factor

which

consideration.

POWER HACKSAW BLADES

Although different

the basic from that

operating of other

motion of the hacksaw is sawing machines,

46 -

the material

the blade

from which

is constructed

is

similar

to bandsaw

blades. Hacksaw Blade Material

2.2.1

Power hacksaw blades materials:

in two different

are available

a

a.

blade

All-hard)one-piece Tungsten a hard

will

alloy

or

sometimes used if

a stainless;

more

be made of molybdenum steel,

better

toughnessv

Standard

soft

is

steel

made of high

jobs.

blades

The all-hard

commonly

for

and often

metals,

are

the

which

provides

and heat

sometimes

expensive

for

cut

all

of

resistance.

used

'one-of-a-kind'

is

blade

often

molybdenum HSS blade

and least

used

the workpiece

wear resistance,

tool-steel

speed steel.

is

off

the more

power

hacksaw blade.

A welded

edge blade

steel

cutting

alloy

back.

equal

or better

consisting

high-speed a of

to a carbon

edge electron-beam'welded The high

speed cutting

-

edge delivers

a

all-hard prone

blade

cutting

hard blade,

if

the alloy

while

to breakage, it

perfotmance

especially is

suddenly

steel shatter; dropped 4

47 -

compared to the back is than

less the all-

on the work,

bends in

the cut,

or is

creating

a hazard

for

Hacksaw Blade

Hacksaw

blades

are

usually

Standards

British

saw blades.

teeth in

teeth

pitch

this

order,

of

teeth

per

x overall width,

blade (mm)

eg or

250 x 13 x 0.65

(18) 1.4 x

regular

tooth

set Details

in the

BS 1919 (48). used

dimensions

and the

25 mm) are always

expressed

shown as follows:

x 1.4

characteristics

their

are made.

found be can

overall

250 x 13 x 0.65

teeth

to

the teeth

and nomenclature

The principal

length of blade between centres holes, the pin of (MM)

Saw blade

they

Institution-publication

(number

loads.

pitch,

from which

13 shows the terminology

Figure

permits

according

and definitions

of the nomenclature

blade

feed

classified

dimensions,

overall

etc,

and nearby

bi-metal

higher

rates

Specification

and the material

pattern

for

for

tensioning

2.2.2

principal

the operator

Furthermore)the

personnel. greater

fed at too high

vary

in

for

which

form Figure

x blade thickness, (mm)

shape depending the blade 14b (1)

48 -

x pitch (number of teeth per 25 mm)

on the work

The was designed. I (49), is the one most

Faces of the cutting

commonly used.

to the back of the blade,

cular

and rounded

to promote

form Figure

14b (ii)

is

chip

material.

are full

The skip

curl.

a much wider

and this This

are perpendi-

and the gullets

for makes

flatter,

relatively

ductile

good

teeth

makes the

gullet,

to break

tends

which

up very for

ideal

tooth

skip

tooth

0

aluminium,

large

cutting

skip

is

to cut harder the

blade that

bite to

heat

promote

which

and bind

in the

the width

The following

feed

thick

slot

cut

of the

to the

positive

rake,

cross

edge of

set patterns

the

manufacture,

the blade

or kerf,

used

sections.

and the

high

by the. blade.

slot,

is

form

cutting

generate

to

The gullet

rates.

during

between

otherwise

similar

This

curl.

or set,

achieved

would

is

make up the

which

is

chip

with

laterally,

clearance

determines work.

teeth

lighter

with

materials

are bent

produced,

when

especially

has a slight

it

that

except

more rounded

Some of

blade,

14b (iii)

form Figure

a better

provide

and similar

etc,

solids.

The hook tooth tooth,

brass

soft

a standard

can clog

which

metals

magnesium,

copper,

so slot

frictional It

0 cut

also. in the

are common, Figure

14a,

0

49 -

(i)

Alternate

(ii)

Raker

(iii)

set.

set.

Wavy set.

In the alternate The raker

left,

right,

is

set

the teeth

raker

a general

tooth

serving

as a chip

solid

uniform

work.

unset

and three

forming

a sine

2.2.3

Cutting

Examinations

pattern,

teeth

set

to the

left,

the

cutting

edges

produce of

the

to the next.

for

one

the wavy set teeth

formed edge

cutting differs

as shown in Figure

50 -

by heat

treatment The actual

the major

15.

the tooth

followed

edges.

teeth

is due to the

in which

considerably

For most blades

blade

hacksaw

This

and heat

and the milling

cutting

(unset)

suitable

to the right,

of

by gang-milling

is produced

badly

of

Edge Geometry

method of manufacture

treatment

consisting

The straight

have shown them to be inconsistent.

profile

and right.

wave.

of

traditional

left

function,

clearing

set

set

sequence.

of three

Wavy set consists tooth

purpose

tooth

straight

are

from

cutting

processes profile one tooth

angles

are

By describing

the

cutting

edge profile

measure of the magnitude

and variation

has been made.

profile

later.

discussed

radii

less

25 n=-. (TPI),

per

measurements.

profile

of the blade,

the

Because

of

profile

Figure

these

tests

Table

1.

range

blade

are

in

in).

edge radii

variation

shown in

was recorded

of

-

51 -

edge the body number

the

edge-

cutting

edge of the

tests.

The results

form in

Appendix

differences

0.02 mm.(0.0008

of B,

occur

same blade, in)

the teeth

representative

and 10

to measurement.

on the

of all

To

of the total

considerable of teeth

enabled

with

of the extreme

tabulated

between

line

in

teeth

early

Appendix

which

to cutting

one third

these

The average

was considered

The results

the

nature

They show that

of 50, and

4,6 of each

were subjected

shown in

of approximately

(0.003

All

16, the curvature

was measured

pm)

blades

out on

to be measured.

were subjected

inconsistent

teeth

the cutting

six

approximately

on the blade,

of teeth

(7

is

radii

were carried

was produced

inches

edge radii

check cutting teeth

0.0003

than

this

of

gave a magnification

template

transparent

a master

The influence

which

some

of the tooth

These measurements

projector

an optical

as a radius.

giving

in a

to 0.07 mm measured on a

blade. the whole of

B indicate

one blade

that

some

and another

having

the

butymore

same pitch,

and 10 teeth

4,6

blades

Slot

2.2.4

Another which

produces

blade

is

blade

after

in

changes

in the

from the

set teeth

blade the of

the metal

to the extreme

steel

a travelling Appendix

that

future

bar.

then

B shows the

thickness assessing

widths

were

and the

results

results

7% to variation up

for

the three a slot

microscope

to blade

edge on one side

above were used to produce The slot

of

these

was occurring a parameter

ratio, blade

is measured

edge on the other.

having

blades of sample random

of the of the

thickness

thickness

extreme

manufactureq rate

removal

overall

The overall

setting.

the

test

differ.

during

variation)introduced

the variation

considered

25 mm did

per

for

Width

geometric

across

averages

significantjyýthe

performance.

52 -

teeth

in the mild measured

compared. tests.

in the which

pitches

It

slot

using Table

2

was seen

width

is used in the

CHAPTER 3

3.0

PERFORMANCETESTING OF HACKSAW BLADES

3.1

INTRODUCTION

a British

Although

grain

hand hacksaw blades, of only

has

work

in

HM Dockyard

in

of both

power and

relates

to testing

the

Hacksaw

have in

past

these

adequate behaviour

the

show the

tests

the

test

and the

53 -

search

for

(56),

and

great

over material,

sawing

by

Specifications

Admiralty

reproducibility of

tests

been undertaken

also with

their

individual

Manufacturers)

performed

blades

HSS power-hacksaw

of

characteristics

by both

undertaken,

conditions

the

blades

power-hacksaw

of

British ýThe

connection

The results

establishing

machine

still

for

test

performance

period

being

fixed)standardised

of

testing

(BHMA) sub-committee,

Association,

in

of

and users.

manufacturers

(51).

the above standard

amount

and is

has been,

similar

etc,

hand hacksaw blades.

A considerable

under

such as

properties

hardness

size,

for

exists

dimensions, of

details

metallurgical

configurations,

composition,,

BS 1919 (48)

provides

which

specifications, tooth

Standard

difficulty

an indefinite the

conditions

saw not

a

only

Many manufacturers programme

f

tests

cutting

performance

of their

or to their

own standards.

within

a firm

to firm

reproduceable and obtaining

an absolute

manufacturer

different

value

different

variables

of

blade

the end product. testing

used

from

the

time

to

collecting

of

o'r user

testing blade

to place

importance

The criterion of users

54 -

or

a

of the many

the performance

affect

test,

procedures

performance.

appears

could

has

This

time.

usefulconsistent')

different

value

a sawing

by the majority

and

conditions

on the relative

during

performance

and the test

of

which

competý'tors

of their

out

possibility from

the

compare

are carried

differ

data

Each blade

blade

under

the tests

which

usually

the

eliminated

from

blades

they

that

with

assessing

under

from firm

of the

independent

in which

product

used for

differ

the

blade,

on power-hacksaw

arbitrarily

the conditions

indication

are engaged in a continuous

and users

chosen conditions

The criteria

number of companies,

effects.

extraneous

of

in'a

are a true

of the power-hacksaw

performance these

the results

that

ensuring

company but

individual

in the

the

used for appears

condition

of

performance to be qualitative

Some users

more than quantitative. impression,

a general

on the

operations brand

blade of

floor; shop

on a cost

purely for

some specifications

United

Kingdom (51,57)

-,qhilst

they

performance,

(i)

Test

Test

blade

shall

exceed

there

are

in

the

testing

(52,53,54,55),

assess

out

which',

under

standardised

blade

the

'x'

sections

bar. 1ml sections

satisfactorily fdr

the

'mth'

section

will

minutes.

strokes

exceeds

the number of different

cut

taken

'n'

satisfactorily

test

shall

time

Number of section

cut

standard

blade

and the

(iii)

blade

carried to

criteria

However,

a

eg

from the (ji)

tests

upon

use various

conditions,

hacksaw

power

on

in different

would purchase

basis.

and abroad

based

are

others

choice

of time. of the

a period

of a number of brands

performance

relative

over

gained

base their

pitch

required the

stated

strokes

being

teeth.

55 -

to cut

a specified

number of strokes., different,

for

not

(iv)

Each sample blade,

in accordance

and nurnber of teeth/25 through for

time

final

the

the criterion

blade, by be a to made final

cut

to be less

Some tests

aý various

specific

and the

time

the cutting

dimensions. and

Similarly

the

when the

is

of

Most testers relief

on the return

rarely

specified.

and with

it

stroke, Tests

lubricants,

i: ý. not

but

out

geometry

blade hacksaw the of with

the

one tester

to

size another.

and the

stroke

the blade

the quantity

conditions.

carry

blade

the

of the

are carried

but

tension

both out

is

dry cutting

and type

of cutting

specified.

is not surprising

of control

length

required

test

others

varies from

range

the

stipulate

to

load

mid-stroke

and has a large

blade

fluid

at

specific-

there

amount,

speeds,

according

machine

than a.

to make the

taken

standardise

speeds

tests

less

is

number of cuts

to

attempt

specify

cut and the

by most foreign

than a specified

to be little

appears

cut

completely specified,

section

preferred

to be the

appears

ations

sections

type

stated.

maximum value Although

mm, shall

the number of

its

with

of the test

from the above)that)due conditions,

56 -

to the lack

and the variables

which

influence the

the metal

BHMA and other

blades

in formulating

a test

a blade,

so that

characterise

quantitatively

s'awing operation,

testing

organisations

difficulty

experienced

in the

removal

have

which would the results

be consistent. would (56) BHMA The

that

quantifying,

the test

results

is not

obtained hacksaw

machine

3.2

It

previously

Performance

of

a Blade

previous

Test

the difficulties

is clearfrom

manufacturers

in

the results chapter

on power

blade

is

test

the process

17) that

57 -

the

by the hackdiscussed

of the

to quantitatively

of the blade

efficiency

been shown (Figure

Assess

and the findings

the best

of a Power-hacksaw

and controlling

to

encountered

and users

chapters, )that

measure the cutting identifying

are a major

characteristics.

a Cutting

performance

considering

the

of

in the previous

without

obtained.

Formulation

blade saw

also

in

out,

inconsistency

to the

surprising

author

pointed

characteristics

contributor

at all

by the

have both

the machine

and a large

factor

This

(50), NEL and

whilst

variables.

the measured

It

has

load

frame saw

to the

applied

dynamic the measure of

_essential

in order

conditions,

for

A method

3.2.1

during,

to obtain

a mean thrust

assessing

the

blade

the,, stroke,

Thus, lt

are used.

be measured

load

an accurate

during

acting

hacksaws

the thrust

that

load

thrust

when hydraulic

especially

is not

at mid-stroke

is

operating

load parameter.!

performance Ab

In this

methodregard

of cut

achieved

thrust

force

blade

by a particular

18)

directly

component,

teeth

on the

sawing machine.

that,

for

a6

TPI

depth

of

to the mean thrust,

proportional

thus, Kf

6a=

is K where

.

the depth

dependent

is

by the

that

sawing machines,, the average

and various is

fact

of the

have shown (Figure

cut per tooth force

taken

component generated

Test. results blade

is

for

a constant

a given

tm

*oooooo***

workpiece

material

and

spacing. 4

3.2.2

Consider

Determination

the blade

itS from. x

position

of

the

average

to be initially at

the beginning

58 -

depth

displaced

of

cutper

tooth

by an amount

of the cutting

stroke.

removed as the blade

The volume of material

Ax from this

by an amount

displaced

further

is

(Figure

position

19)

is tnC

A(vol)

(3.2)

Ax

Where (vol) L,

nc=

number of teeth in contact broad for Bp workpieces = breadth

p=

the

instantaneous

thrust

load

of

blade

teeth

depth

of

during

varies

depth

instantaneous

the volume of material

stroke

becomes

As the

of

cut

it

depth is

achieved

the

per

tooth

cutting

strokel

the

per

tooth

removed during

varies.

also

one cutting

(3.3)

dx

c

instantaneous

experimentally, depth

js

stn6

the workpiece

achieved

cut

achieved

cut

Hence,

(vol) I..

with

of the workpiece of

pitch

the Ax

of the blade

thickness

As the

duripg removed blade the of

= Volume of material displacement small

of

cut

to

convenient during

59 -

is

the

difficult

to measure

introduce

cutting

the

stroke

average per

tooth,

defined

as fs

6 dx

ooooo*o. oo

(3.4)

Where 6a = average these

Combining compared

stroke

of

of

blade

the

teeth,

gives

(3.5)

material

removed

be found

from

For a rectangular

workpiece.

is broad

when the workpiece

sa

the

may also

(Vol

pitch

s=tBP

The volume

per tooth

of cut

expressions,

the

with

(Vol)

depth

)s = w. B.

the

during

the

lo.,ss in

workpiece

ds

cutting

volume

this

of

becomes

9oo*oo99*o(3.6)

Where

w=

of the

width

slot

in the Ss - increase stroke = D/N depth N=

produced depth

slot

of a rectangular

these

expressions

produced

per cutting

w6rkpiece

number of strokes required workpiece rectangular

Combining

the

gives

60 -

to cut

through

the

Sa

The ratio

(w/t)

thickness

blade the of

the is

is

known as the

of the

the ratio

slot

of the blade

which make contact

cutting

at the beginning not

travel

equivalent complete

Therefore,

breadth

number of teeth traverse,

Ne=S.

of

the

which workpiece,

(3.8)

the workpiece

with

do

stroke

The

of the workpiece. may be said

to make one

Ne, may be shown to be

P.

(3.9)

ooosoosoos for

the expression

cut per tooth

*es*

0

the full

and

the workpiece

and at the end of the cutting

across

edges of

is

Nc,

which. are in contact

the teeth

or the

material,

with

Nc = (S + B)p

However,

(3.7)

z.

ratio,

stroke,

width,

from the outside

measured

thickness

The number of teeth the

oooooo. s..

to the thickness

set teeth,

during

1 S. p

D. N

the average

depth

of the

be may written

'ea

-D. ,9F z-

z

W/t

seesoosoes

61 -

(3.10)

3.2.3

Determination

load

The mean thrust

workpiece blade

tooth

per

as the mean load

defined

during

equal

per

acting

the cutting

thickness,

carries

mean thrustload

per

tooth

thickness

unit

per

the

of

between

stroke that

assuming

unit

each

thickness

may be

the blade

and the

per tooth tooth

in

per unit contact

load. a

The mean total

thrust

load

(F

is

given

by

and the workpiece

Ft

Fým =1

tm

) acting

dx

between

the

blade

*

Where

Ft=

instantaneous of the blade

The mean thrust f

tml

is

obtained

tm

load after thrust from the beginning load per

tooth

a displacement of the cutting

per unit

blade

x stroke

thickness

from

soosessess

tm 4c

62 -

(3.12)

For broad workpieces f=F tm

F. p.

and its

developed

variation

type

between

during

of the

load per tooth

machine parameter Combining

6=Kf

which

the blade

the cutting

and characteristics

mean thrust

etc.

per unit

is

the following

ftm

cut

N. FS

sawing machine,

the

blade

is a

thickness

by the machine

setting

equations

*. *. ooooo*

=F tm B. p. t.

esooo. eass

a rectangular

D.w B. . K. s.

or

depends on

tm

the number of cutting through

and the workpiece,

stroke,

controlled

S. p

gives

(3.13)

euetetetee

tm

As the load

the

may be written

this

strokes,

(3.13)

to

workpiece

1 F

N, required

(3.7)

*9*seoo-as(3.14

)

tm

z*D.w. B -constant X

63 -

...........

(3.15)

In

(3.1)

equation

of cut

achieved

thrust

force

for method Further during c)

the

stroke

thus

the mean

giving

a

K.

have shown that

(F

thrust

force

and cutting

t)

to

proportional

other,

each

20 giving

see Figure

F

F=C.

and or

(f

empirical

equation

(3.17) energy

of

relationships

it

removed,

of material

(3.1)

equation

to determine

is possible

the

and thus

and

specific

assess

the

of a blade.

The Establishment

The specific

(3.17)

)mean = C. (f )mean h c

From the

performance

(3.16)

ooootootou

Fem = CF tM

cutting

for a given material cutting

the

directly

are

and f,tm

Brand'XIblades

using

depth

average

stroke

the constant

tests

cutting

the ,

can be measured,

per, tooth,

components

3.2.4

the cutting

determining

the

cutting

parameters

during

cutting

Sa

process,

energy

(Energy

Parameter

Efficiency

of a Cutting

per unit

Volume,

is a measure of the efficiency

the lower the specific

value the more efficient

the cutting

64 -

cutting

process.

of the

energy

The specific

cutting

f*t.

energy 6

B +ft. tm*

cm

k is f

a-

t. B .6a6af

tm

6a«B.

a

k=C

or

R

(3.18) for

A convenient

method

efficiencies

of blades

depth

average force

of cut

the

used

throughout

blade

performance.

3.3

Instrumentation

cutting

relative

is by means of a graph per

tooth

the

the blade

The higher

KIreferred

showing

woýck for

and_Testing

efficiency

K.

to as the cutting

present

the

the mean thrust

against

of the graph,

slope

The above parameter

the

assessing

component per tooth/mm.

the greater

is

tm since

cm .f

19 cm =f

constant,, the

assessing

Hacksaw

for

Procedure

Blades

21, shows the power hacksaw with

Figure which

has been previously

to placing width

the blade

and thickness,

the blade 'finger' the nut

described

tightening specified

in Chapter

in position. )the

it

turns

with

nut,

a spanner-,

65 -

Prior ie blade

a micrometer.

was tensioned

the hexagonal

2.

dimensions,

were measured using

was in position,

the instrumentation

When

by initially

and finally simulating

giving current

industrial

practice.

of the dynamometer,

to the top

stroke

in the vice

secured

it

that

did

not

the

thrust

at mid-

in turn

which

The operation

of the' saw.

to ensure

saw was checked

fastened was

The workpiece

was

of the on the return

cut

stroke. from

The outputs

cutting

force

against

the position

required

components

through

load

setting. was

experiment

(Appendix

of

Averagedepth Thrust

between load

stroke

the

specimen was recorded

for

Consider

of the

various

saw.

machine

The time for

a

hydraulic

as shown in Table

tabulated

Cutting of

Force-per

thrust the blade

setting

machine

the

repeated

and

3,

B).

Processing

typical

force

onan X-Y plotter,

were recorded

and the results

settings

3.4

in

to cut

particular The

dynamometer,

the

is

load

Cut

Test'Results

Sa,

per_Tooth,

Tooth

per

developed

Unit

shown in Figure

Blade

during

and the workpiece

the column in Table setting

to

for

66 -

and'the

the

Mean

Thickness

the cutting

stroke

a particular

22.

3 (Appendix

(2).

Determine

B) relevant

to

Using

the

a planimeter

2

Area

the

under

Length

curve

base

of

92 cm =

16 cms =

curve

of

= 5.75

Mean height

Mean thrust the cutting

force during (F stroke tm) (3J3)

From equation

ftm

cms

129.26

lbf

F

=F tm B. p. t.

tm nct

129.26 6x2

.

NOTE:

The load

lbf,

due to

time

being

The average

the in

in

the

above

depth

Sa

case

expressed

caltbrated

at

in the

units.

of cut

(3.10),

D. 3

has been

being

instrumentation

imperial

equation

using

lbf/mm/Tooth

10.77 =

ftm

*.

per

tooth

Sa,

has been determined

thus

z 7e

the results again from Table : 91.2 and Ne -2 S. P. - 5.5 x6-

Using

3 machine

N=

33

from cutting and

tests

z=w-1.362 T

67 -

setting

(2)

25 91.2

1.362 33

Sa I= 11.32

3

The values for

x 10-

6a and f are tm

of

machine

various

irm in Table

shown tabulated

3,

settings.

EXPERIMENTAL RESULTS - PERFORMANCETESTING OF HACKSAW

3.5

BLADES

3.5.1

The Cutting

Cutting

tests

have shown (Figure

of cut

tooth,

depth

Action

achieved

per

Calculations

most applications. faents of the cutting that)in less

blade

the than

of

cutting

significance Observations

of steel

the action are produced

light of

examinations

discussed

chips,

vary

of these

6a, is

type

very

of

of the

saw teeth, depth

Thus,

the

of

in Chapter

show

The

4.

by hacksawing

confirm

in

is

cut

hacksaw

tool.

cutting

that

under

the chips The

Microscopic

size.

show evidence

68 -

in

small

mode of deformation.

considerably chips

the average

6a and the measure-

produced loads,

thrust

by a shear

and debris

radius.

as a blunt is

235 that

appýications)the

edge

may be classified of this

chips

edge radius

majority

the

New Blades

of

of

surface

shear

lines,

produced

blunt of

oxidation,

surface

load,

the chips to

similar

radius

Figure

of

Blade

thickness

for

workpiece

and blade

23 thus

better

than

these for

for

K. f

Figure

change

of cut

in

achieved

edge profile

load

Pitches

Different

depth

per tooth

and blades parameters blade

a given

a given pitch

of

the average

En la workpiece

may be written size

the cutting

the mean thrust

to each other

proportional

This

tool.

thrust

of material

by the depth

in

can be seen that

It

curls

Performance

23 shows the variation

pitch.

result

by a sharp

than

When

teeth.

Comparison

against

show evidence

ol a large

are continuous

about

of the

temperatures.

the action

under

larger

blade the on

per tooth blade

high

brought

significantly

3.5.2

indicating

produced

is

formation

being

the chips

produced

chips

in front

Frequently

materialq

soft

cutting

chip

edges.

cutting

'piles-up'

as the material

workpiece

of cut

per unit of different

are directly This

pitch. material,

thus

tm

indicates

that

the 6 TPI,

which

the

4 TPI

performs

10 TPI.

69 -

blade

better

performs

than

the

It

be noted

should

the values

that I

for

a given

the blade

tooth

and the values

be used with

only

the

blade

existing

the design

with

from Figure

obtained

of

23 should

design. 0

Blad6s

of

have different

most probably

will

manufacturers

other

vary

will

spacing

K

of the constant

K

value P.

good, provided width

the slot

24 shows the

Figure

the

against the

with

obtained curves the

is measured

for

reciprocal

of

the

workpiece.

Each point

by carrying

out

similar

constant

to

the

in Figure

The results These effects

K: n:. a+b. When 2p
of

tests

of

the

in

graph

has been

En la

25 rrm f or En la

K. n

70 -

the

individual

as follows:

a particular

6

contact

and producing

24 show a significant

(for p.

constant

teeth

23 and determining slope

and

tested.

cutting

on this

be may summarized

When B >. 25 mm for

the

number

cutting

Figure

K from

each blade in

variation

to be very

load measurement

includes

test

every

has been found

test

of this

The repeatability

blade)

value curves.

size

effect.

of

breadth

Where B=

of the workpiece

nC=

number of teeth

p=

of

pitch

a, b, c=

the

of

The method previously

this

comparison

which force

component,

with

of cut,

possible

for

The results (i)

depth

from these

tests

against

with

In Figure

tool

was ground

details

71 -

as follows:

a superior

blade Figure

large

the upper boundary

can be su=arised

blades.

25, '

a lathe-parting-off

of hacksaw blades.

by the Brand'Z'

of

the mean thrust

the parting-off

25 and 26 indicate

the Brand'X'

manufacturer's

25 and 26.

shown indicates

the performance

performance

The results

manufacturer.

edge and was used at comparatively

the result

Both Figures

with

Since

from one manufacturer

blades

of cut

obtained

has been included.

depths

'X'

Brand

a result

a sharp cutting

Different

of

shown in Figures

shows the average

tool

type

has been used to compare the

from another

blades are

Performance

outlined

of several

'Z'

and Brand

blade

a particular

Blades

Manufacturer's

performances

the workpiece

with

teeth

for

constants

material Comparison

3.5.3

in contact

blade

the

-

compared 26 gives

of the BrandIZ'

some

blades.

(ii)

By inspection

cutting

sharper is

(iii)

the Brand'Z'

a microscope

under

than

smaller

it

is

those

on Brand'X'blades.

of the chips

loads

cutting

Brand'X'blades

(iv)

their

with

The tooth

design

support

is possible

the Brand'Z'

lower

working

more resistant (V)

Figure blades

to a lathe action

many irregular

of the Brand'Z'

gives

edge and enables

the Brand'X' cutting

temperature

of

the

chips

much more more heat edge than

design.

edge will

single

edges.

cutting

This

means

operate -at a

and should., therefore)be

to wear.

25 compares the performance I having 4,6 It and 10 TPI.

the cutting

applied

away from the cutting

with

28 and 29,

is achieving

at all

'blunt'

to the cutting

to be conducted

that

in

results

compatible

blade

The cutting

tool.

by the

see Figures

action

similar

and an action

point

-

blades,

cutting

a much superior

edge radius

produced

the Brand'ZI

that

has a'much

edge,

and Brand'X'

clear

blade

ie the cutting

From-observations Brand'Z'

edge of the blades

of the cutting

edge performance

72 -

of

Brand'X'

is

seen that

of these

blades

is

improved

as the number of teeth

Extrapolating does not between

these

account

however,

trends,

for

inch

per

the differing

the Brand'X'blades

decreases.

to 3 TPI perf6rmance

and the Brand'Z'

3.. -TPI

blades.

It

can also

be shown that

for

required

the

specific

blades

the Brand'Z'

is

cutting.

far

less

energy

than the

Brand'X'blades:

ie

for

Brand'X'blades:

From Figures

C=1.20

the

18 and 20 we have 2 /lbf mm

and K=0.00144

specific-cutting

energy

k=C 17

1.2 x 4.448 0.00144 p giving

10 x

k=3.71

For Brand'Z'

blades,

9

Nm (or 3 m

so*

Joules/m

from Figures

2.2 and K=0.0055 The specific

x 10

6

cutting

25 and 26 we have

rrm2/lbf

energy

73 -

3

k

= 2.2-x

these

Comparing

with

9

x 10

Joules/m

3

blade

is

low value

the

values,

energy

the Brand'Z'

also

consistent

obtained

its

with

superior

action.

cutting 3.6

x 10

k=1.78

giving

4.448 0.0055

6

SOME FACTORS INFLUENCING THE CUTTING PERFORMANCEOF POWER HACKSAW BLADES

different number of

tests

Brand'X'power

standard

the

assessing

on the cutting

hacksaw blades of-some

performances

inch per

were subjected

previously

described.

reduced

30.

a view design

geometric

to parameters

of the blades.

A random sample of Brand'X'blades

Figure

with

out on

Spacing

Teeth

3.6.1

influence

have been carried

This

to that

These results 6 and 10 teeth

figures

to the cutting The results

inch per

4,6

tooth

obtained

in

the cutting blades

74 -

differ

and 10 teeth

performance

shows the cutting

of a single show that

with

tests

are shown in performance

the blade.

performance considerably,

of the 4, a

conclusion Also,

show that

they

taken

for

different

width

does not,

having

4 teeth

than the teeth

in performance

geometric

needs

discussed

in

blades

in

of

different

the teeth

;

10 teeth xplanation.

on a blade

per inch, '

This

a

variation

3.7.

Section

it

was decided

the cutting

it

edgesof

was considered

was an important

was less

in

for

to look the 4,6

and

inch.

earlier,

depth of cut

the differences

slot

Edge Geometrv

differences

10 teeth. per As stated

having

of the above tests

As a result

piece

is

Cutting

3.6.2

radius

which

for

taken

to be 150% more efficient

appear

on a blade

spacing.

in

30 shows that

inch

was

Variation

spacings.

explain

width

were

widths

spacing.

slot

same teeth

shown between

per

result

surprising

teeth

Figure

spacing.

the slot

therefore,

performance

cutting

teeth

different

having

same teeth

an average

having average

the

tests.

10% can be

of about

having result

blades

all

However,

blades

last

the

In obtaining

a variation

blades

between

obtained

by earlier

has been confirmed

which

per

tooth

than

geometric achieved

0.050

the cutting

parameter with

(0.002 mm

75 -

that

the mild inches))the

edge the

andysince steel

test

radius

which

was important

io teeth

the teeth

of the cutting

nature

It

in

given

is

blade

seen that

per

result

earlier

the cutting of which

it

did not blades of

blades

of cut

edge profile

radius,

has been observed

in

appears explain having

that

cutting

tests

the average

same teeth

76 -

in

but, more

confirmed

achieved which

the cutting

cutting the cutting

spacing.

is

an

less

explains

action

carried

one

and 10 teeth

of 4,6

a fact

the difference the

te'sts

between

spacing

measurements

the depth

that

From subsequent

blade. blades

These

differ.

did

inch

of these

same teeth

for

averages

significantlyjthe

the mean

than

rather

was recorded

the

of the

1.

some variation

and another

blade, the on

the curvature

The results

B, Table

having

approx-

Because of the irregular

edge.

Appendix

to

projector.

number of teeth

was measured,

of the cutting

and

were subjected

on an optical

edge profile.

of the teeth

tip

radius are

with

to measurement.

were subject

of 4,6

the body of the blade,

of the total

one third

imately

very

line

in

blades

total,

measurement

edge profile

cutting

in

edge of the

extreme

edge radii1six

36 blades

inch,

per

to the

confined

To check cutting

blade.

All

was

than much

of a

out on these edge radius performances

shown in

The trends

these

conclusive.

It

edge profile

was only

side

due to

the

with

that

distortion

In conclusion,

a number of

small

having

Brand'X'blades

a fact

consistent; cutting

performance.

3.6.3

Slot

which

different may lead

by the

blade

from the edge of the

set teeth

blade

to the

in this

width

set

teeth

dimension

led

having

teeth

of

geometrically

differences

to variation

test

previously

in

across

side.

the

of the

Any variation

in the volume of materials the cut.

described,

77 -

dimension

on one side

on the opposite

be must removed to achieve which performance

geometric

Width

was controlled

The slot

operations.

are not

to their

there-

the

of

blades the

pitch

and,

important

between

As a result

spacing.

true

setting

but

the

differs

of the teeth

by the

was produced

teeth

different

was that

was also

have been observed

differences

to quantify

size

This

spacing.

Another

of the teeth

setting

the overall

with

considerably fore,

the

shape of the cutting

spacing.

teeth

difficult was

which

angle

the

considered

one of a number of differences

of different

between blades difference

be that

may well

were not

measurements

In the cutting

the ratio

of the

slot

to the blade

width

calculated

of this

value

30.

It

same teeth

the

were

used

The slot

to

produce

2, Appendix

Table

width

blade

thickness

important was

blade

tested

ative

value

that

B shows

that

and that was not

in

the same teeth does not blades variation

slot

sufficiently was the major

spacing

different of was taken

of

into

spacing, account

78 -

It

slot it

show that for

be measured

accurate.

compared.

in the

The results

every

or representbelieved was

It

of the

explanation

shown in Figure

teeth

bar.

tests.

these

was occurring

performance

the differences

considered, test

steel

the use of an average

the cutting

explain

width

random

and the results

results

ratio.

the

the variation

differences

the

of blades

pitches

mild

the

sufficiently

thisla

teeth

the

up to 7% variation

was seen that to

To verify

the three in

that

possible may vary

were then measured

widths

the data

in performance

spacing.

a slot

An average

tooth.

was considered

blades)having of sample

in the

when calculating

differences

to cause the apparent having

per

by Brand'X'blades

produced

width

of cut

was taken

ratio

shown in Figure slot

depth

average

was a factor

thickness

between blades 30.

However,

in performance as the in these

slot

of it

between width

comparisons.

of the

accuracy

into,

in the cutting

7% variation

that

was suggested

the

in the manufacture

operation

setting be looked

blades

the

it

tests

of these

As a result

as it

of

up to

was causing

of the blades I

performance

produced. Effect

3.6.4

Of Power

The blade

Hacksaw

is

width

the

loads

cutting

to

workpiece

The purpose

of

these

these

changes alter

Prior

to these

blade

width

by blade

tests

for

a different tests

the cutting it

it

large

relationship.

investigate

that

were carried

79 -

deflection

edges are presented

performance

blades.

blade

of

whether

performance.

was thought

thus, tests

the action

under

With

to

thickness.

is made more

geometric was

blade

a given

the cutting

on the cutting

wear,

and controls

produced

i. 9 increased.

in

parameter

of the blade

and therefore,

the teeth, the

design

and the deflection

flexible

Performance

Blades

a major

the width

Cutting

on the

of the blade,

the beam strength By reducing

Width

Blade

of

the effects may also

of

be affected

fiew both and worn out on

blade a new on

The tests

it

and subjecting

400 mm long

to the cutting

performance

to give

a reduced

340 mm long,

section,

performance

difference any

due to

adopted

described

to that were

It

40 mm wide.

t, ests

reduction taken

the

in

performance

long

and the cutting

performance

32 shows the comparisons

reduction

to

80 -

eliminated

was similar

the

tests

Figure

x wear

standard

and its

3.6.6,

section

31 shows the had

due to the wear that was then ground

a central test

before

in width.

re-subjected

400 mm long

Figure

performances

and after

to 340 mm

section

repeated.

of the cutting

the new and worn blades

a central

performance

blade,

subjected

of 19 mm over

give

both

The cutting

The back of the blade

a new width

was then

procedure

blades

worn

re-assessed.

in cutting

place.

for

as described

tests

edge variations.

on a new 6 TPI

perfomance

cutting

cutting

was then

procedure

blade

This

tests.

the

above.

out

carried

x 40 mm wide

of 17.5 mm over

width

and the modified

to the cutting

The procedure

a

The back of the blade

described.

previously ground

blade

6 TPI production

standard

of taking

consisted

the

of

of the blade

The reduction of its

value,

standard

imately

eight,

in the cutting despite

the

considering

(i)

(ii)

resistance

of the blades the blade

was not

life

Figure

limits

may be applied,

that

and,

width

the although

thereforelreduces

rate

of the blade. the fatigue

may lower

to an extent

to blade

that

this

life.

the blade

characteristics

when

on the wear

obviously

removal

the blade

Reducing

be noted

was not measured.

width

measured

blade the of

a limit

width

load

the maximum metal Reducing

produced.

produced:

of'reduced

this

change

new or worn blades,

should

The effect

Reducing

any measurable

in deflections

points

results

maximum thrust

(iii)

produce

differences

the following

However,

by approx-

stiffness

of either

performance

the large

its

reducing did not

times,

50%

to approximately

width

width

affects

of the Wickstead

8.

81 -I

the

load

saw, see

becomes

The principat

blade

of Blade Tension

Effect

3.6.5

is

produced

the blade

to stiffen

by the action

The important

forces

tension

applying

of

effect

applied

be considered

to

force

component of the cutting

the deflection

to minimise

of externally

teeth.

The effects The Thrust

This

force

forces

of

undergoes

cyclic high

frequency

of

this

vertical

the

of

lateral

stiffness,

instability

in

the blade

the thrust produce vertical blade.

Cutting

blade

significant plane

which

The effect

and the

is

much greater

vertical

vibrational

is unlikely.

However, force

the vertical

reduce

deflections

this

82 -

blade

stiffness

deflection.

in

the life

may affect

the

As-the

small

blade

of applying

-

during

variation

is

set

Force

componený of the cutting

to increase and thus

of the

magnitudes.

the

than

the

variation

I stiffness

loads

are as follows:

Component

and reaches

stroke

thrust

and the lateral

applied

forces.

cutting

the

are

by the engagement and disengagement of these

a hacksaw

to

will the of the

tension

is

of the blade

b.

in

As each tooth

with

compared

forcesythey excitation is

left

the

that

forces

these of

the

to the blade

which)if

the

set pattern

resonate

to

mode of vibration. lateral

deflections,

is

tension

a

fracture:

and even blade

of blade

in

or set up chatter

large

finish

surface

to considerably

increase

the

lateral

stiffness

and,

increase

the

natural

frequency

of

In doing

so a more dynamically

effects

cutting

force

lead

therefore,

the

stable

blade.

set of

may be achieved.

conditions

The analysis

are small

lateral

This

operating

occur.

to give

in a lateral

The effect

variations

components

the blade,

poor

bent

may combine

regularwill

would

is

that

engages and disengages force

is believed

it

Set Teeth

set pattern

lateral

the workpiece, Whilst

the

or the

to the right

by the

Applied

Forces

Lateral

in Appendix

C, shows some of the

of the above forces

acting

on a hacksaw

blade.

The most impo'rtant tension

is

effect

to increase

83 -

of applying

both

the vertical

blade and

lateral

of the blade.

stiffnesses

increased.

is

stiffness the vertical

of these

deflections

for

the natural

frequency

for

a given is

increases load

a given

teeth

a lateral that

pattern

are

pattern

helps

Further

work in

to

overcome

displacement lateral

set

difficulties.

(26).

by the above for of the cutting

By the cutting

the

edge shows that

a large

I such" that. the- components

force

teeth

balancing

84 -

can be achieved

edge adopting

of the cutting self

lateral

namely,

to the vertical

are

The theoretical

of the blade

equilibrium

angle

set

the above area has been carried

in a number of ways, (i)

and the

balanced these.

of.

possible,

pitch

by Thompson and Taylor - out model proposed

is

chatter

The

regular.

of the set

to the blade

load

when the tooth

particularly

to reduce

of vibration.

and disengagement

such a frequency

tension.

4nd to increase

The engagement apply

more than

considerably

stiffness

The effects

The lateral

acting in

on the the

set

lateral

direction

little

and that

or no restraint

is needed due to the elastic

distortion

of the blade. (ii)

lateral

For the

force

to be opposed by

due to the elastic

the restraint

distortion

of the blade. (26)

The analysis

edge to wander

cutting

the cutting the

set

pointed

that

the

blade

but

force

and the

it

angles

of

(26)

have

in

the

during

elastic

also

depends

position

on the the

of

hack-

power

depends on the geometry

only

sawing not

variation

by a blade

imposed

in

due to variances

Thompson and Taylor

teeth.

restraint

is

of the

the tendency

and setting

efficiency

out

that

shows

blade

of the tensioning relative

workpiece

to the blade.

3.6.6

Blade

The geometric to determine this tooth

work it height

Wear and its

shape"of suitable

body of the blade

on Blade

to measure

and the

that

was examined

As a-result

wear parameters.

teeth

Performance

worn blades

many partly

was decided of those

Effects

in

the reduction

are in

line

with

shape of the cutting

85 I

of

the

edge

saw

These

profile.

wear tests

Initial

in worn are

produced of

the

set

to

increase

depth

of cut.

is

in

are the

the

of

number

to that

similar

loss

single

cuts

tooth

made.

The

regions.

rounding

of the profile,

During

the earlier

height

is proportional

the

this

of

flank

is

increase is

graph

wear on a

produced

during

of the blade

part

a given

and

shows secondary

region

produced

wear

achieve

with

shape

and it

A primary

tertiary

height

corners

this

of

to

by measuring

tool,

is

and the outer

needed

in

obtained

cutting

point

load

thrust

flat

amear

The effect

rounded.

40 shows the

Figure.

-1

tooth

such a way that

of each tooth,

at the tip

fed

a gravity

TPI blades.

300 x 25 x 1.25 x6

hacksaw and power The teeth

50: 1.

out using

were carried

on a optical

out

carried

of

a magnification

using

projector

were

measurements

by the

manufacture. the loss

life,

to the number of cuts

in is

made; this I

the secondary

region.

with

rapid

increase

that

under

normal

to

The tertiary in wear.

applied

region

is associated

Wear can become so pronounced

thrust

cut.

86 -

loads,

the blades

ceases

wear tests

Further

Wear on the blade

in

,,;as adopted the

and the

produced

proposed,

using

cut

per

for

thicknessv

unit

be that-wear seen can shifts

the

that

indicates is

in the graphical cutting

force

were those

blade

the wear produced

force is

whilst

of

piece. depth

tooth

per

wear. and

constant axis.

It

This

before

material

worn.

cutting

between

per

needed

and the average

components

average

stages

shown in Figures

results

achieved

is

the

cutting

thrust load

some initial

when the

removed,

the

test

steel

load

three the

reduces

along

curve

in

the

of

previously

procedure

mean thrust

a blade

taken., using

were

cuts

between

variation

and the

tooth

the procedure

25 x 25 mm mild

a square

41 shows the

Figure

assessment

the

previously

by measurement

En 44E barfollowed

circular

wear

performance,

of

a number

which

ie a 36 mm

testers;

Therefore,

possible.

was not

standard

bar was circular,

test

the blade

place.

the

using

was produced

As this

assessing

described

as wear takes

by some hacksaw blade

En 44E bar.

for method

of

teeth

bar adopted

diameter

the change in the metal

to assess

blade the of

capability

removal

test

were carried

TPI blades

40 x2x6

400 x on out

the tests

87 -

mild

4ý and 43 the depth steel,

of cut however,

shown had been

whilst

produced

assumed that steel

the number of cuts

bar produced

wear and they

negligible

loss

The initial

42.

has not been included

in

therefore,

the

represents

height

in tooth

produced

function

linear was a required

tooth

height

The principal average

for component The result

of

of

0

36

Figure

a given

cutting

energy:

6a

is

C-

ft

steel

the

thrust

applied

K

time,

wear were to

and increase

cut

mild

The loss

stage.

43, It

cut.

a criterion a loss

in

in).

blade

m 2 1 mm lbfEn 44E

The wear graph,

testar. -., producing

changes

No of cuts

wear

the cutting

of these

the specific

due to manufactilre

by the wear tests,

(0.010 mm

effects

depth

in height

of the number of sections

0.25

of

shown on the wear graph,

secondary

hacksaw blade by some used

was

are not

the measurements.

to double

36 cuts

It

the mild

made using

in the number of cuts

included Figure

the En 44E bar material.

cutting

decrease force

cutting

load,

see Figure

to considerably

Fcm F tm

increase

kC K G Joules/m

mild

steel

mild

0.0017

0.85

2.21

0.00133

1.20

4.02

88 -

the

steel

3

42.

show that

The above results

during

has been doubled flat

The wear

to that

first

load,

which

applied

load

In fact,

it

and did led

metal

generated

into

this

pressure

over

and was present

degree

of wear had been achieved. be considered

the

use of the a useful

the cut

surface,

accelerated

was due to the

no matter

The applied

what thrust

to be made up of these

components.

89 -

effect.

of energy,

and hence,

The second component

cutting

The

over

dissipation

normal

and

two components.

achieve

heat,

considerable

action

the applied

was a redundant

by itself

processes.

penetration

of the wear flat

of wear.

therefore, may,

removal

blade

to considerable

sliding

energy

was similar

results

a contact

not

cutting

means that

divided was generates

component

the rate

above

the

governs

flat, the wear area of

which

the

in many other

of cut,

due to the

in

specific

test.

flat the wear of

The presence

the depth

the

produced

produced

thrust

the

load two

flat the wear of

The presence

The wear test

is

in

a reduction

the

In the terms

increased

wear as the cutting

whilst,

these

were the effects blade, the of

performance

them to specific One important

the teeth,

due probably

- it

should

previously

regions

be noted mentioned

that

ýide

rounding

cutting

corners

-

90 -

of the

of the corner

temperatures action

the design

&se

profile.

to the production

to the high

in

IbI

the above expression,

in the teeth

changes

was the considerable

by the

in the performance

has been done to relate

in addition

effectq

reported,

edge deteriorated.

little

geometric

as

of wear on the cutting

flat, wear

in these

as previously

used in

blade. the of with

to the right

and therefore,

slope,

is

41 show the

curves

effect,

load

a certain

any material

performance

The other

wears.

that

of Figure

results

movement of the cutting the blade

before

to the blade

must be applied removed.

implies

obtained

of the teeth.

of the Brand

were given

of

IXI

special

by grinding

treatment This the

on each tooth

the better

may go some way to explain bla8e

Brand'Z'

(25)

influencing

blade in

wear.

analysis

(57)

associated

identify

using

the

Trent

(58).

Some of

the

features

blade

influence

has also

fundamental

of

wear mechanisms

wear

proposed

been

the

parameters

wear

rate

been made by the above

hacksaw

power

have

to

operations

system of classification

the

involved

some of the engineering

hacksaw

Some attempt

blades. of

and

a method based on dimensional

relates

power

with

of

some of the factors

the wear mechanisms

They adapted which

performance

of power hacksaw blades

to identify

have attempted

(25)'to

have studied

the wear rate

ddge.

cutting

exp`eriýn-ced.

previously

Thompson and Taylor

a corner

by Wright

'

and

which

operations

identified

involved,

(25),

as

is

-rubbing

f ollows: (i)

the

surface

is newly little

(ii)

the

cut

time

surface

been severely involved

in

against

which

the blade

from the work material for

oxide

on which

films

forming

-

the chip.

91 -

is

to form.

the blade

work hardened

and there

is

rubbing

in the plastic

has processes

(iii)

the temperature face

be in

could

energy

the teeth

workpiece

can vary

the depth

between

and hence the geometry the blade

throughout

by the

(vi)

stroke;

strokes

per minute

sawing

decreasess

formation

This in

operation,

varies

variation

tests

of chip

carried

out

during

is

variation

each

of speed at

from zero

76

to a maximum of

per minute.

the thrust

load

thickness

also

acting

per

per tooth

140 Nm

per unit

throughout

varies

The variation

a maximum of strokes

the

sinusoidally

typical

cutting

stroke.

the

with

a power hacksaw operation

speed during

approximately

72 metres (vii)

life.

action,

Author.

the cutting varies

of chip

has been confirmed

geometry

contact

per tooth

achieved

of cut

of 5-6 GJ/m

3

10-30 percent'.

wear during

teeth

specific

cutting

are in actual

the time

as the blade

the order

inter-

sliding

and the

an intermittent

due to sawing being

(v)

high,

can be exceptionally

cutting

at the

and pressure

observed

92 -

the cutting

was from zero

at a cutting

minute.

blade

rate

of 76

to

Microscopic the

of the

examinations

secondary

(linear the wear of

stage

(25),

have been undertaken

and Figure

suggested

(i)

two main processes:

superficial

plastic

process

44 has been compiled have

wear has been produced

hacksaw blade

the following

phase)

Thompson and Taylor

from the above observations. that

during

of teeth

sections

by

-

defonnation

by shear

at high

temperatures.

(ii)

3.7

deformation

plastic

THE VARIATION

of the cutting

edge.

OF BLADE PERFORMANCEWITH BLADES OF

DIFFERENT PITCH AND WORKPIECES OF DIFFERENT BREADTH

Introduction

3.7.1

From the test tooth

results

has been found

varies

with

that

the cutting

constant,

as a measure of the efficiency the pitch

with

workpiece

breadth,

Initially

it

two possible

of the

Figure

was thought

blades

of different

and on workpieces

pitch

defined

obtained

of different breadth, which

it

has been

of the blade,

teeth,

Figure

this

variation

23,. and the

24.

that

causes: -

93 -

was due to

blade

deflection

and the

such deflection

produced

in

teeth

.any effects

a minor

role

blade

deflection

the to

small

feature some the

I Piles

UP' in

around

the tooth

cutting

forming

front

removal

effect

of the

mode of

pieces

was due

chip

(23),

by further

ation

zone associated

(Appendix

large

and not instantaneously

tooth

first

94 -

removal.

this

with

makes contact

The author

with

D),

in front

of

is

established

metal

'ploughed'

away from the main

of debris.

once fully

unaffected

removed

some is

zone is produced

which

formation

some metal

established

one

saw.

and some breaks

each tooth

of

when considering

of each tooth,

a deformation

and

performs

the metal

stroke

small

has previously that

the

of

During

deflection

cause investigated

second possible

chip

blade

stroke

cutting

complete

32 (b),

and the overall is

However

on the cutting

Figure

in determining

blade, the of

rate

(ii)

deflection

has been shown that

individual

w_orkpiece.

have been checked,

constant it

of blade

movement

between

the

with

contact

relative

The deform-

steady state established

is

when the

the workpiece.

0

During the

the earlier

stage

deformation the of

size

is known (23)

it

force

cutting increase

a final

corresponding

steady

fully

to the

tooth

,

increasingý

the components

on the

acting

until

zone is

both

that

formationý)when

of chip

of the

gradually is achieved,

state

deformation

established

zone. to this

According teeth

in

just

force,

thrust

commenced their force

a thrust teeth

the

with

contact

a constant

the author

that

the cutting

makegbefore

reach a steady

action

valueýis

the

given tooth

geometry,

and does not

in the cutting changes the blade

in

performance

the breadth

a tooth

49,

vary

constant for

with

must on it

acting

components

below helps

on by

be acted

of cut

Figure

material,

have

which

the movement of the

approximately

workpiece

The model presented

teeth

been shown by

length

force

on by

be acted

will

with

has also

It

some of the

will

those

whilst

increases

which

(23)

workpiece

cutting

the cut.

along

formation

model of chip

for

a particular the depth

to explain

teeth.

95 -

of cut.

the variation

of power hacksaw blades

of the workpiece

a

with

and the pitch

of

From a simulation (23)

of the cutting

length

in the period

of cut

load

thrust

the

is

From the results ihe

following

3.7.2

If

y=

to remain

with

established

Thompson (24)

presented

model.

Theory

length

of cut made by a tooth length

and yC =. critical fully

of cut

made by a tooth

a deformation

establish

to

zone

thus when y
-ft

and once steady

state

M. =

is ft

ie when y

>, yc

where M is

the cutting

established = ma

osoosooose

for

constant

fully a

(3.8.2)

established

chip. (a)

Chip Formation

Once the Deformation

is

Full)r

Established

The model

figure

50(a)p

proposed

96 -

the

constant.

by the author,

obtained

tooth

established

zone is

deformation

considered

increases

to the fully

prior

Once the

defo-.ýEnation zone.

load

the thrust

shows that

the author

of a single

action

by Thompson (24)

a

Lee-Shaffer based the on and fully is

AC ,a

plane

ponding

the

saw tooth

wedge of material a chip.

Figure

Moh-.s stress

diagram

edgelforming

The workpiece

zone.

with

makes contact

shows the

by a shear plane

from the chip

separated

the chip

model

deformation

established

(59),

the

along

the cutting

surrounds 50(b)

AB and

shows the corres-

from which: (3.8.3)

The thrust

component

determined

by considering

on the

plane

shear

ft

in

acting

50(a),

Figure

giving:

8.4

this

with.

(3.8.2)

equation

gives (3.8.5)

(cot

Equations

constant

(3.8.3)

M for

determined

friction (b)

for

The tooth

(3.8.5) and

enable

a fully

established

a given

apparent

and material,

The Average

-

cot

=k6(.

Comparing

A'B

forces

the

can be

force

of the cutting

Thrust

loading

Figure

chip to be

coefficient

97 -

of

51.

Load Per Tooth

and chip

the cutting

size

Per Unit

for

Thickness

individual

in contact

teeth

is

s6wn

in contact,

the number of teeth number of teeth zone is

in Figure

having

is

a partly

5 and when one tooth

is

52, when n 6 and nt,

cy

the

formed

deformation

about-to

begin

loading

per unit

its

cut.

(3.8.1),

The equation

can be written

thickness, ftl

= M.

6.

y=

ip

since and

the tooth

(ni 1n

ooo*oooooe

Thus the total

(3.8.7)

oseassoo.

yc = nt . p. load

thrust

acting

is given

(3.8.6)

by

nnt Ft

tf ti

+f

ti

nt0

.1

or

n Ft =M (S t

n

98 -

(3.8.8)

in experimentally

due to the difficulty loads,

the individual unit

blade

f

tooth

an average

load per

is used and is given

thickness

by

Ft

ta

oooooo*ooo

ndt.

By combining

f

measuring

the

above

(3.8.9)

equations

oet

00

ta

(3.8.10)

Where i-ntn n tn

n, n.

- nt +>(i

Tt

L0

and n

nc

4t n t;

that

nc10n

load

per

t)

Constant

experimental

a linear

average

(3.8.12)

1

The Cutting

Previous

cn

depth tooth

work,

relationship of cut

exists

per tooth

per unit

-

Figure

99 -

23, has shown between

the

and the, mean thrust

thickness.

ie

6a=Kf

".........

tm

(3.1)

where f

and

F

tm

osoooso,

tm nt c D1 9

da =W.

depth

The average

S. p

of cut achieved

per tooth

has been defined

stroke

one complete

9. o. v. oe..

'a -1 sJ

aý

Combining

Sa '1f

this

with

**99soo.

ta

M*s

during

(3.3)

3.8.10

equation

is

(3.7)

as

s dx

(3.12)

dx

by definition s

f

m1f tm s

ta

dx

0

Sa

Combining

KI

tm

mf this

with

equation

3.1

seoeoeos.

(3.8.13)

The above expression to be related formation

the cutting

enables

to the characteristics in

and variations

constant

of the chip

the cutting

copstant

to be investigated. has shown that)as

The above analysis in contact

teeth

fully a

with When

for

24,

each tooth

and the

associated

thus

from

apparent

of

model,

above

from cutting

obtained

(61),

3.8.13

M. K.

M=1* co

-

101

51.

from

Figure

51,

results

see Table

coefficient

Theoretical

friction

of

experimental

tests

(K) n

apparent

Figure

coefficient

with

From equation

pttch

from

may be obtained

corresponding

obtained

good agreement

but

the

1 -om

friction

values the

chip,

established

The values

of

the value

approaches

nK

Figure

increases,

the worýpiece

with

constant

cutting

the number of

3(a),

using gave

a

obtained Appendix

B.

therefore

co Experimental using

obtained

53 shows the the chip force

computpd

factor

index

force

index

n=1.0

Figure

54,

the

with

different of

per

that

a cutting

for

for

required values

a force

into

the proposed

the results

obtained

workpieces

in contact

of

that

will

of n-1.0

values

with

obtained

the average

critical

to fully

establish

14.8 mm.

values

breadthsa

have a partly 102 -

breadth

of workpiece

experimentally.

Constant

in the Cutting

model demonstrates

small

agreement.

From the above results

pitch.

of the Variation

of differing

25 mm.

the reciprocal

index

experimental

zone is

close

of

(y ) made by a tooth C.

of cut

of the cutting

10 teeth

length

Explanation

teeth

of

calculated

Substitution

for

the reciprocal

Thompson (24)

a deformation

pitch

Figure

53 indicate is

were

as above.

values

having

shows computed factor

of

various

of Figure

blades

values

a blade

with

of the chip

3.7.3

for

The results

together

(3.8.13),

equation

( 0,

factor

of the chip

values

It high

trends is

similar

suggested

proportion

established

and tooth

(24)

of the

deformation

to that)

Thus)the

zone.

becauselfor possible.

This

indicating

an apparently

This

zone.

24.

figure

the deformation

establish (23)

not

controls

workpiece

thrust tooth

load and,

(24).

required therefore,

established cutting

breadth,

workpiece

by the pitch

cut

to

needed

in contact associated

These factors

to achieve

a given

the average

103 -

of cut

However the pitch

and the number of teeth zone.

extent

in the cutting

on the depth

the number of teeth

formed deformation

deformation

a low

influenced of

proportion

the of

fully

zone has been shown by simulation

to be dependent

of the teeth

or the pitch

length

a high

to

are

pqrformance.

by the fully

For a given

The

cutting

be to a large

reduction

is

cut

constant,

established

leads

situation

of

cutting

large

produced

blade a of

performance

teeth,

teeth

load

of the blade.

cutting

tests

will

constant

on the thrust

efficiency

the

have a fully

and, thus I an apparent

constant

blade is

more effective,

depths

a high

to

improved

in contact

deformation

appears

larger

of the workpiece

zone and the cutting dependent

leads

condition

When the breadth of the teeth

load,

applied

a given

load

thrust

applied

tooth

with with

of the the a partly

the total

affect depth

per tooth,

of cut

loading.

per

The cutting

and,)thus)the

constant

the blade,, increases (Figure

Costs

frocess

3.8.1

Considerable

cost

is

quoted in

not

typical

of

detail

sufficient

two cost

and circular

pitch

to enable

be difficult known to are the occasional

is

rate

is very

high.

this

type

of user

is

frequent

user is

cost also

workpiece

to cut.

It

It

blade

materials

which

is concluded is

low. the

with

situation

104 -

For the

the predom-

the cutting offers

to increase

the

to benefit

time.

is high,

cost

that)for

is because

this

the cuttiiig

would be possible

of cost

and

The change most likely

this

figures

cost

day costs

utilization

cost;

to reduce

the total

the

has under-

whose time utilization

significant;

for change.

for

the time

cost

However,

a breakdown

on present

whose time

user cost

predominant

(21)

based

condidons

operating

at

power

and the data used wre-not

The author analyses

for

sawing.

arriving

fully,

stated

(3,4,8)

available

method

to be undertaken.

cost

in the tooth

effects.

data is

the

in many cases,

inant

of

and the Machine

band sawing

hacksawing,

taken

efficiency

ECONOMICSOF RACKSAWING

3.8

given

an increase

with

due to these

23),

cutting

time

more scope

the cost

I

benefit

cost

overall

the higher

could

or by increasing (3.15)

Equation

shows that

load

strength

considerably

blade

depends

load has been shown to undergo

the maximum thrust

than

be reduced

load load

is developed.

the number of cutting

strength, if

the mean thrust

to the maximum thrust

load.

loadw4reincreased

To achieve

load would need to be uniform

strokes

this,

throughout

the

stroke.

The other strokes

the

blade. the of

less

cutting

by either

used

considerable

the thrust

needed

or by increasing

and the mean thrust

relative

strokes.

of cutting

variation

needed could

the

saw through

can be satisfactorily

that

the thrust

For a given

the

reducing

can be reduced

on the breaking

However,

time

stroke.

The maximum load

ultimately

provided

the number of strokes

the mean thrust

of the

an

produce

the cutting

by either

the rate

the workpiece

through

increasing

reduce

needed to

strokes

number of cutting

and still

be significant,

could

can be reduced

time

workpiece

of user

life.

the blade

The cutting

length

which

machine

cost

and increase

to cut

type

to this

of the m.achine

possible

way to reduce the number of cutting

be increase to would -

the machine stroke 105 -

for any

fixed

In use,

such a machine

large as

workpieces

The blade

225 mm. length

being

length

of usable length

the

by the

rarely

cut

a reasonable a machine

with

the cutting

is

be

only

used would

would be discarded

For

capacity.

375 mm with

of blade

a

the remaining

unused. way to reduce

Another

the cutting 70-120

speed,

strokes

it

However, rates

as the maximum machine

and a blade

of 150 mm stroke,

only

would

with

to be accomm-

size

75 diameter say mm

workpieces,

average,

deterrained

is

of which

size

operate

machines

and the maximum workpiece

size

odated.

small

the

stroke,

blade

Most existing

size.

workpiece

the

3.8.2

per

to si=late

(25), wear

typical

that

Blade (27)

Life,

of

their

and blade

the

parameters

method enables laboratory

effects previously

test -

106

machines.

stroke

unstable.

earlier

a computer

the power hacksaw operation

rate;

Rate and Cost

Cutting

and developed

present

the higher

at

combined

to increase

the. stroke

becomes dynamically

investigate to programme machine

is

minute

saw machine

Thompson and Taylor on blade

ie by increasing

has been found

Estimating

time

work programme

and used the of some of the discussed.

data to be converted

The

to

cutting

thus

and cost,

rates

a particular

of workpiece

combination

to be made in

terms

of realistic

and used by those

understood

an assessment

providing

intending

and blade

material which

criteria

of

can be

to utilise

the

hacksaw operation. the data used by the above relates

Although

and difficult

to cut materials,

are believed

obtained

be obtained

.

Figure

The results,

the

average

greatest

choice

operation)a

that

high cost, cutting

is

rate

high

show that

cutting

cutting

of the

the most economical the rate for

rate

for

to be optimised.

which

pro4Uces Thus,

each material.

the power hacksaw

The results

can only

of the criteria.

performance

must be made as to whether

rates

would

materials.

influence

three

than

which

and the breadth

stroke

optimum conditions

when choosing

cutting

45,

is much smaller

rate

of those

common workpiece

on the

respectively

workpiece

stroke

force,

thrust

rate,

to be typical more

trends

many of the

and 48 show the

45,46,47

Figures stroke

the

with

to unusual

be obtained

cost

or

also

show

by incurring

and low cost can only be achieved at low

rates.

Thompson and Taylor

the power hacksaw operation

is

operation.

107

(27)

concluded

a low cost, low cutting

that rate

46 shows that;, -over

Figure

force

developed

by a. hydraulic

cutting

rate

reduced

as the

thrust

reaches

a minimum value

be further

having load

range

these

high

the cost

and the

En 44E.

rate

could

be increased

of

the cost is

are

longer

effects the

of

workpiece

shown in Figure per

little

of

cut

in

the

the cutting a machine

at the higher to fracture

be prone

the range

inch

for

at

also

is

per cut affected.

48.

pitch

on the

is

reduced It

three

the

blade

teeth

and the average

has been suggested

108 -

and the

performance

life

of

available.

presently

of

of a

the development

They show thatlas

increasedthe

output

the development

strokeýwith

the

the average

show that

those

a maximum

reaches

rate

by combining

than

considered,

stroke

of

both materials

cutting

an adjustable

which

The combined

teeth

would

average

The results

with

breadth

that

However,

minimum values

reaches

for

blades

approximately

is

loads.

considered

machine

life

by developing

range.

blades

existing

the

The cost

is possible

46 shows thatywithin

Figure

are

increases.

increased

load

an extended

thrust

of

and the blade

at a load It

of the range. could

rate

load

range

sawing machine,

increases

average

middle

typical

the

criteria

the number of is

increased,

cutting (27)

that

rate the

trends are

in the predicted

sensitive

performance

to the workpiece

109 -

shown in Figure

material.

48

CHAPTER 4

INTO THE CUTTING ACTION OF BLUNT TOOLS

4.0

INVESTIGATION

4.1

INTRODUCTION,

The hacksaw blade a blunt

due to

tool,

has been classified

tooth

large

its

the cutting is

approximately

the

formation,

which

the

interesting

saw tooth

to those

initial

results,

which

work

went

in

some of the phenomena observed

the

chip

of modes of

produced

(23)

a long

(23),

action

cutting

were similar the

conditions,

operating

combination

Whilst

hacksawing.

normal

to

per tooth

achieved

a complex

revealed

has shown (21)

Under the above cutting

one third.

simulating

tests

of cut

under

edge radiusp

conditions,

-

of the depth

the ratio

edge radius.

cutting

work on hacksawing

Furthermorelexperimental that

as basically

during

revealed

way to

sawing

some

explain

tests,

the

work was in no way exhaustive. This

has led

of blunt

action chip

to further

thickness,

or less

condition

interest

in examining

tools

under conditions

or the

layer

than, the cutting

which exists

of material

edge radius.

where the undeformed removed, is This

when removing material

-

110

-

the cutting

is

equal

a cutting

by sawing.

to,

In the present

work great

accuracy

of tests

removed,

under

was

give

above

and the forces

the chips It

the

the metal

removal

was also

thought

the possible

fied

and considered field

slip-line

cutting 55(a)

cutting

a single

blade

the

edge radius tooth

in order

could

be quantimethods.

manufacturing to enable

to be predicted

on performance

action..

experimentally

to a hacksaw blade

when examining

Behaviour

showing

radius.

portion

Near

the

schematic

the effect

and is described

Point

Tool

diagrams behaviour

the material

Whilst

shows a small

the rounded

for

and possibly

'pl oughing'

thickness:

performance

55 shows various

(32,35,37)

sawing action,

to determine

would

results

5.

Material

Figure

of

mechanism during

formation

so called

chip

of

combination

model has been developed

of edge sharpness in Chapter

above

in the

benefits

that

nature

I

relevant

on the cutting

ratio

have been examined.

the

of the undeformed

effect

produced

process

highlight to way some go It

The relevant

of the chip

picture

a clearer

of material

conditions.

the

that

anticipated

on the

layer

to the actual

regard

with

has been placed

emphasis

proposed in

by researchers

the region

of the

the diagrams are not to scale Figure of material

portion of the -

tool ill

edge. -

accumulated As the

tool

in

front

progresses

of

above the horizontal

all

material

the

form of a chip,

front

of the cutting

the ploughed In Figure

material

will

be removed in

this

point

55(c)

Figure h=

where R is

R(l-sin"dc)

rake nominally

with

the height

be very would

ploughing surface

If,

metal

height does not

however,

larger ably

tools

is

with

recovery

compared with cutting very

small

coincide

with

the cutting

the

it

surface. was possible then

edge,

point

stagnation

below

the material tool

and elastically Rubenstein

(35),

recoverý

edge radius

and yc is

the diagram. an estimated

This

suggests

(32)

cutting

rake angle

of 700

would be h-nr 0.5, um, which

the undeformed Whilst

tests.

of

of material

7pm and a critical

of material

small

in conventional

as shown in

sharp

of the order

edge radius (36),

angle

portion

flow

if

and all

underneath

phe cutting

as

the workpiece

known as the

the height

that

a small

of the workpiece.

part

suggested

the critical that

remaining

action

of a built-up

the form of a chip,

be compressed

will thus

recover,

'D'

above the point

and becomes

this

was assumed that formation

the

the edge without

round

it

into

in

of the metal

into

was assumed that

and 55(c)

remove4 in

portion

described

would be pressed

metal

55(b)

small

is

is pressed

(32)

Albrecht

Furthermore)it

ploughing.

the

edge, which

chip.

ofthe

part

all

including

dashed line

suggests

chip

thickness

the above suggested that

the new machined

the base of the tool.

edge radius

of the tool

(0.56 mm), as in the present

112 -

tests,

was considerthen according

to the model suggested

behind

recovering

thickness

The depth

to or less

of cut

of material

the contraryjthat

the

the base of the tool.

during

of the chip

than

the cutting

cutting

tests

chip

edge radius

tests

of these

which

are

are,: thickness

or undefor-med chip

edge radius

is

an initial)relatively

56 shows schematic

of the cutting

occur

process

edge radius,.

cutting

of

orthogonal

is

large,

the

giving

large

negative

cutting

rake which

0 from vary would -90 to zero rake. Figure

in

small.

The cutting

point

was found

where the undeformed

conditions

The two main features

very (ii)

with

the nature

from conventional

distinct (i)

cutting

was equal

the tool.

It

aim was to measure the magnitude

and observe

under

cutting

butIon

line

experimental

the forces

mm).

of

Approach

Experimental

The general

the height

was no evidence

the tool, was in

surface

machined

there

that

tests

the present

4.2

(0.034

would be considerable

recovery

(35),

by Rubenstein

imediately

in

diagrams

occurring assuming front

of the possibilities with

no build

of the

to

nature

is establishing

the true

depth of cut as compared with 113 -

up of material

One of the diff-

in cutting

of this

finite of

tool.

iculties

tests

a tool

the nominal depth

of

base of the tool It

as compared with

has been previously

56(c)

is

with

that

is

a combination

of interest

to establish

cutting

representSthe

several

researchers of the models

process.

cutting

of the models

which

and, in particularpthe

action

of material

proportion

of

surface.

when cutting

process other

of the

Figure

that

Whilst

radius.

56, represent9the

shown in Figure It

of the cutting

finite a of

have suggested

the machined (35,36)

suggested

representative

tools

the position

establishing

and)furthe=ore.,

of cut

going

into

the chip

compared with

elsewhere.. With

to

a view

investigating

have been conducted using

single

point

on the cutting strength while

still

cold-rolled

continuous

with

It

might

retaining copper

copper

HSS tools

edge.

of copper

the

of

had a radius

ground

the

permit

on a larger

well

cutting forces.

low yield scale

Furthermore;

behaved, producing

work hardening.

114 -

tests

workpieces)

was hoped that

fairly

chip and little

and steel

which

manageable is

above., a series

a

Apparatus

Experimental

Cutting

tests

machine

in Figure as shown

a single

were carried

57,

plate

force

dynamometer component

ground

was bolted

material which

plate,

locating

a dial

for used

measuring

The output

the

layer

holder,

movement of the

tool,

be monitored

during

with

allowed

indicator,

the tool nominal

behind

of

cut

and

59(b)

Incorporated the

tool

allowed

cutting the

to the machined processes.

to the tool

on the ground

115 -

out

were

the cutting

to

The

removed.

which

fastened

59(a)

Figure

recorder.

relative

carrying

Figure

of material

and located

depths

for

set-up,

gauge transducer

vertical

line

steel

of cut,

immediately

an air

second dial

top of the

from the dynamometer

edgejwas

surfaceýto

58..

as a datum

violet

fastened

Figure

machine,

bridge

on an an ultra

in the tool

A ground

was in turn

to'the

depth

indicator

signals

displayed

was used

of nominal

measurements

to hold

modified

operation.

which

of the milling

to the work table

milling

to the top of a Kistlerthree

was secured

steel

workpiece

suitably

in a planing

tool

point

out on a universal

be applied

holder steel

in plate,

accurately.

for

Initial

tests

(= 6.00 mm wide),

workpiece

0.56 mm, under of inconsistent

low

the cutttng

with

planing

the width

a cutting

Machine

forces

specimen

variations

deflection

cutting.

Figure

Miller

stiffness

measurements

holder.

the

conditions,

showed that depth

of

under setting

2 2.2 kN was produced,

of

cause a machine

Parkson

at the position

at a nominal load

thrust

to change

60 shows the

The results

of 0.04 mm,a thrust

to: -

attributed

set depth

the nomtnal

the tool

inconsistent

due to the high

during

could

were

to

reduced

were

causing

which

produced

were still

loads

test

was kept

of the dynamometer.

These

tool

random,

depth

set

3.5 mm, the results

and unrepeatable.

edge radius

produced

the high

of the copper

approximately

(i)

having conditions

0.05 ýmm)because

than the

wider

The nominal

results.

were beyond the range With

tool

tool

deflection

of

m 0.04 mm. (ii)

Considerable altered

spreading

the geometry

thus

giving

chip

thickness

a false

of the workpiece of the workpiece

impression

and the quantity

116 -

material, specimen,

of the undeformed

of material

going

which

into

3.55 MM,wide copper

initially

of 0.25 mm, under a tool

using

tool

the

than

spread, plus

the chip)was

During

conditions

cutting

0.56 mm, with Calculations

the workpiece.

the total

equal

the undeformed

side

to the volume thickness.

chip

geometry

of varying

chips

Figure

and shape were obtained,

in the

of material

volume

the above tests,

set depth

at a nominal

edge radius

showed that

in

specimen machined

orthogonal

of cutting

wider

contained

.

cuts

consecutive

eight

with

of an

61 shows a cross-section

Figure

the chip.

62, under

identical

conditions.

cutting In order tests

to eliminate

were carried

groove,

the tool

out with

is more realistic

which

subsequent

all

sidespread,

cutting

of plane

in a

strain

conditions. 4.2.2

Preparation

The tools speed steel For groove

used for

of

the

orthogonal

cutting

Tools

and Cutting

simulating tools

tests,

of

tests

portion

3.5 mm width

117 -

Geometry

were standard.

15 mm square

the cutting

was ground to approximately

Tool

with

high

section. of the tool

one degree

side

clearances,

was to prevent

which

binding

the tool

in the grooves. A machine

was capable

vicewhich

hold to planes, was used . rake and clearance

It

was essential

and the rake

radius

uniformly.

The radii

63(b)

was set

pivot

of

(ii)

to

edge radius.

be accurately into

the.

as shown in Figures

centre

follows: was as line

of

its

diameter

in a bore, concentric

with

-

the using

was accomplished

to half

and set the axis

the jig.

The machine slide tool

in grinding

faces blended

adopted

the

This

point.

a peg, relieved vertically

should

jig,

using'a

and the procedure

The tool Jig

radius

and cleatance

were ground

stage

the

grinding

of the cutting

this

that

ground

63(a),

The final

was the production

the tools

for

blank

the tool

faces.

in two

of swivelling

tip

The slide approximate

'Just'

was advanced so that

the

touched the side of the wheel.

was backed-off desired

cutting

to the value of the edge radius

machine handwheel set to zero.

118 -

and the

(iii)

The tool

63(c)

Figure

and the machine

to the desired (iv)

to; l could

of the

side

the wheel (V)

(vi)

slide

The tool

was advanced

rotating

grinding

Figure

set

the axis faces

the tool

64(a)

Finally

the clearance

tips

side

of

the

towards

the value

the wheel

until

of

holder

The tool

of

beyond

to just

the tool,

to the wheel)as

face,

faces

was

touched

while shown in

size

I

cutting

edge radius,

were lapped

remove any scratches,

tool

the

and 64(b).

the rake

The actual

slowly

wheel until

on both

advancing

and jack

(ii).

in

was reached.

about

squarely

the

was withdrawn

reference

rotated

packing

touched

the zero

radius

again

squarely.

The machine

the

advanced

be advanced until

just

tool

slide

of the radius.

value

By means of the adjustable screwsithe

shown in

to the position

was rotated

gently

to

burrs'etc.

and profile

of the resultinj

were checked by means of a shadow

-

119 -

and

-

by comparing

graph ground

a series

on a transparent

sheet

to

as the projector

lens,

(x 50),

65(b)

the

showing

shadowgraphs

profile

Figure -and

radius cutting.

eoge

Workpiece

4.2.3

with

screen

glass

image on the

the magnified

drawn

of radii

same magnification

65(a),

see Figures

of the cutting 65(c)

showing

edge the

specified

geometry.

and CuttinE

Specifications

Material

Conditions

Copper

Electrolytic

Copper: -

0.03%

Density

0.013%

Fe,

Free Cutting

Steel: -

89.196%Fe,

0.11%C,

212 HV.

from

1.1% Mn, 9.02%Si, 0.06% Mo,

95 mm/min.

Measurements

depths

Kg/m

3

115 HV.

0.16% Pb, 0.001% Al,

4.2.4

varied

x 10

3

0.13% Cr,

Speed: -

were

to

8.96

0.1% Ni.

As,

0.043% P, 0.18% Ni,

Cutting

The nominal

P, 0.05%

of Copper:

Cold rolled

99.807% Cu,

of Nominal

of 0.05

cut

used

mm to

and True Depths during

2 0.5

120 -

the

mm ie

of Cut

cutting

equal

toor

tests less

the cutting

than During chip

of the tools.

edge radius

preliminary

(depth

thickness

the undeformed

tests

cutting

groove

in three

was determined

of cut)

ways: (i)

By weighing

(ii)

the chip.

a dial

Using

bridge

indicator

The nominal

set

depth,

were not at

I

easily the

which

(Appendix with

cutting

B),

a tool

having

First,

for

nominal

set depth, did

a chip not

each cut,

not

layer

of material

methods.

forces

between

This

obtained,

the results

Furthermore A variation

the nominal removed,

was also

Figure

set

5,

cutting mm. the

showed that

the repeated

by weighing did

tests

of 10-20% discrepancies depth

in

66, although

121 -

0.50 of

obtained

as determined

reflected

of cut

Table

groove

while

obtained

depth

which

depths

out.

edge radius

the actual

agree.

small

carried

obtained

a cutting

show agreement.

occurred

were

shows results

for

the reasons

due to týe

tests

a DTI.

machine using

showed discrepancies, determined

by advancing

as applied

the knee of the milling

The results

reading.

and the actual by the other

the magnitude

two

of the

the magnitude of the

forces-did

follow

not necessarily

magnitude

of the

the chips,

they

layer

tests

cutting

of material

the discrepancies

were not

as severe

where considerable

previously,

was noted,

material

On examining

removed.

to be of a consistent

appeared

Although

nature.

the t: rend of the

obtained as those

in the above

obtained of the workpiece

spreading

neverthelessýjthis

shape and

variation

in results

had to be eliminated. By carrying

placing

out

dial

(i)

tests,

gauges at various

to

similar

depth

indicator

of cut

away from

the tool

machine

table,

milling

machine in

obtained reason,

measuring

the nominal 100 mm.

the knee of the

when advancing

the depth

some

thus, any movement of the

tip,

could

and

were due to: -

was approximately

contribute of cut dial

the particular

to the error

applied.

For this

gauge used for

the nominal depth of cut was fastened

measuring to the tool possible

used for

applied,

above

and the conditions

to the above discrepancies

The dial

those

on the machine,

points

were identified,

of the problems contributing

further

holder

in line

to the tool,

-

and as close as

see Figure

122 -

59(a).

(ii)

On the first that

the

layer

actual

(iii)'

deflection,

the

layer

the

dial

three

readings

The variation

in

length

Further

tests

the blunt for

carried

(0.5

applying in

see Table

6 and Figure

agreement

between

above,

were also

found

67(a)

conditions, the

along

the dial

and 67(b).

indicator

123 -

average

depth

and the depth

The trends except

results,

There was a good

set depth,

the chip.

to be similar,

using

more consistent

readings,

-

state

of cut moved to the position

produced

the nominal

by weighing

steady

cutting,

groove

with

depth

cut measured by the bridge

59(b).

cutting geometry

and

obtýined.

r= radius)

described

obtained

of the

identical

during

out

the nominal (i)

see Figure

the magnitude under

was carried

of the workpiece

taken,

of the chips

tool

as measured by

by the variable

was reflected

load.

of the results

set-upp

positions

obtained

would

the corresponding

removed, bridge

indicator

the average

forces

removed

the accuracy

of material

out along

material

caused by the thrust

to improve

In order

(iv)

of

was understandable

set depth minus

be the nominal machine

it

taken,

cut

for

of

of cut

of the

forces

the first

cut,

did not

Test

Rl,

which

this

is

reflected

steady

reach

in the geometry

see photographs

of chip

state

conditions,

of the chip to Test

corresponding

produced, Rl,

Figure

67(a) . (R1)

The chip

far

is

more heavily

Rl has maintained

R4 or R5, and the chip face

tool

the

throughout

cut,

This

rise.

'discussion

for

a procedure

(see Section in

ancies

4.3)

in

force

cutting

later

in detail

under

the preliminary

carrying

out

the

cutting

tests

the errors

was adopted

and discrep-

obtained.

results

Between the Base of the Tool

and the

Surface

Machined 9

In order is

(Figure tool

out

the conditions

(Figure

68) allowed

56) the air

the distance

and the generated

cutting. air

to establish

carried

to

4.4).

which minimised

Relationship

4.2.5

discussed

gained

the

the

with

component have continued

(section

of results'

From the experience tests,

is

situation

contact

hence, both

force

component and the thrust

than R2, R3,

compressed

gauge to the

-

cutting

gauge transducer between

initially

height, same

which

the base of the

to be measured during

surface

Furthermore-by

under

using

124 -

setting slip

the tool gauges,

and

the air

b.e used for

gauge could

From the experimental

contact.

of material

was no evidence the

although

air-gauge

be attributed

to changes

There

the the

was also

possibility

misaligning,

this

magnitude cutting

edge of the

any change

The full capable

during

encountered

in

tool,

reading,

and horizontal

on the air

thus, the height

by Connolly by Rubenstein

(44)

56) by Rubenstein the cutting

rake angle,

providing

this of the

at the

did not

gauge meter

show

recovery (35),

is

edge radius

there

was

According (35)

and Rubenstein (36),

et al

the critical

to be in the order

have estimated

of material

where R is

but load

tests,

(+ 0.05 mm).

)ýc has been estimated

0, 50-55 and others

(Figure

fixture

tool

the cutting

t 0.002"

obtained

path.

I

to the model presented

rake

gauge

air

and the air-gauge

deflection

of monitoring

angle

the

could

and

reading.

scale

and results

finish

air-gauge

a normal

+

mm), which

the

of

small

by applying was checked

in

the tool,

between

surface

fluid

cuUing

to give

(0.0075

the

7) there

behind

fluctuated

readings

mm) and + 0.0003

of

(Table

recovering

in

tool-workpiece

results

0.0002"(0.005

displacement

the

establishing

it

0 70

to be

as postulated given and

by h= Wc is

R(l

Yc), sin -

the critical

is no side spread of the

125 -

of

According

material. of material

recovery

shown large

readings

during

groove

the base of the tool

a tool

using

the present

on the air cutting

would be expected

tests

blunt

coincided

would have

Further

transducer.

with

of cutting

that

toolsconfirmed

the generated

with

cutting

surface.

PROCEDURE FOR CUTTING TESTS

4.3'

The set-up

A slip

and instrumentation

of the equipment

gauge was wrung on to the ground of the

the position loosely

in

the tool

holder

rest tool

holder

by means of

was seated

of the

adjusted A cleaning

the

by the tool

to give

cut

then replaced

reading

was first

taken

to the same heightl

tip

table

the air 126 -

the

the front the tool

on the

slip

gauge meter

68 (b)).

a sharp blunt

in

was then moved so

and the air

with

to

allowed

in both that

(Figure

the appropriate

using

was placed

same position

tip,

a zero

with

located

below

plate

was then clamped

The machine

gauge occupied

gauge as vacated

tool

holderensuring

tool

squarely.

the air

and the

screws

steel

The tool

The tool

gauge.

slip

side

holder.

tool

on/the

and the

was as i described.

58 and 59, and as previously

shown in Figures

that

the tool

of 0.034 mm to 0.13 mm, which

to be in the order

tests

behind

0.5 mm as in

edge radius

the height

to the above model proposed

tool

tool.

It

was

and re-set

gauge transducer.

The tool

and the tool

gauge

beginning

at three

piece

the workpiece the tool

was running

tool

conditions

cutting

fluid

observed,

the forces

the chips

were collected.

oil)

The tool

returned

to its

readings

were taken

cuts

Further

results

to give

uniform

the cutting was

gauge reading

and, at the end of each cut, ., Prior to weighing, the chips they

to remove any cutting

was cleared

original

at

same three

obtained

at

points

the

(Table

127 -

same nominal 7 and Figure

bridge along

the layer

specimen, enabling Using

and

Final

position.

the

oil

the workpiece

of

starting

again

were taken

59

was used during

removed to be measured.

several

(Figure

recorded

of the workpiece

of material

front

of results,

the air

in a solvent

were cleaned

the

irregularity

the

and reduce

cutting

that

The approp-

meter.

mm increments

In order

commenced.

During

to ensure

and measured using

with

operation.

moving

to th e unmachined'surface,

0.002

(sulphurised

of the work-

across,

gauge,

on the air-gauge

indicator

cutting

the length

and air

cut was applied

and cutting

present.

was traversed

parallel

reading

nominal

dial ted moun, (a)),

the

past

a zero

giving riate

The table

specimen.

readings

length

the

along

points

to the

bridge

Dial-indicator

the air

using

of the workpiece

cleared

of the cut.

were taken

was established

contact

workpiece

this

procedure

depth

setting.

69) by the

showed that

above procedure defined

as the depth

surface,

as measured

the undeformed

from the uncut bridge

by the

surface

depth the as

de.fined

the first

this

cut;

in better

accurately

to the cutting

possible

two

after

the nominal The simple

(a)

on subsequent

set

to the

surface these

with

results

on

tool

the results

were

the nominal

depth

cuts

showed that)providing

of cut was applied

4.3.1

the nominal

agreement.

The above results

removed

to the cut

was due to the machine

effect

However,

deflection.

Also

from the uncut

base of the tool. was in disagreement

thickness,

and by weighing

readings

in the good agreement. were chips, of depth,

rhip

to

and measured as close

tool, three

the

layer

subsequent

of material cuts

wcts equal

set depth. analysis

Analysis

Consider

below

shows

of Overcutting Case I -. Tool

this

to

be true:

and Undercutting Overcutting

- 128 -

as

-

to

XQ

I

X1 t

Displacement

Let

Amount

y-

Total

of

overcut

slot

depth

(vertically)

and Workpiece

between machined

Distance

x-

of Tool

surface

and the tool

+x-

achieved

Bridge

reading

x-

kS

For lst

cut

Let

y

0

0

where k

constant

So =Ax

+ x

0

0

k

Yo

+

Yo

1 + k)

4

129 -

kA

)

For

2nd cut

X

1

61 =A-

kA

61 = A(l

-

ks

..

kä(l

ä(1 - k) + kä(l

61

*** yl

, a(l

k2) -

For 3rd cut

=A-

62ýAk6l

Ak)

=a62m

=

=

&(l

k

-k+k

k2 &k +&2)

X2 = A(k --kz

+ k3)

y-d+ ***

-130-

k) -

For

4th

6=A-x 32

cut

&k

&k

=A

&(l

63 =

k2 - k3)

-k+

kS

=k+k2:'3x

=

t(l

3) +

-k+k2-k

&(k -k

2e

k3-

L(l &**

6=

t(1

-k+

&(k - kz

x=

k3 .......

k2

kn) +

+0+')

+k3

Yn

Examr)le: Say tool yo

by 20% of

overcuts

(1 0.2) + =& ä(1

1 Y2

" A(l

Ys

'

A(l

0.2 -

1.26 2)

+ 0.23)

k6)

the applied

- 0.966

.

1.008&

- 0.999,936A

cut

This

the

shows that

the nominal

approaches (b)

4.3.1

slot

depth

set depth, Case II

Consider

achieved,

y, very

rapidly

A.

Tool -

Undercuttin&

O. _ -a-------

_.

If ------------

xf

-TX

Initial

cut

60-A xo = k6 bridge

initial yo =

0=

kA

reading

after

r9=60-0

=&A(l

-

-132-

the first

cut

-Z

Second

cut

k6 =

x,

6, =A+

=A (1 + k)

61=

0. a

kA(l

+ k) 2)

A(k +k 61-

A(k + k7-)

= &(l +QA(l

y1=

Third

-

k2)

k6

x2m

cut

62ýa

ka

=A+

62ý

A(l

+k+

X

= A(l +k+

k2)

-

A(k +

-A-A

A(I -

-133-

k2

+

k3)

+ k2A

k2)

These results

also

'y' removed

approach

4.3.2

Chip-Tool

during

0.56

Prior with

length

steel

to starting felt

black

Measurements

workpiece

ink.

the low temperatures. The experimental

did

not

procedure

the cutting

force components, contact

of the tool

the

using

was coated

coating

described

depths

of cut

on completion

length

of

speeds and. hence,,

the ink

affect.

previously

to measuring

tool

out

specimens.

The low cutting

In addition

the chip-tool

a radius

sharp

face

the cutthe tip

were carried

having

tools

mm and a nominally

and leaded

very

'A '.

measurements for

cutting

mm, 0.81

Length

Contact

readings,

depth set

the nominal

contact groove

copper

of material

by the Bridge as measured

quickly

Chip-tool

layer

the

show that

used.

was followed.

and recording of each cut

was measured using

a graduated

eye-piece. 70(a)

Figure showing increase fall chips

shows the results

the variation in depth

inttwo

bands.

produced,

of

of chip-tool

of cut.

contact

The graph

On examination

the higher

initial

tests

carried

length

- 134 -

with

shows the results

of the corresponding

band shown by the dotted

out,

to

line)c: orrespondsto lumpy chips,

line steady

reaching Further

tools.

the cutting

which

test

type

above)latter

lower

are results

conditions

by type

of a continuous

by the blunt

as produced

stated,

compressed

band indicated

70(b),

shown in Figure

results

conditions

by heavily

produced the

as compared with

the continuous chip

the results

for

when the

were obtained

was produced, as shown in Figure

of chip

70(c) 70(b)

Figure

shows also

tool

with

a higher

chip

tool

contact

by the cutting comparison tool

shown.

within

will

during

Nature

In the previous

in

(0.81

appear

be found

useful

the next

chapter action

tests

the for

is no evidence of material 135 -

This

slip-line

field

predicting

the

blunt of

it

an empirical

thickness.

tools.

of the Chip and the Dead Metal

experimental

sharp

the chip-tool

chip in

For

tested.

enable

between

The

to be influenced

the range

The above results

the cutting

mm).

from a nominally

the results

and the undeformed

model proposed

there

does not

by a blunt

obtained

edge radius

to be established

length

relationship

4.3.3

length

purposes,

relationship

forces

cutting

edge radius,

are also

contact

the results

Zone

has been shown that

recovery

behind

the

Furthermore)test

tool.

geometry cutting

(Figure

conditions

'still' show

(cutting

0.56

edge radius

shown in it

tests

71(c)

Figures

the

far shear was of zone or

tool

(Figure in

shorter flat

Furthermore

tool.

sharp

type

71(d)),

71(c).

Figure

72(a),

tool,

(b),

obtained

under

a fairly

(c),

with uniform

72(d),

and increases

steady

state

is

for

blunt

groove

tools,

reached,

this

the

plane

effective

tool

than

and

conventional tool

sharp

show some features

In most casesp starts

cross-section,

state

of

a blunt

cutting)using

steadilyp

the

the blunt

using

compressed

the

are

cutting

a fairly

steady

136 -

identical

obtained

chips

the chip

thickness

tool

otherwise

conditions.

rectangular in

(cutting

tool

obtained

when using

cutting

cutting,

the blunt

heavily

(d), and

whilst

identical

when machining with

produced

and 71(b)

approximate

as compared with

of chip

71(a)

During

the chip

was very

length,

Figure

the chips

less

identical

blunt and a

mm), under

that

under

sharp

and 71(d).

was observed

shown various

orthogonal

The corresponding

conditions.

cutting

during

(0.0006")), mm,

4 0.015

edge radius

Figure

a nominally

using

copper,

62).

taken

pictures

machining

been produced

to have

chips

of

have

results

to form, Figure

until

the

feature

is

also

steady

is

state

but no longer

cutting,

the typical

Figure

being

72(c)

to build

is uniform

state

shows a sketch

up without

steady

formation

it

was decided

behaviour the and a-Fea region

graphs 4.3.4

of

of

the

sections

edge

of

was quickly

copper

stopped

in the direction

'

conditions.

in the mode

to examine the chip-root in the

material

by taking

photomicro-

cuts.

blunt

with

by reversing

was repeated

reverse

the milling

several

It

result

of

table

'freezing'

The measured time

and interrupt

was considered this

that,

procedure

(See Appendix

137 -

action

machine

procedure

times.

(95 speed used mm/min), a satisfactory

the cutting

the milling

machine table

less than 0.05 seconds.

tools,

This

of cutting.

the cut

to give

has continued

observed

radius,

'frozen'

sides

Photomicrographs

When machining

cutting

which

of the workpiece

cutting

the

with

of the groove.

state

Due to some of the above variations of chip

72(d),

of a chip

reaching

of the

cross-section

by the walls

restrained

in cross-

In the case of groove

rectangular. steady

When the

obtained.

was as shown in Figure

obtained

of the chip

traces

the chip

reached,

section,

chip

force

in the

reflected

F).

to

the cut was at the low was adequate

Specimens were cut the chip set

and root

area,

in conducting

then polished

washing

regularly.

Finally

the

pads down to

Ferric.

Chloride.

1 micron

when mechanically

of the copper

specimen continuously

of the

specimens,

taken

stated,

Figure

whilst.

with

The above resu lts

to exist

This the

of the relevant

the cutting

conditions microscope,

of a projection

of the chip

area

root

electron-microscope.

clearly

show evidence

of a metal

cap

between the envelope enclosed by the cutting

edge radius machined

the

a microscope.

75 shows a picture

on a scanning

because

and by examining

under

the aid

experienced

became deformed.

73 and 74 show photomicrographs

Figures

taken

under

Alcoholic

using

specimens

specimens

by experience,

overcome mainly

on 6

was initially

the

polishing

wheels,

were. polished

and etched

Some difficulty

were

soap and water

with

specimens

and

specimens

down to 600 grit

specimens

the

micron

areas

The mounted

120 grit

using

ecompassing

12 mm square,

approximately

bakelite.

thoroughly

surface

from the workpiece,

out

extending

surface.

discussed are

from the base of the tool

The implications

in detail

in the next

138 -

of this

section.

and the

metal-cap

was

4.4

4.4.1

DISCUSSION OF RESULTS

Cuttinz

Tests in

The discrepancies tests,

with

the nominal could

and the

of cut

be attributed

to two major

The-stiffness

cut

(ii)

layer

layer

depth,

set

from the uncut

surface

of the material

earlier,

Figure

61, which

machined

It

surface.

Rubenstein

(35)

consecutive

which was reported

occurred

the tool

that

whilst

the cutting

of the relative

was initially material

and the postulated

was actually

edge and recovering

Explanation

carrying

wider than the

impressions

this

behind

of the phenomenon of

139 -

1%

of the tool.

the base of the tool

between

position

tool.

with

gave false

workpiece,

the

tests

It

cuts.

as the depth

to the-base

spread

out cutting

effects

system,

defined

The side

beneath

tool

removed was within

of material

of the nominal

removed,

of material

the third

after

between

causes: -

of the machine

has been shown that

the initial

the relationship

can be overcome by repeated

of which

the

during

obtained

to establishing

regard depth

the results

by going

spread

material

workpiece

(62).

Form and Bellinger

Under cutting

is wider

tool

where the

has been given

than

conditions

are applicable

of the

specimen.

Figure

the centre

the vertical

force

is

hand,

is being

is

the material

thus

bi-axial workpiece,

bulge

out,

causing

due to the higher tools,

although

the above cutting sharp

the

on the

other

of the of the tool

the vicinity

Towards hand,

to bi-axial

because

This

material.

in

on the other

to tri-axial,

face,

Near the centre

state.

changes gradually

in the

compressed

and a

to a tri-axialstress

subjected

strain

immediately

in the x and expanded along

the y and z directions.

tip

Owing to

of the workpiece.

to the relief

compressed

workpiece,

what

the x and y directions;

z and expanded along material

76 illustrates

face

,

at the centre

only

component; the material

on top of the tool

adjacent

conditions)

the workpieceplane

strain

happens near

by

the edges of the

the

stress

and the

the material

spreading

formations conditions

tools. 140 -

strain

state

becomes free

to

of the workpiece

is more pronounced forces.

state

than with of burrs

with

blunt

nominally occurs

when machining

tools sharp during with

The model presented 55 (c)

Figure

face.

However,

both with I

the tool

as represented the orthogonal force

cutting

the cutting to

the

force

by Figures

groove

variations

displacement.

workpiece.

The relevant

The results

show a variety

the corresponding

77(a)

formed chip

are

shapes

force

some of

trace

of

the

Wtial

141 -

stages

the

shown.

also formed

of

As

was proportional

under

the chip

obtained. 77(a)

(b), and

have not been reached.

conditions

shows that

axis

displacement

shown in Figure

obtained,

state

the

The geometry

in

steady

Figure

of

conditions.

In the results the

chips

cutting

reflected

time

and

time.

against

Figur. e 77 shows

during

recorded

the thrust

testý,

the

the base of

with

(d). and

56(b)

were recorded

out

and,

occurring

line

cutting

speed was constant,

workpiece

similar

of this

was in

surface

components

the flank

and during

the workpiece

gave no evidence

the machined

behind

recover

be

would

of the experimentsýcarried than

wider

in fact,

During

some material

and would

the results

the tools

cutting,

grouve

the tool

(35),

and Rubenstein

that

suggest

would

below

compressed

by Connolly

of the chip

is

the

have

form,

conventional

an apparently

a thin

with

starting

-

section

but

heavily

deformed

which

is

deformed

state 77(c)

increasing

shows results of Figure

is case

former

force

cutting

trace

and, yet long

case is

components

shows an apparently

produced

at a low depth state

reached

steady

heavily

compressed.

at a nominal

set depth

conditions

The differing characteristics

Figure

geometry confirm

(0.15

ratio..

type

flat of

mm), which it

is

still

shows the results

of 0.5 mm under

to Figure

more stable

thickness

although

77(e)

identical in the

lower

conventional

conditions,

Figure

obtained

chip

of cut

steady

achieve

in the

and higher

of

The increased

chip.

reflected

is

conditions

the chip

thin

section

similarly.

varies

from cutting

77(d)

Figure

cutting

77(b)

77(b)

and does not

obtained

a fairly

in this

efficiency

force

short

up to a heavily

shown in Figure

thickness the

conditions;

to those

chip,

The chip

by a very

building

and finally

chip.

gradually

followed

section,

thinner

lumpy, to a up

building

then gradually

otherwise

has very

obtained idential

77(d).

of the chips the earlier

142 -

produced results

above and their obtained

simulation

tests

all

the test

results

display

have also

been reported

transient

forces

explain

workpieces

The

test

three

cutting

with

a.

of different

basic

types

blunt

is

of these

pitch

conditions when

produced

is

which

in

increases

and forms

thin increases

and then

ness of the chip

of various

to

progresses.

initially

This

condition.

chapter

the cutting

are

lumpy chip

manner,

progresses

which

-

as the cut

which

under

of chips

tools:

conventional

C.

The effects

that,

thickness

(Figure

forces

breadth.

indicate

deformed

cut

transient

of hacksaw blades

A heavily

A chip

the

have been used in an earlier

results

stated,

Furthermore,

earlier.

the performance

with

(23).

by the Author

in

in thickness

reaches

reflected

and fairly

in a

a steady

as the state

by the uniform constant

cutting

thickforces

78).

A combination segmented chip,

(a) of

(b) and

and a continuous

(more pronounced

of rut). 143 -

at very

or

low depths

Ploughing

highly

the

of

However,

tools.

beneath

flow

from spreading

it

prevent

of plane

more realistic In

the

explained rake

of

ahead of

the

the

tool

tool

is

This

condition

with

the high

occurs

effective

by Koenigsberger

of

et al

the

when the

bulk shear

negative (36).

to

sides

is

which

some material

of

the

plane

material

to go into

material

ahead of the

tool

the chip

is ploughed.

144 -

up ahead

material. angle

angle,

Under this

is available

negative

and piles

rake

is

ploughing

high

radius,

deformed

leaving

without

the

of

conditions.

edge

heavily

conditions

a condition

phenomenon

cutting

extreme

the

sideways,

at

Owing to the very

as follows.

blunt

of material

the

under

strain

to

appears

same as has been

restrained

' the

context,

present

at

is

with

above when using

of

Furthermore,

Mechanics

when machining

no evidence

and recovery

material

cutting,

groove

tool

(35,37).

suggested

described

has been

there

the

occurs

Chip

tools)certainly

the conditions

under

exist

which

material,

rake angled

negative

Zone and the

Dead Metal

Ploughing,

4.4.2

coincides

as suggested

condition and,

thus,

no the

From the

photomicrographs

evidence

of

develops

in

the

cutting Further

rise

a steady

until

the

chip

begins

steady

79 (a)).

This

between

It

'cap'

a severely

chip, not

tests.

the

reach

will

steady

building

this

very

chip

If

the

56(d).

tool,

force

when the

tool is

giving

traces,

-Any a fairly

of

(Figure

compressed

tool

during

produced

conditions .

chip

rake

were

severe

face and the,

was produced

'quick-stops'

that root

only

stagnant

zone

To study would

Under cutting

145 -

for

represent

instant.

at a particular

quick-stops. of number

tool

which

did

conditions.

the chip

up Of the

heavily

was commonly

chip,

'piled-up' state

stage

'cap'

Figure

the

of

of the

friction

and the

be appreciated

the area around conditions

after

of

the

of

the

components

are reached,

face

although type

front

the rake

produced

chip

cutting

in

the

force

shown in

that

cap

after

of

geometry

conditions

state

time

short

as shown by the

forces,

thickness,

uniform

to

changes

to leave

subsequent

the

of

This

tool.

cutting

The active

is

there

The development

accumulates

material

the

of

transient

78.

edge thus

74,75)

a very

cut.

primary

Figure

in shown

within

the

of

commencement results

cap ahead

a metal

of material

(Figures

require

conditions,

studying the cutting the gradual a large the

size

of the cap may vary

and geometry

identical

casespunder

formation

of chip

it

Earlier

be unstable. may

cutting

during changed

The changes

in

metal

thickness

of

an unstable

at

conditions

cap grows very

between is wedged and machined

surface,

Friction

conditionson to give

increased

base

tendency

to cause increased

surface,

sufficient

secondary

to cause

obtained deformation

described, a chip reaches

whilst

steady

state.

'cap'

the

have

will

deformation. in

face

Ihe situation 146 -

a

the photoshowed a

and some deformation

formed is

Evidence

which

intact

cap stays is

tool.

drag on the machined

Under the conditions

thickness

the of

in

73 and 74),

on the rake

the metal

increasing of

of the tool

are

were present

frict

metal

of the tool

'cap'

the

surface

(Figures

surface.

on the machined

of

the

of the cut

geometry

conýact

shear

two situations the above of micrographs

face

to metal

the

the

stages

the active

the

altering

edge radius

the rake

to

Thus,

initial

the cutting

metal

furthermore;

region;

naturelthereby

the

'altering

the thickness

of cut.

interface.

at

rapidly

some

geometry

be attributed

could

'cap-chip'

the

length

the

chip

cap being

random

and, - furthermore,

occurred

of the chip

conditions,

in

that

was mentioned

'cap'

the

andjfurthermore

previously the tool)

with

and finally

reflected

in the

and tI

force

traces

Figure

78.

Workpiece

is space cap

then

could factors

anisotropy grain

intercept

size,

diameter,

5=

grain tool

can contribute

is

the influence

a= 231

cutting

r_ut; could some part

of

face

"m.

the

the tests

centred)cubic

lead cutting

This

the

the

'metal

of

the

type

random

size

Measurements

and

of the

9Lve a mean linear a true

gives

high

relatively

material,

grain

value

of

compared with

to inhomogeneous

phase

structure.

147 -

of

defo=ation

The copper

process.

material This

in

workpiece with lattice

the

a

558 /.jm and low depths

of

was a single lattice

altering

of the grain

131 Am which

edge radius

possibly

used

to

material.

of the work-piece

size

for

and)hence

of the cOPPer workpiece

size

79(b),

Tigure

itself.

which

of workpiece

the vacated

The formation

re-establish

geometry

of chip

of the cap

pieces

entering

the chip,

formation.

chip

of

geometry

Other

into

extruded

the required

or the workpiece.

the mode of defo--mation

changing

cap'

the chip

subsequently

material

with

the

the

cutting

to support

collapses

away with

thatlonce

further

with

established,

carried

operation,

the possibility

also

and consequently

being

the cutting

of the cap is unable

structure forces

is

There

cap is

metal

during

obtained

a

could

structure

62 28 x 10 lbf /in

in

(100)

direction

(63).

(64)

for

high

The graphs

up to

0.3

(0.56

0.8 mm and

of in

increase is

the

This the

0.3

slopes

is

is

decrease cutting

proportion

also

of

the

0.5

curves

possibly

edge radius to

the

(layer lines-

blunt

using

overall

mm undeformed to

tend

due to and

the

it

decrease decreasing

would

in the

be

forces.

cutting

of the proce. ss as the depth reflected

tools

a copper

machining

mm and up to

in efficiency

increased

whilst

80,

straight

thickness

chip

mm radii)

Beyond

thickness

approximately

are

(Figure

thickness,

chip

undeformed

mm undeformed

workpiece.

r

the

removed),

of material

reduced

variat3-. CnS-

forces,

cutting

state

steady

against

influence

the

Forces

Cutting

State

of

81. and 82)

slightly.

in

has been reported

it

that

copper

of

6- "2 10 lbf/in

and-10_x

Furthermore,

purity

Steady

chip

directions

modulus

64%/. be as as much can

in hardness 4.4.3

(111)

ie

effects,

may have a Young's

of copper

grains

adjacent

to anisotropic

rise

give

specific

This

of cut

cutting

84 85, Figures the and where specific curves, energy. W beyond level 0.3 tends to off mm undeformed energy r. utting leaded steel workpiece, For the thickness. using chip blunt

tOOlSv the cutting

force

-

components

148 -

are

straight-l'ines,

the

within the

of

range

decrease

shows a dramatic

The high the

depths

low

in

of undeformed

and has

force-

However, at that

force

small

thus

of

particularly

all

surprising.

if

the

(Figure

83).

researchhas

large

force

is

forces

cutting

tools

values on the

acting

of the

proportion

neglected

edge

with

cutting

cut,

that)at

been

above,

(35,36,65,66,

force

undeformed tool

at

cutting

a small

thickness.

chip

experienced

sharp

the

only

values'of on the

acts

and significantq

chip

in

the

past.

thickness/the larger,

proportionally cutting

edge

radius

large. to the high

Furthermore)due tool

with

ploughing

forms edge

cutting

r-utting

depth

metal

thick-nessj

chip

not

also

energy,

that)when

has been considered

It

67,68).

than

previous

as the

identified

values

are

zero

higher

force,

The above

is

steel

cutting

indicate

approaching

considerably

tool

specific

cut,

of

80y 81 and 82 all tools,

blunt

been

leaded

the

energy

cutting

specific

very

Figures

are

in

As with

tested.

cut

85, from 0.05 mm to 0.3 mm undeformed

Figure

at

of 84,

Figure

workpiece,

copper

depths

the

cutting

edge,

some deformation

I

material between

may-occur, the tool

stresses

which

leads

near

týe

of the wol

to increased

and the machined

149 -

acting

surface

contact over

an area

at

the base of the cutting

cutting

tests

(Figure

74),

depths

which would make the

of cut

having

frictional

force

This

edge region.

the

total

cutting

force

will

force

at

The above mentioned) removal

of

form

force.

The existence

of

this

effects

Isize

(69),

effect',

(Figures

thickness that

the rapid

low values

propoxt-Ion

inversely

area,

84,85).

increase

constant

of the total

cutting

thus I the portion

to

of

the

of

of

the

cutting

overall force

the

so called in

of undeformed

cutting

thickness

energy is

spec_ific.

150 -

(69) at

a greater

The specific

to the cutting undeformed

chip

due to the

and thus forming force.

in

results

increase

to the

to.

contribute

has been suggested

is proportional

proportional

proportion

part

specific

chip

cutting

-'does not

It

in

radius,

the tool

force

low values

small

of cut.

redundant

being

energy

depths

refers

at

of undefo=ed force

redundant

cutting

energy

cutting

specific

in

and can explain which

of

cutting

a large

small

chip,

important some

a large may act

redundant

even more

the conditions

form

but

the

the present

situation

under

and a tool

a substantial

contact

cap has been reported

where a metal

Thus; when cutting

severe.

in

increased

further be area would

This

edge radius.

chip

force

and

cross-sectional

cutting-energy

resulting

froi

the redundant

force

will

increase

decreases.

151 -

as the chip

thickness

CHAPTER 5 5.1

FIELD

REVIEW OF SLIP-LINE METAL CUTTING

zone models, form

The shear plane, or shear the analysis their

-

shear plane

so called

on which

the assumptions include:

and, thus

of the

or primary

shear

zone.

in Some of

are based

Chip

formation shear

field

passing

takes plane,

regular carried

state

fixes

plac7e or

through

Chip separation

at which

is

analyýis

called

which

with

continuity, by steady

out

state

'

The stress

in

the cutting

on the

edge. is uniform,

by an angle

of the is

The deformation

so

plastic

shear plane

can be described

formation

the

a plane,

a triangular

the orientation

chip

in

shear plane

asstLmed to take

place.

(v)

fields

stress

such calculations

occurs

the

mechanics.

(iv)

despite

Chip formation

(ji)

for

the models-are

all

the calculation

around

the basis

mechanism today,

Practically

shortcomings.

centred the

formation

of chip

THEORY APPLIED TO

I

is under

152 -

plane

strain.

(vi)

The forces

the cutting

through

been generally plastic

or strain

-Ernst's

(71)

deformation

shear

tool

tip

an analysis

this

(i)

the

(ii) (iii)

86)

rate.

narrow

be idealised

which

as a from

extends

Merchant

surface.

(33)

the

developed

shear model

under

and no rubbing

or

the

is

tip

sharp

the

the deformation

is

the str'esses

homogeneous and ideally

zone,

zone could

between

occurs

simplicity

in a fairly -

based on the thin

tool

has

and films,

(figure

assumptions:

following

for

from photomicrographs

occurs

free

the

to

can

passing

at a constant

observations

that he assumed and simple

material

hardens

plane

force

as isotropic,

treated

surfaces

edge.

the workpiece

Furthermore,

tool

by a single

be represented

that show

on the

acting

tool

ploughing

and the workpiece;

two-dimensional;

on the shear plane

are uniformly

distributed; (jv)

force

the resultant shear plane applied

is

equal

to the. chip

on the chip and opposite at

the chip

153 -

applied

at

the

to the force tool

interface.

From these energy

for

a solution

obtained

in terms

shear plane

metal

the minimum Merchant

cutting,

the inclination the rake

of

of the

ý

angle

between X

friction

of

mean angle

ih

applied

principle

that

and assuming

conditions

the

and the

a tool

and chip,

so 7r

4

tests

Experimental

showed agreement

and steels

ýgreement

with the

assuming

function

of the normal

assumption

the

analysis

of a single

theory

deals

was not

exceeded

shear plane

with

to the

a uniform

slip

lines

shear plane, 154 -

by

was some

shear plane.

the stress

while

slip-line

the yield

in at triangular

parallel Figure

the

retaining

applied

that

forces

the

with

about

shear plane,

plastic

brought

were only

only

(60),

ensured

when cutting

stress

on the

and thereby

By considering

perpendicular

stress

on plastics

relationship

the'yield

of

Lee and Shaffer

of the material chip.

steel

and makes no statement

distribution.

field

value

Merchant's and

on the'chip

for

the theoretical

that

Ernst

theory

with

The results

only.

materials into

out by Merchant

carried

least

part field

to and 87,

they

stress of

the

above

derived

the inclination

of the

is

that

shear plane,

for

expression

a similar

L .4

figure

In the above solution, the

across

line

shear

ST.

fictitious

plastic

field

regiono

The reason

for

in

field

RST is

plastic

perfectly (i)

for

(ii)

the high

strain

rates

approach

for

certain

between

The direction

operations

values

line

slip

examine

the tool

the

face

of

AC being

of

the rigidbecause: -

falls

rate and so

stress. which

occur

said

of the material

solution

rigid

force.

strains

are

the ideally

the

to be justified

said

large

constant

Lee and Schaffer's able

for

values

strength

to

a

the

of

need

the work-hardening

a near

it

force

is

reaches

yield

the

entirely

of

consideration

machining

material

machining

limit

the

the use of. the concept

most metals

to small

RST being

is

ST.

minimum

In the above process

triangle

with

surface the

to give

chosen

the

associated

shearing

occurs

which

of the machining

transmission and the

the

87t flow

during

to raise

the

and to make

plastic.

was found not to be accept-

of the parameters

155 -

a and

The above solution cutting conditions

the built-up

ated with

and sliding

quite

independent to (i)

stem

has

associ-

These

the

88.

been

disagreement

been

were

compared between by several

confirmed discrepancies

appear

from: -

the

assumptions

absence

of

the

material

the

fact

of zero

experiments,

(ii)

arise

between

have

theories

(82,83).

workers

friction

and the This

marked.

would

shown in figure

above

results

experimental

them is

is

nose and the

and hodograph

nose with

the

of

processes

field

material

The predictions with

line

The slip

considered.

tool

these

under which

the case of

and built-up

chip

a continuous

with

to cover

was extended

any

plane

strain

hardening,

strain

due to

effects

the

line

slip

an upper bound solution tion

some parts conditions (iii)CLcomplex

It

chosen.

is

of the

the

temperature

on

and lubrication.

properties

that

in

conditions

field

for

is

solution

the particular

thus

quite

stress

field

possible the

configurathat

stress

are violated. friction

situation

-

156 -

on the rake

only

face.

at boundary

Permissible

by the

plane)implied

(72),

suggested the depth

of cut,

friction of cutting

may not

experimental

conducted

the position Hill

range. in terms

of

and the coefficient and the final

initial

if

stable Similar

condition. from results by Low (72)

I

from

obtained and Low and

(73).

Palmer

Christophersono previous

angle

have been reached tests

he showed that

of cutting

be possible

depends upon the

conclusions

Wilkinson

the rake

have

solutions,

to a certain

solution

a unique

of

to be violated,

was limited

of the shear plane that

in which

were not

criterion

the end of the shear type

shear plane

been examined by Hill the yield

at

conditions

stress

-

assumptions

and Oxley

that

(75),

deformation

(76)t takes

the

examined on a

place

by developing an experimental, technique of shear plane .0 films Cine Subsequently of the process. the taking mechanics in plane

of machining

In the

zone observed

modified ie

strain-hardeningt strain.

Estimates

plasticity.

were made, using

were investigated

for

of cutting

Hencky equations, values

of k that

slow speed experiments2the

from the Cine films

157 -

record

as a problem force

etc,

to allow vary

with

deformation enabled

the

for

individual lines.

crystals

results

field

to which

They

work-hardening.

(i)

(ii)

the plastic

The correlation

of

between

the

tensile

def ormation

stresses

When examining

ie

a tool

the mechanics which

the length

was elastic.

defined,

the length

where the

its and

distribution

the tool

tip

at

the free

surface.

over

face

between

unknown and not well of region

I

of the orthogonal

has a rake

of contact

face,

near

stresses

and compressive

occurrect

up the tool

occur

width

zone and

and tool

chip

of

were smooth curves

in the plastic

curved

in a zone some distance

using

flow

passing

where

of theory

zone was of a considerable

from the work to the chip,

the

a

-

streamlines

contact

constrdet

the effect

and the

the chip

(iji)

that:

concluded

slip

emerged from their

which

by including

was improved

and experiment

to

the

Hencky equations

the modified

89.

shown in figure

to ascertain

was possible

The picture

be applied.

is work

it

From the

slip-line could

to be followed

of infinite

the chip

the question shear

the contact

158 -

cutting length,

and tool arises

stress length.

is

is as to

acting,

(78)

Bhattacharyya

over which

the

the

between

the chip

be assumed can presence

stress

which

for

fields

conditions the

expressions

for

The hodographs

, not

backIthe cut (81)

Usui

et al

with

cut-awaY

johnson

(77),

chip

for

similar

various

for

90,

various

together

component

of the

at the chip

is more oblique

so that.,, if

the tool

to rub the

tool

to those

159 -

has presented

the above show the chip

plastic

contact

stress of the

tools,

figure

which

tend

have presented

tOOlsy

in

face,

would

of contact

(79),

of friction

a direction

than the rake

the vertical

frictional

the horizontal

interface.

along

a constant

geometry,

and the coefficient

directed be to

length

(77)

contact

a power law.

restricted

contact

force

cutting

and an upper following

Johnson

restricted tool

a region

the-complications

eliminates

of cutting

tool

face,

is,

that

constant

of

and rake

common to divide

decreases

of the second zone.

line

with

is

a tool

with

When machining

is

two regions,

stress

shear

over which

region

slip

into

length

the contact

it

showed that

fields

was

face.

associated

proposed

lengths.

to

by

They

(81)

chip

tool

chip

thickness

is above.

field

and tool of

composed

of friction

further

has

Johnson-Usui

modified

the

in shown

figure

presented

that

restricted

cannot

with

field

straight

for

and 94, and has

the natural face

is

contact

about

with

2.6

stress of coef-

artificial

length7the

results. for

fields

slip-line

92.

model

fields

modified Kudo

(82)

further

tools.,

unrestricted shown from

the

length

the un-

times

for

the depth

as

models

of cut.

as compared to Johnson-Usui

solution cutting

solutions)resulting

in

defo=ation steady

the

fields

93

necessarily

variation

experimental

figure

lower gave

solution,

and two

and has presented

slip-line

tool

contact

as shown in

Furthermore)Kudo's

line

face

explored

tool-contact

restricted

the rake

correlation

close

(82) Kudo

for

of the tool-chip

restriction provided

at

treatment

the

of undeformed

The stress

fan

one centred

knowing

values

rake angle.

and quantitative

ficient

various

91),

Based upon the above proposed

fields.

slip-line

for

length

contact

from conventional

obtained

(figure n and e

to set the angles

tools

of

data

have used cutting

resistance. lower

be regarded

cutting

Whilst

resistance;

as more realistic,

mode.)associated 160 -

with

slip-

smaller

a

cutting

appears

resistance,

Kudo's

resistance.

for

resistance

was unlikely for of

results

in

observed the

with

tool

the

is

however

cutting

has presented

edges,

assumed

that

in is removed ness

figures only

that

or 95(a)

part

field

of

the

only

where

these

undeformed

chip

face.

qualitatively.

161 -

for

solutions

In

and

The remainder

and recovers

results

qualitatively

(b).

behind

explained

some phenomena

approximated

the material

his

sLLr_V%

has been

nose

is assumed to be compressed flank

any

The

machining,

the form of a chip.

the

that

model.

orthogonal

edge radius

cutting

but

angles,

were feasible.

slip-line for

cutting

than a certain

be explained

plastic

higher

a built-up-edge

revealed I could

eool-contact,

by straight it

study,

with

revealed

rake

rake angles

rigid-perfectly

restricted

larger

with

zero or positive

actual

(79)

Johnson

solution

negative

his

face

His investigations

plastic for

those

showed a constant

of tool

94(c).

rigid-perfectly

solutions

solution

lengths

Figure

limit,

than

more realistic

underneath

models thick-

of the tool

Johnson has,, however)

5.2

DEVELOPMENT OF THE SLIP-LINE A BLUNT TOOL

it

Initially, blunt

the

of the undeformed

part

form ofachip

in the removed was below

that, when cutting

was postulated

tool,

to

tool,

FIELD FOR CUTTING WITH

behind

recover

was compressed

flank

the

a

thickness

chip

and part

with

face,

has -as

been previously

suggested

field

slip-line

which that

the assumption thickness

(6),

point.

'P'.

I

chip

tool

force

a thrust force,

since

dependent

which

machined

would completely

field boundary

stress

can be considered

The point

'-T'

is

the

metal

is

ý

of

than

greater

same*level

cap and the

this

not

nature

UP is

has a minimum value

which condition

points line,

and the undeformed chip.

162 -

gives

the horizontal

on face

stress

into.

the

and have

field

same horizontal

be going

at

unspecified

A stress

Under this

surface,

chip

point

the hydrostatic

be the on would

on

'PI

on the angle

135 degrees.

the undeformed

and the

continuity

lengthare

been drawn to scale.

96 shows a

The above stress

chip.

The dimensionsof

contact

Figure

the above situation, of

part

the

provided

as a singular as point

only

satisfy

fit

would

into goes

hodograph and conditionsp

(35,41).

'T'

'P' and

coincident chip

of

thickness

with

the 161

If

the undeformed

the

slip-field

field

is

below

the

experimental

(Chapter

4),

there

work

the machined

and that

surface

to the nominal

conditions

were reached.

Some preliminary

front

work (21),

tools plasticine,

of

Further

the

extreme

(figure cut, ting

figure in shown

state

the

that

tools

being

giving

the

coincided

of material

have been reached.

163 -

removed

state

the

action

cutting

model

a tool

of

figures

97(a)

the

above

of. the

and showed

at the

the geometry

tool is

in

(b). and

cap existed

the tool

It

and

cap developed

The cap has been approximated part

with

once steady

a metal

confirmed

edge radius,

tool

layer

a dead metal

'UPQ' and became an integral conditions

the

edge radius,

74) that

98.

of

a perspex

using

blunt

with

of material

on simulating

work

experimental

evidence

them

and the

exist

out

set depth,

showed

cutting

base

the

was equal

striped

the tool,

On the contrary,

the tool.

that

suggested

evidence

carried

was no, evidence

compressed underneath

of

below

does not

tool

goes into

completely

invalid.

From the

blunt

flow

does not

chip, and material

'A'

thickness

chip

the

by

once steady steady

forces

state

the

which

here

considered

situation

deformation the and theory

The theory

is

flow

in plane

at a constant theory

to the problem

must satisfy

the equilibrium and nowhere

conditions

the boundary

equations,

the

region

plastic

by the

must

regions

rigid

without

in

of

producing

deforma-

the stress

and stress

yield

stresses

be capable

plastic

cutting,

stress

conditions

which

is assumed to flow

the

the

the

allowing

material

equations

violate

machining

to be applied.

strain

of metal

that

and the condition

ties,

strain,

In applying

satisfies

solution

complete

orthogonal

so the material stress.

yield

The

predicts.

assumes a rigidjideally-plastic

does not work harden,

tion

one of

in plane

occurs

of plastic

model

proposed

boundary

criterion.

and velocity

stress

and veloci-

transmitted being large

from

withstood plastic

f low. 98 shows the mode of deformation

Figure

represented which

is

by the general

(47).,

contact

length.

for

cutting

with

state fields

to the slip-line

similar

Johnson

steady

a tool

164 -

ahead of the tool slip-line suggested of restricted

field, by

Consider

to be stationary

the tool

the tool

approaching

Near the cutting particles of

state finally

tool, a highly

stress

remains

free

body.

98 and consists

field

triangular

lines

straight

is

boundary

surfaces free. along

QR, such as abc,

'a' Thus,

QR is

Ic' and

is

only,

to the

PQS.

the

stresses

since

and shear

surface stress

shear yield

165 -

The

point

the

surface under

stress stressed

on the the

on the

acting 'b'

of

yield

the

separating with

PQR,

family

in equilibrium

and shear

the normal equal

of

0y 45

Figure

field

intersect

Each element

regions.

of the normal

action

lines

These straight

until

shown in

stress

up to

is

stress-

on each element

stress

the

as a rigid

an orthogonal

and stressed

QR at an angle

and unstressed boundary,

rigid

is

by a fan field, of

value

region

triangular

consisting

of the material. free

face

Subsequently

stress

field

steady

and the material

occurs

the plastic

to be

developed.

region.

The stress

tool

fully

at the yield

of a uniform

to the

under

is

flow

stressed

leaves

the material

connected

velocity,

plastic

enter

and stress

unit

ie when the chip

conditions,

state

with

and the workpiece

k.

I

In the plastic lines

also

PQS, -the lines

region

of

and the

the uncut

frictional the so

rough tool that

the friction

be severe not stress

of

as those

the

fan

base the of on is

98(b),

suggested velocity

slip

stress

also P is

discontinuity

field.

tool

recognised face

as a

vary

stress

face

tangentially

k and)since

stress the apex

a common point

indicat-

PCs

to the

appropriate

are conveniently

QQ' will

The hydrostatic

The shear

Particular

166 -

of the

non-uniform

on UP, Pp=

shows the hodograph line

PQ will

the figure. UP is

is assumed

is

PQ'.

meet the

0 90 the point

the hydrostatic

Figure

lines

the tool

it

the tool

the

and

be perfectly

whilst

the region

in n

angle

region

the whole

along

the tool

of

as shown in

and normally

of the tool

in

yield

cap it

will

along

conditions

The slip

PQS.

field

stress

PC on the face

function

surface

'k', be to assumed

is

face

ing

contact

chip

workpiece

the plastic

Due to the metal

workpiece.

the tool

the

satisfies

between

boundary the on

condition

that

which

region,

plastic

the uncut

separating

stress,

PS)which

of RS, is also a curve

is normal to QS and continuation of maximum shear

The arc

stress.

maximum shear

to PS are

normal

lines

of

defined

tangential by the

in

letters

two regions

the

for

vector

oa = unit

hodograph the of The arc

across in

arc

the

shear

the

with

the

tool. direction entering

material

The line

discontinuity

velocity the

SR and ob represents

origin

changing

zone QPS.

deformation

the

the

stationary

the

represents

the hodograph-represents line

o is

of the workpiece

velocity PS in

separate; while

workpiece,

and corresponds

of the absolute the

the

the hodograph

in ob

they

which

across of

velocity

exit

ab

chip -

a knowledge

With

field

5.2.1

qý;raight

in

zero,

Mohr's

Circle

the

static

98 is

stress

which for

stresses

the is

state

99(a),

a uniform

hodograph

and

slip

suggested conditions.

-P,

equal

to

stresses

of

ap

167 -

in

figure

terms 99(b).

of

on the plane by the

represented origin

field

stress

stress

an incompressible,

can be expressed

material stress

the

boundary

velocity

Assuming

figure

The principal plastic

figure

lines.

slip

QR are

flow

the

Fields

II

The. region

from

velocities

the

satisfies

Stress

the

of material

continuity

applying line

of

of

is ideally

the hydro-

the

Thus: -

a,.

where

k

-p

a2

-P

a3

+k -P > az

a3

........................

> al

According

to Hencky's

following

equations p+

where

2ký

p-

2ko

ý is

the

Considering surface

Pat

Considering

hold

angle 0

of

stress Pb'

since

UP is

along

II,

$-line

a

the

of

a'

)

line.

slip

-a

line,

is

straight.

since

slip

line

b'

x, cl

5.2

.....

b' %,

'73 ""-

I,

-

an a-line

free,

field

Pct = k(l a's

pp = k(l

alonv

plasticity)the

lines:

slip

rotation

field

stress

The hydrostatic

along

= constant,

=k=

of ideal

theorem

= constant,

stress

QR is

5.1

since

line

-a

+ 2n)

stress

on the

+ 2n) = prt

a continuation

tool

flank

UP is 5.3

.................... of

the

The same Mohr's

circle

that

be for used ran

region

I provided

line

slip

was used for

168 -

the

'T'

RSP.

the region axis

is

II shifted

the-r

field

line

The slip

stresses is

axis

under

in going PQ are

along

to 01,

shifted

principal angle n.

However) in order

angle length,

length

contact

n will

and the

relationship

(figure

cutting

tests

5.2.2.

Calculation

The cutting

force

of

terms

of the

the results)the

the

chip-tool

The

chip-tool

contact

An empirical

thickness.

chip

contact

length

has been established

thickness

chip

the undeformed

the

in

has to be determined.

undefo=ed

between

From the

to quantify

be a function

then

answer

and hence the

stress

can be calculated

stresses

chip-tool

a qualitative

consideration.

the hydrostatic

field

line

gives

proposed

action

to the cutting

given

through

99(a).

figure

C

if

by the circle

given

slip

Thus the

to point.

from point

n turned

to the angle

in proportion

and

from

70(b)).

forces

of cutting component

for

a tool

from the model of width

W is

by: (P cx Fc = [k(1 Fc=

((l

PQ x W) + (k x UP x W) FQ +kx + 211) x-

UP]W

F-O. 2n) + + UP1kW ............. x 169 -

5.4

force

The thrust

component

is

by: -

given

UF) FT =-- E(pp x + (k x PQ]W FQ-]kW 2n)UT + ................ UP = Cutting

edge radius

So equation

5.4 becomes

R.

+ 2n)PQ + R]kW

Fc = [(l

5.5

soosoooooo.

oso

5.5 becomes

and equation

2n)R + PQ]kW 5.6 and 5.7 give

Equations

in

f orce components fan

R the

field,

length,

contact

terms

cutting

the

of

the cutting the

edge

angle

force ný the PQ the

radius,

shear yield

of the

From the geometry

slip-line

Sinn =xIFS X'

where x=A-

RS - RS cosn

PQ QS RS = = also .*,

5.7

stress

and thrust angle chip

of

sinil

m

ä-

xt PQ

170 -

field

the

tool

k and the width

W.

of the tool

and x'=

5.6

figure

98,

PQ-+ PQ cOsn. PQ

sinn 0 f0

cosr, - sinri

=1-ä5.8

PQ 5.8 enables

Equation

law relating

the empirical

To compare the experimental

yield

The shear the for

Von Mises leaded

the

Due to

the

low

outpthe

carried

on the material

theoretical and

steel

the

copper

0.81 and

speeds

of

effects

steady

groove

using

the analysis

171 -

100). were

into

account.

the experimental

of

edge radius

cutting,

and

and temperature

forces

cutting

and a cutting

Although

tests

have not been taken

state

using

(figure

which

rate

test.

be 230 MN/M2

to

under

strain

properties

rrm during

material.

and

material

workpiece

404 MN/m2,

workpiece.

cutting

a compression

was found

relationship

zero rake

nominal

piece

from

k for

stress

the workpiece

101 and 102 show the variation

Figures

length

the calculated

with

forces,

Y was determined

stress

yield

results

of the

values

theoretical

contact

of Results

Discussion

5.2.3

chip-tool

using

thickness.

chip

undefonned

n to be determined

the angle

for

tools

of 0.56

copper proposed

of mm,

workis based

ideal upon

be pointed

which the

the basis

is

tool

chip

in

the

(F

force but It

length

contact

C)

interest are of directly

pointed

to the work of

the ratio where range which [211.

The results

within

the range

for

of cut,

the Author

arising

during

the thrust

over

cutting

of cut,

the results the results are in the

sawing process component

by the analysis

as predicted

T)

up to 0.3,

the

force

the cutting

by 15-20%, whilst

estimated

that, whilst

approximately

(F

increases.

of cut

is

A K

the situation

the

low depths

depths

the

results

whilst

at

out

the higher

at

relevant

is

cut,

from

force

thrust

as the depth

be further

from

experimental

in good agreement

is

is under-estimated should

of

n,

obtained

measurements

the

with depths

of

range

is

It

values.

of the angle

The predicted

good agreement

whole

the value

of the calculations,

results.

experimental is

that

out

show fairly

force

the thrust

especially

good agreement, should

the above results

theoryg

plastic

forces

are underare in

good agreement. The experimental cutting

force

FC/F

tested,

the range analysis

ratio T

increases

whereas

increases

same range.

of the

Further.

two components

of

the

from 1.1 to 1.4 within

the ratio

predicted

from approximately experimental

tests

by the

1 to 1.15,

in the

showed good

and

repeatability For

results.

comparison

experimental

identical

with

agreement

steel,

figure

those

obtained

when the chip-tool cutting unityt

and for

chip-tool

From the chip-tool (leaded giving

force

steel), a chip

tool

ratio

will

length

good

conditions to the

be equal less

is

less

thickness

chip

to

than the than unity.

figure

curve

length

contact

fairly

equal

ratio

the undeformed

results

cutting

is

length

contact

under

experiments.

for

contact

edge radiusythe

cutting

from

the force

edge radius,

tool

103, are in

length

contact

Components

The analytical

the model proposed,

On examining

102 shows the

the force sharp

conditions.

cutting

the leaded

for

for

a nominally

with

when machining

analytical

Figure

Purposes

obtained

results

the

with

correlation

70(b) value

to the radiu s

equal

toollis the of

approximately

0.125

mm, whilst

resultsifigure

1031give

value

to be approximately

this

experimental

0.20 mm. Figure for

104 shows the

field

slip-line

model drawn to scale

I

the cutting

obtained practical

conditions

from the model test

results

stated. (r

(rc

The chip

compared to the

c=0.08)/as = 0.1)

agreement. 173 -

ratios

are

in

fairly

good

105(a)

Figures

for

curves

and

show the

the cutting

energy

morelthe

depths

small

for

explanations energy

for

of cut this

Backer

reported.

of cut

et al

the concept

of

a higher

yield

having

shear plane recognising

these

high

the high

accompanied tool

rake

factors

additional high of

observed

dynamic nature

Whilst

the

during

the

of the

situation the tool

angl-e of

due to

further drag at

and examination the

explanation

of cut.

the flank described,

cap previously

that

specimens

depths

to be considered.

speed films

the Author

smaller

in the

shear

by the metal caused

the phenomenon

increase

possibilities

by the high

cutting

was the

edge radius,

cutting

specific

An alternative

smaller

negative

effective

ie

stress.

at

in

at

Various

tools.

explained

effect,

(85) Tamura Nakayama and by length

further-

tools;

have been previously

(84),

size

the blunt

increases

rapidly

increase

energy

As expected )

for

sharp

the blunt

rapid

depths low at

is higher

energy

cutting

specific

cutting

stated.

the nominal

as compared with

tools

specific

conditions

cutting

the specific

with

(b)

174 -

are

From the results of

shear-plane

initial

of the

stages

the chips

produced;

zone was of a of

the cutting

with

action,

The model proposed weaknesses.

under-estimations. to

presented

and practical

simplicity

the length

assumed along where is

valid is

to be k,

assumed in

the

to

the

face

rake

force,

in

in question the material workpiece

this

friction

of

the

closer

agreement

practical

is

the value

calculated specimen.

test

of

the

chip

value

is

friction

of

the

of

force

ratio

the

would be greateý

force

with*the

Another

yield

above

the

over-estimate

results.

only

eventually

from the compression

175 -

stress

this,

the shear yield

The value

shear

The effect

tool.

therefore,

the

has been

of the tool

Beyond

In reality

which wouldýgive obtained

ie

where the

point

First,

occurs.

occurs,

be to theoretically would

assumption thrust

the

the model

face

the rake

although

are

why the difference results

cap regi6n.

metal

decreasing

leaves

contact

chip-tool

the

of

components

maximum friction

of the model,

are in

predictions

examining

the reasons

consider

between analytical for

is worth

It

has certain

force

of the

the ratio

good agreement,

force

the thrust

Although

were reached.

state

present

in its

as the cut

conditions

state

steady

until

progressed

decreasing

the shear angle

stress

ratio point

of

test

of the

stress

taken

of approximately

was at a strain

yield

,

the

indicated

strains

on the copper

tests

Hardness

calculations

strain

shear

Merchants from and

force

stress

ively.

This

would

indicate

stress

taken

from

value

the theoretical the force

that

forces

yield

stress)

using were

chip in

measure-

excess

test

equations,

of

3.

specimen, gave shear

the value

176 -

oil the shear

test

results

and an increase would

by 20-30%p whilst

ratio.

i

the

the above value.

the compression

an under-estimation

k, the shear of

in

2§6 MN/m2 and 320 WI/m2 respect-

yield

is probably

of

an increase

compression

balance

values

yield

than

the true

although

possibly

greater

at strains

stress

From the shear mentsp

indicated

curve

stresS7strain

1.1,

in the

have increased not

altering

CHAPTER

THE PERFORMANCE OF SAW BLADES FIELD TESTS AND THE SLIP-LINE

PREDICTING SIMULATION

6.1

Forces

Predicting Sawing '-

tool

force in

model

FT

LT_

+ 2q)

R The

sin

cos

provided

from

(5.7)

kW ---------------------

R',

the

slip

line

following

n-

shown in

3.8

combining

F(l

A PQ

figure

106,

A

tool

Figure

this,

FrOM figure

FT R

FT can be predicted

R

the

the chip

To obtain

PQ RR

predicted.

(6.1)

field

equation

model derived

may be in

5,

chapter

form

by

from

determined

point

single

-E-11ý1

Ti in

fan-angle

in

Energy

kW -------------------

+ PQj

+Q

FROM THE

5;

chapter

through

Divided

the

satisfactorily

component

2n)R

1+

be

Cutting

enables

model to

performance

The thrust the

field

line

The slip

Specific

and

DERIVED MODEL

for

(5.8)

--------------------

contact 70

(b)(c)

length

PQ is

was

replotted

and 6.2

in

106.

steel

workpiece

(6.2)

-------------------------------6.1

known.

gives:

-

+ 2n) + 3.8gflj MR -------------

177

7

the

By combining I,.

used f

force

thrust

mean

in

equations

the

tooth

per

per

is

calculation

sawing

(1.415R. +3.8

FT

tm

and 5.8

49R + 3.8 A] kW

FT The

6.3

6a)k

ft.

thickness

unit

.1

by

given

6.4

------

-w

since

for

6a

A=

Substituting

shear

k

404 MNM-2 and

R

271im. - -into for

expression

ccqparison

yield an

for

stress

average

radius

edge

force

of-'sawb1ade-s derived

following

the

gives

thrust

mean

performance.

steel,

cutting 6.4

equation the

saw blade

with

per

tooth

per

unit

thickness: f

16.14-

tm

This

+ 15356

Nmm

single -point- cutting

tool

for

can be obtained, force

cutting

obtained

to be ccnpared with

sawing tests. Similarly, an expression energy

---------

the re ults

allows

expression

6.5

the

using

with

results

specific

the

expression

[(l R]

+2+

Specific

cutting

Esp

FC

Esp

f

kW-----------

5.6

energy,

[(l

+ 2n)FQ

178 -

+ R]

k

obtained

cutting

component:

F

the rnodel of the

for

f=

.0

Combining

this

6.2

-

gives:

[5

61 +Rk -

Esp

107

Figure the

of

a Single

of

Comparison Performance

from

------------

6.6

the

cutting

specific

different

for

values shear

tests,

The model

predicts

conditions, The

lished.

to

those

of

yield

The

appears

to has

in

obtained the

range

from

obtained

forces

does

for

the

when not

in

workpiece

slope

of

the

depend

on

geometric

been

Blade

the

23.

differences

changes

pitch.

which

with

is,

and

6a within

of

the

model

provide

which

results

Figure

that

Tool

values

hacksawing

blade saw

Point

the

compares

model

power

due

and

k.

stress

6.2

for

5.8

equation

R and material

radius

edge

cutting

allows

be calculated

to

energy

a]

expression

The above

with

expression

chip

is

state

fully

estab-

include

parameters

blade

performance

breadth

and

varying

in

figure

107

curves

previouýly

steady

factors,

noted

in

a problem

Chapter

3.

1 Although

some

attempt

has

179 -

been

made

previously(24)

to

the

explain

on blade

The slope

of

in

parameter

6.3

the

the

results

obtained

from

the

simulation

confirms

that

there

is

saw blade

performance

the

analysis

Performance

Tests

(88).

of

blade

that

The

not

109.

figure the

factor

show The

pitch causing

A further

series

4 and 6 T. P. I. dition

any

of

teeth

by

results

obtained

agrees

from the

with

on

a standard

trend!

the

was

not

which

appreciably of

in

cutting

these

tests

was

not

the

4 T. P. i. to

modified

relieving pattern,

of

tests

blades.

influencing

then

set

change

in

change

factor

tests.

out was

teeth

the

of

model

figure

sawing

performance

results

an

tip

of

was

repeated by

altered

the

modified

performance, clearly

showed

geometrical

performance.

were carried The blades

in

out

on standard

their

new con-

CUtting

performance

were then modified

by completely

were subjected

The blade

blade

teeth,

modification. did

carried

The

three

the

slipline

Effect

blade

tooth.

other

sets

this

same

2 T. P. I.

apparently

from

108,

the

This

tooth

a single

were

The

from

the

as the

figure

tests.

and that

Pitch

defined

pitch,

a geometric

for

the

of

in

been

has been plotted

This

obtained

obtained

results

Examination

every

pitch

be a performance

shown to

different

of

with

the

107,

hacksawing.

power

together

model

figure

K, has been

blades

various

blade

have

explanations

in

curves

constant

cutting

of

and

actory.

unsatisf

for

the

performance,

breadth

workpiece

of

effect

to the

tests.

every

removing

size.

gullet the

modified 110

Figure

for 6.4

the

shows

pitch

for

broad to

inadequate would

increasing

the

results

blades

make

subsequently

was depth.

gullet

these.

of

tests

---

blades.

radius There

acco=odate

of

the

depth

are

all

a possibility

was

the

gullet

size

the

chip

produced.

gullet

the

that

so and

ineffective

gullet

Some dimensions

designed

gullet

workpieces

the

blade

the

are

similar.

geometrically that

by

teeth,

the

of

6 T. P. I.

to

Geometry

and

hacksaw

Standard

subjected

and modified

standard Size

Gullet

The

the

again

were

tests.

performance

further

blades

The

increasing

thus

tooth,

other

by

was

chip

This crowding.

f or

geometry

standard

blades- are shcwn belcv. Root-tip

Blade

height (mm)

Root

Pitch (mm)

radius (mm)

4 T. P. I.

3.3

1.14

6.35

6 T. P. I.

2.28

0.69

4.1

10 T. P. I.

1.4

0.43

2.54

Preliminary

hacksaw

calculations

operating of

workpieces removed

in

difference crowding

as

conditions

50 mm breadth, less

was far

blade

that

showed

than

- 181 -

normal

when cutting

steel

the the

performance

such.

under

volume

gullet

of

metal

volume.

was not

due to

So the chip

Observations

have

Condition'l

tooth

and does not

Under

these

form

the

chip

-

at

obstructed to

by

applied

spread.

the

is

face

of

the

of

ill.

the

gullet. to

appears

per-

it

until

or become

break

the

above

gullet

Condition

the

root,

Any

further

metal to

chip

the

tooth

the

base

of is

removal t: he back

these'conditions

pressure

to

hits

the

locked

into

are

the

even the

-

of

in

IV - Finally, in

travel

this

conditions

chip

182 -

where

can either

position.

gullet

some cases, situation,

curling.

it

root the

around

paramount

this

the

around

workpiece

energy

extra

travelling

chip

perimeter

by

of

causing

owing

continues

three

occur. s. However, caused

the

- Under

The chip

gullet

face

rake

the

obstruction.

in

expended

radius.

is

workpiece

workpiece

difficult

III

Condition

the

up

increasingly

made

the

figure

the

root

a broader

For

travels

formed, is

In

chip - fo=r.,,

rake

blade

the

conditions

11

and

is

the

reach

hacksawing

at maximum efficiency.

Condition is

of

up the

travels

chip

in

of various

breadth

the

--When

the

formation

chip

the'production

revealed

small,

the

of

radius

and

importance.

chip

curl

back

pressure

112:

Figure that

be

can

The

cut

II

III

and

The above

above

and

the

Since

anism.

the

zone,

mation

the

results

of

pared

(figure

formance

standard 108)

with from

obtained well

. with

There

appears

to

shape

and

blade

performance.

agree

in

the

is

valid,

without point

the

gullet

chip

to

the to

mechby

chip

defor-

the

altered.

provided

modified

the

single

QR is the

any obstruction, tests.

tooth

The blade

chip

98,

it

free. is

However,

is This

allowed

as was the

- 183 -

in

results results.

that

the

influences

gullet

stress

test

an

com-

per-

model

factor,

Figure

is

tool

point

hacksaw

test

the

blades,

model.

a geometric

the

from

calculated

the

presented,

region

simulation

the

pressure

and

the

be

of

size

model

the

that

K,

coni3taiit'.

cutting

in

Results

of

Discussion

broad

sawing

offered

is

for

gullet

modifies

field

condi-

E).

obstructed

a back

stress

of

of

thatwhen

resistance

blades.

pitch

(Appendix

thus

applies

shape

gullet

The

are

workpiece

criteria

size

confirm

chips

the

the

of

various the

on

blades

The obstruction

space.

6.5

based

observations

workpieces,

the

for

are

similar

geometrically

length

efficiently

calculations

tion

limiting

the

shows

-the

assumed assumption

to

case

flow in

additional

the

freely single back

of

be

can

pressure the

in

chip

tional

pressure

cutting

force

force

FT and

value

6a,

of

is

believed

is

in

fact

tm

Figure

108.

results

of

K and

a 'cavity'

or blade

in

Further figure

to

blades root the

are

the

contribute variation

same

figure

in

23 lowering

of

effect

the

the

of

to of

It

tip

which

184 -

showed was increased

size

teeth.

were

geometrically

differences

in

and the

that

to

the

refer

the to

respect

with

contribute

pitch.

-

the

23)

to the change in blade blade

in

(figure

gullet

height

believed

is

in

tested curves

the

explains

obtained

blade

the

effect

This

when gullet

blades

of

be a pitch

to

exists

where

pitch

size

all

in

the

effect.

The overall

root

performance.

chip

thrust

the

for

performance

performance

the

gullet,

gullet

performance

tooth.

radius,

if

increasing

thus

appears

110(a),

the

a single

and

undeformed

curves

confirmation

The 41 6 and 10 T. P. I. and

same

addi-

thrust

the

the

this

energy.

altering

similar

obstruction

of

that

have

what

in

the

the

will

that

improvement

effect

increased

of

slopes This

difference

without

is

constant.

It

the

f

hence

cutting

specific

for suggests

model

the

both

increase

to

components

the

cutting

The

gullet.

is

decrease.

will the

the

The

thickness.

on QRowingto

applied

perimeter the

the of

blade

above differences

performance

with

the

The

results

results

obtained

breadth

increased

This

mance. is

in for

an

that

been observed as it

thickness

the

cutting

the

chip

remains

of

on the

cutting

of

certainly

tance

interaction

of

well

correlates 113.

figure the

ing single

edge

as

This

an

is

the

radius

the

blade

the

of

the

extreme

discussion

is

now

summarized

point

formation

tool under

measured

high,

study free

significant,

blades,

the

increas-

of

the

it

edge

radius

of

for

the

values has

been

used

condition.

:-

confirms chip

-

but

and

confirming The

dis-

with

model,

effect

tooth,

average

a little

perhaps

the

tests.

simulation

with

of

shows

thickness.

more

the

point

tool

factor

is

results

also

of

force

from

flow

185 -

the

has-

up td, the

cutting

dominant

tt

constant

uniform

obtained

test

fairly

of

root

indicator

The single chip

energy

effect

Single-point

in the

not

perfor-

of steel'r

face,

chips

gullet

figure

tool

point

root.

with

with

The

70 Vm compared blades

chip

cutting

specific

The

gullet

is

travel

tooth

of

tooth

increase

the

that

suggests

up the

gives

blade

cutting

ba:ýed on

explanation hacksaw

impinges

the

breadth

workpiece

power

wheft it

This

in

In

travels

steel

.

work-piece

pitch,

adecline

of

explanation

forces.

transient

blade

the

of

as the

a particular

to

trend

24 where,

indicating

alter-native

the

confirm

figure

decreased,

constant

112

Figure

of

mechanism

conditions.

of There

is

factor

in- blade

energy

in

the

tion

forces

of

the

obtained

by

constraint

of

detailed

for

future

the

the the

in

chip

the,

would

explanations

tests,

of

to

clearly

cutting

specific is

compared

can

be

with

explained

Investigations

saw gullet. to

be

a fruitful

only

to

the

seem

effect

Or frictional

deviations

the

model,

consideraThe

When

saw blade

the

into

gullettis

energy.

the

:-

obstruction or

in

topic

work.

The results Whilst

of

blade

cutting

that

geometry.

chip

cutting in

from

to

the

of

specific

as obtained

energy,

due

specific

than

take

not

a deciding

are

follows

as

or

size of

higher

does size

gullet

walls

is

value

explained

study

forces,,

the

on

increase

that

tool

effect

additional

any

The

tests

is

This

point

The single

test

saw blade

the

and

geometry

gullet

performance.

results.

model

for

the

that

evidence

presented

adequate

single

copper

workpiece

data

perforinance,

on the to

above

copper

point

refer

(chapter did

test

cutting

not

be made.

186 -

4), allow

data

steel

was available

insufficient the

workpiece.

comparison

sawing of

blade

CHAPTER 7

GENERAL CONCLUSIONS

1.

load

The thrust

the

2.

characteristics

At high

dramatically.

vary

machines

lozýd is

thrust

effective in

A method

assessing

the

removal

rate

on the metal

be used

of

and the

this

tests

comercial

blade

speeds,

the

based

performance,

is

has been

every

to be very

found

out on a load

includes

test

which

The

test.

be carried

could

of the (3.2)y

proposed

control

test

saw provided

due to

reduced,

and independent

as a quality

repeatability

good,

power

characteristics,

saw machine could

the

recipýrocaltion-

hacksýaw machines.

instability

of

of the power hacksaw

measurements. 3.

Cutting cut

tests

achieved

per of

applications

together

have shown that

with

teeth

show

depth

of cut

the cutting that,

in

is

less

blunt

cutting

tool.

metal

removal

takes

formation.

small

hacksawing.

the

of

majority

than

saw the

applications,

edge radius.

be classified may

with

of

measurements

of the

the cutting

Under these place

depth

in most

These

edge radius

the hacksaw blade

Therefore,

of chip

is very

tooth power

the average

cutting

a complex

as a

conditions, combination

4.

The specific

that

than

usually

cutting

relative1jinefficient The cutting measure blades

blade

different

of

teeth

From the

pitch

experimental having

tools

a large

as a with

both

and workpieces

of

when machining edge radius

thickness,

flowing the

there

beneath

flank

as

the

as has been

suggested.

When cutting cap enveloped

with

surface,

unstable

in nature.

instability

blunt

It

to exist, is

believed

188 -

metal

edge radius which that

to the variation

produced.

-

a stationary

the cutting

appears

contributes chips

tools,

between

machined

of

chip

behind

and recovering

previously

type

the

varies

cutting

of material

was no evidence

7.

indicating

of a hacksaw blade.

observations

compared to the undeformed

tool

with

has been used

performance,

times

breadths.

different

with

the

to four

when cutting

thus action

which

constant,

of

obtained

(turning)

tools

sharp

nominally

5.

fn the hacksawing

has beeen shown to be three

operation greater

energy

cutting

and

could this in the

be

8.

blunt

with

tools,

confirms

A usefUl tool

build

and the

presented

which

influenced

by the

cutting

the

found

is

theory

of

found

to

to

appear

plasticity-,

the

chipthickness

chip

within

be the

weaknesses

field

slip-line but

point

slip-line

boundary

all

gives

(Figures

experimental

depths

as compared with

arise

force in

ratio

processes

construction

Fc 4 FT such

189 -

has

presented

the

Both experimental at very

the cutting 1,

its

good

101 - 105) with

have shown that

results

the

fields

and fairly

results.

and analytical of cut,

fan and

conditions.

model

a qualitative

agreement

quantitive

plastic

The associated

with

satisfy

The simple,

could

the

edge radius

field.

and velocity

of stress

radius,

author.

to be composed of one centred

slip-line

one straight

single

does not

which

tested.

By applying

are

by the

undefo=ed

is

of cut

up forces,

between

relationship

length

when machining

length

obtained

has been

field

11.

transient

empirical

contact

range 10.

as the

results

previous

process

decreases

causing

progressed

9.

of the cutting

The efficiency

a situation

as sawing,

low

edge which grinding

I

on the tooth 12.

The results

by the

predicted tooth

(Figure

tests

tooth

configuration

performance.

blade hacksaw a blade

of different

the effects

to study

can be used

The model presented

and broaching.

model for

the*oretical

and results'from

experimental

107 and 108) fall

into

a simple

pattern. The cutting

edge radius

be satisfactorily can

13.

The model

the

assists

blade

with

performance

by the model which

predicted

correlation

shows close

on blade

effect

explanation

figure

tests,

the

of

workpiece

I

breadth

and blade

the influence

pitch

effect

in conjunction

with

of the gullet.

The work undertaken geometric

factor

affecting

the blade

demonstrates

due to gullet

that

there

is a

shape and size.

performance.

The model and single

point

tool

study

qualitatively

relates

to the blade

performance.

In order

quantify

the results

the analysis

has to be

to

I modified

to take

into

the above

consideration i

geometrical

aspects.

-

190 -

113.

SUGGESTIONS FOR FUTURE WORK

1.

Saw Machine A feasibility

and investigations

study

to improve

carried

out

hacksaw

machine.

some of

the following:

(i) (ii)

6 a variable dynamic

the performance improvements

These

the power

should

include

saw machine at

stability

speeds of

the higher the

force

the mean thrust

to be closer

cycle

of

-

stroke

iprocation

be

should

rec-

available

saw machine

during

the cutting

to the maximum thrust

orce load

a thrust

saw machine, load

force

maintained

(v) (vi)

system,

tooth

per

which

would

workpieces,

cross-section

a blade

tensioning

a quick

return

the

enable

value.

useful

and This

when cutting

and measuring

system

mechanism on the idle/return

191 -

the

to the

to be monitored

would be particularly

stroke

I-

facilities

to a pre-determined

of varying

into

system built

feedback

with

applying

thrust

measuring

Saw Blade

the blade

Assuming that treatment

is work

increasing

the

the

reducing

data

for

This

and

tool

point

the effect

of gullet

size

different

using having

would

study

in

loss

a larger

provide

use of the

more effective

The single

different

(rake

of the blade

tools

edge radii.

cutting

cutting

sharpness

teeth

tests

and cutting

materials

the

the kerf

simulation

out

the

of

thickness

order to reduce Tests Simulation To carry

can

which

edge,

angles)

clearance

4.

sharpness

of the blade

geometry

3.

cutting

and maintaining

edgep

(iii)

the

of

the

by. --

be improved (i)

in improving

required

and life

efficiency

heat

are as good as can be achieved,

at present

then further

and its

material

should

workpiece range

comprehensive field

slip-line be extended

and geometry

of

model.

to include

when machining

materials.

Sawing Tests

Blade perfo=ance different

workpiece

comprehensive

data

tests

be carried should

materials. for

the blade

This user

would

out using provide

and designer.

more

APPENDIX A

Appendix (i)

Suggested

(ii)

conditions

Comparative

(iii)

How to for

(iv)

Power

and blade

most

universal

costs

Hacksaw

Blades

- some of

the

problems

solutions

B

Table

1

Tooth

Table

2

Measurement

of

Table

3

Performance

testing

Table

4

Cost

Table

5

Cutting

test

results

for

Blunt

Tools

Table

6

Cutting

test

results

for

Blunt

Tools

Table

7

Cutting

test

results

for

Blunt

Tools

Table

8

Computer

Table

9

Theoretical -.

Appendix

C

AnalysiS

of

Appendix

D

Simulating Appohdix Predicting

machine

sawing

application

and their Appendix

the

Bandsawing

times

cutting

choose

your

for

the

radii

measurement

for

data

slot

the

cutting

the

Limiting

width of

Blades

a hydraulic

programme

effects

- results

from

results

of

Power

slip

-

Blade

action

Data -

line

Hacksaw

field line

slip

Sheet

field

tension

of

a single

Hacksaw

Blade

Tooth

EI Length 193 -

of

Cut

for

Blades

of

Various

pitch,

Appendix

A

SUGGESTEDCONDITIONS FOR BANDSAWING(4]

Material

Work size and blade teeth per inch Under 3 in 3 to 6 in Over 6 in

Feed pressure (lb)

Saw band velocity (fpm)

SAE steels 1020

8 or 6

6 or 4

4 or 3

75 to 200

225

1050

8 or 6

6 or 4

4 or 3

75 to 200

200

1110

8 or 6

6 or 4

4 or 3

75 to 200

250

1120

8 or 6

6 or 4

4 or 3

7S to 200

200

1320

8 or 6

6 or 4

4 or 3

75 to 200

175

ý340

8 or 6

6 or 4

4 or 3

75 to 260

165

3135

8 or 6

6 or 4

4 or 3

75 to 200

150

4140

8 or 6

6 or 4

4 or 3

75 to 200

140

5140

8 or 6

6 or 4

4 or 3

75 to 200

130

52100

8 or 6

6 or 4

4 or 3

75 to 200

125

9260

8 or 6

6 or 4

4 or 3

75 to 200

100

8

6

4

75 to 200

75

10

10

10

75 to 100

22S

Tubing or channels (heavy wall)

8 or 6

6

6 or 4

75 to 200

225

Brass, SAE 72

8 or 6

6 or 4

4 or 3

75 to 200

250

Bronze: SAE 73

8 or 6

6 or 4

4 or 3

75 to 200

225

Aluminum alloys

8 or 6

4 or '3

3

75 to 175

300

other

metals

High speed steel Tubing or (thin channels wall)

Al TABLE 1

SUGGESTEDCONDITIONS FOR BANDSAWING(4]

APPENDIX A Comparative

1

Figure

Cutting depends

(a)

ability, of. the ýr'n

cutting

blade

times,

costs

(b)

time for bandsawing machinon material and beam strength saw blade 4tt-E6V/00SV 100 IYQ18001170

00

per

[4]'

workpiece

Power hacksaws can apply feed pressures adjustable hss blades to tensioned by backup blades supported

140r

10 0 0// 80 OIV707

60?

U,

50 0'

C .5

U

40%

Q

0

0

0 0)

Machinability of material

<

10

2T

12 24 Time of cut Example: Given 48 sq inches 50% then time machinability 12 min

016.03

Time of cut(minutes) Example: Given 20 sq inches 1007o then time machinability 1. -min

4 Cc)

6-

Blade

cost

off with diameter at $18.55 1 (YI670%

per

workpiece

in

(d)

cut

bandsaw varies with and machinability, a blade 30% 20% 50%

6

Blade cost per workpiece cut off with power hacksaw is ba-sed on tungsten hss blades at $4.22 a blade

M% 50%

30%

1 20V.

ai u Qj CL

40

0

E2

ý-2 (U G a 0

0

10

Slade. cost per

15

0

piece (cents)

A2

IIIIIIIII1011111 r-I in

Irl

Blode cost pe-r piece (cents)

')I

0 0 cl. 14 a asw

0

Q.

'A

* 00

'o

r-

40

*0

.

'0

00

0

.0

*

M.

3v

a

4

.0

&

-E

3.

6d

C

31

cr V z -tp Mw C) 0N

1c, *0 *

1

.0-

1

1 4F

=;

I

a

0 c

I

ý. *Z s

4ý as &. I

* . r. 12

1

4 0*

1

1

1

* I ý*

1 *

4 0 *

.9" I ý

-0 I I

44 :;

-0

-W

64

2 0

it

4.1

-2

-

*0 *. rqp 'A

0

4ý

0 40P. 4

0 4F

4op

43

to

-0

4p

31

Is

40

ta

a I-

.

a

.

a

vi

0

vi

-

a

I.. L* vs c

9 2

0

,w

Iu

M

.

9

a

41

to

L.

0,

JS

0 0 ! as .4 . Z

AM

1 V2

000 cý

0 = 12 ..

-s

"i

"i

2 . , v

w 1.

su o

c

oq= PUT

aw2.

" t0C

c C C

A3

9. .

C

02

2

.i Cu S I..

. 'Appen'dix TABLE

A

3(a)

POWER HACKSAW BLADES:

SOME OF THE PROBLEMS AND THEIR

SOLU'rIONS,

PROBLEM

CAUSES

Blade breakage

1

Blade contacting beforý cutting

2

Blade not cutting straight

[13]

SOLUTIONS

1

Start machine with blade work and allow automatic to make contact *

Cutting in'the same slot with a new blade precut by worn blade viously

2

Always start a new cut with a new blade, or turn material over and saw to meet the old cut

3

Insufficient

3

Check the blade for 3 or 4. cuts after

4

Excessive feed when thin sections cutting

4

Reduce the pressure

5

Using a worn out blade

5

Fit

6

Material

in, vice

6

Hold/Clamp especially cutting

I

Insufficient

1

Check blade for tension 3 or 4 cuts after

2

Blade worn out

2

Replace with new blade - an blade is both a time over-dull and money waster

3

hard spot in Excessively blade forcing off material straight path

3

Turn material over and start If set has become a new cut. unevenly worn replace with new blade

4

Excessive

5

Saw frame worn in slide or out of perpendicular alignment

5

Inspect adjustment of machine and adjust as necessary

6

Excessive

6

Reduce to correct

7

Bladefails to lift return stroke

work

tension

loose

tension

above feed

tension

new blade firmly. material in multiple

Reduce the pressure and watch the improvement in alignment

pressure

speed on

.7

A4

speed

Inspect machine for probable necessary adjustments

Appendix

TABLE

3(b)

POWER HACKSAW BLADES:

SOME OF THE PROBLEMS AND THEIR

PROBLEM

Premature wearing out of teeth

I

Excessive

2

Teeth. facing

3

Incorrect

---------- --Blade breaking pin hole

(13]

SOLUTIONS

SOLUTIONS

CAUSES

Teeth ripping

A

1

Reduce pressure

2

Teeth should face towards the machine if drawcut type - away if push out machine

of teeth

3

Replace with

4

improper cutLack of'or ting compound or coolant

4

Use reliable coolcutting ant with correct mixture for material being cut

5

Excessive

tension

5

Do not apply excessive pressure in tensioning blade

1

Blade not mounted

correctly

1

Make sure blade is flat against the holders and pins are drawn up to the end of eye before final clamping and tensioning of saw

2

Worn pins size

or improper

2

Replace with rect pins

3

Too many teeth large material

3

Select etc

1

Sawing against corner or a sharp edge

1

Carry out 3 tooth rule being cut material

2

Material moving during cutting

2

Hold/Clamp especially cutting

at'

out

pressure wrong way

pitch

for

A5

correct

pitch

new and cor-

correct

tooth

pitch

on

firmly material when multiple

APPENDIX

Table

I (a) OF TEETH RADII

RESULTS BLADE

B

SPECIFICATION:

x 10-3

Radius

i

'X' BRAND -

400

x '40 92x4

TPI

inches

BLADE No 1

No 2

No 3

1

1.1

1.6

3.0

2

2.5

1.2

0.9

1.5

1.6

3

0.8

1.0

1.4

1.5

0.6

1.4

4

1.0

1.4

1.0

1.1

1.1

1.2

5

0.5

0.6

1.1

1.2

1.9

6

1.0

0.5

0.8

1.4

0.6

0.6

7

1.1

0.5

1.4

0.8

1.1

1.1

8

0.8

0.8

0.7

1-0

0.7

1.2

9

1.4

1.4

1.0

0.8

0.55

1.4

0.6

10

0.9

0.8

0.8

0.6

1.2

11

1.4

0.9

1.0

1.2

0.8

0.4

12

0.7

1.4

1.2

1.5

1.1

1.0

13

0.8

1.2

0.9

0.9

1.2

1.2

14

1.2

0.5'

0.7

1.1

1.1

0.9

15

0.8

1.4

1.5

1.6

1.2

1.1

0.9

16

0.8

0.9

1.2

1-1

17

0.7

1.0

1.2

0.8

1.4

1.0

18

0.6

1.1

0.9

1.6

1.2

1.1

19

1.2

1.5

0.8

1.1

1.4

0.5

20

0.9

1.5

1.2

1.0

1.5

21

1.0

0.8

1.4

1.

1.5

1.1

22

0.8

1.2

1.5

1.6

1.257

1.1275

1.045

TOOTH

Average Radii

0.957

-

,2

1.100

No 5

No 6

'0.7

........

Bl

No 4

1.0619

Table

I

RESULTS OF TEETH RADII CATION: --; BRAND 'X'40G

BLADE

SPECIM

Radius

x 10-3

x 4G X '2 *X 6 Tpj

inches ...........

: 111, ....

.

...

..

No I

No 2

No 3

No 4

No 5

No 6

Radius

Radius

Radius

Radius,

Radius.

Radius

1

2.6

2.8

1.5

2.6

1.4

1.4

2

2.6

1.1

1.6

1'

1.5

3

1.8

1.1

1.5

1.8

4

0.9

1.2

1, *8 1.9

*8 2.2

1.5

0.9

1.2

1.8

5

1.5

1.1

1.4

1.4

1.5

1.2

6

1.6

1.5

1.6

1.1

1.4

1.5

1.4

0.9

1.1

BLADE TOOTH

....

...

.

7

1.8

2.2

1.2

8

1.0

1.8

1.5

0.9

1.1

1.2

9

1.6

1.2

1.2

1.9

1.6

1.4

10

1.1

1.2

1.0

1.5

1.2

1.0

11

1.2

1.4

1.2

1.8

1.8

1.2

12

1.4

1.4

0.6

1.0

1.4

0.9

13

1.1

1.2

1.6

1.4

1.2

1.1

14

1.5

1.2.

1.0

1.5

0.55

0.8

15

1.6

1.5

1.5

0.8

0.7

16

1.5

1.2

1.6

1.9

1.2

17

1.1

0.4

1.6

1.4

0.6

0.6

18

0.9

1.8

1.1

1.5

1.2

0.6

19

2.4

1.9

1.0

0.7

0.8

0.55

20

0.9

1.4

1.5

0.8

1.4

0.6

21

1.2

1.5

1.6

0.9

1.4

0.8

22

1.2

1.4

0.8

1.6

0.5

0.7

23

1.8

1.6

0.9

1.8

1.4

0.9

24

1.9

1.5

1.6

0.9

1.4

1.2

25

1.4

1.1

1.9

1.5

1.5

0.6

26

1A

1.0

1.1

1.6

0.8

1.1

27

2.4

1.6

1.6

1.2

1.0

28

1.4

1.2

1.0

1.1

1.2

0.9

29

1.0

1.5

1.4

1.8

1.4

1.5

30 31

o. 8 1.4

1.2

1.5

1.6

1.6

1.4

1.2

1.5

1.4

1.6

2.6

32

2.5

1.5

33

1.0

4.0

1.6

1.0

0.9 1.2 -

1.5

Average Radii

1.4878

1.512

1.376

1.409

B2-

1.224

1.2

1.1

1.134-

Table

I

RESULTS OF TEETH RADII BLADE Radius

SPECIFICATION: x 10-3

-

BRAND'X'

400

x 32 x

1.6

x 10 Tpj

ins

No 1

No 2

No 3

No 4

No 5

No 6

Radius

Radius

Radius

Radius

Radius

Radius

1

1.8

1.6

2.5

2.4

2

1.6

2.5

0.9

1.2

2.0

1.2

3

2.2

0.9

1.4

0.8

1.6

1.9

4

1.9

1.6

0.6

0.6

1.0

5

1.0

2.5

6

1.6

1.4

0.8

8

2.0

1.5

9

BLADE TOOTH

1.2

2.2

-1.4 0.9 1.0

0.6

0.8

0.7 1.8

1.2

1.0

1.0

1.5

0.8

1,4

1.6

1.5

0.6

1.8

2.0

0.6

10

1.5

1.4

1.2

1.6

1.1

1.2

11

1.6

1.2

0.7

1.4

12

1.8

1.1

0.8

13

0.9

1.6

14

1.2

1.8

15

1.2

16

7

1.1

2.4

-0.7 2.5

0.9

1.5

1.8

1.2

0.4

0.5

1.4

1.1

0.7

0.3

0.5

3.0

1.2

1.1

0.7

1.8

1.0

2.2

1.0

o. 8

17

0.8

1.6

1.4

0.7

1.2

1.1

18

1.4

0.9

1.2

3.4

0.7

1.2

19

1.0

1.6

0.7

1.4

1.2

1.2

20

2.0

1.1

1.1

1.4

0.5

1.2

21

1.1

1.6

0.9

1.4

0.9

0.7

22

1.6

1.6

0.7

1.4

0.5

1.3

23

1.4

1.2

1.1

1.5

1.4

1.2

24

1.8

1.6

1.2

0.8

1.5

1.8

1.0

1.5

1.6

2.4

26

1.5

1.2 1.9

1.0

0.6

1.0

0.8

27

1.5

1.6

1.6

1.2

1.4

1.0

28

1.4

1.0

0.8

0.7

1.5

1.2

29

1.2

1.8

0.9

1.6

1.2

1.4

30

1.5

1.9

1.8

1.5

1.9

1.2

25

B3

.

BRAND'X'

400

No 1

No 2

No 3

No 4

No 5

No 6

TOOTH

Radius

Radius*

Radius

Radius

Radius

Radius

31

1.8

1.4.

2.4

1.0

1.4

32

0.7

1.4

0.7

33

0.7

2.0

0.9

1.6 . 1.6

1.6

1.1

1.1

0.9

34

0.8

1.1

1.5

1.2

1.2

0.9

35

1.0

1.6

2.4

1.6

1.0

1.1

36

1.2

1.5

1.6

1.6

1.1

1.2

37

1.5

2.0

0.9

1.4

1.2

1.1

38

1.2

2.6

1.0

2.5

0.8

0.8

39

1.0

1.6

2.4

2.4

0.9

1.5

40

1.6

1.8

0.9

1.4

41

0.9

2.6

1.2 1.4

1.2

0.8

42

1.5

1.5

1.6

-1.9 1.9

1.4

1.0

43

1.4

2.0

0.8

1.9

1.5

44

1.5

2.6

1.4

1.1

0.7

0.4

45

0.6

1.8

0.9

0.6

46

1.1

1.4

1.5 1.8

2.5

1.4

0.7

47

1.9

1.4

1.1

1.8

1.8

0.8

48

1.6

1.2

0.7

1.2

1.4

1.2

49

1.6

1.5

1.4

0.6

50

0.6

1.5

1.1

0.7

1.1 0.9

1.1

51

1.5

1.5

1.6

0.7

0.55

1.4

52

1.6

1.6

1.8

1.9

1.1

53

1.2

1.4

1.4

54

1.6

1.5

1.9

2.0

1.6

1.4

55

1.6

1.4

1.0

0.9

1.2

56

1.6

2.2

2.0

2.0

1.4

1.0

57

2.0

1.5

1.6

2.8

0.9

0.7

58

2.6

2.2

0.9

-

0.9

-

59

3.4

-

-

-

-

Average

1.440

1.587

1.247

1.598

1.2098

BLADE

SPECIFICATION: x 10-3

Radius

BLADE

.

-

x 32 x

1.6

x

10 Tpj

continued

ins

Radii

B4

0.7

1.087

B

Appendix

TABLE 2 (b) MEASUREMENTOF SLOT WIDTH 400

10 TPI

x 32 xbx

Width

Width of Bla d e b mm

Blade No 1

Mean 2 2 2

Mean 3 3 3 3 Mean .. .......... 4 4 4 4 Mean 5 5 5 5 Mean 6 6 6

w mm

Slot

2-. 0125 2.1685 2.280 2.1825

2.26 2.50 2.585 2.045

1.5062

2.1608

2.347

1.525 1.560 1.570

2.3675 2.3475 2.2550

2.180 2.170 2.6025 2.6675

1.5516

2.3233

2.405

1.605 1.665 1.665

2. -2525 2.255 2.190

2.295 2.825 2.1485 2.140

1.645

2.2325

2.3521

1.555 1.590 1.585 1.575

2.555 2.485 2.400 2.3875

2.3580 2.5775 2.245 2.292

1.5762

2.4568

2.368

1.595 1.570 1.570

2.2225 2.2325 2.3175

2.255 2.420 2.385 2.4225

1.5783

2.2883

2.370

1.60 1.61 1.60

2.340 2.335 2.340

2.4875 2.710 2.785 2.200

.

2.3383

1

Az min

.

0993

b

z

wi I

b zi

1.4346

1.5582 .

1.4973

1.550

1.3571

1.4298

1.5586

1.502

1.4498

1.5016

2.5456

1.4584

1.5877

Mean

1.4593

1.5215

1022 7% = Az max = . =

wI

wi mm

1.52 1 r, 1.5.1.5 1.475 1.515

1.6033

Mean

of

-

Azi

= 6.87o

Azl

B5

max = . 091-7 = 6.38% 4.35% min = . 0662'=

TABLE 2(b) MEASUREMENT OF SLOT WIDTH 400

x 40 xbx6

Width Blade

Blade No

Width

of

b mm

1 1 1 Mean 2 2 2 2 Mean 3 3 3 3 Mean 4 4 4 4 Mean 5 5 5 5 Mean 6 6 6 6 Mean

Az Inax = Az rnin

TPI

=

. .

w mm

of

Slot

wI

1 w mm

1.910. 1.915 1.930

2.715 2.6765 2.7475

3.02 3.020 3.040 3.0025

1.918

2.713

3.0206

2.02 2. .01 2.00 2.01

2.9375 3.1625 2.820 2.990

3.1475 3.165 3.3275 2.8875

2.01

2.9775

3.1318

1.77 1.78 1.76

2.645 2.66 2.535 2.750

2.500 2.700 3.145 3.000

1.7"t

2.6475

2.8365

1.915 1.91 1.90

2.930 3.1650 2.705

2.955 2.930 2.965 2.820

1.908

2.9333

2.9175

1.94 1.95 1.98

2.992 3.055 3.090

'2.915 3.335 3.165 3.100

1.9566

3.0456

3.1287

1.885 1.900 1.875

2.650 2.865 2.7425

2.8925 3.2025 3.1975 3.135

1.8866

2.7525

b

z

wi /

b

zi

1.4144

1.5748

1.4813

1.558

1.4957

1.602

1.5373

1.5290

1.5565

1.599

3.1068

1.4589

1.664

Mean

1.4906

1.5878

0762

= 5.11%

Azl

0659

= 4.4275

Azl B6

min = . 0588 = 3.7% max = . 0762 = 4.797o

2(c)

TABLE

MEASUREMENT OF SLOT WIDTH 400

x 40 xbx4

]

TPI

Width of Blade b mm

Blad No 1

1 1 1 Mean 2 2 2 2 Mean 3 3 3 3 : ýMe: ian 4 4 4 4 Mean 5 5 5 5 Mean 6 6 6 6 r-M-e-a; ý1

Width w mm

of

Slot

w/

1 w nm

1.885 1.89 1.94 1.88

2.6125 3.000 3.0850 2.7525

2.6125 2.855 2.905 2.875

1.89875

2.8625

2.8115

1.94 1.96 1.94 1.93

2.9875 3.015 2.995 2.685

2.8175 2.8725 2.875 2.920

1.9425

2.9206

2.87125

1.97 1.985 2.01 2.01

3.1275 3.115 3.515 3.075

3.127 3.255 3.125 3.0925

1.9937 '99

3.2081

3.1498

1.975 1.97 1.99 2.01

3.1425 3.305 3.035. 3.07

3.0925 3.1750 3.2625 3.150

1.98625

3.1381

3.170

1.84 1.83 1.86 1.835

2.5425 2.3100 2.865 2.6775

2.7465 2.835 2.740 2.545

1.8412

2.5987

2.7166

2.02 2.03 2.02 2.01

2.825 3.230 3.390 2.865

2.955 3.085 3.100 3.030

2.02

3.0775

3.0425 Mean

67, max. =

&z min

=

. .

b

z

b

zi

1.5075

1.4807

1.5035

1.4781

1.609

1.5798

1.57991

1.5959 .

1.4114

1.4754

1.52351

1.5061

1 1.52ý48

1 1.5193

11108

= 7.297o

Azl

max =

08652

= 5.687o

Azl

min

B7

wi /

=

0766 . .

0439

= 57o = 2.8%

B

Appendix TABLE

3

PERFORMANCE TESTING

400

BLADE CONDITION:

New

WORKPIECE MATERIAL:

(2)

Area

92

mm Hydraulic Dynamometer 22.48 lbf/cm

x 40 x2x6

sensitivity

Tpi Saw stroke

= 5.5

Air

FLUID:

Machine setting

-

DATA SHEET

76 strokes/min

SPEED:

BLADE SPECIFICATION:

CUTTING

200

Wickstead

SAW MACHINE: CUTTING

OF HACKSAW BLADES

25 x 25 mm, En la

(4)

(6)

(8)

(10)

(12)

89

105

127.15

163

213

5.75

5.56

6.56

7.96

10.18

14.59

129.26

124.98

147.46

178.94

12.28

14.91

CM2

Mean height cm

FTM

228.8

327-96

lbf fTM lbf/mm/ tooth

10.77

Time per cut sees

72

Strokes 6a

X 10- 3 MM

10.415

66

63

19.06

27.33

51

42

31

53.2

39.3

19.41

26.2

91.2

83.6

79.8

64

11.32

12.35

12.94

15.98

I

Remarks:

B8

.6

inches

TABLE 3a - APPENDIX B

N=ber

of blade 25 nm

teeth

per

10

The apparent friction of the model

coefficient from obtained

The apparent coefficient from friction obtained of force measurement

THE APPARENT COEFFICIENT

0.77

0.70

0.67

0.77

0.73

0.72

OF FRICTION

THE MODEL AND FORCE MEASUREMENTS (24)

B9

OBTAINED FROM

COST DATA FOR HYDRAULIC POWER HACKSAW

4-

TABLE

Cost per cut for 75 mm diameter Time

utilization

the M

of

a En 58J

machine

20 40 60 80 100

Cost

per

Time of

cut

for

C1 M

CZ M)

4 3 2 2 1

61 45 36 30 26

a En 44E steel

utilization

C1 M

the machine C110

6 5 4 3 3

20 40 60 so 100

C, = non-productive time CZ = cutting

C3 = total C4 = scrap

austenitic

stainless

C3 0110) 18 27 32 35 38

C4 (70)

69 56 47 40 35

time cost per cost per cut

C3 M 20 31 39 46 50

Total pence

17 25 30 33 35

workpiece,

cost per

in Cut

39.0 26.2 22.0 19.9 18.6

75 mm diameter

workpiece,

CZ (FO)

steel

C4 M 5 8 10 11 12

Total pence

cost per.

in cut

24.2 15.0 12.0 10.5 9.5

cut

blade cost cut per cost material per cut

COST DATA: cost cost cost (i) (ii)

of of of En En

machine blade workpiece 44E 58J

= E710 = El. 12 material

labour rate Operators Annual weeks worked by the Hours worked plant time Non-productive per cut time cut cutting per

(ii)

En 44E En 58J

= C145 per ton ton = E790 per = 60p. per hour - 48 = 40

Time to change blade Width of cut Blade life in cuts (i) En 44E (ii) En 58J

75 see 2.35

mm

24 = 16

= 30 see

=6 min - 8.5 min

4 data Table The cost above are based on a hydraulic shown in 400 40 TPI blade a mm x saw, mm x2 mm x4 and two workpower diameter, 75 both En 44E and the other is En 58J, one'is mm Dieces The blade life time stainless steel. and cutting austenitic 6-7 load a setting on at a rotational obtained speed of were 104 strokes per minute. the cost of the sawing machine It is assumed that is writtenis paid on the over a period of 10 years and no interest off involved. The operators hourly labour is based capital rate is assumed that ratess and it he is semi-skilled on current two this is machines simultaneously; operating assumption to represent trade believed current The workpiece practice. is assumed to be manually clamped in the vice. All power and fluid have been ignored. costs cutting

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Appendix

C

ANALYSIS OF THE EFFECTS OF BLADE TENSION

The distribution

stress

of

in a hacksaw blade

the

under

force the components and the applied cutting action of blade is load the the cross-section of subjected tensile bending of a action the moment and a to combined The stress distributions load. due to longitudinal these

loads

and their

is

combinations

shown in

figure

33.

Notation b= d

breadth

the

E

Young's

e

displacement centre

Ft

blade

depth

of

the

blade,

depth

of

the

teeth

of

effective minus

the

ie

the

actual

ýýpth

bending

from

modulus

of

of the

instantaneous

cutting

the

cross thrust

neutral

axis

of

section of the (or vlartical)

the

blade. component

of

the

force

frequency I=

second moment of area length ie the effective

free

length

between

end supports M

bending

N

number of

n

number of teeth

F

tensile

RPM

revolutions

moment teeth

in one set pattern per unit length of the blade

load per minute

cl

of the

sawing machine

the blade

S

= stroke

U

= tensile

factor,

V

= cutting

velocity

W

= applied

load

w

= load

per

defined

length

unit

in

the

of

from

the

the

text

blade centre

of

in. the

text

the

cross

blade

the

of

section deflection =

6

longitudinal =

stress

The longitudinal cen tre

This

st7ess

12 My

P

bd 3

bd

neutral

axis

.P eR-

d2

the cutting A typical

moment. in Fig 33(b).

Before

blade

at

from

anydistance

the

is

bending

the neutral

depends on the ratio

Blade

of

acting

th is

stress

is

zero

and hence

12

shows that

towards

the

of

section

the

defined

factor,

deflection =

At

saw

distance

= vertical

y

the

of

of bending is displaced edge of the blade by an amount which load to the bending of the tensile

position

axis

of

the neutral

axis

is

shown

end supports blade

deflections

and stiffnesses

can be estimated

to know the method of holding the blade at its holding the device restrains the to and extent ends which blade movement. is necessary

C2

it

It

the end hole

through

direction.

vertical that

It

the lateral

passes

than the

be assumed in what follows

will

in

simply supported in the lateral plane.

and built-in

the vertical

plane

and Stiffness of the Blade be assumed that the thrust it will

Deflection

Vertical

in

is

the blade

which

to be c,lamped between is fixing to give method of

this

of

to the blade

support

greater

by a pin

the blade

and for

The effect

side plates.

to be held

the blade

for

is normal

force

For simplification force is the acts and concentrated cutting of component blade. This the the severe most gives of the centre at The that the blade wil-1 experience. loading condition 34(a) be Fig simply shows supported. assumed will ends together

this

configuration (Smax). deflection

týie equations deflection central with

As tiie

beam loaded

simply supported tension longitudinal

at

the centre

for for

central a

but without

is:

Smax = -T8-E, when P=0 ý gives

the factor

of

application deflection the of -The reason is tension

the reduction

tension. factor

Fig

it

is

introduces

due to the

35 shows the variation

ý, against

why deflection that

in deflection

reduced

the

tension

factor

by the application

an idditional

bending

U. of

moment

by loads. the moments produced vertical which , Fig 36 shows the determination of Young's Modulus for the oppo§es these

M2 high blades.

of Brand X saw used in the manufacture induced in a Brand X 37 shows the tension

speed steel Fig

C3

TPI blade

400 x 40 x2x6 for

nut

The vertical

w - 6max

Wicksteed

and the

blade

37.5

d=

Data:

2.0

is

given

by:

48EI - L3ý1

based

Calculations

of the tension

machine.

of the'blade

stiffness

Stiffness Sample

Hydromatic

the Wicksteed

the turns

against

on the Brand

X 400 x 40 x2x6

TPI

saw

power

mm tin

400 mm 198.7 GNm-2 (M2. high

E=

M,

P=7.5

by approximately

produced tension

PL2 U

4E,

when

1

(37.5

of

the

10-12

-=8.78

12

8.78

or 88%.

x

This

x 10 -9

M2

0.415

10-5

the example the deflection

shows that under the tension is reduced to 88% of its

value.

un-tensioned stiffness

)3X

12

3x0.4 2 10 7.5 x u 7A x 198.7 x 109 x

in used

one turn

nut

bd 32x

From Fig 35ý = 0.88

speed steel)

-

48 x 198.7

x 10

(0.4)3

x 8.78

x 10-9

x 0.88

.

1.487

x 106 N Hi

load produced by the Wicksteed power thrust The mid-stroke load (1112 No 8 is 250 1bf setting N). The maximum saw on deflection

of

the Brand X6

C4

TPI blade

under

the action

of

is,

load

this

Smax ==0.748 Stiffness

X 103

1.487

x 106

determined

Experimentally fig

1.112

(0.0295 mm

in)

-

in are shown

stiffnesses

vertical

by the above than those predicted These are smaller is believed to be due to movement The difference

38.

theory.

in load. However, the blade change under ends the of in blade tension increase due to well agrees stiffness with (iv)

the above theory.,

frequency blade the natural and of Lateral stiffness lateral be in the natural stiffness will of use As the main load is the considered uniformly frequency cý.Llculations distribution the to distributed simulate of mass along blade. The be blade the the length ends of of will the Fig 34(b) shows this configuration built-in. be to assumed for deflection. the the equations central with together ý2 again--gives

The factor

to the application lateral

will

stiffness

stiffness

frequency f

tension

in deflection

and is

be taken

shown in to be,

fig

due

35.

The

A 384EI - dmax -L 3ý2

The most convenient frequency of lateral the blade

of

the reduction

for method vibration

to be concentrated at is then given by) -s /iTtfRec Fine s 7r tive mass V C5

determining is its

the natural

to consider centre.

the mass of The natural

one half

where the effective the blade.

mass is

Sample Calculations

based on the Brand X 400 x 40 x2x6

Wicksteed the and

blade Data:

d=

12 mm

b=

37.5 mm 400 mm

E=

198.7

produced

U

plý

4EI

From fig StiffiAr-00

(2)3 x 12'

37.5

; =/7.5

4x

103

speed

TPI

steel) one turn

of

the

nut

X 10-12-

25 x 1(7-12ý' m4

(0.4)2 x

198.7 x 109 x 25

17 ý=0.148 -

high

by approximately

tension 3 bd IF2

mass of

power saw

GNnf-ý2 (M2, M,

P=7.5

the actual

of

X

7.78

10-12

or 14.8%

384 x 198.7 x 101 x 25 x 10712 (0.4 )3 x 0.148

The mass of the Brand X6

TPI blade

is

='201.38

0.236

kg,

103 N E

therefore,

/-2-01.38 1 208 f =. ýir ý cs-1 = 118 Fig

39 shows the experimentally

its and a tension

variation

with

of 7.5 M

approximately

blade

determined tension.

the measured natural

180 cs-I,,

C6

It

natural is

frequency

seen that frequency is

at

(v)

frequency

Forcing

the blade

due to engagement and disengagement

of

teeth

given to the blade teeth was Suppose the set pattern length in its the teeth and number one of along periodic lateral frequency forcing N', the then was complete pattern due to engagement and disengagement

of

teeth

becomes

Vn N'

the cutting

Since

the maximum value RPM To-

Vmak

21TR

Sample

cAlculations

Data:

RPM = 140

S= n=

(a)

velocity is

'. RPM lrS . . = 60 for

the

undergoes

fmax

variation

in which

Vmax. n = N'

Wicksteed__Hydromatic 1

140 mm

240 teeth

a fmax 0,

M

per

metre

(6 TPI)

140 x IT x 140 x 240 . 60 x N'

Frequency individual

242 NI

cs -1

due to the engagement and disengagement teeth ip-.

of

I is fmax

242 cs-I -o

Frequency

due to alternate

ie N' =2

is

fmax - 121 cs7l

C7

set eg right-left-right

set,

(c)

is

ie N' =4

set,

set 'right-centre-left-centre

due to the Raker

Frequency

fmax = 60 cs-I (vi)

Blade

or chatter

resonance

engagement

A blade

the

of

is not

frequency

due to engagement and dis-

blade

likely

teeth

to vibrate

a nodepoint establish must workpiece With the workpiece at blade length.

lateral

fundamental

the presence

above since

as calculated

its

with

of the the

somewhere along the centre

of the

having is a vibration possible blade a second node of frequency fundamental than four the times greater frequency 39.

fig

in shown

for

The frequency

this

and a tension

of

5.0

Assuming a blade and of similar

RPM =

x 40 x2x6

TPI

blade

kN becomes

with

ie N=2 set pattern, to the Brand X6 TPI blade, the

an alternative

proportions

speed of be would

frequency

the

considering

140 = 560 cs-1

4x

rotational

vibration X400

Brand

the

machinet

Wicksteed

mode of

the machine

560 x 60 x2= 0.140 x 7r

needed to achieve

this

631

x 240

is speed

large

compared with the maximum hacksawing it is tempting machines with commercial power used 1! hacksaw blade that a of the proportions to conclude As this

rotational

considered

would be dynamically C8

stable

at normal

operating

types out on other carried of machine work speeds. be frequencies that can achieved at chatter of tools show fundamental frequency, hence the 1/2v 1/3,1/4 at etc of However,

totational

315,210,159 of speeds

RPM etc.

dynamic analysis would enable these chatter A more extensive to resulting frequencies amplitudes and their of vibration Even if blade fracture be determined more accurately. was blade lateral by finish the chatter of surface not produced badly be the cut would

affected.

C9

-

APPENDIX D

APPENDIX D

the Simulation cutting action of blade tooth hacks'aw single

of a

M. Sarwar and P. J. Thompson

SUMMARY has large radii edge cutting tools very with The cutting action of been investigated. These actions have been classified according to in the thrust and cutting the formed variations and the rVpesof chips includes The discussion force a obtained. the cutting of components the to cutting the obtained implications results of the summary of blad" hacksaw power of action Introduction haveshownthat Koenigsberger' Groszmanand Rubenstein, a sharp single point ortho. using when occurs ploughing is negative and the angle rake tool when gonal cutting During angle. ploughing the plane shear with coincides is compressed front in the tool cutting of part of the material is plastically deformed to. part and recovers and elastically bulk. Thus from the separating without spread sideways from the is workpiece. removed material no have shown that some ploughing Other researchers"Al finite tool of a single point using when can take place action some of the material in In this cutting sharpness. is removed, whilst some forms and a chip tool the front of is compressed by the cutting edge radii to recover elastic. In to the conventional addition tool passes. the as ally cutting process these force diagram of the orthogonal have developed a more complete force diagram researchers interface force, from the tool the chip which separates due to the radius of the tool. This work forces ploughing large depths of cut compared with with out carried was

the cptting edge radius of the tool. The cutting edge radius was estimated to be in the order 7.62 pm-1 5.24jum and the depths of cut greater than 127 pm. Under these condi. tions it was concluded that the ploughing force due to the cutting edge radius was insignificant. Kregelski I in his work on abrasive wear has considered the transition between different deformation modes of a surface loaded by a spherical sliding Indentor. The depth of indentation was small compared with the radius of the indentor and Kregelskl concluded that for most surfaces, plastic conditions are established under light loads. He also discussed the transition from plastic Indentation to a process involving 'piling up' In front of a spherical indentor being pushed along a surface, virtually 'cutting or tearing. Previous work on metal cutting has not dealt with the situation where the depth of cut is far less than the cutting edge radius, a situation known to exist in some metal cutting processes. Current work on power hacksawing has shown that the depth of cut achieved per tooth is small compared with the cunt.ng edge radius even when the blade is new. Fig. I shows the geometry of a single tooth in a power saw blade. The cutting edge radii have been found to be in the range 20pm-ý776pm for blades of various pitch of teeth. The depth of cut achieved per tooth has been found to be 2-30 F&m. depending on the thrust load applied by the saw frame. This has led to an interest in the cutting action of a tool

M. Sarwar studied mechanical engineering at the Thames Polytechnic (formerly Woolwich Polytechnic) London, and was awarded an honour3 degree at London University in 1968. In the sameyear he entered the machine tool engineering division of the Department of Mechanical Engineering UMIST for post-graduate studies. During this period he carried out research Into problems associated with dynamic testing of machine tools. After completing his MSc In January 1970, he worked In manufacturing for International HarvesterCompany of Great Britain for approximately two years. In 1971, Mr Sarwar entered the Department of Mechanical and Production Engineering, Sheffield Polytechnic. as technical officer for James Neill (Services) Ltd. Sheffield, Orrying out researchInto the mechanics of sawing. He was appointed to his present post as lecturer In production technology In 1973.

ADA M

P. J. Thompson, commenced his engineering education In 1953 as an apprentice development engineer with Messrs Accles Er Pollock Ltd. In 1958 he was awarded a Whitworth Society Prize on the results of the Ordinary National Certificate examinations. and a Tube Investments student apprenticeship. He studied mechanical engineering at the College of Advanced Technology, Birmingham. and was awarded a first class honours; degree. After completing four years as a lecturer at the Harris CcIlegle, Preston. he joined the UKAEA as a senior scientific officer in 1965. Whilst at the UKAEA he worked on the development of hydrostatic extrusion. and obtained an MS4:. by research, as an external student of the University of Aston in Birmingham. Following a further two-year period as a senior lecturer at the Harris College, Preston. he obtained his present post as principal lecturer In production technology at Sheffield Polytechnic. His main research Interests are the mechanics of metal cutting during sawing operations. intermittent metal cutting and lubrication of wire drawing. He has been a consultant to James Neill (Services) Ltd. Sheffield, since 1970.

The Production Engineer- June 1974

ISO

DI

having a larger cutting edge radius than the depth of cut. It appears that with this geometric arrangement the action of 'ploughing' and 'piling up' combine to give-an unusual cutting action. It is believed that this action can be applied to operations other than power hacksawing, such as filing, cold chiselling, scraping and possibly grinding. Norn,W10Ihe vmrkpiece"faca

RakeAngie

56 da% a«nxjW

FIg. 1.

Toc)I-cutting

of these tests are shown in Figs. 2.3; 4 and S. It was found that cutting actions observed could be classified into three groups: a metal removal by a ploughing and 'piling. up' action; b metal removal by ploughing and continuous or seg. mented chip formation; or c metal removal by a combination of a and b. Metal removal by a combination of ploughing and 'piling up' was obtained when cutting the copper workpiece, Fig. 2 shows a result from these tests obtained at a depth of cut 0.12mm and at a speed of 3.34m/min. These tests show that. due to the very high negative rake at the extreme cutting edge radius woftiece material is initially heavily deformed and some is displaced sideways, indicating a ploughing action. As cutting begins there Is an accumuration of material in the sector-enclosed by the envelope of the cutting edge radius, the point of contact of the tool and the surface of the workpiece to form a built up edge effect As cutting progresses metal 'piles up* as indicated

edg* geornstry.

and testing Instrumentation The cutting tests were carriedout on a universalmilling hold in to the tool, to order modified suitably machine The conditions. cutting orthogonal obtain steady-state bolted to the top plate three of a was material workpiece to the secured was workdynamometer which component Only two the components of machine. milling the of table force the namely cutting comused, were dynamometer force FT. The component two thrust the Fc, and ponent dynamometerwere the of from channel each outputs to displaced on amplifiers via an ultra. simultaneously violet recorder. cutting

------------

tooll

from 4: 18: 1 high-speed tool made orthogonal A swndard The geometry was 5mm was used. I square steel and (Fig. 1) deg. -4 rake angle: 56 deg. wedge angle: 38 deg. clearance angle: 0.406mm. cuWng edge radius: A radius was ground on to the cutting edge and measured Finally, in to give the cutting order projector. optical an with blade to finish that of a tooth, saw similar the surface tool by heat treat. tool oxidised was the cutting of the surface I ment.

77 Flg. 2.

Piling-up action..

VV*Ikc. n ffom,. * Mbd rAM Q"Ya opma 33&lwm DwmclQc*vwm Langftof *A, IMmm

wo

d odwo

4"".

MOUIS Workpiece As 30M. HP rolled condiCon I Alul"inium. SS 1477,0.7Mn, 1.oSi, 0.8mg. 85 VHN

Bright drawn. 178-182 VHN EMA type Mildsteel., 2 Cu: 99.85% 1172 BS 3 -coppersheet Fe: 0.03, P: 0.013, Pb: 0.01, As: 0.05 Ni: 0.1, VHN: 64-68 ' 60CU-4OZn* 4 Brass. 5 Lead:Commercial,as received. 145mm 145mm dimension: x x1 Workpiece test results cutting Cutting tests were carried out using workpieces made from depths listed at of cut ranging from above 09 metals 32mm/min 0.2mm of speeds and cutting and to 0.02mm 3.34m1min. During each test the thrust and cutting comforce were recorded against time, the cutting of ponents the time constant speed. was axis was cutting the as Some tool displacement. to the cutting results proportional

Fig. 3.

Discontinuous

piling-up action.

in Fig. 2, and also shown in Figs. 6 and 7. This piling-up action continues resulting in a very heavily compressed chip. Results of thi3 type of action show that there exists transient build up of the thrust force over an initial distance ye corresponding to the formation of the chip by the 'piling up* action. When the chip is fully formed the thrust force reaches a steady value. which is then maintained for the remainder of the cut. Fig. 8 shows an analysis of the transient state of the build up of the thrust force component for various depths of cut It C3n be seen that there exists a relationship between the instantaneous thrust force and steady state thrust force, for the transient state: Th* Production Engineer- Jun* 1974

194

D2

(FT) (FT)

1

1........... 11)

10

for y4y. and n from graph - 0.35. in force point instantaneous thrust at any (FT) Where Idistance travelcorresponding yand state; the transient led by the cutting tool. force compo(FT) Iw steady state value of the thrust by the distance travelled nent; and ya - corresponding formed i. fully e. when chip, a to produce tool cutting (F (F T) 11. T)Iy opy, 9)

(Fig. the tool depth gives cut of intercept at zero The the results obtained confirms force which ploughing noseor of this the magnitude ', 1. Although

by previous researchers be due to to be it high, explained may force is relatively the extremely large cutting edge radius. and ploughing by of combination a Metal removal both cutting formation when observed was chip segmented by This accompanied was action mild steel and aluminium. debris. form in the of of metal the release of small particles a very showed in the thrust force component The variation Vj, kpws Mnwv* AkPww" DqMdCur. CW2"n CumV Wman"n"m

Fig. 4.

Discontinuous

piling-up

Figs. 8 and 7.

action.

Pila-up

as cutting

Pfc)grGss*s-

in the chip 1hickness. These off ects are shown in Fig. 5. During the early stages when piling up was occurring the thrust component of the cutting force gradually in. creased, In a similar manner to the increase obtained with copper.

CNP

Discussion It has been shown that the cutting action of a tool having a large cutting edge radius involves complex combination of modes of chip formation previously observed with sharp cutting tools. Ploughing, as previously defined by Rubenstein, Grozzman and Koenigsberger,plays an important role in the three cutting actions observed. The important 1 P§MW pur%-difference between these actions and the action of sharp cutting tools lies in the way in which metal removal is achieved. The principal method is by an action which Kregelski 'piling This Involves the gradual called up'. pz-ýaccumulation of material in front of the tool until a type of formation. loading to continuous chip piling-up action chip is formed. With metals which lack ductility the piling 5. Fig. 0.12r"m; 32mm1min. ) depth cutUng speed., of out: jejd; (Workpi, ce.. up action can lead to a form of segmented chip formation so that the metal is removed in the form of small chip Increase followed by a gradual decay to an segments and debris. initial rapid . The force feature of the type of cutting distinguishing Another cutting components; value. steady approximately increase investigated is throughout the the total cut the high value of the thrust compo. action however, gradually 145mm. The be effects may seen was made nent of the cutting force compared with the cutting compolength of cut finish bj The 4. In this produced cutting surface 3 addition. considerable variation in the thrust nent. Figs. and in beginning In poor. the the very component occurred at of each cut. was action Metal removed by a combination of ploughing, 'piling up' piling-up action the thrust-load gradually increases until formation was obtained a steady state has been reached. This steady state is associ. type chip of -continuous' and a initial in The between termination lead. the the ated metal cutting action produced growth with of contact cutting when The in front is has the the tool. tool, tool that to progress along the of to chip and up similar piling by the metal This piling up action abruptly ended cut for a considerable distance compared with the depth copper. with obtained formabefore Is the cut to steady of chip a conventional continuous state condition achieved. way and gave has This fall in transition associated The was the a significant eff act on the cutting action of a with a rapid tion force and a decrease multi-point cutting tool such as a powerýhacksaw blade. the cutting of force component thZt

re .

1 owwmuw -r -7mb.!

.rbq production Engineer- June 1974

197

D3

As previously described the geometry at the tip of each Depthof cutblade tooth is similar to that which gives rise to the complex 12MM action observed in the tests. Metal removal cutting metal . by sawing is achieved by applying a thrust load to the 20MM 0blade, this is shared between all the teeth in contact with 1-0 Cutting . speed constant , The depth depends the workpiece. actual of cut achieved on the metals involved and the geometries of both the blade and the workpiece, but is proportional to the applied thrust load and is equal for all the teeth in contact. The -9n 4.4 thrust load variations obtained during the tests when a al W 'pile-up' action was observed indicate that for the hacksaw blade teeth which have just commenced their cutting 2 action, the thrust load per tooth will be small compared .5 L with the load acting on the teeth which have achieved a Siope n-o-3s -4 longer length of cut It follows that the thrust load per hacksaw blade tooth is not uniform along the length of 3 contact with the workpiece. This gives rise to the size effect 2 observed when sawing workpieces of different widths. If the width of the workpiece is smaller than the distance needed for each tooth to fully establish a chip, the thrustV load per tooth will never obtain the relatively high steady ' io 1-1 1-2 in hence -1 -2 these tests .3 -S depth .3 .7 .8 .9 .4 and the observed state values larger for be given applied load. As the will achieved logloy/y cut of c width of the workpiece is increased the effect of this tran. Fig. 8- Analysis load becomes less build thrust of thetrensl*nt zone (issultstakenfrom'coppaf of significant since tests)-(Depth up sient fully-developed of be cut and curing speedshownin figure.) associated with a teeth will chip more and hence the depth of cut achieved will be small for a given load. thrust applied AEFERENCES 1. Rubenstein,C, G(oszman,F. K. Koenigsber, F. Procý.Int. Indus-

trial Diamond Conf. Oxford. 1966. 'Force Measurements during cutting tests with single point tools simulating the action of a single abrasive Grit! 2. Albrecht. Pý Transactions of the ASME, Journal of Engineering lor1ndustrv. 'Nsw developments in the theory of Metal Cutting Part 1. The ploughing process in metal cutting, ' p. 348, Nov. 1960 * C.. Inst. Rubenstein, J. Macir. R.. Tool. Des. Res., ' rho Connolly, 3. Mechanics of Continuous chip formation in orthogonal cutting. ' VOL 8, pp. 159-187. 4. Masami Masuko. Trans. Society of Mechanical Engineers pjpan). Vol. 19, js3. pp. 32-39. 'Fundamental Researches on the Metal Cutting. 1. A now Analysis of Cutbng Force'. 5. Kregalski, X,, Friction and Woof, London, Butterworth's Press, 1965. G. Albrecht P. Transactions of the ASWE. 13.34a. No. 1960. 'Now Proces& Part 1. developments in the theory of the Motal-Cutting The ploughing Process In Metal cutting'.

Cuttihg SPeed-3-34mjýý_ z 0-2-

E E 0 -5 S_ IM

0-1

7. Wallace, P. W. and Boothroyd, G.. Journal Mech. Eng. Science.

Vol. 6, No. 1,1964. "rool Forces and Tool Chip Friction in orthogonal

machining.' S. Wallace, P. W. Boothroyd, G.,Journal Mach. Eng. Science, Vol. 8, No. 1,1964. 'Tool Forces and Tool Chip Friction In orthogonal machining'. 9. Zdrev, N. N. Prom 1, Mach. F_Conference on the Technology a/ p. 255,195& EngineeringMS"I"t"fe-

D4

_PIt"fing

I F;Orca Forca C

0 2345a IF;Orc:e dueto Nose Radius) Thrust Fo= Fig. 9. Intercept Ploughing fares.

Ft X103N

at zero of cut showing the tool nose or

The Pr(Wuctlon Enq.'neor -Juno

1974

E

APPENDIX

below

The calculations

(a)

is

the

(b)

is

limit

of

assume

that

II

condition (length

reached, limit

of

of

of

condition (length

reached,

for

Cut

the

Blades

gullet

of

perfo=s

with

until:

maximum efficiency the

Length

Limiting

the predicting Pitch Various

of

(Gullet

fig.

height),

cut

B

III

(Gullet

cut

B

Ill

or fig.

perimeter)

2 I

a knowledge

From

BI

cut

and

B2 can

be

chip

(c

ratio

blunt

with

cutting

workpiece

the

of

tools,

calculated

h

the

and

is

Gullet

Pitch (mm)

height (mm)

in

shown

Limiting of B 1

Gullet Perimeter (mm)

the

of

table

length c ut B 2

(MM)

(mm)

11

35

4

6.35

3.3

6

4.1

2.28

7. o5

7.6

23

10

2.54

1.4

4.32

4.66

14

14*

1.79

0.94

3.00

3.14

9.7

18*

1.41

0.73

2.33

2.44

7.7

*These the

have

calculations

blades

geometrically

were

of

the

10.5

steel

length

limiting

below. Blade T. P. I.

for

0.3)

been

based

same type

similar.

ignore Calculations the root and chip thickness but radius to have minor can be expected 112 on Fig. effect

E.

on the

as 4,6

assumption

and

10 T. P. I.

that and

F

APPENDIX

QUICK-STOP TESTS In

the

principle, should

action

has

work-piece time

the

function

used

for

the

to

in

less

ten

cent

of

per

high

the

the

CIRP (62)

have

recom-

thickness

'were

above

(200

be 400

-

(Figures

to

73;

been

has

recommendations

the to

intended

zone

difficulty

needed of

tests

cutting

tests,

present

time

the

than the

should

equipment

deformation

complex

the

applying

speed

the during

recommendations

above

in zone

results,

time

cutting

shear

the

process.

satisfactory

the

a particle

go through

a stopping

to in

produced

ienced

stop

the

conventional

Owing

m/min).

to

move

The

in

applied

74)

to

chip

time

interrupting

that

so quickly

obtain

has

which

zone.

shear

to

needed

thatv mended be

no

for

used

equipment

the

exper-

simulation

tests. time

The

to

required the

interrupt

cut,

the

reverse

as measured

on

mechanism,

was

less

sidered

thatq

the

low

cutting

normal

problems

associated

with

timer

much

reduced

milling

at

the

and

machine

table

prove

useful

than

(95

and

recorder

violet

seconds.

speeds

It

con-

was

the

mm/min) techniques

quick-stop adopted

for

to

give

adequate

table

machine

an ultra

0.05

procedure was

milling

were the

reversing a satisfactory

result.

It

would

to test

the performance

when machining saving

at

to

out

carry

of the speeds

further

interrupted

comparablc

process. i

work

cutting with

that

in

this

action in

the

area

REFERENCES EMERSON C How to American Machinist

2

3.

4

5.

6.

cut-off Special

metal Report

428 1956

Band machining ANDERSONRA and friction sawing I. Mech. E. Proc. Conf. Tech. of Eng. Manufacture REMMERSWAALJ Lp MATHYSEN MJC Economics of of the cutting-off 1961 15(4) August, Microtecnic,

metals 140-150

Bandsawing NELSON RE or hacksawing? Volume 109 No 24. November Am. Mach. Pages 90-93 Tolerances Sawing to Blueprint Machine and Tool Blue Book Volume Page 98-102 Carbide saw slices The Iron Age June

the superhard 16 1966. Page

82

Pushbutton bandsaw handles huge loads Page 56 The Iron Age August 11 1966.

8

Estimating CORKER J Fabrication Weldýng and Metal Fabrication June

10

BILSTON S&L Iron & Steel

1966.

Tage

230

High speed hot sawing December 1967. Page 524

Cutting JOHNSTON CA the cost per April 17 1972. American machinist

MORTIMERJ Blade breakthrough hacksaw exports The Engineer 16 November 1972. 12

22 1965.

60 No 2. February

7

9

1958

cut Page 90

to get

the edge in

Page 42

GREENSLADEA Metal sawing today Sheet Metal Industries August 1976.

Page 125

1965

13

lift Sawing developments Production Metalworking

14

JABIONOWSKI J Fundamentals of Sawing 15 1975. April Page 54-68 American Machinist

15

HAYWARDJ Compare the costs in cutting off May 1977. 47 Page Metalworking production

16

Trends in sawing Tooling and Production

17

18

cut-offs status December 1975. Page 43

January

1978.

Page 70

RAKOWSKI R LEO Know your saw blades July 1978. Machine and Tool Blue Book

hacksaw's bite tests Cutting survey June 1979. Metalworking production

Page 84

Page 133

19

Sawing Sophistication comes in very slowly Report Metalworking Production. Special 1980. Page 113 February

20

(Bandsawing) Get your basics right Production. November Metalworking

1980.

Page 149

21

SARWAR M Power Hacksawing THOMPSONPJ& 15 MTDR. Conf 1974. Proceedings Page 217

22

SARWARM 'Hacksawing' G&S Section. I. Mech. E. Lecture. North Midlands November 1974. Sheffield Branch. City Polytechnic

23

SARAR M&PJ Simulation of blade tooth The Production

24

THOMPSON the cutting

action

Engineer.

June

of 1974.

a single

hacksaw

Page 195

THOMPSONPJA theoretical study of the cutting action of power hacksaw blades Int. J. Mach. Tool Des. Res. Volume 14 1974. Page 199

25

26

TAYLOR THOMPSONPJ& into An Investigation hacksaw rate of power analysis 16 Blade Wear Testing

RW factors blades

influencing the dimensional using

MTDR Conf

wear

1975

TAYLOR RW THOMPSONPJ& lateral displacement the An analysis of influence hacksaw blade and its on the 16 MMR Conf 1975

of a power of cut quality

27

TAYLOR RW THONPSON PJ& A computer of the power hacksaw operation simulation in blade life, its estimating rate cutting use and and cost Engineer. January 1976. Page 25. The Production Volume 55 No 1

28

THOMPSONPJ influencing Factors during power metals technology. metals

29

ductile hard the sawing rate of hacksaw and bandsaw operations Octobý--r 1974. Page 437

MALIN RA THOMPSONPJ& How angular of the workpiece motion time Welding and Metal Fabrication.

sawing reduces 1979 July/August

30

HEAVER GR THOMPSONPJ& Characteristics of saw operations when cutting sections circular November 1976 Technology. Metals Page 522-28

31

THOMPSON PJ TAYLOR RW& A study of bandsaw blade wear rates and economics cutting 1976 17 NTDR Conf Birmingham

and its

effects

on

32

ALBRECHTP The Ploughing process in metal cutting Trans. Am. Soc. Mech. Engrs. Volume 82 (Series B) Page 263 1959.

33

Mechanics MERCHANT ME J. Appl. Phys. Volume

of the metal cutting 16 1945. Page 267

process

34

Fundamental MASAMI MASUKO 11 A of new analysis cutting. Soc. of Mech. Engrs. Trans. Page 32-39. 1953.

35

CONNOLLYR& RUBENSTEIN C The mechanýcs of chip in orthogonal formation cutting Volume 8 1968. Int. J. Mach. Tool Des. Res. Page 159-187

36

KOENIGSBERGER F RUBENSTEIN C, GROSSMANFK& during Force measurements tests cutting with single the action tools simulating of a single point grit abrasive Industrial Diamond Conf. Int. 1966 Proc. Oxford

37

PALNER WB& YEO RCK Metal flow near the tool point blunt tool a with cutting Page 61-70 MTDR Conf. 1963.

38

39

40

41

42

researches on the metal force" cutting (Japan). Volume 19

OKUSHIMA K& KAKINO Y Study'on the generating process J,SME, Volume 12 (1969). Bull. CUMMINES JD et al A new analysis in of the forces J. Eng. Ind. Volume 90 (1965). BITANS K& BROWN RH An investigation of the cutting J. Mach. Tool Des. Int.

during

of*machined Page 141-148

surfaces

orthogonal cutting Page 480-486

deformation Volume

orthogonal

in

5 (1965).

HASLAMD& RUBENSTEIN C Surface and sub-surface work-hardening operation a planing Annals of the CIRP Volume XVIII 1970.

orthogonal Page 155-165

produced

by

Page 369-381

HEGINBOTHAMWB& GOGIA SL Metal cutting and the built-up nose Mech. Engrs. Proc. Inst. Volume 175 (1961). Page 892 4

43

44

45

KRAGELSKI Friction and wear London Butterworth's

Press

1965

LAL GK BUSURAYP K, MISRA BK& from ploughing to cutting Transitions blunt tools with machining (1977). 43 Page 341-349 Volume Wear, SHAW Mc BACKER W Rp MARSHALL ER& in metal The size effect cutting Volume Trans Am. Soc. Mech. Engrs. Page 61-72

during

74 (1952).

46

NAKAYAMA K& TAMURA K in metal force Size effect cutting Volume 90 (1968). J. Eng. Ind. Page 119-126

47

JOHNSON W& MAHTAB FU Upper bounds for restricted edge machining (1965). 6 Conf. Advances in MTDR Proc.

48

Standards British for Specification

49

Machine

50

NEL Divisional to assess the Power Hacksaw

51

Admiralty

52

American

Specification

53

Canadian

Gove =

54

Australian

Standard

55

USSR State GOST 664

Standards

and Tool

Institution BS 1919 Hacksaw blades Blue

Booko

Report. feasibility Blades.

1974

1978

A survey undertaken test of a cutting 1969

Specification:

ent

July

Page 447-462

No 1055B August -

by NEL for

1964

GGG-B-451 d 1968 specification July

46-GP-1

1968

Saw blades -

for

metal

cutting.

56

Testing carried out by BHMA Sub-Committee on "A for Performance Test in their search testing for HSS Power Hacksaw Blades". (Confidential). 1969 Jan.

57

The Governm ent Department Specification Hacksaw Blades Stores No. TG81 1941. Frames and Power Machines.

58

COLDING BN A-Three Dimensional Economics. Trans ASME.81,1959

Tool-Life

for General for Hand

Equation-Machining

pp 239

59

TRENT EM WRIGHT PK& Appraisal Metallurgical of Wear Mechanisms and Tools. Processes on High Speed Steel Cutting Metal Technology Jan 1974

60

LEE EH& The theory machining. 405. p

61

SHAFFER BW to a problem applied of plasticity of J App Mech Eng; Trans ASME 1951, Vol

SARWAR M THOMPSONPJ& Report Confidential on Power hacksawing (Services) Ltd. Sheffield 1973 Neill C Report on Terminology research.

62

CIRP Group for turning

63

FORMGW& BELINGER H Fundamental Considerations formation Annals of-CIRP Vol XVIII

64

65

and procedures

in Mechanical

Chip

pp 153-167.1970

VAN VLACK LH "Materials Science for Engineers" Publishing Company (1975) Adison-Wesley MOTT BW "Micro-Indentation 73, Butterworths p

to James

Hardness Scientific

Testing" Publications

p 198

(1956)

73,

66

1 HAHN RS

"On the Nature Process"q Advances of the Grinding in Machine Tool Design and Research, p 129, 1962 Pergamon Press Ltd, Oxford:

67

68

69

70

71

BROWNRH EJA& ARMAREGO "On the Size Effect of Metal (1962), 75 1 Vol Res, p

Cutting",

BOOTHROYD G WALLACE PW& friction Tool forces and tool-chip Mech Engrg Sci. J Vol machining, 0 1964 BOOTHROYDG Fundamentals of Metal Machining BdoK Company, 1975, McGraw Hill

Int

in orthogonal 6, No 1, p 74,

tools.

and machine p 71

sHAw MC BACKER W Rq MARSHALL ER& in metal The size effect cutting Vol 74 (1952), Trans Amer Soc Mech Engrs, ERNST H Trans Symposium Cutting, Metal of

J Prod

on Machining of Metals Trans Amer Soc Metals

I.

61

Physics 1938

72

HILL R "The Mechanics of Machining". a new approach, Vol 3, p 472 1954 i Mech Phys Solids,

73

LOW AH "Effects initial of conditions NEL Report No 49,1962

in metal

LOW AH& WILKINSON PT An investigation of non-steady NEL Report No 65

state

74

75

OXLEY PLB PAINER WB& Mechanics of orthogonal machining, Vol 173, No 24,1959 Engrs,

cutting",

cutting,

Proc

Inst

Mech

76

PALNER WB CHRISTOPHERSON D G, OXLEY PLB& Cutting Orthogonal of a work-hardening material, Vol 186, p 113t 1958 Engineering

77

JOHNSONW fields "Some slip-line Vol 4, pp 323-347,1962

78

79

80

81

82

BATTACHARYYA A On the friction process Conf, p 491,1966

Machining",

....

in

metal

J Mech Sci,

6th. MTDR

cutting,

JOHNSONW Cutting with tools having a rounded XIV, 315-319,1967 Vol CIRP the pp of JOHNSON W& MELLOR PB Plasticitys Engineering

Int

Van Nostrand

edge.

Annals

483-484,1973 p

USUI E KIKUCHI K, HOSHI K The theory to machining applied of plasticity ASME 63, No tools, Prod 5,1963 paper cut-away KUDO H for two-dimensional Some slip-line solutions Int J Mech Sci, Pergamon machining. state 1965 Vol 7, pp 43-55t

with

steady Press,

83

ROWE G W, SPICK PT to determination A new approach of the shear-plane in machining. angle Trans ASME Jnl of Eng Ind, pp 530-538,1967

84

PUGH HUD "Mechanics Process", of the cutting Engrsv London, Mech England. of Conf on Tech of Engrg Manufacture,

85

The Institution 1958

BACKERW Rv MARSHALL E R, SHAWMC in metal cutting, The size effect Trans Mech Engrs, Vol 74,1952, p 61-72

Am Soc

86

87

88

89

NAKAYAMA L& TAMURA K in metal cutting Size effect (1968). Vol 90, p 119-126

force,

J Eng Ind,

SARWARM& THOMPSONPJ Tools. Cutting'Action of Blunt 1981 22nd Int MTDR Conf. SARWARM and HALES W Effect Blade gullet geometry of on -The in Power Hacksawing Performance (To be published). ROWE CW Principles Processes, p 24-25

(if Metalworking Arrtol ck tq"T7,

LIST

OF FIGURES CAPTION No.

Fig.

1

Method used to instrument

a Power Hacksaw

2

force thrust Variation of for various saw machines

against

3

hydraulic Simplified sawing machine

4

during the cutting The load developed stroke, hydraulic by blade the the a workpiece between and load settings saw on various

5

(a)

Main features of the restricted hydraulic for a machine method

(b)

thrust A theoretical diagram displacement non-cutting a rigid, influencing

unit

the

of

angle

the Wickstead

hydraulic

'back

flow'

blade load against for such a machine blade

6

Factors

7

deflection blade Effect of developed by the Wicksteed

.

crank

effective

and-

wedge angle

load on the thrust hydramatic machine

8

force developed by the in thrust Variation Wicksteed hydramatic saw on a common load setting different blades widths of with

9

to cut through a The number of saw strokes 25 mm x 25 mm mild steel bar using a Brand X force developed blade against the mean thrust 6 hacksaw machines power various -by

10

Geometry of the sawing in the tooth factor Geometric workpiece

action

showing variation

between the relationship breadth and the effective

saw stroke, blade length

and high

for

12

load variations, Thrust the Wicksteed saw

13

Some features of power hacksaw blade, action cutting

14

Hacksaw blade

15

Cutting

16

Saw tooth

17

force Comparison between the mean thrust for various -force at mid stroke position machines

18

The depth of cut achieved by an Brand X blade TPi cutting the mean thrust mild steel against by various force per tooth per unit thickness, power hacksaw machines

19

Paths followed workpi'ece

20

force component against Instantaneous cutting force component for a. instantaneous thrust Brand X6 TPi blade cutting mild steel

21

Hacksaw machine and associated for blade testing

22

loads developed between the blade Typical thrust during the the cutting workpiece, stroke, and for various machine load settings

23

The average depth of cut per tooth against the load thrust per tooth per unit thickness, mean for blades having different teeth pitch

24

The cutting constant the number of teeth

the reciprocal against of in contact with the workpiece

25

Comparison

performances

teeth

slow

and its

patterns

edge geometry profile

speed,

of a hacksaw blade

of a6

TPi blade

by individual

of blade

tooth

teeth

and the static sawing

through

6

the

the

instrumentation

26

'Z' 3 TPi blade and a between Brand. the Comparison instantaneous d'X'6 TPi blade cutting showing --Bran force components .

of the

Brand

'Z'

3 T_Pi tooth

27

Profile

28

Samples of metal chips obtained when cutting for various 4 TPi blade, Brand 'X' machine settings

29

with Samples of metal chips obtained when cutting for various Brand'Z'3 TPi blade, machine load settings

30

The effect edge radii, of tooth spacing and cutting blades Brand'XI Of the Performance cutting on

31

Effect

32

deflection blade Effect of blades new and worn

33

(a)

longitudinal stress distribution load bending moment, a tensile combination

(b)

Position of the due to a central

34

of blade

Deflection

wear on the cutting

models

(a)

A simply tension

(b)

A uniformly factor

35

Deflection

36

Load/extension blade

37

Tensile number

against

curve

for

of

due to a and their

axis of bending for a hacksaw blade for:

and equations

loaded

performance

on the perfo=ance

neutral load,

supported

with load

-

blade

with

longitudinal

blade

with

built

tension

in ends

factor

High Speed Steel

in a saw blade load induced of turns of the tension nut

against

the

38

blade The effect of blade the ness of

39

frequency Natural blade tension

40

(a)

Blade tooth wear against sections cut

(b)

Tooth profile

on the vertical

tension

lateral of

vibration

showing

stiffthe

against

the number of

wear

41

The average depth of cut per tooth against the load for tooth thrust thickness per per unit mean a blade in three stages of wear

42

The effect

43

Loss in sections

44

in both the blade and the Deformation occurring compiled from micýroscopic observations workpiece, during wear tests

45

The effects blade life, factor

of'the cutting average cutting

46

The effects the average

of the thrust cutting rate,

load on blade life, and the cost factor

47

The effects the average

of the cutting

of the saw on blade and the cost factor

48

The effects of the teeth pitch and the breadth of* the workpiece the average cutting on blade life, and the cost factor rate,

49

Variation of the increase

force the cutting in length of cut

50

(a)

A fully

established

(b)

Mohr's stress diagram deformation zone

of blade

tooth cut

height

wear on its

cutting

performance

the number of

against

stroke rate on the rate and the cost

stroke rate,

components

deformation for

all

life,

with

zone points

in

the

51

in Predicted variation the apparent coefficient deformation established

52

Thrust

53

Comparison between-the computed values of the factor for the chip various values of reciprocal force index the and experimental cutting values of

54

Comparison between the computed values of the factor for force the chip of cutting reciprocal data obtained with index of one2 and experimental blades of various pitch

55

Diagramitc representation of having tool a a large with

56

Diagramatic representation of the relationship between the nominal set depth, layer of metal removed and the machined surface

57

Machine tool for simulation

58

View of

59

Close-up

60

Machine tool measurements

loads

acting

of

the

constant against for a fully

on the 'saw teeth

and the testý

the cutting

the cutting of friction zone

the cutting process cutting edge radius

associated

tool

bridge

4equipment

workpiece dial

gauge

(Parkinson Miller) at: the position of

Cross-section of an initially machining, specimen, after

62

Chips of varying geometry produced tool copper workpiece with a blunt at 0.25 mm nominal depth of cut

63

(a)

Tool radius grinding machine grinding

(b) (C)

Essential

features

set-up arrangement

stiffness the tool

61

used

holder

3.55 mm.wide copper showing the side spread

jig,

when machining (0.56 mm radius)

set up on the surface

of radius

grinding

jig

64

(a)(b)

Close-up photographs when grinding face and flank of the tool

65

(a)(b)

Shadow graphs profiles

(c)

Tool

66

of the

tool

the

edge

cutting

edge geometry

cutting

for a during Forces obtained groove cutting (0.1 depth of cut mm) using nominal constant (0.51 blunt tool mm edge radius)

a

67

forces and the corresponding Cutting chips for cutting, a constant obtained when groove (0.25 blunt depth a of cut mm), using nominal (0.51 tool mm edge radius)

68

(a)

Measurement

(b)

Initial gauge

(a)

Force traces obtained blunt using a cutting nominal depth of cut

(b)

Chips (ý9(a)

(a)

Variation of chip-tool con tact length ' depth increase in of cut, for different type of chips

with

(b)

Variation length of chip-tool contact increase in depth of cut, for various machining copper and steel

with tools,

(c)

Photograph of the chip-tool and the appropriate chip

69

70

71

of workpiece

setting-up

obtained

of

recovery

the tool

and air

during groove tool at a constant

corresponding

to

contact

formation Photographs the showing chip length the along of cut positions (a)

Sharp

tool

figure

length

at various

Blunt (c)

-

tool

Chip produced when machining sharp tool nominally

copper

Chip produced a blunt tool

copper. with I

when machining

with

a

during

72

Some features of copper chips blunt a using groove cutting,

73

Photomicrograph showing primary deformation zone when machining

74

Photomicrographs

75

Electron-microscope

76

Material

77

(a)(b)(c)(d)(e)

78

forces during groove cutting Variation of cutting secondary and steady state showing, primary, regions and the relevant chip

79

(a)

Schematic diagram of the chip formation tool when machining with a blunt

(b)

Schematic diagrams showing layer of material being extruded around the chip root area

behaviour

showing

picture at

the

produced tool

and secondary with a blunt tool

chip-root

area

of the chip-root

the centre

of

area

the workpiece

Variation forces of the cutting during groove cutting, when tool cutting with a blunt and the appropriate chips

80

forces and the corresponding Variation of cutting length with the increase in chip tool contact depth of cut (0.56 mm cutting edge radius)

81

Variation forces and the corresponding of cutting length with the increase in chip tool contact depth of cut (0.81 mm cutting edge radius)

82

forces Variation and the corresponding cutting of length increase in the tool with contact chip depth of cut (0.56 mm cutting edge radius, worksteel) -piece

83

forces with increase in Comparison of thrust depth of cut, for a nominally sharp and blunt tool

84

in specific Variation in'depth of cut, for piece - copper)

85

Variation in depth

cutting energy with increase (workblunt and sharp tools

in specific cutting using of cut, a blunt

increase energy with (workpiece tool -

steel)

86

Single

87

Lee and Schaffer's single shear plane

88

Slip-line

89

Diagramatic

go

Slip-line restricted

field tool

solutions contact

91

Slip-line

field

in machining

92 93

Modified restricted

94

field Slip-line for restricted solutions chip-tool contact unrestricted

95

field Slip-line and hodograph for restricted tool contact, where cutting edge radius is approximated by straight edges

96

Slip-line to flow tool

shear plane

field

model line

slip

field

solution

for

a built-up

and hodograph

sketch

of

suggested

cutting

a

nose

process

and hodographs

with

for

cut-away

for

tool

Johnson-Usui for slip-line solution and unrestricted chip-tool contact

field beneath

(invalid)y the

tool,

where material when machining

and

is assumed with blunt

97

in horizontal Deformation produced patterns and layers of plasticine, when simulating vertical tools, the cutting of blunt using a action model tool. perspex

98

Slip-line and the

99

Mohr's

100

True

(a) (b)

field in machining with hodograph. corresponding circles

stress

figure

tool

98.

from

curves

stress-strain

Copper Leaded

for

a blunt

tests

compression

steel. forces

theoretical

increase

101

Experimental in depth of

102

Comparison and sharp

103

Comparison tool, blunt

104

Suggested slip-line conditionscutting

105

in Speci'f id Cutting Variation and steel). cut (copper

106

Chip Chip tests.

107

Comparison of different

108

Comparison blades of

of the different

performance pitch.

of

new and modified

109

Comparison of the 4 T. P. I. modified

performance -Blade.

of

a standard

110

Comparison of fied blades.

performance

of

dtandard

ill

diagrams Schematic for various Gullet

112

Influence cut (steel

and cut.

- with

theoretical copper.

forces

of experimental and theoretical leaded machining steel.

forces

of experimental and blunt tools., machining

Contact Tool thickness/Edge

of

field

Length/Edge radius

single pitch.

the

to

point

scale,

for

particular

energy

with

depth

radius derived

showing chip formation in sawing. situations

of blade pitch workpiece).

on the

Undeformed simulation

vs from

performance

limiting

of

and blades

and and modiin

the

length

of

FIG.

METHOO USED TO INSTRUMENT HACKSAW.

--

"

-

_______ ----

___

______

A POWER

-

---

____

--

27

Unear Transducer

I

0

AC signal Kistler Piezoelectric Load Platform

Amplifier

ChargeAmplifier

y j y

x

inpqt

input

x X-Y Plotter,

vig. 1

SPEED ,

64 STROKES/MIN

0 0 ob

0

troke

Return

(1) MACHINE SETTINGS SHOWN THUS

2(A) FIG

VARIATION OF THRUST FORCE AGAINST CRANK ANGLE FOR A KASTO POWER SAW AND THREE MACHINE SETTINGS

84 STROKES/MIN -SPEED

a

ob

S Return MA61NE

203) FIci

(1) SETTINGS SHOWNTHUS

VARIATION OF THRUST FORCE AGAINST CRANK 221 POWERSAW AND ANGLE-FOR A KASTO VES FIVE MACHINE SETTINGS

120 STROKES/MIN SPEED -

0

a

)ke

Cutting

2(c) FIG

VARIATION OF THRUST FORCE AGAINST CRANK ANGLE FOR A WICKSTEAD HYDROMATICPOWERSAW AT THREE DIFFERENT SETTINGS

.... '-.... 120 _CuTiiNG-SPEED ......

.... ...

...... .... ...... SjRoKEsPMiN-

roke

utýnc

FIG

2 (D)

VARIATIOR-

QF THRUsT

...... .... .... FOR'C'E AG'A'INST CRANK

ANGLE FoR A

.... .... -OWER .... THRUST' ..... SAW-111TH-DIFFFRENT .I. LOAD--SETT NQa

=ULO-SPEED

Return

FIG 2 (E)

6B STROKESIMIN

ýroke

OF IHRu5T FoRcE Ar,A'iNsT CRANL.La Ific 'STEADPOWERSAW'(SWR CLIYF'E'lELD D--LU--_LE-Em-A EQUMEN1.0

.... .... .... SPEED

.. . .... I ... .... STRoKEs/Mi-N

120

oke

utti

FIG 2 (F)

ýARI

'THRUST FORCE AQ3A, AT'l QN-o,F-* l, NSf-CRAN, K .... ..... .... A .... MARVEL ...... .... 110 9 POWER'SAW

Return

-roke

.....

....

. ......

....

....

. ......

....

Dau-PoT-ADJUsTbENT IN Mir)-PosjýAR*l'A'Tl'ON-'OF ... rORCE-AGA'T'NST (G) 2 THR'US*T FIG .-..... .... ...... ..... .... . POWER .. CRAN SAW 311DER

Swing an'n Pivot

0-0lrZ! --.0,

Crank connectim

ýx

Workpiece Double actinq------ý hvdraulic cylinder

Flow control valve

oi 1 tank

FIG.

3: ' Simplified hydraulic

hydraulic unit sawing machine

of the Wickstead

FIG.

4:

stroke The load developed during the cutting between the blade and the workpiece by a load settings 200m hydraulic saw on various

1800

1600

1400 C. /)

1`1200 1000

8

800

%\ 600

0

400

200

0 Blade Workpiece Speed

:

400 x 40 x2x6T. P. I. (H. S. S. ) 25=. x. 25um, En la 76 strokes/min

STROKE (140 irm)

Fig.

H

Swing arm Pivot

Flcw ccntro valve

Double acting hydraulic cylinder

Oil tank

3Ak ( c
(b)

x 2R

A= cross-section area of the hydraulic k= flow valve constant R= crank radjUS of the crank w= angular velocity FIG.

S(a): (b)

cylinder

for back flow Main features the method restricted of a hydraulic machine' load against blade displacement A theoretical thrust blade for such a machine and rigid, non-cutting (21)

diaqr"10' 11 rig. 5 (a)

(b)

influencing

FIG.

6:

(a)

Angle due to blade

Factors

the effective

wedge angle

deflecticn

SWING ARA SUIEW

0 %

04.

-0

. LOADED CM= OF THE BLADE

56

UNLOMED CENTPE LINE OF THE BLADE

tl

irachine wedge angle angle due to blade deflection angle due to rretal removal wedge angle effective

END FIXING POINT OF THE BLADE

(b)

END FIXING POINT CF THE BLADE*

Angle

due to metal

removal SWING ARM SLIMQZ

A= 0ý,-p

BIAM

CUITIMG EDGE POSITION.

CF DIF=ICN BLADE MMEMENT

load 138 iýf

ET

DISPLACEMENT

FT

iTmrI nh load 3261bf =

, Fig.

FIG. 8:

in thrust force developed by the Variations Wicksteed Hydrarnatic saw on a commonload different blades widths of with setting

300

0

200 C-

I-

76 40 100

Stroke

,

inches

FIG.

I

9;

The nunber of saw strokes to cut through a25nm by 25nm nild steel bar using a Brend 1XI I. 6 T. P. blade against the iman tilnL,, -t force developed L-1 various -x7aer hacksawing r,,adlines

300

=

x0-

Wickstead Saw

M-

ý-iidmtead erdrcmatic

Iýasto Saf

200

(A

m

100

0. 0

100

200

MeanThrust Force lb f Ftm FIG. 9

FIG.

10:

Georretry of the sawing in the tooth factor (a) (b)

U

showing variations

action

When S >, BB= When S4BS=

Breadth of workpiece Machine stroke blade length Effective

L=

0

F---'ý

Blade

ýqorkpý ýc in initial

position

BB 22e,

S-R

L_ lB Bn

,

orkXiec

z

in fi al!posi tioni

L

Slade su Ppo' S'

Blade supportF

C) u

'81

A

IB 4BI

Bl,ade B 2 yorkVece in ipi ial L!--

(b)

yiorkgec,e @

in -ij position

L

10

between saw stroke, Geometry relatimships blade workpiece brezidth and the effective length

FIG. 11:

1.0 100 80 0-8

Percentage of blade length enclosed by the workpiece

0

A= B=

0 4--

Cn cc C: a)

't-M

O-E

Kasto Wicksteed

'

0

GJ C3

ro CO CO

Limiting

0-4

workpiece breadth

aj Cj u>

.a !duCu

C- 4-0

Percentage of blade length which make!9 contact with workpiece

N

0

04

0.2

0-6

0.8

Saw Strokes S

10

Effective

1.0

Blade Length L

20 stroke

0.8 40

-j . I.CO

0.6

0) C-

A=

Kasto

B=

Wicksteed

0

-j "D ro

efficiency

Cu

ru

ED

0-4

Cu

Limiting

workpiece breadth

(Ij u Qj C0 uj

0.2

Percentage of blade length which makes contact with workpiece

0

0-2 0-4 ' 0-6 0.8 Saw Strokes S , Effective Blade Length L

1.0

J C 0

Q (I)

r-

SLMq MACHINE

(68 STROKES/tIM) SPEED

STROKE

M.

,i2

a 0

Q 9 FCl)

HIGH MACHINE SP:: -" r-

12 t-IG.

U20 STROKES/Miti)

STROKE (14 0 rn

THRUST LOAD VARIATIONS DURING CUTTING STROKE FOR WICKSTEED HYDRAULIC SAW

/

'Flank

Pin

e Ut ting Face

Root

hole

`ýAxis

edge-

radius

Side Toothed

Back

edge

Edge A typical ered set

----Teeth Pinhole

A typical

25-mm Overall

type

type

of

stagg-

of

wavy

No 6f-teeth '(10 in this

set

exampl'e)

length

'R1n Aa I am n t7+In

j

4. Ile

-Thickness t, dimensions Linear

lWidth '

(diagrammatic)

Gage -LSide Clearance

^.. -L Slot

width Side End View", ý Clearance Angle i

Rocker

U. Straight Feed FIG, 13

Return

Strok

SOME FEATURES OF poWER HACKSAW BLADES-AND THEIR cUTTING

FIG.

14:

Hacksaw blade

Alternate .III

teeth

pattems

Raker Wavy

M Regular tooth

(i i) SkFp tooth

NO Hook tooth (b)

FIG.

15:

Cutting

edge geanetry

of a hacksaw blade

tooth

No mal to the workpiece surface

4Rake

angle . 0,- 4 d@g (Negative)

Wed-geangle 51ddjp

Workpiece suýface

Clearance angle38de8. Cutting edge radius 0-02mm-0 -076mm

s. 14/15

LLJ C)

M LO CD Lr) x

0

U)

LLJ

LL CD Of CL

LL) z ý-Il

= 0 0

F-

(/)

LiD

U-

FIG. 17:

force and between the man thrust Carparison for various the force at mid-stroke nosition sawing machines

00

4. -

-12

c:

5200

It: .IA 0

CL

(a x

0

t..1

10

E

100 -1.

0

0

100

Mean thrust force lbf

200 ,,tm FIG.

17

FIG.

18:

The depth of cut ad-deved bv a Brand IXI 6 T. P. I. blade cutting r,&ld steel against force develoced, bv various the n-nan frmmt pcwier hacks-mring mchines

20

(a Leo

E

10 %1ý0

_c d-c2CLJ

CD

0

10 Mean thrust

force per Unit thid=-Zs

f

tmlbf/rrm

per tooth

FIG.

18

FIG.

19:

Diagrarroatic representation by each tooth

of the paths

followed

Thrust force Fi: Blade

Paths &I followed by individual teeth through

the workpiece

---V

Workpiece

B

Fig. i. 9

FIG.

20:

force ccmponent against Instantaneous cutting force ccnrxnent for thrust the instantaneous blade I. P. mild steel cutting a6T. 25 r.n, workpiece breadth: Blade: 400 x 40 x2x6T. Stroke: 5.5 inches 76 Strokes/min

P. I.

Maker

Set)

300 .m -k-

c: w

200 a

cn C= :4-r_

0

C: ra 4. -

00

0

0

100

200

300

Instantaneous Thrust Force Componentlbf (Fý-) Flc;. 20

I

FIG, 21

HACKSAW MACHINE AND ASSOCIATED INSTRUMENTATION FOR BLADE TESTING

b--4

xZZ:

0

CN

ui

x ck:

CM

b-4 Z

Lr%

%.ý. c"li (n LU le-

X

Ln 0 23x CD C:) (M r-, LU

cn

LLJ CL 3: .: ui .

cý . CD

LLI L)

LLJ a. 2Z w LLJ

ui Im U

co LLI

LLJ LLJ 0-%

C%4

LLI

Cz uj Fa- LLJ

C)

U)

LLI

-i

LLJ im

> w

C)

to

LLJ

Cý4 cl-j

LU U)

Ip-i

I

Ill ON -1

Cl -j

22(A)

FIG'.

ci

I I _ht

III

U. 3 II

%ilk.

c

FIG

.

22(B)

ci

P

nrUST

rorce

FIG. 22(c)

cu

FIG. 22(D)

ci

n

Fl G.22 (E)

uj cu -ýd 0 V)

11

Thrust Force

FIG 22(F) -"'

FIG. 23:

The avertige depth of cut rx--r tooth against the thrust ýoothý-per load per for blades having unit týickness different teeth nitch.

25mn, 25mm, Enla cutting x specimen: fluid Cutting : Air cutting : 76 strokes/min speed Machine : Wickstead 20Cm Hydrmratic

S.-w

E E rn 1IC> ra 11-0

zv

40

60

80,100

f tra Nmm'-l

120 FIG. 23

14C

FIG. 2 4:

:-5

The cutting constant against the reciprocal of the number of teeth in contact with the workpiece

Workpiece fluid cutting Cutting speed Machine

: : : :

Breadth(B) x 2-'ýrm, En la Air 76 strokes/min Wickstead 200= Hydrmiatic

0

Saw

/6TPI

-4

B= 50mm 6 75)m

B= 38mm /10TPI

13

_4TPI 25m.m

"? IR

0

//

1.0

x

E E

Blades as supplied (H.S.S.) 13- 400 x 40 x2x4TP 0-

400 x 40 x2x6

TP 1

400 insx 32 x 1-6x 10 TP1

0.1

0.2

0.3 7-1

FIG. 25:

Carparison

of blade perfonriances-

Machine: Kasto Pmper Saw

'A-

(Brand

'Z')

(Brand

'X')

*3 TPI 4. TPI

'X')

6 -.pi

(Brand

.

(13rand W)

10 TPI

' ..

rri I e--) Ir-

0 J= -I. CL (Ii Cl

10

0

Mean

thrust

is

20

25

force per un it tiiickness lbf/irrn (ftd

FIG.

u U-6

26:

Instantaneous Brand

force components 1XI 6TPI Blade

for

30(

4.0

ci

CL

(31 Li 90

20

cn C:

t/I :3 0 C: ro

10

100

3CO

200

Instantaneous thrust force componentIV (Ftý FIG. 26

C4

Is

FIG.27

PROFILE OF THE

BpAvT3

ToPol,

BLADE

411 opok '17

1

LU LU A a1v

dp Wit.

17

Z: LIJ m

Z ý Z:

cz LLJ

LU ýz

CD 0 (n üý c- -::3LU

"Alp*

V

LL _zr CD

IN

* V0 Iw*0

LU

cn LU -i 2:

<

00 CN

X

gý

tie lik

ja IP

-0

I LLJ LIJ U)

c:l _j

z

z

U) LL) Cif

u (n Z-3CL LO u

Lu

Q < < LLJ CLL 0

U) Lu CL z

z0 cn

FIG.

48

30: The effect of tooth spacing and cutting blades the of cutting nerforrrance on,

Cutting cutting

edge radii

1'

specimen: M. S. 25=25mm fluid : Air

blades in as received condition cutting speed : 76 strokes/min rachine : Wickstead saw

4T

44P

1-127 0-957 36 A

3.2 .

28

6TPI

0

24

1512

1-13 20

16

yo

OTPI 1-ý87 r 1-598

12

8

in inches denote X10numbers average radii 4

16 20 12 (ftm) lbf mm -1

24

28 FIG. 30

32

FIG.

31:

Effect

of blade

wear m the cutting

per.. =ance

rn x ra 1-10

0Z468

'10 12 1L 16 18 20 22 24 lbf mrrfl

26 28

30

Fig. 31

FIG. 32: Effect of blade deflection new and woxn blades

cn theperfo=nance

25rrm x 25rnmMild Specimen' I: Air Cutting fluid: Cutting speed: 76 strok-es/nin

of

Steel

C

L

0

8 4 Mean thrust (ftm) lbf rrr,-'

28

24 12 20 16 force per tooth per unit thickness

400 x 40 x2 x6T. P. I. Blade No. 6 New blade 400 x 17.5 x 2x6T. P. I. Blade No. 6 New blade 400 x 40 x2 x-6 T. P. I. Blade No. 2 Worn blade 400 x 19 x2 x6T. P. I. Blade No. 2 Wom blade

X

Standard

0

Reduced width Standard width

uridth

Reduced width

ric;.

32

41

-11. -

10

-

LLul ro

tn r-i le ul d, 2 .9 Ini

ý T-lc:

1.

12

0

En En

43

4-) 41

a,

En 404 LL.

4j

4J

En 8

44 0

A

M M 0)

ul

4J En En

4

-j V-1

$4 .-P U) ,48 mI

04

ulzC'14 V-1

Cl.

c3 rýW

rig. 33

FIG.

34:

Deflecticn

models and equaticnS

(a) w

-W

2L2 A simply

22 supported

bladerAdth

6 max 01

vAiere

WL3 48EI

longitudinal

tension

01

tanhU

=U-

1/3 U3 J-ýPL2

U=

and

A4EI

(Load/Unit

Distance

P4P LK W(

22

A uniformly loaded blade with built-in

6 nux

where

and

02

WL4 3MI

= 24.' T U2

212-

ends

02

UooshU -U sinh U

U Fig. 34

FIG.

35:

Deflectim

factor

against

tensim

factor

loý L. 0 ro LL. C:

M

10

Tension Factor U

Fig. 35

FIG. 36: Load/extensicn

s

curve

for

H. S. S. blade

(Brand Ix').

1

d

-4-

C 0 I"0 (0 0 -J

048

12

14

16

24

Extension x 16'4 inches

1

2'

0.071*

0- 976"'

9

FIG.

36

FIG.

37:

load induced In aTensile 4CO x 40 x2x6T. P. I. blade nuTher of tums of the tensim Machine

: Wickstead

Hydramtic

against nut

the

8" x 8"

10

8 _L,

2

0

0-25 0.50 1.0 0-75 Turns of the tension nut

1-25

Fig. 37

Tension nut

Position Amfloe4i-inn

of the wcrkpiece

ý,fien the

t%mq Try-3A-q=PA

1.6 1.2

En 44 "-i 41 Ea

a4

Blade Tension-kN (All -measurarent: k made durin cutting) .g

FIG. 38:

The effect* of blade tensim of the blade.

on the vertical

stiffness

ricr. 38

FIG.

39:

frequency Natural blade tensicn for 4CO-x 40 x2x6T.

vibration of lateral a Brand 'X' P. I. blade

against

28

240

2 Theoretical trend assuning built-in ends

6O

E:3ýerimental L-trend

U C= ci

12C = cr (Ii L. U-

/

0

0

80 4(0

Vbde of vibration

amsidered

40 Wicksteed 811x 811Hydramatic machine

0

468 Blade

10 Tension kN

Fig. 39

lý ý -;;, '-cu'

I ;ý A 18 -K CN CO x ul

F

ýw

CO LM (n

r4 0*

*0

00

0*

tu

-A .

1v

LLJ

cn LL 0

%0, 41

V

44

dw

En w

-ci !5 c: r 0, vi vl

-

C>

(U

-_r

Wen

10-1mm x

(a) 40 Fig.

'-14 M Eý pj

o\O

ýý4 > c, 'W cq Ln

ý2 ,4

9 LA Co Ul

Ln

9-

a) 4-

IA

%#- 4ro 0,

CC13 (31 rn : ý: co

(0

:i

5 8 E,

Fig. 40 (b) , %W

lb

FIG.

41:

The average main thrust for a blade

depth of cut per tooth against the load per tooth per unit thickness in three states of wear

IKorkpiece : Cutting speed : Blade : Machine :

25rrm x 25rmnEn la 120 strokes/min 400 x 40 x2x6T. P. I. (HSS) Wickstead 200m Hydrarratic saw

2e

24

2C

E16 rnE X 22 I-V

8

4

0

20

40

60 ftm

80 1 Nm6

100

120

Fig. 41

14

FIG.

42:

The effect

of blade wear--on its

cutting

performance' Blade Speed Machine

201-

: 40Ox4Ox2x6 T. P. I. : 76 strokes/min : Wickstead VxV Hydranatic

16

12

(U

cn ro L-

0

48.12 Mean Thrust Per

14m

Unit

Force

thickness

ft.,.

-16 Per Tooth lbf

20

miýl

160

New Blade 36 cuts After

E

0 12 tut

80

for wear tests En 44E

:Z

40

0

for load measuremnts; 5nm M.S.

40 80 120 160 Mean Thrust Force r-tm lbf Fig. 42

ý %I0 cn

m

C:)

rýq m

cm

c14

-T CN

4-3 8

c.,J rc 44 0

%0 T-

(N

Co

-. t

(

Wear x 16"mm

Fig.

43

13 LU U)

Blade Tooth

Rake Face Chip Plastic Flow Lines in th e Base of Tooth

Metal Breaking Away from the rear of the Blade Tooth

Nb

Cracks IN

Direction of 81,ade Motion

Workpiece

FIG. 44

/ ee *0 00 0 1/ Heavily DeformedLayer Below Cracks the and Workpiece Surface

:>-%

DEFORMATION OCCURRING IN BOTHTHE BLADEAND WORKPIECE COMPILEDFROMMICROSCOPIC OBSERVATIONS DURINGWEAR TESTS ON EN44E (25)

200

aj 0

200

0 60 -

300

-

ýEn 44E (cootant )

tA Wi (Li m

600

700

9 tcoolaýntý)

En9 (dry)

En 44 E te)

20 -E fai > 0

500

, --'--ýýEn

Ragge of P xis ng machi

m cn 0 l=

400

00

200

300

400

Soo

600

0.4

0-31

16J m

0.2 LL. . 6-

VI

En'9 (coolant

0.1

0

FIG. 45:

Cost Ratio =0- 5 700 600 Soo 300 400 200 100 Cutting Str6e Rate in Strokes I min , The effects blade life,,

of the cutting stroke rate an average cutting rate and the cost factor

(27)

45

00

W

4-

cu

-20-

3000

2000

1000

0

Tg pic aI Pange for a ydr gulic 'Machine

18.

This load apprc3cheIs the breaking strength at standard blades

14 ,.; LL.

do(ant

.1 VrIC

cst ost

04 . 0 FIG.

46:

11

Ratio =0-5

4-II 1000 Thrust Force N 2000

3000 .

The effects of the thrust load cn the blade life, the average cutting rate and t!he cost factor (27)

rig. 46

I

"ý80C -

En 9 (coolant) I

lEn 9

dry)

260 . ypical range for the st andard blades

V) .5 ej

II 11

-. 1

2DC

0

En 44E ( coolýnt) En 44E ( dry 200

10D

300

4W

5DO

I 60-

600 En9( coolant) En9 (dry)

lTypi*cal stroke too sting machines .....................

=-2 40

En 44E(coolant

Ln En 44E (dry)

20ml CL C>

<

0

300

100.200

400

Soo

600

En 4A E (dry) 1 En44E (cooLant) 0-2,

Cost Ratio 0 -5

0-1-

En9 (dry ..........

0

FIG. 47:

100

200

3v'O--- 400 Soo Stroke ot the Saw mm

En9 (coolant) 600

The effects of the stroke of the saw cn the blacle life, the average cutting rate and the cost factor (27) Fig. 47

ci

m

20

0

40

60

60

100 120

-60

EO

100

140 160

10TPI 6 TPr 4 TPI 180 200

c210

c7> ai

120

140

160

180

2

4TPI

0-4

0-3ý

Cost Ratio = 0-5

6TPI. m

0.2TPI

20

FIG. 48:

40

60 50 100 120 140 160 180 Breadth of the Workpiecemm

200

The effects of blade teeth pitch and breadth of wrkpiece the average cutting on the blade life, rate and the cost (27) factor

Fig. 48

C:

.0 4u ro Cni. M cn a

z

LO Z:

u

44 0 144

8 U-) -0

;zl. col CD 4-4 84 44 0 Ul 0 rq 4t -IY4

Fc

Ft CUTTING FORC E

Fig. 49

FIG.

SO:

defo=ration

(a)

A fully

(b)

Mhr' s stress diagiCUL for in the deforaation zone

established

all

zcne points

(a)

Chip-/ 0 C jL G (zr

V1

$aw Tooth

5"/

B It up Edge

50 -Fig.!

in the cutting Predicted variation constant of friction against the apparent coefficient developed deformation for a fully zone

FIG. 51;

: En la (k= : -4 degrees

Material Rake angle

461.87

Nmm-2 )

2

1.

m IC:

)

Irx

LL

01

0

-1.0

-4 -2 -6 .8 Apparent Coefficient of Friction

Fig. 51

FTG. 52:

loads

Thrust

acting

on th6 teeth

(24)

Blade L=. G , £;=O

C-ijE) MG

76

i c v

lic-29.5 tv 4ý3 'm

Wor-kpiece , *,

Fully

established

Defonnation

Note:

Zones

'ý isccnstant

for all

teeth

Fig. 52

FIG.

between the Ccaparison for factor the chip of index and experinmtal

53:

of the reciprocal cornputed values force values of the cutting various values (24)

1.

3.

3.1

2.

2-

2.0-

2"

1"

1.01 0

-2

n

3-0-

2-5-

-3

O-B

10 TPI Blad-(

1-0

1

2.5-

2-0-

011

-

L0

-1

0-

2-0

1-5

1 oL 0

1-5-

1 11

'OL

12 -wcMaterial

En la

3

1 Fig. 53

FIG. 54:

between the carputed values of the Carpariscn for cutting force of the chip factor reciprocal data obtained with index of 1 and experimental blades of various pitch (24)

4.

3

2

1.0 1vJ

nc

Fig. 54

JA.

Albrecht

(32)

Fig. a. -

%%

Uncut Surface (37) Yeo & Palmer

Fig. b.

&q/

Work

lýB

/V y

Uncut Surface

(35) Rubenstein & Connotty Workpiece Fig. CFIG. 55:

e

za

If,

00 I

Diagra=ntic representatim of the cutting process a tool having an extreme cuttiiýg edge radius

Cut

Surface with

r4g. 55

h=Material Recovery.

fo=Nominal Set Depth.

Deflection. x=McLchipe

tl=Layer Removed.

MachinedSurface

to > ti (CL)

i

-,

to 14 T-! -. ined Surface

(b) to=tl

to

MachinedSurf ace

I> (C) t,0 tj

to

ined Surface to=tj

(e)fo

FIG. 56:

to

MachinedSurface tj

10

Diagrmmmtic representation of the relationshil, between the set depth, layer of material removed and the machined surface Fig. 56

LLJ

z

C/)

0 Lim ui C/)

z Lli

Z:

LLJ Cý

0 cn

0 0 LLJ

U

rýLr) LD Lj-

kir

to air gauge

Air

gauge

Tool

Dy eads mplif

FIG.58

VIEW OF THE CUTTING TOOL-WORKPIECE, SET-UP FOR SIMULATION TESTS

to ie

(A)

(B)

FIG,59

CLOSE-UP

OF THE BRIDGE

DIAL

GAUGE ARRANGEMENTS

FIG. 60:

Stiffness

measurermnts at position

of tool

holder

(Parkscn Miller) f

tz

0

.6 5

4 = 'C3 ro 0 -j

2

0

20

40

80 60 DeflectionAm

100

120

CD U) 0 z

crLLI LL z LU u Li

LU (L CL CD u LU 3:

Ln

LL 0 z 0 0ý Fu ui V)

1=ý < uj X CL

w

Lu

ýý

Lo

r--i LO

rQ

cký Lij CL CL 0

u <

Lr)

LU M :3: Lr) clsi ui u

C: )

C)

Fu

>(If

U0

Lu Z 0 LU

M FaLU

CD

cn

>

Of

LL 0

Z Z:

U) LO al U-) C: )

CI-4 Co (D

ag-

1

(.

FIG,63(A) TOOLEDGE RADIUS

GRINDING JIG

SURFACE GRINDING MACHINE

SET-UP ON THE

Wheel

Grinding

Pin on Axis to relieved diameter

of Jig half

Rotation axis of

about Jig

-.

Clamp screws to hold tool in jig

(B)

Capable direction graduated grinding

Grinding

in movement by means of handwheel. of table machine

of

Wheel

(C)

FIG.63

ESSENTIAL

FEATURES OF RADIUS GRINDING JIG

this

mm "

(A)

I

f

41k, %-

''

(B) FIG. 64

CLOSE-UP

VIEWS

OF THE TOOL

WHEN GRINDING

THE FACE AND FLANK

'11ý

CIO cl,

LU

LLI

LLJ LU

UD r--i Ln 00 CD C: ) ý-,

1-1

C/) LLJ

LL. 0 0I 0 0

0 V)

ullý (.CD

t

I

I.,

,0

p;»

cu

F= E co

E (D U'ý

4 4

cn C:

. 4=3 t-. i

de Ln %D

Fig. 65

-i I

0w 0 ý- r-i

Ln

CD = C=) P-4

Uj U uj b-.4 CL

LLI Ua-j CL 0 U=

C)

LLJ

I

z cn w LLI 2: :3 LU = CL M: 0U) ý: -j = U)

z z

(D LIN = Cl b-4

6ý

0" Ur. " 14

IIU) Z Z: 00

C=) 00

LU

0 U

i

0

gZ LU (n CD:: w

I-

w

0

w u

F-

0.

LLI u U)

LU =

FZ

gn

cxi

LU uZ JY0

cm

U. C%4

t4,1 C, 4 i ... (N>I) -30UO:l ouiano

r--i

3NN

LD

LsnbHl

L9 U-

b-4

(n =

cn

UN CN cý

-

E2

LL

KL w

Z: Z: CZ) 00 0* LL. w w

kw > r w< 0

0 Z

0-, (D

b--4 w=w CL "-i 12.

CL C)

Ln

-3 :D. 0 CD

92

im 0-4

1cn

1Z0 .. LU -1 LL L) w (D ZZ 0-%

f-41% "

(NA) 30HO:1

no

T--4

(N)I) 3:DNO:l

0

0 (D

tf) Z wZ -i 0 LL

TT

___

Li LrIA

LL

u LL. LL-

Z: 2: CZ) 00 r--i im LU cn ci:: LU

LU

cn

LL

U

LLJ

U, U-

30ýOJ

Transducer

meter

Air

Gauge

ce

FIG. 68\(A)

MEASUREMENT OF WORKPIECE

RECOVERY

4

Tool

Slip

Ground

FIG, 6ul(B)

INITIAL

Gauge

Base Plate

SETTING-UP

OF TOOL AND AIR GAUGE

0 C:)

1

LU

LU

_j

(n -

LU CL

(D =

:r 12-

(D =

1

i

-. CD

<

ZD

0

h- 2: L) LU Z

UD

L',ý

Lu CL ýz

cr Lu 0CL C:)

Z:

2:: LL Cý cn 1-ý :D 2:: 5-

cl-i CD

CD U-

(2-

CL LU

CD F-

M:

z

7-

z

00

F--

00

LLJ V) Cýf LLI

ui C/) of LL)

(D U-

Of

uj u 2: LJ

LLI u

Lil Q) 2:

cn

U)

LU

C)

CD C:)

mi

VI II

LLI C/)

LLJ cz LU Z

LLJ 0 Ld C=

2r

CD

LLJ C:) LLZI,

(0)

Ký

cl-j

r--i

33ZýO=l ONiiino

N"%

r-I

(NN) 33ZýOd isndHi c71 LD

<

(9

(5

L 1=ý LLJ u

0

E)

LL-

FLU m U) 0-

LL 0 U) CL

0 0 Cl-

O-T

(E)

41

o-%

CIQ

CD

'1

0 r

P -04

H

........

00

1,9 vi

Ln CN 6

4J 41

U)

ro

(U -4V)

Tj CM

C.,4

c

(Li

4-

c3.

ul C>

41

(sl\

.0

44 0

44 0 44 0 -ij

(d

0

Lr) C) <6 0

rm

--t

CD

rn

'Contact Length (mm) Fig. 70 (a)

Ln 6

E

..

'1 cu a

T

CL

-0

10

Er= *s E E: - E c:" 3

CL (DIr- ,Lr Lnco m D M M. ... r= C) CD vi r= W to

Ln E: 1: c2% 1 _Y. . c2 gci : ý: CJ

(1 c2. Ic c2. ', 2 (T 0 . .

r7 C>

Ln

-,t-

g . vi ; P-%

-4

x

0

'3(

CN

le-

C>

Contact Length (mm)

Fig. 70 (b)

--T 0

= -cr FC) C-) LLJ

C) 0

:F u

E E C) CA ui bid

cc

In ui LU

ce CC ui UJ Ui UJ &9 40 )cb cm tn

-i s

tv.

uj M: cr1.

C-)

uj UC)

w

a ui -J

E ,g,.

d=

:2

ce. ui 3.-

Ul

tn ,

x ,

..

ui

: 2, vi

4.3

uj

+ 0 r- 2;

-i U-

_j

=

!LJ

; r. UJ g -»

= ei

0 :X

cr. = ci u

c) >-

C N.

I10

J-

(ýotu)

HION31 10VIN03

1001 dIH3

1%

NomINAL CUTTING CONTACT

0.5 mm EDGE RADIUS: 0,81 mm LENGTH: 3,81 mm

DEPTH OF CUT:

COPPER 14ORKPIECE MATERIAL: CUTTING SPEED: 95 MM/MIN

FIG. 70(d)

ToOL-CHIP CHIP

CONTACT LENGTH AND THE APPROPRIATE

FU

0 -I LLJ

(D

C:)

0

CD

LL

UCL x <

V)

C)

-J

0

Qo Lr) z

C)

-j 0

-

121 LU w z

Z u

CD 0

<

F-

z

2-1 M

LLJ

=

3: LL) u

W

1

-i

M

Ljr)

U)

(n

< LIJ LU

m

CZ)

LL

0

LLJ

U)

=D

cf)

CD (D z z

0 L)

(D LL

I (D

0 Z:

M U

_j 0 0

31ý 1.

Lu cn

z

CD LLJ m -E (1) -!:

U)

U) C)7)

13LLJ

<

1::)

u

m

:: ) F-) 0 W-

F:3:

FLu U)

_j LL

aU)

CL

w

-J <

(D m

m

CL

m: (-j

u

LU ilCL 0 0 u ; 21-

LLJ LLI

:D L-)

Top surface of many compressed iýetal of

chip showing layers

777

Side from

(a)

surface contact

showing pblish resulting with side of groove

Length of ,ýteady chip state formation-

(b)

Steady state reached

(C)

of

Cross-section

chips Towards

At beginning

of

end of

cut

cut

caused

FIG.72

not

Straight sides by groove conta

SOME FEATURES OF COPPER CHI*PS P'RODUCEDDURING GROOVE CUTTING

CHIP TOOL

CAP

wo R.Y.?I t, cz

TOOL cifir

RAKE rAc::

v

a,

C'Th, Ip TOOL

TOOL

cHip

RAKE FACE

": CE,, NOMINAL DEP"-ý

%4

CUTTING FLU" CUTTING TOOL.

AZjIUS

: T. -"

le

FIG.733

PHOTOMICROGRAPHS OF QUICK

STOPS (MAGNIFICATION

COPPER ý'!ORKPIECE.,

NOMINAL

DEPTH:

0,25 mm

CUTTING

FLUID:

SULPHURISED

CUTTING

TOOL:

0,56

16) x OIL

MM RADIUS

«-1 U

j

ctj

0 0

co Q4

la4

r--l 0

0

ý4 0

Q4

-4 Q4 4-)

1 u

0

'-I

0

04

0 0

I

04

-4 0 0 E-4

4J 2: u

A»

Z)

4-J

ý4 0 0 E-4

04

u

*L

4&L-

Q4 Q4

CL4

r-4 it 4J

04 U

to E-4

COPPER WI TH BLUN1

(NOMINAL SET DEPTH

0.25 10'

»k clq Kl%

x 0 u 0.UI,

lit,

k' to -

Z -

I.c::

U-

i

FIGURE

74

PHOTOMICROGRAPHS AREA WHEN ROOT CHIP OF THE RADIUS) MM TOOLS (0.56 CUTTING COPPERWITH BLUNT (NOMINAL SET DEPTH 0,25 mm) -

;

(/ 000

FIG.75

ELECTRON-MICROSCOPE PICTURE OF THE CHIP ROOT AREA !'!CRK PIECE MATERIAL. COPPER NOMINAL SET DEPTH: 0,25 CUTTING TOOL: CUTTING FLUID:

TOOLWIDER

mm

0,56

MM RADII

SULPHURISED OIL

THAN WORKPIECE

z

x Y

FIG.76

MATERIAL BEHAVIOUR AT THE CENTRE OF THE WORKPIECE

WORKPIECE MATERIAL:

COPPER

GROOVE CUTTING

BLUNT TOOL: 0.56 MM RADII TOOL WIDTH: 3.4 mm CUTTING SPEED: 95 MMIMIN CUTTING FLUID:

SULPHURISED OIL NOMINAL DEPTH OF CUT; 0.15 mm

QJ

i-

Lengfh of Cut

(a)

ýIG,

178 m

77

VARIATION OF CUTTING FORCES DURING GROOVECUTTING WITH A BLUNT TOOL AND THE APPROPRIATE CHIP PRODUCED

WORKPIECE MATERIAL:

COPPER

GROOVE CUTTING

0.56 MM RADII TOOL WIDTH: 3.4 mm CUTTING SPEED: 95 MM/MIN BLUNT TOOL:

NOMINAL

DEPTH OF CUT:

CUTTING

FLUID:

0.1

SULPHURISED

MM OIL

L

180 m-m Length cf Cut

Fig. 77(b)

CUTTING

CONDITIONS:

AS ABOVE

0-1%

/ Fc

180mm Length of Cut

RKý' I

LLL

GROOVE CUTTING

0.56 MM RADII 5.4 mm

BLUNT TOOL: TOOL WIDTH: CUTTING

SPEED:

95 MM/MIN

CUTTING

FLUID:

SULPHURISED

OIL

z

Ze Iu- 2 1

180 mm Length of

Cut

Fig 77 (d) WORKPIECE MATERIAL:

COPPER

---.

..,

, ýý.

I.

0.56 -Z

FLUID:

NOMINAL DEPTH:

GROOVE CUTTING BLUNT TOOL:

CUTTING

/I

MM RADII

RAU

z a) I-

0

LA-

180mm Length Cu ol

Fig 77 W

SULPHURISED OIL

0.5 mm

--_---i:

-

-------

-

"--;

I

49

>%

- 10 0

08,

CJ

Q)

404 tr) CD LLI L. )

LU

-3:

ci

4-

A,

(M

rn

cl

>1

4,0 4.4

01

U-

0

0

44

ci V) a

.2 QJ .! =

44

cl .

Z

-0/ r>N

uj I

co

V4

E C-

m

C14

C>

MM80ý Fig. 78

Ul cl

I t

FIG. 79(A)

SCHEMATI DIAGRAM OF THE CHIP FORMATION WHEN ,C MACHINING WITH A BLUNT TOOL

FIG. 79(B)

SCHEMATIC DIAGRAMj SHOWING LAYER OF MATERIAL BEING EXTRUDED AROUND THE CHIP ROOT AREA

Chip Too[ Contact Length I (mm m

C*14 LL

Ln

LL#-

I

Cn

04

Ln a.

00

....

06

4.9:

It5

1

r-4

ER ý413 -I

4

4M

ILJ

E-4

44 0

Cu

E CI-4 Ci

-10-'d

4-

6-0C=

Cn C:

ý

4

ro

UU0

"A

C: LA = =3 C3.

C9 00x

El-

%0

Lrw

--t

Force kN

m

C14

C)

T-

Fig. 80

(WLU)

cu Li t-

%0

Li

ý

4-

vi C -

c: Ln Lj

ru

E

e

4 'Ii

'-I

I-

T-0

E' C... ci

44 0

CN

6 4ý4

44

b t; rd I

a Kr-4

C-41

W t7l

co

ký4

ý '40-ý

C5

Ln

m

Force(kN)

C*4

C1.14

.?,

Chip Too[ Contact Length I( mm) 00 %0 -1-T C)

Ir-

rL

Cý

C)

IU(ý4 co

06 LL

"r7 -J

Yo.,cn

C: 0 C:

Ln 6

CJ

78 4-)

0.4 u

44

rO

C4 Hzg

.

1-

12

Ln (3)

Ln .

*0

0'0004000 rd ro 44

00

E-4

Ln.,

--t

Force M)

rn

T" MG.

82

ir -i

EýG ca. l= UP

(U

LL

CD

0

rg

..

*.

.0....

cE>

týro ro 44.. U)

t3 tn S;

r-4

8 E-4 x

cu

c)

m 44 0

vi

x

1

92 4. .

4

en co

8

-Ln

-4

m

. Thrust Force FT(k N

V-

Fig. 83

ý c:

a

8

CL

fu

x

Ln

--t-= IS ct) im .LýI

..

-ý 01

E4

W 0

U

MCI.

CL

%. J

ru -a

(n V)

9Q80.,

12 tu

M. x

44

«a

044

0

4

0

0,0

e8ý

Co

r CI

jr 4

SP

7cu

m2

11

GN/m

Fig. 84

0

Ln 6 a

0

ci tn

0

E5IS ýJ m L2 o tr

«ci

0

4-4 0

CN

0

C)

Ln Co

0

,

Co

r-

Specif ic

Ln

m

Cutting

Energy GM/m

Fig. 85

FIG,86'

SINGLE SHEAR PLANE MODEL

(70)

(a)

line

Slip

f ield

-

(b)

Mohr

circle

for

stress

-ý,

j

W,

field

11

0=

11

4

LEE AND SCHAFFER'S SLIP LINE FIELD SOLUTION FOR A (59) PLANE SINGLE SHEAR

FIG.

field 88: Slipp-line and hodograph for-bq1t-up Lee fter Shaffer (66) and a; nose

(a)

Built up rcse

(b)

FIG.

89:

Diagrannatic sketch (74,75) process

VT%dl

of suggested

cutting

m

Figs. 88/89

FIG. 90:

S1Jp-line fields soluticns and hodcgraphs for ýrestricted tool contac: L (77)

Tool

h.

P.

0B

A Wcrkpiece

aJ

(a)

u:i*r-Slip--J: Lne field

- Negative Rake

(b) (b)

Hodograph - negative rake, tool (-Vc)

b

a

(a) Slipr-line

field Positive

Rake

(b)

0

Hodograph - pcsitivo raka tool (+Ve)

Fig. 90

FIG. 91:

Slip-line

field

in machining wit2f Cut-aFay* *tool

(81)

C, s.

Tr8P-J

7-

w

FIG 92 MODIFIED JOHNSON-USUI SOLUTION FOR RESTRICTED TOOL (A) SLIP LINE FIELD FACEv (B) HoDOGRAPH (82)

eo. 2) .4 f'ýý 2.3

4EdF (177)

'%ý (W)

FIG, 93

r+'

I

MODIFCATIONOF FIG. 92 FOR UNRESTRICTED TOOL FACE-I' (A) SLIP LINE FIELD (B) HODOGRAPH (82)

4, J

(W)

(A)

IE

MODIFCAT ON OF FIG. 92 FOR ZERO RAKE ANGLE AND STICKING 'I' SLIP LINE FIELD AND HODOGRAPH*, ' (82) FRICTION,

C4 t

//(77)

"I (W)

-2

/, E

/

0.

11

1

Ew T, 7- Z

FIG, 93 MODIFICATION (B) FOR ZERO RAKE ANGLE AND STICKING OF SLIP LINE FIELD AND HODOGRAPH (82) FRICTION,

y

FIG.94

SLIP-LINE

SOLUTIONS FOR RESTRICTED AND ' UNRESTRICTED CHIP-TOOL CONTACT*, (82) FIELD

FIG. 95:

field and hcdograph for restricted Slip-line tool ccntact, where cutting edge radius is -approximated by straight edges (79)

(a)

ts

Id'

_

Fig. 95

w

LU

w w

LL.

Cz F> %-o

0-40-4 U. :3. w I

c71 LL.

cm

FiG. 97

DEFORMATIONPATTERNSORODUCEDIN HORIZONTAL AND VERTICAL LAYERS OF PLASTICINEi WHENSIMULATING THE CUTTING ACTION OF BLUNT TOOLSp USING A PERSPEX MODELTOOL,

Ic

:5

51

4-4

r-4 P-4

to Co CN

f

.4

810 0 gn 41 c) ci pl w 4) 41 Ul 41 (4

44 0

I

4J Ul ul

c14 ji

U)

0 41

Pf 01

0

lu c4 P., f-t Z00 ri 0 ji c:

r. 110u

JJ C0 Pf N4

0 RU

u tu Fig. 98

I

Shear Stress T

01

FIG.

99 (a) :

Mohr' s stress 98 Fig.

circle

Mohr's

circle

for

slip-line

field

in

0

FIG.

99(b):

stress

Fig. 99(a); (b)

cl%j T-t-

E C4

cl

LLJ

C7%

x ui 44

CC)

DI

CD w cc:

tý4

0 u 0

LA. W u w 0bid C)

Ln CN

0 4J -P En a)

Co

(LI

w

M 4J 00 rd 0 $4

cu

CA: M

0M -ri EO 0 Q) En 0

cl: w a. 0 u w Op LA.

rn

$4

C- L(Ij (U C3. C3. C3. CL 00 ,L.j L. J

00 U 4j 0 r-4 rd

cl:

w cl:

X0

rd P rd ý4 r. -r4 P CO (a 4J

%.0# CD

C)

rn

%i

r-4

MNIM2(y) Stress True

V-

C*-4

'17

01%

CC)

w ciz IW w

r. -

ck: w

C:)

cr. U. -i Q) w =W Ln 6,2

Q tj ce LL. LU cl:

rn

V-14 CD

(n w cr. V)

eq % C)

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True Stress

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x

C3 <>

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(W 33aOJ Fig. 102

ci

ci

Cy

0)

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x

CC) C7%

LU

-b.-

(11

ci

LJ -4-

0)

ai

CU

F= - Z: CL x

LU

Ln

Ln C;

Cý m tA -rl cl

E E

cn C: Cj CD __j Ln C: C) Lj0 0 cm =3 L. J

CL

= t-j

rn

N

la

ai

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5 40

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ei 9.1 cu

(A

LJ a)

(1) ci

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r; =rCD

cn

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L-i

CD

IN

3D80A Fig. 103

ii

r-i 01-*

2:

w

c; -

w

(D Ln

E

Ln -i < c 14 b.-4 LO CDw wl w ý.- C:D

E

00 CD

Uc:C

CD U-

2: 0 w LL

LLC,1-1

6--4 Fcy c) Z:

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0-

CL

Li-

< LU

cl W

_j LLi

Ln C*4

9c cr_I

0X Lii

IL

CL W rM

I .

13

0* . %0 OL

llcn

J_U

Y-\ý

------------"/ tO

0 0 F-

cn

E E:

0 U

0

C) LlLLJ co

08M 2ul/ND

Mum

DljID3dS Fig. 105 (a)

144

a l3 4 Q) Z:

a)

En

W (3. x LL J

Cl U

40) CJ

I vi

ý -P

HT

1. . E u cj C3-

Lil

V7 I

L.J CYJ

an

I

CU In c10

vo,

c II

I

I

I

I

I

I

I

I

I

4-

C)

IT I I I I I I I I IL

co

Lrl

rn

083Ný ONIlin3 DJADUS ZW/N9 rig. 105 (b)

11

I-

:Z C)

tA Ca .c ad

da -9 cc

uj L2

ui co

uj s

LLP

C6 bc ad 0 31

e9

CD c2 U.

-3 uj

00 11

ui U

.aI cc

Lai

cm Am

LLJ cm dm CD w LJ L *, -ý 2>

Ul V) ui

= w

d?

Cl. x cw a 39

in It

Cm

0 cc ui 96 CL. Op

ý-- c: )

.0=

LLJ ui LLJ

4 CD -N

LI C:) vi

ci %0

snlaVH 35a3 / HIDN31

IOVINOO

36 4 TPi

BLADE

SLIPLINE FIELD MODEL PREDICTION (SINGLE POINT)

' 32J

i 6 TP.

9

'C 0

a

A

0

FIG. 107

20

40

ft

so

60

mN

100

mm-1

PERFORMANCE COMPARISON OF SINGLE POINT (FROM THE MODEL) AND BLADES OF. DIFFERENT PITCH

Standard

Blades

(Raker

Set)

I. 40 P. 400 x2x4T. x . P. I. Brand-IXI 400 x 40 x2x6T. 400 x 32 x 1.6 x 10 T. P. I. )

W; 1=

0.

%.. o

«:r

0-

3 c-!

0-

0"

0.

57

TEETH PER INCH

oil

INCREASING GULLET SIZE

FIG. 109

COMPARISON OF THE PERFORMANCEOF NEW AND MODIFIED BLADES OF DIFFEERENT PITCH.

f,

MILD STEEL; 50 mm BREADTHx 25 mm DEPTH WORI(PIECE: BiAND P.II BLADE: 400 x 40 x2x4T. HYDRAULIC SAW MACHINE

3

2

to

0

20

40

ýt

60

mN

FIG.109

so

100

120

mmI

COMPARISON OF THE PERFORMANCEOF A STANDARD AND MODIFIED 4 T.P.1 BLADE.

WORKPIECE:MILD STEEL 50 *nm BREADTHx *X (400 x 40 x2 mm) BRAND BLADE! HYDRAULIC SAW MACHINE 76 STROKES/MIN CUTTING FLUID AIR

25 mm DEPTH

P-1

(6 TPI MODIFIED) (INCREASED GULLET) (6 TP.1 MODIFIED)

3 T.FI

26 TPI

(STANDARD)

2

20

CD x cl COOO

8

4

20

40

60

Ttm

80

100

120

N mm-,

LCJ OF COMPARISON "STANDARD' THE PERFORMANCE OF c FIG--110 AND MODIFIED, BLADES (6 TP1 -3 T.P.1 -

DEPTH 25 BREADTH Somm MM X STEEL MILD WORKPIECE: %--o . --.---II

CDP X cl C.40

As

20

40

ftm

60

BO

log

120

N mm-,

COMPARISON OF THE PERFORMANCEOF 'STANDARD' AND MODIFIED BLADES (4 TPI ---*-2 TPO

o'lolv-

up

!2

ce uj

tn Ln ca WC ui 4A tL

e

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a: i CD

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to

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Let U) Q:

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1:

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C)

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tn tA LU

L-Li (2)

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AMU

9NIIInO

31JI33dS

1