Tolerance Analysis

Tolerance Analysis for Non-rotational Parts Team: Dr. X. Han, S. Yao, C. Fei Advisor: Professor Y. Rong Sponsor: NSF & Delphi Corp.

Tolerance Analysis in Production Planning Tolerance analysis - Part of setup planning - Locating error coupled with process error - Intra- and inter- setups - Process verification and quality control Best Practice - Integration in CAD/CAM

CAD

Part Information Model - Manufacturing feature - FTG (Feature tolerance graph)

Setup Planning - DMG (Datum Machining feature relationship) - Processes with tolerance specification

Tolerance Decomposition

Four steps: – Tolerance stack-up analysis • Tolerance decomposition • Machining error analysis

– Tolerance assignment – In process inspection – Quality control plan In this project, the first step is studied.

Tolerance Assignment Machining Error Analysis

Is error in tolerance zone ? Yes In-process Inspection

Quality Control Plan

End

No

Tolerance Stack-up Analysis • Tolerance stack-up analysis is to evaluate the machining error effects in each setup on the feature tolerance specifications of the final product • Tolerance stack-up analysis – For given setup plan as DMG – For given machining errors in each operation – Evaluate the machining error accumulation through setups

• Tolerance decomposition – The feature tolerances specified in product design can be decomposed into operation tolerances specified for each setup – The machining error in each setup can be decomposed into locating errors (∆ loc) from machine tool and fixture, tool-fixture alignment errors and tool wear errors (∆ tool), other deterministic (∆ o) and random (∆ ran) errors.

∆ =∆

loc

+∆

tool

+∆ o+∆

ran

Tolerance Achieved in One Setup Symbol

•Tolerance decomposition model 1 : Two related features are machined in one datum frame:

Tolerance type

Machine error calculation in one set-up Model1

Model2 Two features have the same normal and

Linear dimensions

with the same tool

∆ = ∆ o + ∆ ran

Two features have opposite normal and with the same tool

∆ = 2∆ tool + ∆ o + ∆ ran

Profile of a line Profile of a surface ∆ = ∆ + ∆ loc tool Circular runout

• Tolerance decomposition model 2: One of the features in the tolerance relationship is the datum feature:

Total runout Concentricity Symmetry Parallelism Perpendicularity Angularity

+ ∆ o + ∆ ran

Two features have the same normal and with the same tool

∆ = ∆ o + ∆ ran Two features have opposite normal and with the same tool

∆ = ∆ tool + ∆ o + ∆ ran

Tolerance Achieved in Multiple Setups • Tolerance Decomposition Model 3 The features in the tolerance relationship are machined in different setups

∆ ∆ ∆

N,N’ N,A

A,N’

=∆ = ∆ ran =∆

ori

N,A

+∆

ran

+ ∆

A,N’

Tolerance Stackup Searching Algorithm In order to identify the factors that influence the machining errors, two steps are needed: • Search the datum-feature relationships that construct the tolerance stackup chain • Calculate the total machining errors Tolerance within one setup: ∆ = ∆ m t + ∆ cu tte r+ ∆ L o c + ∆ ra d o m

Tolerance stackup in multi-setup:

Begin

Tolerance stackup chain searching Searching features of target tolerance in DMG

Two target features are machined in one setup?

No

Yes

No

Begin with the target feature (I) in later set-up, searching related features in stack-up, calculate the variations of i

∆

Is the stack-up chain successfully found?

Machining error calculation Tolerance achieved in one setup

∆ = ∆ mt + ∆ cutter + ∆ Loc + ∆ radom

Yes Tolerance achieved in multiple setups

∆ = ∑ (∆ mt + ∆ cutter + ∆ Loc + ∆ radom )

∆ = ∑ ( ∆ mt + ∆ cutter + ∆ Loc + ∆ radom )

End

Locating Errors Analysis Among the machine errors in one setup, the locating error (∆ calculated:

loc

)can be

0 0 0 0 0 0 • Six locating points(P1 , P2 , P3 , P4 , P5 , P6 ) construct three orthogonal planes

A1 X + B1 Y + C1 Z + D1 = 0 A2 X + B2 Y + C2 Z + D2 = 0 A3 X + B3 Y + C3 Z + D3 = 0

•

A theoretical fixturing coordinate is expressed as

 A 0 (θ ) ( X 0 ) T  T =  1  0 0 0 0

•

X0 is the position of the origin point A 0 (θ ) is the 3× 3 orientation matrix

Actual fixturing coordinate reflects the variation caused by locator errors T = T0 • ∆ T ∆ T = (∆ x, ∆ y, ∆ z, ∆ α , ∆ β , ∆ γ ). ∆ T comes from the given locator errors.

CSf’

parallelism

CSf (∆ x0 , ∆ y0 , ∆ z0 ,

Workpiece

Xi

∆ α β0 , ∆ γ0 ) 0,∆ Locator

X Fixture base Pallet

Machine tool CSw

0 i

∆ T fb

∆ Tpl ∆ Tmt

profile

An Case Study on Knuckle L6 203

201

202

109

204

L3

OP10

105

L5

107 103

L2

102

104

L4

110

101

106

205

108

L1

208 207

0.1

OP20

A

111 209 206

1.2 X Y Z Machining feature GD&T of OP10: 101 Surface A Theoretical fixture CS: 0 1 0 − 27.64  Actual fixture CS  0.999966 1 0 0 − 72.7367    with given locator 0.00558042 0 0 − 1 − 73.8312 errors( + 0.0254 ) 0.00614057 −   

0 0

0

1





0

− 0.00558818 − 0.00613351 0.269581 0.999984 − 0.00128144 0.344082 0.00124717 0.99998 0.334775  0 0 1 

The worse case caused by locator errors: 0.654 Overall machining error ∆ Total = ∆ locating + ∆ mt + ∆ process +∆ tool = 0.654 + 0.013 + 0.254 + 0 = 0.921 mm ∆ mt, ∆ process and ∆ tool are given parameters.

A Case Study on Engine Block | 0.25 | M-S | A | R AA

X

W

Cy5~8

|Φ0.40 M | M-S | A | R |0.05/162 | M-S Cy1~4

YY ZZ L J R

M-S D

DD A

K

XX

B

Datum frames:X-Y-Z, XX-YY-ZZ, A-B-C, M-S-A-R OP10

OP20

OP30~OP170

X

XX

XX

A

A

Y

YY

YY

B

B

ZZ

ZZ

C

C

M-S

OP175~ M-S A

R

R

Cy

∆ M − S , A = ∆ OP 30loc + ∆ tool 1 + ∆ OP 30 mt + ∆ proc1 ∆ M − S , R = ∆ tool 2 + ∆ OP 30 mt + ∆ proc 2 ∆ ⊥ M −S ,Cy = ∆ OP175loc + ∆ tool 3 + ∆ OP175 mt + ∆ proc 3

Summary A comprehensive tolerance analysis framework is established for machining system planning and verification. Tolerance stackup analysis has been studies for non-rotational part. Three tolerance decomposition models are developed for intraand inter-setup analysis. • An inter-setup tolerance stackup algorithm have been implemented. • The calculation of locating errors has been implemented. • The analysis is integrated in CAD/CAM Acknowledgement: Dr. Y. Zhang and Dr. W. Hu contributed to the earlier work of the project.