Theory Of Metal Cutting-theory Of Chip Formation

LECTURE-07 THEORY OF METAL CUTTING - Theory of Chip Formation

NIKHIL R. DHAR, Ph. D. DEPARTMENT OF INDUSTRIAL & PRODUCTION ENGINEERING BUET

Chip Formation Every Machining operation involves the formation of chips. The nature of which differs from operation to operation, properties of work piece material and the cutting condition. Chips are formed due to cutting tool, which is harder and more wearer-resistant than the work piece and the force and power to overcome the resistance of work material. The chip is formed by the deformation of the metal lying ahead of the cutting edge by a process of shear. Four main categories of chips are: Discontinuous Chips Continuous or Ribbon Type Chips Continuous Chip Built-up-Edge (BUE) Serrated Chips

Department of Industrial & Production Engineering

22/2

Types of Chips Discontinuous Chips: These chips are small segments, which adhere loosely to each other. They are formed when the amount of deformation to which chips undergo is limited by repeated fracturing. Hard and brittle materials like bronze, brass and cast iron will produce such chips.

Continuous or Ribbon Type Chips: In continuous chip formation, the pressure of the work piece builds until the material fails by slip along the plane. The inside on the chip displays steps produced by the intermittent slip, but the outside is very smooth. It has its elements bonded together in the form of long coils and is formed by the continuous plastic deformation of material without fracture ahead of the cutting edge of the tool and is followed by the smooth flow of chip up the tool face. Department of Industrial & Production Engineering

22/3

Continuous Chip Built Up Edge: This type of chip is very similar to that of continuous type, with the difference that it is not as smooth as the previous one. This type of chip is associated with poor surface finish, but protects the cutting edge from wear due to movement of chips and the action of heat causing the increase in tool life. Serrated Chips: These chips are semicontinuous in the sense that they possess a saw-tooth appearance that is produced by a cyclical chip formation of alternating high shear strain followed by low shear strain. This chip is most closely associated with certain difficult-to-machine metals such as titanium alloys, nickel-base superalloys, and austenitic stainless steels when they are machined at higher cutting speeds. However, the phenomenon is also found with more common work metals (e.g., steels), when they are cut at high speeds. Department of Industrial & Production Engineering

22/4

Actual Chip Forms and Classifications

C-type and ε-type broken chips

Short helical broken chips

Medium helical broken chips

Long helical broken chips

Desired Not Desired Long helical unbroken chips

Department of Industrial & Production Engineering

Long and snarled unbroken chips

22/5

cutting conditions are the main causes for discontinuous chips     

Very low or very high cutting speed Large depth of cut Low rake angle Lack of cutting fluid Vibration on the machine tool

Department of Industrial & Production Engineering

22/6

Chip Formation in Metal Machining Since the practical machining is complex we use orthogonal cutting model to explain the mechanics.In this model we used wedge shaped tool. As the tool forced into the material the chip is formed by shear deformation. Uncut chip Thickness a1=So sin φ Shear plane

Rough surface

Chip Thickness (a2)

Chip

Shear Angle (β)

Shiny surface

Positive rake

Rake angle (γ) Rake surface

Clearance angle (α)

Workpiec e

Tool

Flank surface

Department of Industrial & Production Engineering

Negative rake

22/7

Deformation of Uncut Layer The problem in the study of the mechanism of chip formation is the deformation process of the chip ahead of the cutting tool. It is difficult to apply equation of plasticity as the deformations in metal cutting are very large. Experimental techniques have always been resorted to for analyzing the deformation process of chips. Several methods have been used: Taking photographs of the side surface of the chip with a high speed movie camera fitted with microscope. Observing the grid deformation (directly)  

on the side surface of the work piece and on the inner surface of a compound work piece.

Examination of frozen chip samples taken by  

drop tool apparatus and quick stop apparatus,

Department of Industrial & Production Engineering

22/8

Grid Deformation Methods The type of stress-state conditions is evaluated by means of an angle index e obtainable from Levy-Lode’s theorem,

e + e − 2e o 1 2 3 = tan (30 − e) - - - - - -[1] o e −e tan30 1 2 r  r    1 e = ln , e = ln 2  1 2 r r  o  o where, e = = = = ro = r1 & r2 =

ro Chip

and e + e + e = o - - - -[2] 1 2 3

deformation criteria 00 for pure tension 300 for pure shear 600 for pure compression radius of circles marked on the workpiece semi-axes of the ellipse after deformation.

Department of Industrial & Production Engineering

r2

Workpiece

r1

Tool

Schematic representation of the translocation of circles into ellipses during chip formation.

22/9

From Equation [1] and Equation [2]

tan(30o − e) = ln r1r2  r 2 tan30o  o 

3

r  ln 1  − − − − − [3] r   2

Case-1: For Pure Tension [e=0]

r = ro (1 + ε) and r = ro (1 − με) - - - - - - - - - - [4] 1 2 2   2 r r r ε ε ε 1 = 1 + ε, 2 = 1 − and  2  = (1 − 2. − ) ≅ (1 − ε) - - - -[5] r  ro r 2 2 4 0 0   Where, ε = cutting strength μ = frictional coefficient=½ since ε is very very small so neglecting ε2

Department of Industrial & Production Engineering

22/10

Now, from equation [5]

 r  r   1  2   r  r      0  0 

2

rr 2 = 1 2 = (1+ ε) (1− ε) ≅ 1- - - - -[6] r 2 0

From Equation [3] and Equation [6]  2 4 r  r r rr 3 ln 1 2 . 1  ln( 1 2 ) 2  r 6 r2  0 r tan(30 − e)  = 1- - - -[7] 0 = =  0 r r  tan300 1  1 ln( ) ln  r  r 2  2 or, tan(300 − e) = tan300 or, e = 0o for Pure Tension

Department of Industrial & Production Engineering

22/11

Case-2: For Pure Shear [e=300]

r = ro (1 + ε + με) and r = ro (1- ε - με) - - - - - - - - - - [8] 1 2  r  r  r r 3 3 1 = 1 + ε, 2 = 1 − ε and  1   2  = (1 + 3 ε) (1 + 3 ε) ≅ 1 - - - -[9] r  r  ro 2 2 r0 2 2  0  0 From Equation [3] and Equation [9]

3

  r r  ln 1 2  r 2 0   tan(30 − e) 0   = r  tan300 ln 1  r   2

3 ( ) ln 1 = = 0 - - - - -[10] r  ln 1  r   2 or, tan(300 − e) = 0 = tan(0) or, e = 30o for Pure Shear Department of Industrial & Production Engineering

22/12

Case-3: For Pure Compression [e=60o] r = ro (1+ με) and r = ro (1− ε) - - - - - - - - - - [11] 1 2 2   2 r r r 1 = 1 + ε , 2 = 1 − ε and  1  = (1+ 2. ε + ε ) ≅ (1+ ε) - - - -[12]  r  ro 2 4 2 r0  0 2  r  r   1   2  = (1 + ε ) (1- ε ) ≅ 1- - - - - - - - - [13] r  r   o  o From Equation [3] and Equation [13] 2

 r12 r2   r2  ln 3    0 r0   r1  tan(30 − e)  0 0 0 = = − 1 or, tan(30 − e) = − tan30 = tan( − 30 ) 0 tan30 r  ln 1   r2  or, e = 60o for Pure Compression Department of Industrial & Production Engineering

22/13