Theory of Metal Cutting Theory of Chip Formation

LECTURE-08THEORY OF METAL CUTTING

- Theory of Chip Formation

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

ENGINEERINGBUET

22/2Department of Industrial & Production Engineering

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 ChipsContinuous or Ribbon Type ChipsContinuous Chip Built-up-Edge (BUE)Serrated Chips


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.


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.


Actual Chip Forms and Classifications

C-type and ε-type broken chips

Short helical broken chips

Medium helical broken chips

Long helical broken chips

Long helical unbroken chips

Long and snarled unbroken chips

Desired

Not Desired


Chip Formation in Metal MachiningSince 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.

Rake angle (γ)

ToolWorkpiece

Chip

Roughsurface

Shinysurface

Uncut chipThicknessa1=So sin φ

Chip Thickness

(a2)

Shear Angle

(β)

Clearance angle (α)

Shear plane

RakesurfaceFlank

surface

Negative rake

Positive rake


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,


Grid Deformation Methods

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

-[1]-----otan30e)o(30tan

2e1e32e2e1e

where,e = deformation criteria

= 00 for pure tension= 300 for pure shear= 600 for pure compression

ro = radius of circles marked on the workpiece r1 & r2 = semi-axes of the ellipse after deformation.

-[2]---o3e2e1e andor2rln2e ,

or1rln1e

ToolWorkpiece

Chip

ro

r2r1

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


From Equation [1] and Equation [2]

]3[2r1rln

3

2or

2r1rln otan30e)otan(30

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

-[5]--- ε)(1 )42ε

2ε2.(1

2

0r2r and

2ε1

0r2r ε,1

or1r

[4] ----------με)(1or2r and ε)(1or 1r

Where, ε = cutting strengthμ = frictional coefficient=½

since ε is very very small so neglecting ε2


Now, from equation [5]

[6]-----1ε)(1ε)(120r

22r1r

2

0r2r

0r1r


Tension Purefor o0e or,

0tan30e)0 tan(30or,

-[7]---1

2r1rln

2r1r.6

0r

42r

21rln

)2r1rln(

3)20r

2r1rln(

0tan30e)0tan(30


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

-[9]--- 1 ε)23(1 ε)

23(1

0r2r

0r1r and ε

231

0r2r ε,

231

or1r

[8] ----------με)-ε-(1or2r and με)ε(1or 1r


Tension Purefor o30e or,tan(0)0e)0 tan(30or,

[10]-----0

2r1rln

31ln

2r1rln

3

20r

2r1rln

0tan30e)0tan(30


Case-3: For Pure Compression [e=60o]

]13[---------1ε-1 ε1or2r

2

or1r

-[12]--- ε)(1 )42ε

2ε2.(1

2

0r1r and ε1

0r2r ,

2ε1

or1r

[11] ----------ε)(1or2r and με)(1or 1r


nCompressio Purefor 60e or,

)30tan(tan30e) tan(30or, 1

rrln

rr

rrrln

tan30e)tan(30

o

000

2

1

1

2

2

30

22

1

0

0


Chip Reduction Coefficient (ξ)

Chip reduction coefficient (ξ) is defined as the ratio of chip thickness (a2) to the uncut chip thickness (a1). This factor, ξ, is an index of the degree of deformation involved in chip formation process during which the thickness of layer increases and the length shrinks. In the USA, the inverse of ξ is denoted by rc and is known as cutting ratio. The following Figure shows the formation of flat chips under orthogonal cutting conditions. From the geometry of the following Figure.

γo

β

ToolWorkpiece

O

AB

C

a1

a2

Chip

]1[sinβ

sinγsinβcosγcosβsinβOA

)γcos(βOAABAC

aaξ 000

1

2


Shear Angle (β)

From Equation [1]

angleShear osinγξ

ocosγ1tanβ

osinγξ0cosγ

tanβ

0sinγtanβ

0cosγ

sinβ0sinγsinβ0cosγcosβ

ξ


Condition for maximum chip reduction coefficient (ξ) from Equation [1]

angleShear 0γ2π

21β

2πcosβ)0γcos(β

2πcos0sinβ)0γsin(βcosβ)0γcos(β

0β2sin

)cosβ0γcos(β)0γsin(βsinβ

0sinβ

)0γcos(β

dβdor 0

dβdξ


Velocity Relationships

The following Figure shows the velocity relation in metal cutting. As the tool advances, the metal gets cut and chip is formed. The chip glides over the rake surface of the tool. With the advancement of the tool, the shear plane also moves. There are three velocities of interest in the cutting process which include:

γo

β

ToolWorkpiece

ChipVs

VfVc

γo

β

Vc

Vf

Vs

90o -γo

90o -β+γo

γo -β

VC = velocity of the tool relative to the workpiece. It is called cutting velocity Vf = velocity of the chip (over the tool rake) relative to the tool. It is called chip flow velocity Vs= velocity of displacement of formation of the newly cut chip elements, relative to the workpiece along the shear plane. It is called velocity of shear


According to principles of kinematics, these three velocities, i.e. their vectors must form a closed velocity diagram. The vector sum of the cutting velocity, Vc, and the chip velocity, Vf, is equal to the shear velocity, Vs. Thus,

fVcVsV

sinβfV

oγ(βo90sincV

)oγosin(90sV

ξVV or,

ξcV

)oγcos(β

sinβcV

)oγ(β090sin

sinβcVfV

f

c

γo

β

Vc

Vf

Vs

90o -γo

90o -β+γo

γo -β


Kronenberg derived an interesting relation for chip reduction coefficient (ξ) which is of considerable physical significance. Considering the motion of any chip particle as shown in the following Figure to which principles of momentum change are applied:

dθμv

dvdθv

dvNFμ

dtdθmvr2mωN

dtdvmF

Vf

Vc

FN

γo

)γ2π( 0


As the velocity changes from Vc to Vf, hence

0γ2πμ

eξ

0γ2πμ

efVcV

oγ2πμ

cVfV

ln

fV

cVπdθ

vdv

)γ-2π(

0

o

This equation demonstrates that the chip reduction coefficient and chip flow velocity is dependant on the frictional aspects at the interface as well as the orthogonal rake angle (γ0). If γ0 is increased, chip reduction coefficient decreases.

Vf

Vc

FN

γo

)γ2π( 0


Shear Strain (ε)

The value of the shear strain (ε) is an indication of the amount of deformation that the metal undergoes during the process of chip formation. The shear strain that occurs along the shear plane can be estimated by examining the following Figure. The shear strain can be expressed as follows:

AMagnitude of strained material

CB

Plate thickness γo

A

BC

Dβ

β-γo

Shear strain during chip formation (a) chip formation depicted as a series of parallel sliding relative to each other (b) one of the plates isolated to illustrate the definition of shear strain based on this parallel plate model (c) shear strain triangle

-[1]-)oγtan(ββcot BDCD

BDAD

BDCDAD

BDACε

γo

β

ToolWorkpiece

Shear plane

Chip=parallel shear plates

a cb


From equation [1]

strainShear βsin cV

sVε

[3]equation and [2]equation From

[3])oγ-(β cos

o γcos

cVsV

iprelationsh velocity From

[2])oγ-(β cos β.sin

o γcos )oγtan(ββcot ε


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Theory of Metal Cutting Theory of Chip Formation