6_n.s. das & c.k. biswas & b.s. chawla

8/9/2019 6_N.S. Das & C.K. Biswas & B.S. Chawla

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INTERNATIONALJOURNAL OFADVANCES INMACHINING ANDFORMINGOPERATIONS,

Vol. 2 No. 2, July-December 2010, ISSN : 0975-4784

A SIMPLIFIED ANALYSIS AND EXPERIMENTAL

VALIDATION OF CHIP BREAKING IN ORTHOGONAL

MACHINING WITH A STEP TYPE CHIP BREAKER

N. S. DAS*, C. K. BISWAS & B. S. CHAWLA

ABSTRACT:In the present investigation, an attempt is made to examine chip

breaking by a step-type chip breaker using the rigid-perfectly plastic slip linefield theory. Orthogonal machining is assumed and the deformation mode is

analyzed using the solutions proposed earlier by Kudo and Dewhurst.Machining

parameters such as chip thickness, chip curvature and bending strain are

computed for different chip breaker positions and height. The extent of Material

damage is assessed from the cumulative shear strain suffered by the material in

passing through the primary and secondary deformation zones. The range of

values of machining parameters for effective chip breaking is established from

actual cutting tests. The experimental results are compared with the theoretical

limits predicted by the slip line field analysis.

Keywords: Orthogonal Machining, Sharp Tool, Step Type Chip Breaker, Chip

Curvature, Breakability Criterion, Chip Breaker Design.

NOMENCLATURE

bF = Chip breaker force

1 2,F F = Forces perpendicular and parallel to chip breaker force

cF = Cutting force

Fc/kt

0= Specific cutting energy

H = Height of the chip breaker

HTR = H/o

t

I = Unit matrix

M = Moment exerted by the slip linesABandBC

CL = Linear Coulomb/adhesion friction operatorP, Q = Standard matrix operators

pC,p

D= Hydrostatic pressure at points CandD

chipR = Radius of the chip curvature

I J A M F O International Science Press

* Corresponding Author: [email protected], Fax.: 0674-2460743


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152 INTERNATIONAL JOURNAL OF ADVANCES IN MACHINING AND FORMING OPERATIONS

ch ip 0/R t = Normalized radius of curvature

W = Position of the chip breaker from the cutting edge of tool

WTR = W/t0

cV = Cutting speed

c = Column vector representing a circle of unit radius of curvature

k = Yield stress in shear of the work material

n = a constant

0t = Uncut chip thickness

chipt = Chip thickness

1 2, = Angles made by the primary shear line with free surfaces

o = Linear coefficient

, , ,b p s t

= Breaking, Primary, Secondary and Total shear strains

= Orthogonal rake angle of cutting tool

= Low stress level friction coefficient

, , , , = Slip line field angles

= Angular velocity of chip curl

, ,C D E

= Friction angles between slip lines and tools rake face

= Scale parameter representing the geometrical scale of the field

n= Normal stress

= Shear stress

1. INTRODUCTION

Modern high-powered machine tools with cutting tools of sintered carbide have increased the

rate of chip formation and it has become necessary to produce properly broken chips for

convenient handling and disposal. The problem attains serious proportions especially in turning

and boring operations where, the tool removes metal for a considerable period and the chips

produced in the form of long ribbons can present serious hazard to the machine tool, machine

operator and also damage the machined surface by scuffing. This has made it necessary to have

proper control on shape and size of chips by bringing into use chip breakers of various forms.

The main purpose of these devices is to produce tightly curling chips and direct them in such

a manner that they strike the work piece or flank face of the cutting tool resulting in intermittentfragmentation of chips.

A number of studies have been carried out in the past to identify the variables affecting

chip breaking during high speed machining. The mechanism of chip breaking by ramp and

step-type chip breakers has been investigated experimentally by Nakayama (1962), Trim and

Boothroyd (1968), Henriksen (1953,1954)and Subramanian et al.((1965). The action of a
mailto:[email protected]:[email protected]


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A SIMPLIFIED ANALYSIS AND EXPERIMENTAL VALIDATION OF CHIP BREAKING 153

groove type chip breaker has been studied by Worthington and Redford (1973), Worthington

(1976), Worthington and Rahman (1979), Jawahir (1986) and Wang and Jawahir (2007).These studies have indicated that in metal machining the controlling parameters influencing

chip breaking are the uncut chip thickness t0, the chip thickness t

chipand the radius of chip

curvatureRchip

and that the chip breaks when the ratio (t0/R

chip) or (t

chip/R

chip) or some function

of these ratios such as the bending strain exceeds a threshold value (Worthington and Rehman,

1979: Jawahir, 1986: Nakayama, 1963: Takayama et al, 1970}. Chip breaking has also been

shown to be linked with the cumulative damage suffered by the material in passing through

the deformation zones (Athavale and Strenkowski, 1997) or with the specific cutting energy

consumed in the chip removal process (Grzesik and Kwiatkowska, 1997). It therefore appears

that for predicting chip breaking under a given set of machining conditions an accurate estimate

of the above parameters is essential.

A lot of effort has been undertaken during the last two decades to establish suitable criteria

for chip breaking. Finite element simulation of chip formation and chip breaking has beenattempted by Shimozoa et al (1996) and by Yang et al (1996). A hybrid algorithm for predicting

chip form /chip breakability has been advanced by Fang, Fie and Jawahir (1996), while a

quantitative relationship between chip breakability and tool wear has been proposed by Yao

and Fang (1993) using neural network. Methods for performance evaluation of Chip breakers

has also been proposed by Lee et al (2006) and Kim at al (2009). Despites these efforts,

however, a comprehensive analysis of the problem of chip control is still difficult and its

solution is generally approached using some empirical rules with limited degree of success.

In the present investigation an attempt is made to predict chip breaking using the rigid-

plastic slip-line field theory. Orthogonal machining is assumed and the analysis is carried out

for a parallel step-type chip-breaker. Machining parameters such as shear strain; bending

strain, chip thickness and chip curvature are computed for different chip-breaker positions and

height and their values for effective chip breaking is established from actual cutting tests. Theexperiment results are also compared with those predicted from theoretical analysis.

2. SLIP LINE FIELDS

Two slip line field solutions for orthogonal machining with a step type chip breaker were

analysed in the present investigation. These are shown in Figures 1 and 2 with their associated

hodographs. Solution I shown in Figure 1 (Kudo,1965) is obtained when the slip line field

proposed by Lee and Shaffers (1951) for chip streaming is modified to account for machining

with chip curl.

Referring to this figure it may be seen that the plastically stressed region consists of the

primary shear lineABDand the secondary shear zoneBCD. The chip boundary is defined by

ABCwhere,BCis theline andABtheline. WithinBCDthe deforming material slides onthe tool face CD in accordance with the adhesion friction law given by the equation (Maekawaet al,1997).

1

1

n

n n

ke

=

(1)


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(a)

(b)

Figure 1: (a) Solution I with Chip-breaker (b) Hodograph for Corresponding

Field (not to Scale)


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where,andn

are respectively the shear stress and normal stress at any point on the tool face

within chip/tool contact region, kis the yield stress in shear of the deforming material, is thelow stress level coefficient of friction, and nis a constant whose value depends on tool-work

material combination.

Referring to the hodograph (Figure 1 (b)) it may be seen that the material suffers a

velocity discontinuity of magnitude on crossing the primary shear line. Hence, velocityalong the slip lineDBAis represented by the circular arcdbin the hodograph. Since the chip

is rotating rigidly with angular velocity , the curves ab and bc in the hodograph aregeometrically similar to the curves AB andBC in the slip line field respectively. Hence,

slip line curveBAis also a circular arc of radius/.

This field is of direct type and the column vector for the radius of curvature of the

slip line CBis calculated from the relationship:

. .D

c =

CL (2)

Where,D

CL is the linear operator that constructs the field between the circular arc db

and the tool face dcconsistent with the adhesion friction condition given by equation (1)

(Dewhurst,1984: Dewhurst,1985) and c is a column vector representing a unit circle.

(a)


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(b)

Figure 2: (a) Dewhursts Solution with the Geometry of Chip-breaker and Cutting Tool

(b) Hodograph for Corresponding Slip-line Field (not to Scale)

The second field analysed in the present investigation is shown in Figure (2) and consists

of the primary shear line AE, the secondary shear zone CDE and a singular fieldBCE

(Dewhurst,1978: Dewhurst,1979)). The chip boundary for the field is defined by the convex

-lineAB, concave-lineDCand the convexlineBC.It may be seen that the material suffers a velocity discontinuity of magnitudeon crossing

the primary shear line (Figure.2 (b)). Thus, the velocity along the slip line EBAis given by

the circular arc eba. Since the chip is rotating rigidly with angular velocity, the linesAB,BCand CDare geometrically similar to their hodograph imagesab, bcandcd.

This solution is of indirect type and the slip lineDCfor this field is obtained by solution

to the matrix equation (Dewhurst,1979: Maity and Das,2001).

( )CI DC c =

CL Q Q CL CL P (3)

Where PandQare standard matrix operators as discussed by Dewhurst and Collins (1973),

CLis the linear operator as explained earlier, I is the unit matrix and c is a circle of unit

radius.


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It may be seen that in Figure.1 and Figure.2 the chip after emerging from the deformation

region encounters a chip breaker of heightHplaced on the tool face at a distanceWfrom thecutting edge. This imposes a curvature on the outgoing chip and helps in breaking long continuous

chips to smaller sizes.

3. METHOD OF ANALYSIS

The slipline fields shown in Figure.1 and Figure.2 are characterized by the field angles , , ( ), hydrostatic pressurep

C(p

D) at points C(D) and the chip breaker distance WRT(=W/t

o). These

variables are determined from the stress and velocity boundary conditions at the rigid plastic

chip boundary. These conditions may be stated as,

(a) The resultant traction perpendicular to the chip breaker force must be zero (smooth

chip breaker).

(b) The net anti-clockwise moment on the chip due to chip breaker force and the forces at

the rigid-plastic chip boundary must be zero.

(c) The outer radius of chip curvatureRcimposed by the chip breaker must be compatible

with that calculated from the hodograph.

Referring to Figure.1 and Figure.2 the above conditions may be expressed mathematically

as:

F1

= 0 (4)

M+Fbxd= 0 (5)

Rc Rchip = 0 (6)

Equations (4-6) are non-linear in the field variables and these were solved by an algorithmdeveloped by powell for solution to non-linear algebraic equations with unknown derivatives

(Koester and Mize,1973). For prescribed values of friction parameters and n, the fieldparameters , P

c(P

o) and WTRwere assumed to be correctly estimated when the sum of the

squares of the residuals were less than 1010. These optimized variables were then used to

construct the fields and estimate the machining parameters. The program incorporated mass

flux and flatness checks as discussed by Maity and Das (1998,2001). The program was terminated

when the friction angle at tool tip became negative or when the rigid vertices at A(Figure 1

and Figure 2) were overstressed (Hill, 1954).

Solutions 1 is unique in the sense that the field involves only three variables. Dewhursts

solution is non unique in nature as there are four field variables and there are only three

conditions from which these are determined.

Once the field variables were known and the fields plotted, the streamlines of flow couldbe constructed and strains in the primary and secondary shear zones estimated. The procedure

followed was similar to that discussed in detail by Das et al (2005). A representative flow

pattern for a specific field configuration is also indicated in Figure 3.


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Figure 3: Dew Hursts Slip-line Field with Streamlines (Chip Breaker not Shown)

4. ESTIMATION OF BREAKING STRAIN

The chip breaking process has been studied by Fang and Jawahir (1996) and according to these

authors the chip breaks due to the development of fracture on the outer profile of the chip (or

on the inner profile of the curled chip) when it reaches its highest degree of straining and its

final up-curl radius. This strain may be given by the equation. (Nakayama, 1963).

chip

chip

1 1

2b

L

t

R R

=

(7)

Where, tchip

is the chip thickness,Rchip

is the outer radius of chip flow circle imposed by the

chip breaker andRLis the final up-curl radius.

RLis usually much larger thanR

chip.Worthington (1979) consideredR

Lto be 2 timesR

chip.

However, as indicated by Nakayama (1963) RLis rather difficult to predict a priori and hasonly marginal influence on chip breaking. Hence, neglecting the contribution ofRL

, the breaking

strainbmay approximately be given by the relation,

chip

chip2

b

t

R

=

(8)


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5. RESULTS AND DISCUSSION

The results from the present theoretical analysis are illustrated in Figures. 4-8 where these arecompared with the experimental observations obtained from orthogonal cutting tests carried

out by the authors. The figures indicate that as WTRincreases, the total shear straint the

primary shear strainpand specific cutting energy (F

c/kt

0) increase while the bending strain

b

and the secondary shear strains(= 10-15 % of

t) decrease (Figures.4 and 5). Chip of curvature

(Rchip

/t0) also increases with WTR(Figure.6). Thus moving the chip breaker away from the

cutting edge not only renders it less effective but also results in consumption of more power in

the chip formation process. These observations from Dewhursts solution (Figure.2) are in

close agreement with those reported by the authors by solution to the slip line field proposed

by kudo (Das et al,2005). There is also seen to be close relation between breaking strainband

chip curvature (Rchip

/t0) as predicated by equation (8) with most of the experimental points

lying within the bounds predicted by Kudos solution and Dewhursts solution (Figure 7).

Figure.8 shows some chip breakability criteria as constructed by the present slip line fieldanalysis and their comparison with the experimental results (authors) from actual cutting tests.

The chips in the above figure are classified as under broken, affectively broken or over

broken according to the ease of their disposability (Henriksen,1953: Henriksen, 1954). It is

assumed that affectively broken chips have a radius of curvature of approximately 6mm (Fang

and Jawahir,1996) and that these are produced when the bending strain bin the chip has a

value within the range proposed by Jawahir (1986) or Takayama et al (1970). The figure

Figure 4: Variation oft

, ,

s

an d with Chip-breaker Position,

N = Negative Friction Angle Limit


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Figure 5: Variation of Total Straint

and Specific Cutting Energy F

c

/t

0

) with Chip-breaker Position

and Rake Angle

, N = Negative Friction Angle Limit

Figure 6: Variation of Breaking Strain, and Radius of Chip Curvature

with Chip-breaker Position


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Figure 7: Variation of Breaking Strain with Normalized Radius of Curvature

Figure 8: Comparison of Various Chip Breaking Criterion,

Numbers within Brackets Indicate References


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indicates that as the chip breaker moves away from the cutting edge ( WTRincreases)b,

(t0/Rchip) and (tchip/Rchip) decrease while the total straint(material damage) and specific cuttingenergy (Fc/kt

0) increase. It, therefore, appears more appropriate to base the breakability criteria

on bor (t

0/R

chip) or (t

chip/R

chip) rather than on material damage or specific cutting energy since

a less effective chip breaker is associated with decreased values of these parameters. The figure

also shows very good agreement between theory and experiment especially in the effective and

under - breaking regions.

Figure.6 demonstrates how the present theoretical analysis can be utilized to determine the

position of the chip breaker during actual machining operations. For given values ofWandt0

(WTA=W/t0), the bending strain

bin the chip can be estimated from this graph. If it lies

within the proposed range (Jawahir,1986: Takayama et al, 1970) the chip will certainly break

and its radius of curvature can be determined from a plot of (Rchip

/t0) vs. WTAFor example in

the present experimental study effectively broken chips (Rchip

= 6mm) were produced while

machining with feed values of 0.12mm /revolution and 0.24mm/revolution with the chipbreaker positioned at 3.96mm (WTA= 33) and 4.32mm(WTA= 18) from the cutting edge

respectively. The chip breaker height HTA for the above two cases were 10mm and 5mm as

shown in the above Figure. It may be seen that the bending strain in the chips for the above

two cases were 0.065 and 0.039 which are very close to the suggested values.

7 . CONCLUSIONS

Two slip line field models are analyzed for orthogonal cutting with step-type chip breaker

assuming adhesion friction at chip tool interface. For both the fields the chip thickness, chip

curl radius and total plastic strain suffered by the material in the primary and secondary shear

zones and specific cutting energy are estimated for various chip breaker positions and height.

It is shown that the total strain and primary strain increases as the chip breaker moves away

from the cutting edge, while the bending strain and the secondary shear strain, decrease. Theanalysis suggests that the chip thickness, chip curvature and the bending strain are the most

important parameters that govern chip breaking. The theoretical and experimental results

show very good agreement with those obtained earlier by Jawahir and Takayama et al.

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[27] Takayama H., Sekiguchi H., Takada H., (1970), One Solution for Chip Hazard in Turning study

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31, pp. 89-101.

N. S. Das

Professor, Deapartment of Mechanical Engineering,

C.V. Raman College of Engineering Janla Bhubaneswar,

Orissa, India

E-mail: [email protected]

Fax.: 0674-2460743

C. K. Biswas

Assistant Professor,

Deapartment of Mechanical Engineering

National Institute of Technology,

Rourkela 769008

Orissa, India


Fax.: 0661-462999

B. S. Chawla

Professor and Principal

Institute of Technology

Korba, Chhatisgarh

Pin - 495684


Fax.: 0775-2414968
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]


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6_n.s. das & c.k. biswas & b.s. chawla

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