6_n.s. das & c.k. biswas & b.s. chawla
TRANSCRIPT
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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
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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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154 INTERNATIONAL JOURNAL OF ADVANCES IN MACHINING AND FORMING OPERATIONS
(a)
(b)
Figure 1: (a) Solution I with Chip-breaker (b) Hodograph for Corresponding
Field (not to Scale)
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A SIMPLIFIED ANALYSIS AND EXPERIMENTAL VALIDATION OF CHIP BREAKING 155
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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156 INTERNATIONAL JOURNAL OF ADVANCES IN MACHINING AND FORMING OPERATIONS
(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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A SIMPLIFIED ANALYSIS AND EXPERIMENTAL VALIDATION OF CHIP BREAKING 157
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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158 INTERNATIONAL JOURNAL OF ADVANCES IN MACHINING AND FORMING OPERATIONS
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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A SIMPLIFIED ANALYSIS AND EXPERIMENTAL VALIDATION OF CHIP BREAKING 159
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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A SIMPLIFIED ANALYSIS AND EXPERIMENTAL VALIDATION OF CHIP BREAKING 161
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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A SIMPLIFIED ANALYSIS AND EXPERIMENTAL VALIDATION OF CHIP BREAKING 163
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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
E-mail: [email protected]
Fax.: 0661-462999
B. S. Chawla
Professor and Principal
Institute of Technology
Korba, Chhatisgarh
Pin - 495684
E-mail: [email protected]
Fax.: 0775-2414968
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