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ABSTRACT
The Finite Element Method (FEM) can be applied onhigh speed
machining processes to get a better
understanding of the chip formation process.Furthermore,
modeling such high speed cuttingprocesses can reveal useful
information which cannotbe measured directly during the machining
process(e.g. temperature distribution, stress over cutting edge)and
which can be used to optimize tool wear as well asthe entire
machining process. In this paper theimportant aspects of a model
are discussed. Theprocedure and requirements for establishing a
highquality model for high speed milling is presented.Finally, the
experimental results of an orthogonalcutting process are compared
with an initial 2D FEMmodel.
INTRODUCTION
Over the past decades metal cutting mechanics werethe subject of
many research publications. The problemwhich is inherited with
metal cutting mechanics is thehighly localized chip formation
process. The way thechip is formed has an decisive influence on the
entiremachining process. It determines the finish of themachined
workpiece surface and is responsible for thecutting forces, cutting
temperatures, and also tool wear.
From this point of view, the chip formation is regardedas the
core of the process. The formation of the chipoccurs in a fairly
small zone under extremely highvelocity. This nature of the process
makes it quitedifficult to conduct precise measurements on the
chipformation in order to understand and get a betterunderstanding
of the chip formation mechanism.
Therefore, attempts have often been made to describethe chip
formation by either analytic or non-analyticmodels in order to
understand the dependencies ofdifferent parameters [1]. Due to its
universal capability,the Finite Element Method can be efficiently
used toestablish complex models to examine the chipformation
process.
BENEFITSOften the question arises what chip formation modelsare
good for. First, these models are basicallyestablished to get a
better understanding of the chip
formation mechanism itself. Due to the tremendousdifficulties
which occur in attempting to measuretemperatures, strain rates,
stress distributions etc.during the process, modeling the chip
formation offersnew possibilities to have a closer look at it.
Second, the model reveals values that cannot bemeasured directly
within the process. E.g. a model candeliver a temperature
distribution across the chipthickness, but in an experiment the
temperature canonly be measured at the chips outer surface.
Third, with a model the interaction of tool and chip can
be examined.
Fourth, if a valid model exists, the model can be usedto vary
certain material or process parameters, e.g.heat conductivity or
specific heat, of the workpiece andof the tool respectively. One
the one hand, this mayhelp to design materials or tools which are
moresuitable for machining operations, and on the otherhand this
procedure can be used to find new optimizedtool geometries.
Also, due the complexity and the number of influences
within a machining processes, it is important to noticethat
modeling chip formation processes has always beclosely accompanied
by an experimental verification.This is the only way to determine
the quality of anmodel and to find out the critical factor of the
modelwhich have to be improved.
PROCEDUREThe objective of establishing a cutting model is
actuallya full 3D model of a chip formation process for
millingoperations such as high speed milling. Due to a lack
ofreliable experimental data (e.g. temperaturedistribution across
the chip/tool interface) for thosecases, the model has to be
developed step by step withincreasing complexity. The chosen
procedure is tobegin with a 2D model. This 2D model has the
Finite Element Modeling
of High Speed Machining Processes
Arno Behrens, Bert WesthoffManufacturing Laboratory
University of the Federal Armed Forces, Hamburg, Germany
Copyright 1999 PTW TU Darmstadt.
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advantage of relatively good comparability to
accurateexperimental data obtained in orthogonal cutting test.In
these kind of tests temperature distribution, cuttingforces,
contact length, chip thickness, and even stressdistributions on the
chip/tool interface can be measuredand used for comparison with
results obtained in 2DFEM simulations.
Figure 1. Procedure to establish a 3D model includingcontinuous
experimental verification
If the 2D model delivers accurate results with respect tothe
experiments, the next step of the procedure is thetransformation of
the 2D model to a 3D model. Thismodel is first used to perform
simulations of turningoperations such as oblique turning actions
which arealso tightly related to adequate cutting tests.
In the final step (Figure 1) the model is used to simulatethe
chip formation of high speed milling operations.
MODEL OF AN ORTHOGONAL CUTTING PROCESS
INTRODUCTIONFigure 2 pictures schematically the different
zoneswhich have an important influence within chipformation. Zone 1
is known as the primary shear zonein which the material is
subjected to a major shearing
deformation. Due to high friction in the tool/chipinterface the
chip is also sheared in the secondaryshear zone (zone 2). The
material separation takesplace in the area close to the tool tip
(zone 3) which issupposed to be highly pressurized. The
newlygenerated surface is also slightly sheared by theclearance
face of the tool which contacts it in zone 4.Further, a general
material pre-deformation is assumedin an area which is shown in
Figure 2 as zone 5.
MATERIAL PROPERTIESThe properties of the workpiece material have
atremendous influence on the chip formation [9]. Forexample, the
materials flow stress determines therange of the cutting force
because the major part of theenergy is used for plastic deformation
within the shear
zone. Therefore, these material properties have to bedetermined
for the computer simulation. The flowstress depends on strain,
stress, and temperature. Weuse for the initial model material data
for a 0.18%carbon steel as follows [3, 4]:
Eq. 1
where
Eq. 2
with Eq. 3
is the engineering strain, the engineering strainrate, and the
absolute temperature.
Figure 2. Section trough the cutting area and resultant
chip, showing the deformation zones [2]
FRICTIONFriction in the chip/tool also has an important
influenceon the chip formation process. As shown in Figure 2,due to
high friction the deformed material is sheared inthe secondary
zone. Furthermore, friction determinesthe contact length.
Concerning the model, it must be determined howfriction in the
interface is to be modeled. In this case,the shear friction model
(Eq. 1) is used to describe
friction due to chip/tool interaction and its shear
frictionfactor ( is the shear friction stress in the interface,
is the shear yield stress) is seen to be constantacross the
interface area.
Eq. 4
For metal cutting problems, Coulombs friction model isnot the
most appropriate model as the material is highlydeformed and under
locally high hydrostatic pressurewhich would lead to an
overestimated shear frictionstress far beyond the local yield shear
stress. Laterwhen a good working model exists, the friction must
bedescribed in more detail by a variable friction coefficientacross
the tool rake face. Further, it is assumed that nocoolant or
lubricant is used throughout the process.
FE-Model Experiments
Ortogonal cutting test forces stress distribution on the
chip/tool interface temperatures contact length chip
geometry
Turning and milling tests global forces temperatures
2D Modelof an
orthogonalcutting process
3D Model
Turning process
Milling process
Transfom to 3D
Y A0 T( ) 1000------------
0 0195, 0 21,=
A0 T( ) 1394 0 00118T,( ) +exp=
339+ 0 0000184B2,[ ]exp
B T 943 23 5
1000------------
ln,+ +=
T
h
h
Shear Plane
Workpiece
KL
Tool
m iY
i mY=
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MATERIAL SEPARATIONDuring the machining process a new workpiece
surfaceis generated. The generation of a new surface is one ofthe
characteristics of the process which also needs tobe part of the
FEM simulation. Because FEM modelsare based on a finite element
mesh which discretize thematerials volume (in the here applied
Langrange
formulation), the material separation model must beclosely
related to the mesh.
Generally, two questions have to be answered toconduct a
material separation in an FEM simulation.First, it has to be
determined when the material failureoccurs (separation criterion),
and second, how thisseparation is obtained by the model. Further,
it can besaid that material separation in machining operationshas
the advantage that the tool geometry and itsmovement already
determine the area of the workpiecewhere the material separates.
Operations insimulations, such as finding a crack path, can be
used
but do not have to be used because the crack path
isapproximately known.
Figure 3. Contact detachment technique
There are two types of separation criteria: one group
isintegrated into geometrical criteria, which meansseparation is
detected based on geometric parameters(e.g. distance tool tip to
mesh node), and the othergroup is physical criteria, which are
derived fromphysical measures such as stresses, strains,
energy,etc. [5].
Furthermore, there is a variety of different methods tomodel the
material failure in an FEM model.Techniques like element
elimination [6] and node
splitting [7] can be applied. Another method is aseparation
technique based on contact detachment [8].Figure 3 illustrates this
process: two bodies are gluedat the area where separation occurs.
Strains, stresses,and heat fluxes can be transferred from one body
to theother as long as they are glued together. Fulfilling acertain
criterion, nodes are detached from the othersurface. Applying this
method on the orthogonal cuttingprocess, two bodies are defined for
the workpiece. Onerepresents the chip volume removed from
theworkpiece, the other body is the volume which remains.The chip
volume which is subjected to a severe
deformation ending up with a very distorted mesh canbe remeshed
automatically without any majorproblems.
DYNAMIC EFFECTSDynamic effects, in this context, means the
influence offorces or stresses on the process created by inertia
ofmasses, may be also have to be taken into account.Especially in
high speed machining it is possible thatdynamic effects play an
important role. They canincrease the stress within the shear zone
or chip/tool
interface which might influence the process. Usually inhigh
speed machining a smaller cutting depth is usedthan with
conventional cutting speeds. The modelallows taking dynamic effects
into account so that it ispossible to use FEM to conduct research
on theimportance of the dynamic influences.
CHIP SEGMENTATIONIn a number of machining processes a
chipsegmentation can occur during the process. Thesegmentation is
due to adiabatic shear bands. In thesebands, a localized shear
increases the temperature inthe shear plane which again decreases
the shear
stress in the plane[10]. But, like the dynamic effects, itis not
definitely clear whether they have a tremendousinfluence on the
important process parameters such ascutting force and temperature
distribution. The presentmodel does not take chip segmentation into
accountyet because this segmentation is not easy to
model.Basically, the same problems are present as with thematerial
separation except that the path of the shearbands is unknown.
First, it has to be determined whenadiabatic shear bands exist, and
second the FEM meshhas to be modified adequately. The second factor
is themajor problem, which is the reason that this is not
implied in the current work.
HEAT TRANSFERHeat transfer occurs in the contact area between
chipand tool and at surfaces exposed to the environment.Due to the
short time of the formation process, heattransfer by radiation and
convection is neglected in thefirst assumptions. Only the heat
transfer between tooland chip is taken into account with a constant
heattransfer coefficient which is needed to determine theflux :
Eq. 5
where is the local chip temperate andrepresents the local tool
temperature.
TOOL AND TOOL TIPDuring the cutting process the tool is heated
up anddeflected by high stresses even if it has a higherstrength
than the workpiece material. For the firstanalysis the tool can be
considered to be rigid withoutany deflections. Further, in the real
process the tool tipcontacts the workpieces newly generated surface
andslides over it. It is also a difficult problem to describe
this sliding within the model. The radius of the tool
tipcertainly has an influence on the chip formationprocess as well
as non-perfect tool tip geometries fromtool wear.
a) b)
hq
q h T Ttool
( )=
T Ttool
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SIMULATION RESULTS
MODEL SETUPThe setup of the model used in the analysis is shown
inFigure 4. The material failure is represented by thecontact
detachment technique. As shown in Figure 3, afull model based on
this technique consists of two
bodies, the chip volume and the remaining workpiecevolume which
are glued to each as other shown inFigure 4(i). In this analysis,
the remaining volume isreplaced by a straight rigid line where the
chip volumeis glued (Figure 4(ii)).
The rake angle used in the analysis is chosen to be0 because the
same rake angle is used in theexperiments. The cutting depth of
0.1mm used in theexperiments is the same as in the simulation.
Thematerial properties are derived from Eq. 1 to 3 for a0.18%
carbon steel [3,4] to attempt to describe materialproperties of the
C15 steel. However, properties may
vary due to different microstructures and heattreatment. The
friction factor was chosen to be 0.4and constant across the tool
face. Heat exchangebetween tool and chip was also taken into
account inthe analysis although the process is almost
adiabatic.Therefore, a heat transfer coefficient of about
20,000W/m2K was defined which is about the same size ofcoefficients
for hot forging processes. Tool temperatureis considered to remain
constant at 200C, but asmentioned before, due to the adiabatic
character of theprocess, this parameter does not have a
decisiveinfluence. If not otherwise described, the analysis is
conducted quasi-static which means that inertia effectsare
neglected.
Figure 4. Model setup based on the contact detach-ment
technique
CHIP FORMATIONA HSC analysis conducted with a cutting speed
of4000 m/min was taken to compare the chip formation
with experimental data. The chip geometry obtained bysimulation
is shown in Figure 5. The contact lengthmeasured in high speed
orthogonal cutting tests can becompared to simulation results. The
experiments
showed that the contact length ranges from 0.22mm to0.28mm which
is a good correlation. Figure 6 presentsthe tool displacement
versus the calculated cuttingforce per unit depth. The curve shows
the beginning ofthe cut and a more or less constant region. The
scatter-like appearance of the force results on the one handfrom
continuous remeshing during the process and on
the other hand from contact detachments of certainnodes.
Figure 5. Calculated chip geometry at a cutting speedof 4000
m/min for a 0.18% carbon steel
Figure 6. Tool displacement vs. cutting force at a cut-
ting speed of 4000m/min (0,18% carbonsteel)
COMPARISON TO EXPERIMENTSIn orthogonal high speed cutting
experiments, cuttingforces, temperatures, and the chip geometry
have beenmeasured. This data was used to compare to results
ofcomputer simulations. Figure 7 shows a microsectionof the chip
obtained in a quick stop test at 4000m/min.With the same scale, the
outline of the simulated chipis transposed with the microsection.
The result shows agood correlation with the contact length.
Further, the
side of the real chip that is not in contact with the
toolexhibits segmentation which was not included in themodel. The
macroscopic formation of the calculatedchip correlates well with
the experimental.
m
vc
(+)(-)
Too
lGlue
Chip Volume
vc
(+)(-)
Too
lGlue
Chip Volume
Remaining Volume
i
ii
vc
KL
25
0.1mm
KL=0.2
5mm
0
100
200
300
Fc/t[N/mm
]
0 0.5 1 1.5
Tool displacement [mm]
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As mentioned above, in the tests a cutting depth of0.1mm was
chosen. Further, the broad dimension ofthe cut was 2.0mm. With this
data the measured cuttingforces can be compared with the analysis.
At a speedof 4000m/min the measured cutting forces are
about290N/mm. The forces obtained from the simulation arearound
180-190N/mm (Figure 6). This great difference
may result from different microstructures and heattreatments of
the material. In upcoming experiments,material properties must be
determined with the samematerial and same microstructure to
overcome thisdifference. Further, the neglected radius of the
cuttingedge may also have an influence on the range of thecutting
force and must be included in future models.
Figure 7. Comparison between simulated and real chipformation
(C15 steel) at 4000 m/min. Highspeed cutting quick stop test were
performedin cooperation with IFW, Hannover
DYNAMIC EFFECTSTo examine the influence of mass inertia effects
themodel was used to compare a quasi-static analysis(without
inertia effects) with a dynamic analysis, takingthese kinds of
effects into account. The result of thecomparison is shown in
Figure 8 for a cutting speed at1200m/min.The comparison shows that
the rage ofcutting forces seems to remain the same. The
cuttingforces predicted in a dynamic analysis seem to oscillatewith
fairly high amplitudes around the forces predictedin the
quasi-static simulation. This oscillation is due tonumerical
problems using a rigid body within a dynamic
analysis, but it shows that at that cutting speed theinertia
effects seem not to influence the processtremendously.
Figure 8. Cutting forces of quasi static analysis in com-parison
with a dynamic simulation
CONCLUSION
It has been shown that FEM models of high speedcutting processes
can be quite useful for theunderstanding and exploration of the
process itself andhelp finding out important dependencies. First
resultswith an orthogonal cutting model in comparison withcutting
tests show that even a simple model with anumber of constraints can
partly deliver reasonableresults. However, the model has to be
improved step bystep. First, more reliable material data has to
be
determined to exclude effects from a mismatch ofmaterial
properties. Further, the complexity of thesimple 2D model has to be
increased by introducing adiscrete tool with a cutting edge radius.
Next, the modelhas to be compared systematically to
orthogonalcutting test to determine its quality and find out
defects.Finally, the model can be transferred to a 3D model tostudy
high speed machining processes such as milling.
REFERENCES
1. Oxley, P. L. B.; The Mechanics of Machining: AnAnalytical
Approach to Assessing Machinability,Ellis Horwood Limited, 1989
2. Warnecke, G. Spanbildung bei metallischenWerkstoffen, Mnchen,
Technischer VerlagResch, 1974
3. Shirakashi, T.; Maekawa, K.; Usui, E.:Flow Stressof Low
Carbon Steel at High Temperature andStrain Rate (Part 1) - Property
of IncrementalStrain Method in Impact Compression Test withRapid
Heating and Cooling Systems, Bulletin ofthe Japan Society of
Precision Engineering, Vol17, No. 3 (1983), pp. 161 -166
4. Maekawa, K.; Shirakashi, T.;Usui, E.:Flow Stressof Low Carbon
Steel at High Temperature andStrain Rate (Part 2) - Flow Stress
under Variable
100
0
100
200
300
Fc/t
[N]
0 0.5 1 1.5
Tool displacement [mm]
dynamicquasi-static
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Temperature and Variable Strain Rate, Bulletin ofthe Japan
Society of Precision Engineering, Vol17, No. 3 (1983), pp. 167
-172
5. Huang, J. M.; Black, J. T.: An Evaluation of ChipSeparation
Criteria for the FEM Simulation ofMachining, Journal of
Manufacturing Science andEngineering, Vol. 118 (1996), pp.
545-554
6. Ceretti, E.; Fallbhmer, P; Wu, W.-T.; Altan, T:Application of
2D FEM to Chip Formation inOrthogonal Cuttting, Journal of
Materials Proces-sing Technology, Vol. 59 (1996), pp169-180
7. Shih, A. J.: Finite Element Simulation of Orthogo-nal
Cutting, Journal of Engineering for Industry,Vol. 117 (1995), pp.
84-93
8. Behrens, A.; Westhoff, B.:Probleme und Heraus-forderungen bei
der Simualtion von Zerspanpro-zessen, XXV. FEM-Kongress,
16.-17.11.1998,Baden-Baden
9. Childs, T. H. C.: Materials Properties Require-ments for
Modelling Metal Machining, Journal de
Physique IV, Vol. 7 (1997), S. XXI- XXXVI10. Burns, T. J.;
Davies, M. A.: Nonlinear Dynamics
for Chip Segmentation in Machining, PhysicalReview Letter, Vol.
79, No. 3, 1997, pp. 447-450
