Mechanical Engineering Journal - experimental studies and modeling of heat generation in metal...

8/7/2019 Mechanical Engineering Journal - experimental studies and modeling of heat generation in metal machining

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Machining Science and Technology, 13:488515Copyright 2009 Taylor & Francis Group, LLCISSN: 1091-0344 print/1532-2483 onlineDOI: 10.1080/10910340903451506

EXPERIMENTAL STUDIES AND MODELING OF HEATGENERATION IN METAL MACHINING

A. Liljerehn, V. Kalhori, and M. Lundblad

AB Sandvik Coromant, Sandviken, Sweden

Heat generation in the cutting zones due to plastic deformation and friction in the cuttingregion governs insert wear, tensile residual stresses on the machined component surface and maygive rise to undesired tolerances and short component life. Therefore, it is crucial that the heatgeneration is kept under control during metal cutting. In this study an analytical model forprediction of heat generation in the primary and secondary deformation zones is compared withresults from finite element simulations and temperature measurements using IR-CCD camera.The used cutting data are altered to study the temperature influence from tool geometry and

feed when machining stainless steel SANMAC316L and low carbon steel AISI 1045.

Keywords analytical temperature prediction, finite element modeling, infrared

charge coupled device IR-CCD, material modeling, metal machining

INTRODUCTION

Metal cutting is one of the most common manufacturing processesused to achieve the desired shape and dimension of components. Standingdemands for higher productivity and better life for processed componentsand cutting tools have historically pushed further development ofexisting tooling concepts. This is to achieve better production economics

and manufacturability, and thereby higher competitive force in themarket. However, increased productivity target must not jeopardize thecomponents quality in terms of dimension accuracy, surface integrity andlongevity.

It is widely known that heat has a major impact on the componentscharacteristics and life of cutting tools. It may give rise to undesiredtolerance deviation, tensile residual stresses at the workpiece surface andgoverns insert wear rate. Therefore, it is of great interest to understand themechanisms that cause heat development in the metal cutting, and thus

Address correspondence to A. Liljerehn, AB Sandvik Coromant, Sandviken SE-811 81, Sweden.E-mail: [email protected]


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Modeling Heat Generation in Metal Machining 489

would, if possible, reduce or control the heat development in cutting zones.The generated heat at the cutting zone is mainly governed by elastic-plasticstrain energy dissipated at the primary, secondary and tertiary deformation

zones and friction between chip and insert on the secondary deformationzone. The heat developments in cutting are strongly dependent on thecutting process parameters and insert geometry. In this study, the thermo-mechanical behavior of the insert-chip interface and the shear plane isinvestigated. An analytical model is applied and the results are comparedwith numerical finite element simulations and experimental measurementsusing infrared CCD method.

EXPERIMENTAL SETUP

Insert Geometry and Cutting Parameters

Several different cutting geometries are selected to study its effect onheat generation within the cutting zones. These are the cutting insertsTCMT 16T 308-MR for roughing and TCMT 16T 308-MM for mediumroughing and TPNG 160 308 with no chip breaking geometry and a rakeangle of 3, manufactured at Sandvik Coromant (Table 1). The tool gradeused was a PVD coated carbide (GC1025), where the coating consistsof a thin outside layer of TiN and a thicker inner layer of TiAlN, witha total coating thickness of 4 m. The cutting speed was chosen to be

200m/min for both workpiece materials, SANMAC 316L and AISI 1045.SANMAC 316L is an improved AISI 316L stainless steel with respect tomanufacturability, produced by Sandvik Material Technology.

Experimental Setup Using Infrared CCD

The infrared charge coupled device, IR-CCD, technique was usedto measure the temperature at the cutting region. The experimentalsetup for temperature measurement in turning, performed at the SwedishInstitute for Metal Research (SIMR), is illustrated in Figure 1. The CCD

TABLE 1 Workpiece Material and Cutting Insert Combinations for theMachining Tests

Test Workpiece material Cutting insert

1 SANMAC 316L TCMT16T308-MR 2 SANMAC 316L TCMT16T308-MM3 SANMAC 316L TPNG1603084 AISI 1045 TCMT16T308-MR 5 AISI 1045 TCMT16T308-MM

6 AISI 1045 TPNG160308


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490 A. Liljerehn et al.

FIGURE 1 Experimental IR-CCD camera setup for tool temperature measurement in orthogonalcutting.

components used in the present camera model are made of silicon-basedsemiconductors that act like condensers. During the exposure phase tothe light flux, the condenser accumulates a charge, which depends onthe number of photons collected by the semiconductor. During the imagereading sequence, the charge of each condenser is transferred to the

neighboring one under the application of an external electrical field.The charges are then transferred from one element to the other. Finallya diode located at the end of the measuring chain permits to readthe charge number and transfer the information as a form of a videosignal. The signal is then directly digitized and transferred to the imagememory of a computer controlled with suitable software. The number ofeffective picture elements 752 582 (H V) ensure the possibility to havea 64 48 mm sensing area. The normally occurring thermal noise of theCCD sensors is here eliminated by a Peltier cooling system, ensuring arepeatable image quality.

Application of the System to the Detectionof Infrared Radiation

The Si-based CCD sensors classically used in black and white imageanalysis are sensitive both to visible (400800 nm) and near infrared(8001100 nm) radiation. The present type of sensors is optimized in thenear infrared range.

The adjustment of an object can be done in the visible range, usingan IR-block filter. The fine adjustment of the image can be done inthe near-IR range through replacing the IR block filter with an IR filter


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(800 or 1000 nm) that will cut the visible radiation. As the area of interestfor temperature measurement in machining is located close to the tool tip,it is necessary to enlarge the zone corresponding to the sensing area of the

CCD-sensors, which is 64 48mm. To fulfill this requirement a specialfixed magnification lens (Navitar Precise Eye) with a working distance of175mm was used. This type of magnification lens, generally optimizedfor visible radiation (8085% in radiation transmission), can also be usedin the near infrared range, however with a slight loss in transmission(7580%).

Calibration of the CCD System

To calibrate the CCD system, two different methods may be applied:

the calibration in front of a black body for which absolute temperatureis known,

the calibration directly against a reference source made of the samematerial (example, cutting insert) as the one that is supposed to beobserved during the turning operation.

In the black body calibration method (BBM), the real temperature of theobject, i.e., cutting insert, is related to the one given for a black bodyderived from Plancks law, as shown in Equation (1)

1Tr

= 1Tbb

+ khc

ln (Tr, ) (1)

where Tbb is the black body temperature, h = 66255 1034 J.s, k =13805 1023 J/K, c = 29979 108 m/s, is the emissivity, and is thewavelength corresponding to the NIR filter (850 nm).

This relation is directly applicable in the case of a monochromaticradiation. Owing to the low emissivity variation of the cutting tools inthe near-IR region investigated, Equation (1) could be employed as a

first approximation (MSaoubi et al., 2002). Furthermore, it shows thatthe knowledge of the real temperature requires the determination of theobjects emissivity.

In the present study, the emissivity values at different temperature weredetermined for temperatures up to 1000C, on the inserts. The measuredemissivities are presented in Figure 2. It shows that for temperaturesbetween 5001000C, the variation in emissivity values is very small.Therefore it was decided to fix this value to = 0386 (0006748) whencalculating the insert temperature.

A calculation of the error propagated on temperature when emissivityvariation is neglected has been done and permits to determine the shift


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FIGURE 2 Results from emissivity measurement for cutting insert TPNG160308.

between the real temperature and the one of a black body, as expressed inEquation (2)

Error = Tr TbbTbb

= Trk

hcln (T) (2)

Table 2 and Equation (2) indicate that the error in temperature isquite sensitive to emissivity variations. The maximal error is 11% foran emissivity of 0.2, below 8.5% for an emissivity higher than 0.3 andlower than 5% for an emissivity value higher than 0.5. In earlier studies,experimental emissivity measurements were carried out for differentcutting tools, such as tungsten carbide and TiN-coated tools. Resultsshowed experimental emissivity values to vary between 0.5 and 0.85. In thepresent investigation the emissivity was found to be 0.380.4. Consideringthe temperature range in this study (


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The calibration of the CCD with a reference cutting insert heated atdifferent temperatures was done in the chamber of a special furnace atSIMR. The temperature is controlled by a thermocouple introduced in the

furnace chamber that is filled with Argon gas in order to minimize theoxidation effect due to high temperatures. A sapphire window embeddedin the chamber enables the observation of the insert. With this method nocorrection of temperature with emissivity is needed and the temperatureof the insert is assimilated to the temperature of furnace.

COMPARISON OF TWO METHODS

Based on the two methods described in the previous sections a set ofcalibration curves displaying either the temperature of the black body or

the temperature of the furnace as a function of grey level were obtained(Figures 3 and 4). Each calibration curve (grey level, n = f(T0)) wasfitted with a mathematical function (sigmoidal with 4 parameters) of thefollowing form:

N = n0 +a

1 + e(TT0)b(3)

Once the parameters n0, a, b and T0 were obtained, this relation wasinverted to obtain a function describing the temperature as a function of

grey level, namely:

T = T0 + bln

a

N n0 1

(4)

FIGURE 3 Black body calibration curves (IR filter 850nm).


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FIGURE 4 SIMR furnace calibration curves (IR filter 850 nm).

TABLE 3 Parameters Determined for the IR-CCD CalibrationCurve at t = 20ms

Method a b T0 n0 Corr.

Black body 334 63 767 57 0.99

Furnace 396 75 815 187 0.99

FIGURE 5 Comparison between black-body and SIMR furnace methods (for t = 20 < ms).


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As an example Table 3 shows the parameters determined for thecalibration curve obtained within an integration time of 20 ms. Based onthe emissivity results and black calibration it was possible to calculate the

temperature of the insert using Equation (2) and compare it with theinsert temperature in the SIMR furnace. Results are shown in Figure 5,displaying a comparison between black body and SIMR calibration curvefor t = 20ms. It indicates a maximal deviation of 40C between T(insert)and T(insert via black body). Possible reasons that could account for this variationcould be an underestimation of the insert surface temperature in the SIMRfurnace. The reading of the gray scale is problematic since both the insertand the thermocouple are placed in the furnace and the thermocoupletemperature has to be read through a small window. Another reason couldbe due to an underestimation of the insert emissivity. Typical treatment to

FIGURE 6 Typical treatment to obtain the tool isotherms (MSaoubi et al., 2002).


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obtain tool temperature distribution in a tungsten carbide cutting insert isshown in Figure 6.

ANALYTICAL MODELLING OF CUTTING TEMPERATURE

The analytical solution handles heat generation due to the combinedeffects of shear plane heat source and the tool-chip interface frictionalheat source and is based on the analytical model suggested by Komanduriand Hou (2001a). The analytical model has however been correctedto follow the stated boundary conditions regarding the location of theimaged secondary heat source. The correction enables the solution tobe applied for cutting tools with a rake and relief ratio different from

90. This change is important since it makes a significant difference intool temperature for tools with large rake and/or relief angles, which iscommon in cutting tool design.

TEMPERATURE RISE IN THE CHIP FROM THE PRIMARYHEAT SOURCE

The primary heat source, in the solution proposed by Komanduriand Hou (2001a), is viewed as an oblique band heat source moving

in the direction of the cut in an infinite medium. This solution hadalready been derived by Hahn (1951), but Komanduri and Hou (2001a)adopted Hahns solution and made two important adjustments. The firstcontribution was a modification of the model to yield for a semi-infinitemedium. This was accomplished by adding an adiabatic boundary on thetop of the chip surface and splitting the solution for the temperature risedue to the primary heat source in the chip and the rest of the workpiece.The image heat source is a reflection of the heat source in the adiabaticplane. Adopting this method for calculating the temperature rise in the

chip due to the primary heat source (Komanduri and Hou, 2001a) andthe secondary heat source (Komanduri and Hou, 2001b) came up with thetwo schematic solutions presented in Figures 7 and 8.

The temperature rise at any point in the chip, including the tool-chip interface, due to the primary heat source, relative to the coordinatesystem shown in Figure 9 and considering the previously stated boundaryconditions, can be calculated with Equation (5):

cs =qpls

2wp

AB

li=0 e(x

(lc

li sin()))vch/2a

K0vch

2aRi+ K0

vch

2aRi

dli (5)


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FIGURE 7 Oblique band heat source with infinite depth, traveling in a semi-infinite solid; afterKomanduri and Hou (2001a).

The distance, Ri, between the point in the chip, M(x, z), and the finiteincrement of the primary heat source, dli, is given by Equation (6):

Ri =

(x (lc li sin()))2 + (z li cos())2 (6)

and the distance, Ri, between the point in the chip, M(x, z), and the finiteincrement of the imaged primary heat source, dli, is given by Equation (7):

Ri =

(x (lc li sin()))2(2tch z li cos())2 (7)

The heat source is moving with the velocity of the chip, vch, and having anoblique angle , that is given by Equation (8):

= (8)

FIGURE 8 Komanduri and Hous (2001b) proposed model for the temperature distribution dueto the secondary heat source in a continuous chip formation process in metal cutting.


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FIGURE 9 Schematic description of Komanduri and Hous (2001c) model for calculating thetemperature rise in any point in a continuous chip due to both the primary and secondary heatsources.

The coordinate system is positioned with the x-axis aligned with, andthe z-axis normal to, the tool rake face. Komanduri and Hou (2001c)positioned the coordinate system for both the primary and the frictionalheat source to have the same position and orientation. The length of theshear plane AB, is defined by Equation (9):

AB = tchcos()

(9)

The thermal diffusivity, a, is a function of thermal conductivity, , specificheat, cp, and density, , as shown in Equation (10):

a = cp

(10)

TEMPERATURE RISE IN THE CHIP FROM THE SECONDARYHEAT SOURCE

The secondary deformation zone is referred to as the secondary heatsource and is defined by the contact area between the sliding chip and the


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insert. The mathematical solution for this type of moving heat source hasbeen a subject of research for Carlsaw and Jaeger (1959), Blok (1938) andKomanduri and Hou (2001b). Komanduri and Hou (2001b) started with

Jaegers solution for a source with a defined length and an infinite width,moving along the length of the source in an infinite medium. The sameimaged heat source approach that was used for the solution of the primaryheat source was used to derive the solution of the frictional heat source(Figure 8). The heat liberation over the contact length is regarded asuniform, which is the same assumption that Komanduri and Hou (2001b)as well as Hahn (1951), Trigger and Chao (1951), and Li and Liang (2005)have made in their calculation models. The solution for the temperaturerise at any point in the chip due to the frictional heat source is presentedin Equation (11):

cf =qpl

2wp

lcxj=0

e(xxj)vch/2a

K0

vch

2aRj

+ K0

vch

2aRj

dxj (11)

where the distance, Rj, between the point in the chip, M(x, z), andthe finite increment of the secondary heat source, dxj, is given byEquation (12):

Rj = (x xj)2 + (z)2 (12)

and the distance, Rj, between the point in the chip, M(x, z), and thefinite increment of the imaged secondary heat source, dxj, is given by

FIGURE 10 Typical solution of the temperature rise in the chip due to the primary and secondaryheat sources.


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Equation (13):

Rj = (x xj)2 + (2tch z)2 (13)

A typical output of the combined solution of Equations (5) and (11) ispresented in Figure 10, where it can be noted that only the temperaturerise in the chip is used in the final solution.

TEMPERATURE RISE IN THE TOOL FROM THE SECONDARYHEAT SOURCE

The secondary heat source is regarded as a stationary rectangular heatsource for the temperature rise solution in the tool, in accordance with

the solution presented by Komanduri and Hou (2001b). The temperaturerise in any given point in the tool, by using the same imaged heat sourceapproach, can be calculated using Equation (14):

tf =qpl

2tool

lcli=0

b/2yi=b/2

1

Rk+ 1

Rk

dlkdyk (14)

The distance, Rk, between the point in the tool, M(x, y, z), and the finiteincrement of the secondary heat source, dlk, is given by Equation (15):

Rk = (x lk)2 + (y yk)2 + (z)2 (15)The calculation of Rk has been re-derived since the equation for thisdistance presented by Komanduri and Hou (2001b) did not use the

FIGURE 11 Schematic comparison between Komanduri and Hous (2001c) model (on the left)and the re-derived model (on the right) for calculating the temperature rise in any point in thetool due to rectangular heat source at the tool-chip interface.


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FIGURE 12 Typical solution of the temperature rise in the tool due to the secondary heat source.

correct mirror plane. The mirror plane in which the image heat source isreflected is located at the tool clearance (Figure 11). This is mentionedin Komanduri and Hou (2001b) but the equation has unfortunately notbeen derived from this standpoint. The re-derived equation is presentedin Equation (16):

Rk =

(lc(1 + cos( + )) x xk)2 + (y yk)2 + (lc sin( + ) z zk)2(16)

where

xk = lk cos( + ) (17)

and

zk = lk sin( + ) (18)Figure 12 shows a typical solution of Equation (14), and it can be noted

that there is only a part of this solution that moves on to the final solution,just like in the solution of the chip temperature.

TEMPERATURE RISE IN THE WORKPIECE FROM THE PRIMARYHEAT SOURCE

The temperature rise at any point in the workpiece due to the primaryheat source relative to the coordinate system in Figure 13 can be calculated


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FIGURE 13 Schematic description of the analytical model for calculating the temperature rise atany point in the workpiece due to the primary heat source.

using Equation (19), and a typical solution is shown in Figure 14.

wps =qpls

2wp

ABll=0

e(xll sin())vc/2a

K0

vc

2aRl

+ K0

vc

2aRl

dll (19)

FIGURE 14 Typical solution of the temperature rise in the workpiece due to the primary heatsource.


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FIGURE 15 Combination of the valid chip, tool and workpiece temperature solutions.

The finite increment of the primary heat source, dll, is given byEquation (20):

Rl =

(x ll sin())2 + (z ll cos())2 (20)

and the distance, Ri, between the point in the chip, M(x, z), and thefinite increment of the imaged primary heat source, dli, is given byEquation (21):

Rl =

(x ll sin())2 + (z+ ll cos())2 (21)

There is only a part of the solution of Equation (19) that moves on tothe final solution, just like in the previous examples. The final solution(Figure 15) of the temperature distribution in the chip, tool and workpieces is then assembled from the valid parts of the solutions obtained with

Equations (5), (11), (14) and (19).

SOLUTION OF THE TEMPERATURE DISTRIBUTION

To be able to calculate the temperature rise and distribution at anygiven point in the chip and tool it is essential to know the fraction ofenergy that goes into the tool or follows the chip. This problem is solvedby calculating a heat partition ratio, B(x), which satisfies temperatureequilibrium along the tool-chip interface, as shown in Equation (22):

cs + cfB(x) = tf(1 B(x)) + tiBtool_ind(x) (22)


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where ti and Btool_ind(x) is introduced to match the heat on the rakeface originating from the shear plane. A numerical solution that onlysatisfies the equilibrium at discrete points over the tool-chip interface

cannot be used to solve the temperature distribution in the chip or thetool. The solution of the heat partition ratio B(x) needs to be describedby a continuous function of xj along the contact length. The suggestedfunction presented in Komanduri and Hou (2001c) was used for solvingthe heat partition ratio B(x), ti and Btool_ind(x). The fraction of heatconducted into the workpiece material is not constant or linear. The powerlaw Equations (23) and (24) are used to solve the temperature equilibriumbetween tool-chip interfaces.

B(x) = (Bchip B) + 2Bx

lc

m

+ CBx

lc

k

(23)

The fraction of heat conducted into the tool is expressed withEquation (24):

1 B(x) = (Btool + B) 2B

x

lc

m CB

x

lc

k(24)

where Btool is defined using Equation (25):

Btool = (1 Bchip) (25)The temperature rise in the tool due to the induced heat source isexpressed by Equation (26):

ti =qpli

2tool

lcli=0

b/2yi=b/2

1

Rk+ 1

Rk

dlkdyk (26)

and the heat partition ratio for the induced heat source is found inEquation (27):

Btool_ind(x) = (Binduced + Bi) 2Bi

x

lc

mi CiBi

x

lc

ki(27)

The coefficients in Equations (23), (24) and (27) need to be solved tosatisfy Equation (22).

INPUT PARAMETERS

The analytical temperature model has been evaluated for six differentexperimental setups. The cutting conditions and output parameters from


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TABLE 4 Cutting Conditions

Test 1 2 3 4 5 6

tc [mm] 0112 0112 0224 0112 0112 0224tch [mm] 016 019 028 018 017 032vch [m/s] 140 118 157 128 132 140vs [m/s] 244 225 236 237 232 236b [mm] 30 30 30 30 30 30 [deg] 350 305 387 326 334 350lc [mm] 023 028 038 023 027 042

TABLE 5 Cutting Forces

Test 1 2 3 4 5 6

Fc [N] 747 773 1296 738 743 1247Ff [N] 564 601 613 513 580 663Ffr [N] 564 641 680 587 618 727Fs [N] 288 332 629 255 273 641

TABLE 6 Thermal Material Properties Used in the Analytical Model

Test 1 2 3 4 5 6

Tcm [C] 485 520 380 477 493 420c

wpp [J/kg K] 720 745 658 685 740 646

wp [J/s m K] 216 221 202 379 376 387tool [J/s m K] 74 74 74 74 74 74awp [mm2/s] 39e6 39e6 40e6 65e6 64e6 78e6wp [kg/m3] 7626 7599 7690 7790 7788 7822

TABLE 7 Material Properties Used in the Finite Element Model (MSC. Marc)

SANMAC 316L AISI 1045 Cutting insert TiAlN

Rp02 [MPa] 240E [GPa] 199 206 580 439 03 03 022 018 [mm2/s] 165e6 16e6 74e6 74e6 [J/s m K] 14 38 120 24 [kg/m3] 7822 7675 14500 4900cp [J/kg K] 445 675 220 551


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the trials are shown in Table 4. Cutting forces were measured during thetests and are presented in Table 5, while the thermal material propertiesused in the analytical model are listed in Table 6 and the properties used

for the MSC. Marc FE simulations are provided in Table 7.

LoewenShaw Model

This model is also based on an idealization of the heat sources (inprimary and secondary deformation zones) that are both regarded asplanes (Loewen and Shaw, 1954). The tool is also assumed to be perfectlysharp and with no chip breaking geometry, as in the previous model.This model does not take into account deformation of the material in thesecondary deformation zone but considers all work done due to friction

at the interface. On the other hand, the model does include the heatexchange of the area of contact when sliding on a conducting surface.

Work in the Primary Deformation Zone

The estimated mean temperature of the material passing through theprimary deformation zone according to the Loewen and Shaw (1954)model becomes:

s =(1

)Fsvs

cptcbvc (28)

where (1 ) Fs vs is the heat per unit time per unit area that flows intothe workpiece and (1 ) can be calculated by Equation (29):

1 = 11 + 1328

acos()

vctccos()

(29)

Temperature in the Secondary Deformation Zone

The average temperature rise in the chip due to the secondary heatsource can be expressed according to Boothroyd and Knight (1989) byEquation (30):

f =Ffvch

cptcbvch(30)

and the mean chip temperature can be found through Equation (31):

Tcm = T0 + s + f (31)


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The thermal dependant material propertiesthermal diffusivity, a,thermal conductivity, , specific heat, cp, and density, have beenselected based on an iterative solution of the average chip temperature.

NUMERICAL MODELING OF HEAT GENERATION

Finite element program MSC. Marc was used to predict cutting forces,chip formation and heat generation within the cutting zones. This isbased on an implicit updated Lagrangian formulation using continuousre-meshing technique to model the chip formation (Kalhori, 2001).Jaumann rate formulation is employed for the rate formulation (Crisfield,1997). The orthogonal cutting condition has been modeled using four-node plane strain elements. The volumetric strain is under-integrated

in order to avoid locking caused through large, incompressible plasticstrains. To predict the chip forming process for workpiece of steel AISI1045 and stainless steel SANMAC 316L, a thermal-elastic-plastic materialmodel with temperature dependent properties and variable hardening wasimplemented in MSC. Marc. The yield stress is updated based on strainrate and thermal softening of workpiece material, formulated using theEquation (32):

(p, , T) = g(p) () (T) (32)

where,

g(p) = 0

1 + p

p0

1/n(33)

and 0 is the initial yield stress, p is the plastic strain and p0 is the

reference plastic strain. The strain rate contribution to yield stress isconsidered using the Equation (34):

() = 1 + 01/m1

, if t

() =

1 + 0

1/m21 + t

0

(1/m11/m2), if > t

(34)

where, is strain rate, 0 is reference plastic strain rate, t is strain ratewhere the transition between low and high strain rate sensitivity occurs,m1 is the low strain rate sensitivity coefficient and m2 is the high strainrate sensitivity coefficient. Thermal softening is accounted for using apolynomial function of order up to five. To predict the material failureat the primary deformation zone a damage model based on hydrostatic


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pressure and strain to failure was implemented in MSC. Marc. The damagevalue for each integration point is calculated using the Equation (35):

D = i

p

i

p

fi

(35)

where D is the dimensionless cumulative damage, pi is the instantaneousincrement of strain, and pfi is the instantaneous strain to failure. Theinstantaneous strain to failure is determined considering the hydrostaticpressure given by Equation (36):

pf

=n

exp

15 Pc J

pf0

(36)

where Pc is a pressure-dependent coefficient, defined by Equation (37):

Pc =13

ln

pc

pt

(37)

and

n

=exp

3 Pc2

(38)

RESULTS AND DISCUSSION

The predictions from numerical and analytical models of cuttingprocess are compared with experimental results. The cutting forces weremeasured using a Kistler dynamometer in a manual lathe (Kping),as described by Kalhori et al. (1997), and the IR-CCD temperaturemeasurements were made during cutting in a CNC lathe. These are

compared with results from numerical studies in Table 8. It is observed thatthe agreement of simulated cutting forces compared to the experimental

TABLE 8 Comparison of Measured (Exp) and Predicted (FEM) Machining Forces

Test 1 2 3 4 5 6

Fc [N] Exp. 747 773 1247 738 743 1296Fc [N] FEM 750 775 1150 800 750 1230Ff [N] Exp. 564 601 654 513 580 614

Ff [N] FEM 550 450 400 510 450 450


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TABLE 9 Comparison of Measured (Exp) and Predicted (FEM) Chip Morphology Parameters

Test 1 2 3 4 5 6

tch [mm] Exp. 016 019 028 018 017 032tch [mm] FEM 016 018 034 018 018 032 [deg] Exp. 350 305 387 320 334 350 [deg] FEM 350 327 333 320 363 350lc [mm] Exp. 023 028 038 023 027 042lc [mm] FEM 018 026 048 025 026 039

values is very good when it comes to the forces in the cutting direction.However, this is not the case for feed forces, especially for TCMT16T308-

MM and TPNG160308 inserts. Several different phenomena, describedbelow, could be the reason for this deviation.

More accurate results may be achieved through further developmentof the material model considering strain localization. The damage modelimplemented in the current FEM simulation model should be furtherdeveloped in order to better capture shear localization at the primarydeformation zone. Furthermore, the friction model used in the numericalanalysis might be further improved. In the current study an averagefriction coefficient for the insert-chip contact area is assumed. Since, thefriction behavior of contact surfaces depends on both the contact bodiestemperatures and contact pressure; it should be included in the FE-model.It is believed that this would improve the numerically predicted result.

The simulated chip morphologies are compared with experimentalresults in Table 9. It is shown that there is very good agreementbetween the simulation and measurements when it comes to the averagechip thickness, contact length and shear plane angle. The measuredpeak temperature over the tool-chip interface for different geometries iscompared to the analytical and finite element simulations in Table 10.

TABLE 10 Comparison of Experimentally Measured (IR-CCD)and Predicted (Analytical, FEM) Peak Temperatures at theTool-Chip Interface

Test Analytical [C] IR-CCD [C] FEM [C]

1 802 8502 890 852 8503 1004 943 9604 657 7505 785 785 740

6 835 823 760


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FIGURE 16 Comparison of analytically predicted, experimentally measured (IR-CCD), andnumerically simulated (MSC. Marc) temperatures for Test 2 (TCMT 16T308-MM tool; SANMAC316L workpiece).

FIGURE 17 Comparison of analytically predicted, experimentally measured (IR-CCD), andnumerically simulated (MSC. Marc) temperatures for Test 3 (TPNG160308 tool; SANMAC 316Lworkpiece).

FIGURE 18 Comparison of analytically predicted, experimentally measured (IR-CCD), andnumerically simulated (MSC. Marc) temperatures for Test 5 (TCMT 16T308-MM tool; AISI 1045workpiece).


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FIGURE 19 Comparison of analytically predicted, experimentally measured (IR-CCD), andnumerically simulated (MSC. Marc) temperatures for Test 6 (TPNG160308 tool; AISI 1045workpiece).

The temperature gradients in the cutting zones for all tests, except for theTCMT 16T308-MR insert where there are no IR-CCD results, are shown inFigures 1619.

The analytical model of heat generation has a tendency tounderestimate the temperature near the tool tip and overestimate thetool peak temperature further up along the rake face, which has itsnatural explanation from the neglected friction forces around the cuttingedge radius. The mean temperature is also lower along the tool-chip

interface than the IR-CCD measured temperature but the model is mostdefinitely suitable for over-all temperature estimations. The reason for theunderestimation, by the analytical model, near the tool tip might have afour folded explanation:

A) Since the cutting forces along the insert-chip interface are not evenlydistributed, the assumption that the heat liberation over the rake facewould be evenly distributed may not be correct.

B) The contact between the tool and the chip needs to be modeled witha stick-slip approach that considers the shear stress variation over the

contact length properly. This would result in higher heat liberationintensity closer to the tool tip and a lower intensity further up wherethe contact state changes from sticking to slipping. This approach hasbeen proven by both Huang and Liang (2003) as well as Karpat andzel (2006a,b) and would also result in a higher mean temperaturebut a lower peak temperature.

C) In the current studies the temperature rise from friction between thetool and the workpiece in the tertiary deformation zone is not takento account.

D) The heat liberation intensity in the primary deformation zone isdetermined based on the calculated average plastic deformation over


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the shear plane. This is not the case during the cutting process.The primary deformation zone is known to involve more plasticdeformation near the cutting edge radius then on the back face of

the chip. This will further increase the temperature rise close to theedge radius and increase the mean temperature over the contactarea.

The results from the analytical models are based on informationfrom measurements; i.e., cutting forces, contact length and thickness ofdeformation that is caused by friction in the contact with the insert.Contact length is hard to predict or measure but a very importantparameter since the results from the analytical model are very sensitiveto the contact area over which the heat liberation is calculated. A smalldifference in contact length can result in a large difference in predictedtemperature.

CONCLUSIONS

From the result comparison between measured cutting forces and thecorresponding values predicted with the FEM simulation model it canbe concluded that the forces in the cutting direction match well in allexperiments. The prediction of the feed force on the other hand needs

to be further developed, preferably with a material model that considersstrain localization better as well as an improved friction model. Thedamage model implemented in the current FEM simulation model wouldalso result in a better agreement regarding the feed force if it were furtherdeveloped in order to better capture the shear localization at the primarydeformation zone. It can also be concluded that the FEM model madegood temperature predictions for the SANMAC 316L workpiece materialbut slightly underestimated the temperature in the AISI 1045 case, whichmight have to do with the underestimation of the feed force in these

simulations.The analytical model of heat generation made generally goodtemperature predictions for the given experiments but the model isvery sensitive to input parameters. The problem with underestimationof the temperature near the tool tip, and overestimation of the toolpeak temperature further up along the rake face, could to some extentbe worked around by considering the rubbing heat source on theclearance side of the tool. This approach demands more in-depth analysisof the cutting force distribution around the cutting edge of the tool.The information that is obtained from the experimental setup in this

experiment is not enough but might be of interest in future work.


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NOMENCLATURE

1 B Fraction of heat conducted into the toola Thermal diffusivity

[mm2/s

]AB Shear plane length [mm]B Fraction of heat conducted into the chipb Depth of cut, ap [mm]cp Specific heat capacity [J/kg K]D Dimensionless cumulative damageE Youngs modulus [GPa]Fc Cutting force [N]Ff Feed force [N]Ffr Frictional force [N]

Fs Shear force [N]J Hydrostatic pressure [MPa]K0 Bessel function of second kind order zerolc Contact length [mm]m1 low strain rate sensitivity coefficientm2 high strain rate sensitivity coefficientPc Pressure coefficientqpl Heat liberation intensity of the frictional heat source

[J/mm2 s]qpls Heat liberation intensity of the moving shear plane

heat source [J/mm2

s]R Distance between the moving-line heat source and pointM,where the temperature rise is calculated [mm]

T0 Ambient temperature of workpiece [C]Tcm Average chip temperature [C]tc Uncut chip thickness, feed [mm]tch Cut chip thickness [mm]vc Cutting speed [m/s]vs Shear velocity [m/s]x, y, z Coordinates of pointM where the temperature is

calculated [mm]1 Fraction of energy conducted into the chip Clearance angle [C]

pi Instantaneous increment of strain

Ratio of chip thickness deformed in secondarydeformation zone

p Plastic strain [mm/mm]

p0 Reference plastic strain [mm/mm]

p

fi Instantaneous strain to failure [mm/mm]

Strain rate [1/s]0 Reference plastic strain rate [1/s]


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t Strain rate where the transition between lowand high strain rate sensitivity occurs [1/s]

Temperature rise [C]tool Thermal conductivity of tool [J/s m K]wp Thermal conductivity of workpiece [J/s m K] Density[kg/m3] Initial yield stress [MPa] Von Mises stress [MPa] Poissons ratio Shear angle [C] Oblique angle [C]

REFERENCES

Blok, H. (1938) Theoretical study of temperature rise at surfaces of actual contact under oilinesslubricating conditions. Proceedings of General Discussion on Lubrication and Lubricants,Institute of Mechanical Engineers London, pp. 222235.

Boothroyd, G.; Knight, W.A. (1989) Fundamentals of Machining and Machine Tool, 2nd edition, MarcelDekker Inc., New York.

Carlsaw, H.S.; Jaeger, J.C. (1959) Conduction of Heat in Solids, 2nd edition, Oxford University Press,Oxford, UK.

Crisfield, M.A. (1997) Non-linear Finite Element Analysis of Solids and Structures, Vol. 2, AdvancedTopics. John Wiley, Chichester.

Hahn, R.S. (1951) On the temperature developed at the shear plane in the metal cutting process.

Proceedings of the First U.S. National Congress of Applied Mechanics, pp. 661666.Huang, Y.; Liang, S.Y. (2003) Cutting temperature modeling based on non-uniform heat intensity

and partition ratio. Machining Science and Technology, 9(3): 301323.Kalhori, V. (2001) Modelling and Simulation of Mechanical Cutting, Lule Technical University, Doctoral

thesis: 28, ISSN: 14021544.Kalhori, V.; Lundblad, M.; Lindgren, L.-E. (1997) Numerical and experimental analysis of

orthogonal metal cutting. Transactions of the ASME, International Mechanical Engineering Congress& Exposition, MED Vol. 62, Manufacturing Science and Engineering, Dallas, Texas 1621Nov. 1997.

Karpat, Y.; zel, T. (2006a) Predictive analytical and thermal modeling of orthogonal cuttingprocess. Part I: Predictions of tool forces, stresses and temperature distributions. ASME Journalof Manufacturing Science and Engineering, 128(2): 435444.

Karpat, Y.; zel, T. (2006b) Predictive analytical and thermal modeling of orthogonal cuttingprocess. Part II: Effect of tool flank wear on tool forces, stresses and temperature distributions.ASME Journal of Manufacturing Science and Engineering, 128(2): 445453.

Komanduri, R.; Hou, Z.B. (2001a) Thermal modeling of the metal cutting process, Part 1:Temperature rise distribution due to shear plane heat source. International Journal of MechanicalScience, 42: 17151752.

Komanduri, R.; Hou, Z.B. (2001b) Thermal modeling of the metal cutting process, Part 2:Temperature rise distribution due to frictional heat source at the tool-chip interface.International Journal of Mechanical Science, 43: 5788.

Komanduri, R.; Hou, Z.B. (2001c) Thermal modeling of the metal cutting process, Part 3:Temperature rise distribution due to combined effects of shear plane heat source andthe tool-chip interface frictional heat source. International Journal of Mechanical Science,43: 89107.

Li, K.M.; Liang, S.Y. (2005) Modeling of cutting temperature in near dry machining. Journal of Manufacturing Science and Engineering, Transactions of the ASME, 128(2): 19.


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Loewen, E.G.; Shaw, M.C. (1954) On the analysis of cutting tool temperatures. Transactions of theASME, 71: 217231.

MSaoubi, R.; Eggertsson, C.; Chandrasekaran, H. (2002) Application of IR-CCD technique tomap tool temperature distribution in single point turning of quenched and tempered steel.

IM Report No IM-2002-563, Swedish Institute for Metals Research.Trigger, K.J.; Chao, B.T. (1951) An analytical evaluation of metal cutting temperatures. Transactionsof the ASME, 73: 5768.


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