Wear 258 (2005) 1479–1490

2D FEM estimate of tool wear in turning operation

L.-J. Xiea,∗, J. Schmidta, C. Schmidta, F. Biesingerb

a Institut fur Werkzeugmaschinen und Betriebstechnik, Universit¨at Karlsruhe (TH), Germanyb Institut fur Werkstoffkunde I, Universit¨at Karlsruhe (TH), Germany

Received 8 July 2003; accepted 11 November 2004

Abstract

Finite element method (FEM) is a powerful tool to predict cutting process variables, which are difficult to obtain with experimental methods.In this paper, modelling techniques on continuous chip formation by using the commercial FEM code ABAQUS are discussed. A combinationof three chip formation analysis steps including initial chip formation, chip growth and steady-state chip formation, is used to simulatethe continuous chip formation process. Steady chip shape, cutting force, and heat flux at tool/chip and tool/work interface are obtained.Further, after introducing a heat transfer analysis, temperature distribution in the cutting insert at steady state is obtained. In this way, cuttingp mperatured bles and theirr unches chipf ol geometry,t perimentalr©

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r es-Usuihod,esiveleyE2res-odee-takeeth-

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rocess variables e.g. contact pressure (normal stress) at tool/chip and tool/work interface, relative sliding velocity and cutting teistribution at steady state are predicted. Many researches show that tool wear rate is dependent on these cutting process variaelationship is described by some wear rate models. Through implementing a Python-based tool wear estimate program, which laormation analysis, reads predicted cutting process variables, calculates tool wear based on wear rate model and then updates toool wear progress in turning operation is estimated. In addition, the predicted crater wear and flank wear are verified with exesults.

2004 Published by Elsevier B.V.

eywords:Tool wear; FEM; Turning operation; Chip formation; Orthogonal cutting; Heat transfer

. Introduction

The main tool failures, which take place in turning opera-ion, include progressive wear (flank wear and crater wear),hipping, partial fracture, plastic deformation, thermal crack,tc. At present, experimental and analytical methods are still

he main ways to investigate every type of tool wear. However,ith the continuous development of more and more powerfulomputers and numerical methods and their ever-wideningpplication in manufacturing, phenomena in metal machin-

ng, such as cutting force, temperature, and even progres-ive tool wear are gradually studied using numerical methodsainly including finite differential method (FDM) and finite

∗ Corresponding author.E-mail addresses:lijing.xie@mach.uni-karlsruhe.de (L.-J. Xie),

uergen.schmidt@mach.uni-karlsruhe.de (J. Schmidt),arsten.schmidt@mach.uni-karlsruhe.de (C. Schmidt),rank.biesinger@power.alstom.com (F. Biesinger).

element method (FEM). The earlier progressive tool weatimate with numerical methods dates back to 1978, whenet al. predicted crater wear and flank wear with FDM metusing wear characteristic equation deduced from adhwear[1]. Later it is reported that Monaghan and MacGinperformed tool wear calculation using FEM code-FORG[2]. And recently, Yen et al. made great progress in progsive flank wear and crater wear estimate with FEM cDeform-2D[3]. It is expected that in the future FEM will bcome an effective tool for the tool wear study and partlythe place of time- and cost-consuming experimental mods.

Tool wear estimate with numerical methods is basechip formation simulation and wear model. Tools with chfered or rounded edge are most commonly used in real cuoperations for highly strengthened tool edges. Furtherminitial sharp tool will become blunt as it wears away. Thefore, chip formation modelling for cutting with roundeblunt and chamfered tool is necessary.

043-1648/$ – see front matter © 2004 Published by Elsevier B.V.

oi:10.1016/j.wear.2004.11.004

1480 L.-J. Xie et al. / Wear 258 (2005) 1479–1490

Table 1Cutting condition

Cutting type Orthogonal cutting, turning operation, dry cutting

Work material Mild carbon steel AISI1045Tool material Uncoated carbide WC-CoTool geometry γo =−7◦, αo = 7◦, rε = 0.0245 mmCutting parameters vc = 300 m/min,ap = 2 mm,f= 0.145 mm/r

The existing wear model can be classified into two types:one is cutting parameters-tool life type, aiming at optimi-sation of machining operation, such as the famous Taylor’sequation, which establishes the simple relationship betweenthe cutting speedvc and tool lifeT. Another one is cuttingprocess variables-wear rate type, often based on one or sev-eral wear mechanisms, such as E. Usui’s wear model derivedfrom adhesive wear, which describes wear rate as a functionof cutting process variables, such as normal stress, contacttemperature, and relative sliding velocity on tool face andsupplies approaches for tool wear estimate with numericalmethods.

In this paper, the FEM code ABAQUS is used as the FEMcalculation tool for chip formation, heat transfer and toolgeometry updating. Tool wear calculation main program andsubroutines are developed with object-oriented programminglanguage Python, which is strongly suggested by HSK[4].

The studied cutting condition in this paper is listed inTable 1.

2. Tool wear estimate program design

Fig. 1 shows the flow chart of the tool wear calculationprogram. Chip formation and heat transfer analysis supply thec uttingf tingt d VBi value

is calculated, and tool geometry is updated. If the VB valueis still smaller than the user-defined tool reshape criterionVBmax, a second tool wear calculation cycle starts with theupdated tool geometry.

2.1. Continuous chip formation simulation

At present there is no general predictive chip formationmodel, because the physical phenomena associated with thecutting process are extremely complex: friction, heating,large strain and strain rate. In addition, different approachesto the implementation of chip separation lead to variation ofchip formation modelling.

2.1.1. Chip formation considerations2.1.1.1. Contact and friction.The contact and friction attool/chip and tool/work determine the cutting power, machin-ing quality and tool wear, they play an important role in metalcutting. Photo-elastic experiment and plenty of evidencefrom worn tools, from quick-stop sections and from chipsshowed the coexistence of seizure and sliding at tool/chipinterface under many cutting conditions, which is consistentwith Zorev’s assumption about slide-stick friction model[5].However, Coulomb’s friction model is still applicable in somecutting conditions and widely used in chip formation mod-e stantf allt holeu

2 dt igh-s flows nec-e anyr ls ford icalm odeld es

car-b ma-t ial int d byV bedb

σ

w

T

w uiva-l

utting process variable values at the steady state of cor the wear rate calculation subroutine. An optimum cutime increment is searched according to a user-specifiencrement value and the calculated wear rate. Then wear

Fig. 1. Flow chart of tool wear calculation program.

lling at present, and accordingly in this paper a conrictional coefficient along tool/chip interface is applied tohe chip formation analysis processes throughout the wseful tool life as well.

.1.1.2. Material model.Very high strain, strain rate anemperature in the metal cutting process, especially in hpeed-cutting (HSC), have strong influence on material’stress. A material model, which includes their relation, isssary for getting better chip formation analysis result. Mesearchers are making efforts to establish such modeifferent work materials through experimental or analytethods, such as Johnson-cook equation. A material matabase has been developed by Sohner and Altan with thupport from international researchers[6].

Several material models are already available for mildon steel AISI1045, which is the most commonly used

erial in research work and was selected as work materhis paper. Among them, the material model developeohringer is used in the following study, which is descriy Eq.(1).

∗v (T, ε) = σ∗

0

(1 −

(T

T0

)n)m

(1)

ith

0 = G0

kln(ε0/ε(pl))

here the constants are determined for CK45, an eqent to AISI1045 in Germany. They are:m= 1.78,n= 0.53,

L.-J. Xie et al. / Wear 258 (2005) 1479–1490 1481

Fig. 2. Initial chip formation analysis. (a) Initial geometry and mesh. (b) Stress field (MPa) att= 0.18 ms.

G0 = 0.58 eV,ε0 = 7.29× 105 s−1, andσ∗0 = 1352 MPa.k

is Boltzmann constant, andT is temperature in Kelvin[7].

2.1.1.3. Chip separation.ABAQUS/Explicit supplies sev-eral formulations for numerical modelling: Lagrangian, Eule-rian and Arbitrary Lagrangian Eulerian (ALE). Among them,Lagrangian and ALE formulations supply approaches to chipseparation in the chip formation process.

Lagrangian formulation tracks discrete material points.Chip separation is normally performed along predeterminedlines of elements on the moving path of the tool edge, bydeleting elements ahead the tool edge when element failurecriterion, such as shear failure criterion, is reached. The fail-ure criterion is usually defined arbitrary because of the dif-ficulty of obtaining the required experimental equipment. Inaddition, the number and size of deleted elements affect pro-duced chip thickness, and fine elements improve simulatedresult whereas at the same time increase sharply the calcula-tion time and cost. Therefore, sharp tool is most frequentlyused in chip formation modelling, because the separation lineis obvious and by using very fine elements along this line anddefining shear failure only to these line elements, the conflictbetween cost and precision are settled.

Eulerian formulation, tracking volumes rather than ma-terial particles, request the steady-state chip geometry andf tor gingc itialc ion.

them eom-e acet etersw oothi tot dgec tionl n ac-c ilurec erialm for-m thef

2.1.2. Analysis stepsIn normal turning operation, cutting depth, feed rate and

cutting speed are kept constant, and steady state will bereached within several seconds after the entrance of tool edgeinto work material. Therefore, it can be said that progressivetool wear is mainly formed during the steady state and thecontribution from the unsteady state can be ignored. The anal-ysis of cutting process’ steady state becomes the first step tothe tool wear estimate. Knowledge about the shape and ge-ometry of the formed chip is the prerequisite of steady-statemodeling, which comes from experiment or simulation. Thispaper supplies a complete modeling method from initial chipformation to the realization of steady state, which consistsof three analysis steps, including initial chip formation, chipgrowth, and steady-state chip formation as described in de-tail in the following parts. The first two analysis steps supplysteady chip geometry for the steady-state chip formation anal-ysis step. During all the chip formation steps, coupled thermo-stress analyses are performed with ABAQUS/Explicit[8].

The work has a size of 0.6 mm× 3.2 mm, which is meshedwith 2725 CPE4RT elements. In order to save calculationtime, only part of the cutting tool near cutting edge joins inthe chip formation modelling, which consists of 327 CPE4RTelements. Moreover, in the first two steps, the cutting tool isd p thec rdert lattert

2 isa rnerh ion ofs e (seeF hen k,e se thec ipa

ndy

ree-surface tracking. With this formulation it is difficultealize chip separation and simulate the cutting with chanhip thickness. Therefore, it is impossible to analyse inhip formation, milling process or segmented chip format

With ALE formulation, the mesh is not attached toaterial and thus can move to update the free chip gtry and avoid distortion. Correct configuration of surf

ypes and reasonable adaptive meshing control paramhich depend on tool edge geometry, will ensure the sm

mplementation of chip separation. ALE is very suitablehe cutting conditions in which a rounded or chamfered-eutting tool is used. With ALE, no predetermined separaine is required and coarser elements can still produce aeptable chip thickness, cutting force, etc. Because no fariterion is required, there is a broader selection of matodels. Therefore, ALE formulation is used to the chipation analysis steps with rounded-edge cutting tool in

ollowing parts.

,

efined as rigid body, whereas in the last analysis steutting tool has to be modelled as a deformable body in oo obtain the necessary cutting process variables for theool wear estimate.

.1.2.1. Initial chip formation.At the beginning, the toolt the right side of the work, and on the work a small coas been cut away at the right side under the considerateeding more nodes along the formed concave surfacig. 2(a)). The work is fixed and the tool is moving in tegativex-direction.1 With the tool advancing into the worlements along the concave surface extend and compohips’ outside surface.Fig. 2(b) shows the formed initial chnd stress distribution at 0.18 ms.

1 In all figures of this paper,x-direction is pointed to the right side a-direction to the top of the page.

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Fig. 3. Chip growth analysis. (a) Initial geometry and mesh. (b) Stress field (MPa) att= 0.09 ms. (c) Stress field (MPa) att= 0.3 ms.

Fig. 4. Steady-state chip formation analysis. (a) Initial geometry and mesh. (b) Stress field (MPa) att= 1 ms.

2.1.2.2. Chip growth.With a user-developed subroutine,variables of the work and the tool about node coordinate, tem-perature, etc. are read into the model file of the chip growthanalysis step from the output database of initial chip forma-tion analysis step at a user-specified field output frame.

In this step, the tool is fixed. The left and right boundaryof the work are defined as Eulerian boundary regions, whosemesh is fixed inx-direction, but material flows in continu-ously from the left surface at cutting speed and flows outof the right surface, as indicated with the small arrows inFig. 3(a). In addition, the work is fixed iny-direction at thebottom surface.Fig. 3(b) and (c) show the growth of the chipwith the material flowing into the control area and the stressdistribution in the work at 0.09 ms and 0.3 ms.

2.1.2.3. Continuous steady-state chip formation.The workand tool variables are read into steady-state cutting analy-sis step model file from the chip growth analysis step whenthe chip geometry near the chip root becomes stable. Forexample, the mesh inFig. 4(a) is read from the frame att= 0.09 ms in chip growth analysis step, seeFig. 3(b). For thesimplification of boundary condition definition, some nodesat chip top are moved, which changes the shape of the chiptop.

The mesh of the chip top is fixed, shown with small trian-g d,a onlyd int rial

flow out of the chip mesh area in place of the visualized chipgrowth.

Because cutting tool is deformable body, its movement isfixed through defining constraint inx-direction at the rightboundary and iny-direction at the top boundary.

Fig. 4(b) shows the stress distribution at 1 ms.By adding the reaction force component in the same di-

rection at all constrained nodes of the cutting tool and thentaking the negative value, the cutting force components Fcand Ft are obtained.Fig. 5shows that the cutting force com-

F ,a

les inFig. 4(a), its movement inx direction is constrainend it has Eulerian type boundary region, which is theifference of boundary condition definition for the work

his step from that in the former step and allows mate

ig. 5. Cutting force history (under cutting condition:vc = 300 m/min

p = 2 mm,f= 0.145 mm/r).

L.-J. Xie et al. / Wear 258 (2005) 1479–1490 1483

ponents change within a very narrow range from 0.7 ms, andit is deemed that the mechanical steady state is realized, there-fore, the mechanical cutting process variables, such as contactpressure (i.e., CPRESS), sliding velocity (i.e., SFLIPR) at1 ms are read out for tool wear calculation. From orthogonalcutting experiment, in which the cutting depth is 1 mm andother cutting parameters have the same value as this simulatedcutting condition, Fc and Ft are 370N and 240N, respectively[9]. According to metal cutting theory, cutting force doubleswhen cutting depth doubles. FromFig. 5 the simulated Fcand Ft are 630N and 300N; compared with the experiment,they have errors within 15% and 38%, respectively.

FromFig. 6(b) within 1 ms, cutting temperatures at mostof the tool nodes on tool/chip interface, i.e., highlighted nodesin Fig. 6(a), have a very slow increasing curves, which meansapproaching steady state, in comparison with the sharp climb-ing curves of temperature with time inFig. 6(d) at the high-lighted nodes inFig. 6(c) inside the tool. This means thatthermal steady state is not realized in the whole cutting tool.Fig. 7shows the temperature distribution at 1 ms. The highesttemperature is at rake/chip interface, and most part of the toolis still at room temperature.

In this study, the heat produced in cutting process includestwo parts, the heat created by the friction between the tooland the work, half of which is introduced into the tool, and the

Fig. 7. Temperature distribution att= 1 ms of steady-state chip formationanalysis step.

heat converted from inelastic energy, i.e., plastic deformationenergy, whose conversion ratio is set to 90%. Part of thelatter heat is transferred to the tool through heat convectionat tool/chip interface.

Fig. 8 shows that the total contact heat flux at the wholetool face has always negative values in the first 1 ms, whichmeans that heat is transferred from slave surface to mastersurface, i.e., from the work to the tool. At the end of the first1 ms, both the total heat flux due to friction (i.e., SFDRA)and the total contact heat flux are approaching steady state.

Fn

ig. 6. Temperature history of tool nodes at steady-state chip formation anaodes. (c) Position of nodes in the tool. (d) Temperature history of nodes in t

lysis step. (a) Position of nodes on tool face. (b) Temperature history oftool facehe tool.

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Fig. 8. Heat flux history of tool/work interface at steady-state chip formationanalysis step.

The sum of their absolute value makes the total heat fluxinto the tool at the whole tool face. By adding the absolutevalue of contact heat flux and the heat flux due to frictionat every tool face node, the heat flux distribution along thetool face is obtained. The heat flux distribution at the time of1 ms is written into the heat flux file of the tool heat transfermodel.

2.2. Heat transfer analysis

In order to realize thermal steady state in the whole tool,heat transfer analysis is performed with ABAQUS/Standard[10] for its qualification in heat transfer analysis. As shownin Fig. 9, the tool used in this analysis includes the part,which is surrounded by the rake face, flank face, bottomface, and the central hole’s surface, and it consists of 640DC2D4 elements. The tool used in the former chip forma-tion analysis steps is only the highlighted part inFig. 9, andin this step it has the same element label, node label, and el-ement connectivity as in chip formation analysis steps. This

Table 2Characteristic constants for carbon steels

C (m2/MN)θf ≥ 1150 K 1.198× 10−2

θf < 1150 K 7.8× 10−9

λ (K)θf ≥ 1150 K 2.195× 104

θf < 1150 K 5.302× 103

makes variable value transfer from chip formation step ef-fortless.

The initial temperature value of the nodes in the high-lighted part is read from the last frame of the steady-statechip formation analysis step. The initial temperature value ofthe other nodes is set to room temperature. At the nodes onthe tool/chip interface, heat flux is defined, and their valuecomes from the chip formation analysis step. In addition, thetool makes heat transfer with the environment through rakeface and flank face. The nodes on bottom face and hole sur-face always keep room temperature because of their contactwith the tool holder and the screw.

When maximum temperature change of 10 K is selectedas steady-state criterion, steady state is reached in the wholetool in 2.2 s.Fig. 10shows the development of temperaturewith time at four nodes in the tool, which are selected atrandom.

In Fig. 11(a), at the beginning of heat transfer analysisthe high temperature region concentrates in a small area nearthe cutting edge, and after 2.2 s this region extends to nearlyone-third of the tool as shown inFig. 11(b).

The temperature of nodes on rake and flank face at the lastframe is read for tool wear calculation.

2.3. Wear calculation

2rbon

s esivew ear,

analys

Fig. 9. Geometry and mesh of the tool in heat transfer

.3.1. Wear rate calculationWhen tungsten carbide tools are used to machine ca

teels, crater wear on rake face is mainly caused by adhear. According to M.C. Shaw’s equation of adhesive w

is, the circled part is the part of the edge engaged in the cutting.

L.-J. Xie et al. / Wear 258 (2005) 1479–1490 1485

Fig. 10. Temperature history of nodes in the tool. (a) Position of the nodes. (b) Temperature history.

Fig. 11. Temperature field (Kelvin) change of the tool in heat transfer analysis. (a)t= 0 s. (b)t= 2.2 s.

Usui et al. deduced the characteristic equation of tool wear[1], given by

w = Cvsσfexp

(−λ

θf

)(2)

where w is wear rate, i.e., the wear volume per unit areaand unit time;vs, the relative sliding velocity at tool/workinterface;σf , the normal stress;θf , the absolute temperature,Candλare constants determined for the combination of a tooland a work material. For the combination of carbon steel anduncoated carbide P20, the values for the constants are givenin Table 2. The latter study[11,12]shows that this equationis able to describe flank wear as well, which mainly resultsfrom abrasive wear.

From previous analyses, cutting temperature and contactpressure have been obtained for every tool face node. Sincethe relative sliding velocity of work material to tool face isoutput only at the position of work nodes, the value at everytool face node in contact has to be calculated according tothe relative position between the tool face node and its twoneighbouring work nodes, which are in contact with tool face.For the convenience of finding out relative position relationbetween work nodes and tool face nodes, the tool face nodesare ordered in counter-clockwise beforehand. At the tool facen tives

After all the cutting process variables are obtained, toolwear rate is calculated at every tool face node using Eq.(2).

2.3.2. Wear directionTool wear expression in geometry can be realized with

two approaches: element deletion and tool face node move-ment. The latter one is adopted in this paper. The move di-rection, i.e., wear direction, is calculated for every tool facenode.

Before calculating the wear direction, the dividing node(the circled node inFig. 12), i.e., the first tool face nodein counter-clockwise order, which has the minimumy-coordinate, is searched by the program (the coordinate ofthe dividing node for the new tool is saved as the edge posi-tion for the latter calculation of flank wear land width). Thisnode separates the tool face into two parts, the first part in-cluding the rake face and part of the round tool edge (namedas rake face part), the second part including the flank face andthe other part of the tool edge (named as flank face part). Inthese two parts, wear directions are calculated with differentmethods.

In the rake face part, wear direction in every tool facesegment is assumed to be perpendicular to the direction ofthe relative sliding velocity of work material and points intothe tool body, that is opposite to the unit normal vector. Everyt eard o the

ode, which loses contact with the work and the chip, relaliding velocity is set to zero.

ool face node is attached with two tool face segments. Wirection at the tool face node is defined to be opposite t

1486 L.-J. Xie et al. / Wear 258 (2005) 1479–1490

Fig. 12. Wear direction vectors (thick arrows) of tool face nodes.

resultant vector of unit normal vectors of the two attachedtool face segments.

In the flank face part, the relative sliding velocity is as-sumed to be in the cutting speed direction because of thenegligible elastic recovery of work material. Therefore, thewear direction at every node in this part is the same, pointedupwards.

Wear direction is calculated at every tool face node, andnormalized to unit vector�wdirection, as indicated with thickarrows inFig. 12.

2.3.3. Cutting time increment calculationCutting time increment means the duration of cutting time

between two successive tool wear measurement. If the toolwear is studied only with experimental methods, it is difficultto predict an approximate cutting time increment value for aspecified tool wear increment value, for example, flank wearland width incrementVB = 0.05 mm, whereas it is possibleby using numerical methods before the tool wear curve is ob-tained since the wear rate is already known from the previous

calculation. This paper uses a user-specified flank wear landwidth increment valueVB to calculate the time incrementvalue, when a flank wear land width increment is within therange of the specified valueVB ± permitted error.

Flank wear land width VB is calculated by a flank wearcalculation subroutineFlankwear(t, wearrate). VB is thedistance from the edge position (which has been saved forthe new tool) to the last moved tool face node. For example,node a is the last tool face node with non-zero wear rate, andin cutting time incrementt, it should move to point a1, thennode b and c will have smallery-values than point a1, whichproduces a bulge on flank face. This seldom takes place inpractice. Therefore, node b and c will move to point b1 andc1 in order to have the same y-value with point a1. VB iscalculated from edge position to node c, because it is the lastmoved tool face node.

The cutting time increment searching procedure is de-scribed byFig. 14. At the beginning, the aimed VB me-dian value VBm is calculated according to the user-specifiedVB increment value. For example, inFig. 13(b), the toolgets a flank wear land width of 0.05 mm from the previ-ous tool wear calculation cycle.VB = 0.05 mm is spec-ified by the user. Therefore, in this tool wear calcula-tion cycle, VBm is 0.1 mm. For saving searching time, theaimed VB value should be given a user-specified permit-t -m rr inF ue arts.D limit -t rr

2e by

E

w

ng proc proc

Fig. 13. Flank wear calculation and cutting time increment searchi

ed error range, the dotted range inFig. 13(b). The peritted error should be a positive value, denoted as eig. 14. In addition, an initial cutting time increment valt0 is given arbitrarily. Then the searching process sturing the searching process, the searching lowert1 and the searching upper limitt2 are changing un

il cutting time incrementt falls into the permitted erroange.

.3.4. Wear calculationWear value is calculated at every nodes on tool fac

q. (3):

� = w · t · �wdirection (3)

ess. (a) Flank wear calculation. (b) Cutting time increment searchingess.

L.-J. Xie et al. / Wear 258 (2005) 1479–1490 1487

Fig. 14. Flow chart of cutting time increment searching process.

where�w is the displacement vector of the tool face node dueto wear.

In addition, some nodes on flank face have to be movedin order to avoid forming bulge on flank face, as mentionedabove.

2.4. Tool geometry updating

In order to visualize the wear shape of the tool and preparetool geometry for the next tool wear calculation cycle, toolgeometry needs updating. This is performed through runningan explicit dynamic analysis job.

The displacement of every node, the circled node inFig. 15, on the rake and flank face is set equal to thewear vector�w as boundary conditions. The cutting tool isfixed at the bottom nodes, marked with small triangles inFig. 15.

In order to alleviate mesh distortion during tool geome-try updating, two steps are used and both employ adaptivemeshing method in the whole tool area. The first step pro-duces the tool wear on the tool. The second step smoothens

zigzags of the crater wear profile and coarsen the mesh nearthe cutting edge because very fine mesh in this area mayresult in negative element areas when tool geometry is up-dated further in the next calculation cycle due to additional

Fig. 15. Boundary conditions of tool updating model.

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Fig. 16. Changes of the mesh during tool updating steps (a) at the beginning of step 1, no tool geometry updating is carried out (b) at the end of step 1, nodeson tool face are moved according to the calculated wear, crater wear and flank wear are formed (c) at the end of step 2, zigzags of crater wear are smoothened.

Fig. 17. Tool wear profiles. (a)t= 0 s. (b)t= 5 s. (c)t= 46 s.

produced tool wear.Fig. 16shows the geometry and meshchange of part of the tool near tool edge between everystep.

3. Results and discussion

With this tool wear estimate program, tool wear underthe cutting condition described in introduction part is calcu-lated. Tool reshape criterion is 0.1 mm, andVB = 0.05 mmis specified by user, permitted error is set to 0.01 mm.The tool wear estimate process is accomplished with twocalculation cycles. After the first calculation cycle, thenew tool in Fig. 17(a) is updated to the worn tool inFig. 17(b). After the second calculation cycle, increasedcrater wear and flank wear can be found on the updated tool inFig. 17(c).

The solid line inFig. 18shows the wear progress curves offlank wear and crater wear obtained from experiment[13,14]under the same cutting condition. The dot lines are predictedtool wear curves. It is found that the estimated flank wearand crater wear are smaller than experimental ones. In ex-periment, after 20 s of cutting, the flank wear has exceeded

0.15 mm and crater wear 0.06 mm, but after 46 s, the es-timated flank wear just arrives at 0.1 mm and crater wear0.03 mm.

The discrepancy may be caused by:

(1) inconsistentness of material combination. Because thecharacteristic equation of tool wear and the tool weardata come from different literatures and researchers, itis unavoidable that difference exists in these tool andwork material’s chemical composition and structure. Itwas tested by Kitagawa and co-workers that the contentand size of abrasive particle dispersed in work materialand chemical composition of tool material could be cor-related with change in the constants of the wear char-acteristic equation both in higher and lower temperatureranges[11];

(2) the simplified friction model and coefficient. Coulomb’sfriction model is adopted and a constant frictional coeffi-cient 0.3 is used in the whole tool wear estimate process,which may simplify the contact at tool/work interface andcause a wide divergence in temperature, contact pressure,etc.;

(3) work material model. The constants in work materialmodel is developed for annealed mild carbon steel CK45.

L.-J. Xie et al. / Wear 258 (2005) 1479–1490 1489

Fig. 18. Comparison between estimated and experimental progress curves for tool wear. (a) Flank wear. (b) Crater wear.

But the work used in tool wear experiment is AISI1045.There may exist difference in chemical composition andheat treatment;

(4) poor mesh control at tool/chip interface. High density ofmesh is localized at the produced surface, which is oppo-site to flank face, and coarse mesh formed on the outsidesurface of chip with the chip growing. This causes thecontact ‘noise’, and at the same time makes some nodeson the tool face lose contact with the chip, which affectsthe cutting process variables, such as heat flux, tempera-ture, and contact pressure seriously and thus crater wear’scorrect profile. In addition, contact problem causes therelative greater error of the estimated tool wear in thesecond calculation cycle with the updated worn tool ge-ometry than that in the first calculation cycle with thenew tool.

4. Summary and conclusion

This paper makes an interesting study in integratingABAQUS/Explicit and ABAQUS/Standard with Pythonuser-program to perform the 2D tool wear estimate in or-thogonal cutting of turning operation. The main findings ofthis study are as follows:

( for-ol,on.and

g ofh,uous

( sis.dis-ced, a

pure heat transfer analysis in tool can reduce sharply thecalculation time for further realizing the thermal steadystate.

(3) Python user program launches chip formation and heattransfer analysis job automatically every time the cut-ting process variables at steady state are needed. Thendisplacement of every tool face node due to wear is calcu-lated mainly with three subroutines including wear ratesubroutine, cutting time increment calculation subrou-tine and wear calculation subroutine. Finally, tool ge-ometry is updated according to the calculated nodal dis-placements and one calculation cycle is finished. ThePython user program continues until tool reshape crite-rion is reached. The number of calculation cycles car-ried on before Python user program stop is defined bydividing tool reshape criterion by the specified wear in-crement. Because of the huge calculation time and costof chip formation analysis, a bigger wear increment ispreferred in order to reduce the calculation cycle num-ber, which certainly will bring bigger errors in estimatedresult. A trade-off value should be found.

(4) In order to improve the estimate result and realize toolwear estimate in quantity, more efforts should be madein several aspects: more reasonable frictional modelling,further mesh control and refinement at chip outside sur-

ula-ear,tionex-

R

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1) ABAQUS/Explicit can be used to analyse the chipmation of orthogonal cutting with blunted cutting towhen ALE technology is applied in chip separatiThrough the reasonable design of boundary typesALE mesh control parameters, the complete modellinchip formation from initial chip formation, chip growtto steady-state chip formation can be used in continchip formation analysis.

2) ABAQUS/Standard is effective in heat transfer analyThrough introducing the heat flux and temperaturetribution from the chip formation analysis’ result onmechanical steady state in chip formation is reache

face in chip formation analysis, consistency in simtion, experiment and characteristic equation of tool wfor example, development of wear characteristic equaand material model for the material used in tool wearperiment, etc.

eferences

[1] E. Usui, T. Shirakashi, T. Kitagawa, Analytical prediction of thdimensional cutting process, part 3: cutting temperature andwear of carbide tool, Trans. ASME J. Eng. Mater. Technol.(1978) 236–243.

1490 L.-J. Xie et al. / Wear 258 (2005) 1479–1490

[2] J. Monaghan, T. MacGinley, Modelling the orthogonal machiningprocess using coated carbide cutting tools, Comput. Mater. Sci. 16(1999) 275–284.

[3] Y.C. Yen, J. Sohner, H. Weule, J. Schmidt, T. Altan, Estimation oftool wear of carbide tool in orthogonal cutting using FEM simulation,in: Proceedings of the 5th CIRP International Workshop on Modelingof Machining Operations, 2002, pp. 149–160.

[4] ABAQUS Scripting Manual Version 6.2, HSK, Inc., U.S.A., 2001.[5] E.M. Trent, Metal Cutting, Butterworths, England, 1977.[6] J. Sohner, T. Altan, Material database for manufacturing simu-

lation (MADAMS): Summary of the Activities and Flow StressDatabase, ERC/NSM Report No. HPM/ERC/NSM-01-R-76, ERC forNet Shape Manufacturing, Ohio State University, 2001.

[7] V. Schulze, O. Vohringer, Influence of alloying elements on thestrain rate and temperature dependence of the flow stress of steels,Metall. Mater. Trans. A 31A (2000).

[8] ABAQUS/Explicit User’s Manual Version 6.2, HSK, Inc., U.S.A.,2001.

[9] J. Sohner, Beitrag zur Simulation zerspanungstechnologischerVorgang mit Hilfe der Finite-Element-Methode, Dissertation, Uni-versitat Karlsruhe (TH), 2003.

[10] ABAQUS/Standard User’s Manual Version 6.2, HSK, Inc., U.S.A.,2001.

[11] K. Maekawa, T. Kitagawa, T. Shirakashi, E. Usui, Analytical pre-diction of flank wear of carbide tools in turning plain carbon steels(part 2)-prediction of flank wear, Bull. Jpn. Soc. Prec. Eng. 23 (1989)126–133.

[12] T. Kitagawa, K. Maekawa, T. Shirakashi, E. Usui, Analytical pre-diction of flank wear of carbide tools in turning plain carbon steels(part 1)-characteristic equation of flank wear, Bull. Jpn. Soc. Prec.Eng. 22 (1988) 263–269.

[13] C. Schmidt, Development of a FEM-based Tool Wear Model toEstimate Tool Wear and Tool Life in Metal Cutting, Diplomarbeit,Universitat Karlsruhe (TH), 2002.

[14] P. Frank, Improvement of the FEM-based Predictive Model of ToolWear, Diplomarbeit, Universitat Karlsruhe (TH), 2002.