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The toolgeometry is incrementally updated in the FE chip formation simulation in order to capture thecontinuous evolution of wear profile as pressure, temperature and relative velocities adapt to thechange in geometry. Different friction and wear models have been analysed, as well as their impact onthe predicted wear profile assessed. Analyses have shown that a more advanced friction model thanCoulomb friction is necessary in order to get accurate wear predictions, by drastically improving theaccuracy in predicting velocity, thus having a dramatic impact on the simulated wear profile. Excellentexperimental agreement was achieved in wear simulation of cemented carbide tool machiningalloy 718.& 2008 Elsevier Ltd. All rights reserved.1. IntroductionNickel-based superalloys, used in the aerospace industry, areamong the most difficult materials to machine. These alloys aredesigned to retain their high strength at elevated temperatures,and machining thus involves forces that are considerably higherthan those found in the machining of steel. In addition, thecontact length is shorter, which gives rise to high stresses at thetoolchip interface 1. Work hardening, which can be as much as30 percent 2, is another problem encountered when machiningthese alloys, as it may lead to severe tool wear at the flank face.The low thermal conductivity of nickel alloys giving rise to hightemperatureisyetanotherproblem3,andtemperaturemeasurements 1 have shown that the temperature is higherthan for steel.The high stress at the toolchip interface, the work hardening,and the high temperature involved in the machining of nickelalloys all contribute to tool wear. It is therefore important tounderstand the wear process in order to predict wear rates andimprove tool life. In the past, experimentation has been the mainmethod used for investigating wear. However, continuous devel-opment of numerical methods such as the finite element method(FEM) together with more powerful computers enables simulationof complicated contact problems such as the cutting processes.FEM has proved to be an effective technique for analysing thechip formation process and predicting process variables such astemperatures, forces, stresses, etc. Therefore, the use of simula-tions has increased considerably over the past decade, andcoupled thermo-mechanical simulation of the chip formationprocess has been used by many researchers, such as MacGinleyand Monaghan 4, Yen et al. 5, Altan et al. 6, Hortig andSvendsen 7. Lately, simulations of the evolution of tool wearhave also been performed by implementing a wear rate equation,such as Usuis equation, in FE software. The method has been usedby Yen et al., Filice et al., and Xie et al. 810 for steel, calculatingthe wear rate from predicted cutting variables, and updating thegeometry by moving the nodes of the tool. Reasonably goodaccuracy was achieved, and the method can be regarded as state-of-the-art in modelling of machining.However,thisapproachforsimulationoftoolwearinmachining nickel-basedsuperalloys hasshown considerablediscrepancy between simulated and measured geometry, espe-cially in the region around the tool tip 11. Consequently, morework is required to enable accurate tool wear simulations. To dothis properly, it is necessary to simultaneously work withmodelling wear and friction at the toolchip interface, as thesephenomena are strongly related. According to Amonotons law thefrictional stress is proportional to normal stress. However, Childs12 states that frictional stress is limited when the normal stressis larger than the shear flow stress. This is the case in the regionaround the tool tip, where the real-contact area approaches thenominal contact area 12. Ozel 13 evaluated different frictionmodels and suggests that variable friction models should be usedin order to obtain more accurate results in FE simulations ofARTICLE IN PRESSContents lists available at ScienceDirectjournal homepage: Journal of Machine Tools & Manufacture0890-6955/$-see front matter & 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.ijmachtools.2008.03.001?Corresponding author. Tel.: +46706513447; fax: +46520223099.E-mail addresses: john.lorentzonhv.se, (J. Lorentzon).International Journal of Machine Tools & Manufacture 48 (2008) 10721080machining. This has not been considered in previous tool wearsimulations, where the friction has been described with constantfriction coefficient over the toolchip interface by the shear model8,9, or by Coulomb friction 10,11.1.1. ObjectiveThe overall objective of this work is to develop a finite elementtool wear model that can predict the worn geometry quantita-tively in cemented carbide tool machining nickel-based alloys. Toachieve this, different wear and friction models impact onparameters affecting the wear process, such as temperature andrelative velocity, have been investigated and used for predictingthe worn tool geometry. Specifically, the details analysed here aredivided into wear and friction (described in more detail inSections 2.1.4 and 2.2):1.1.1. WearW1. Usuis empirical wear rate model 1416, which is afunction of contact pressure, relative velocity and absolutetemperature;W2. For Usuis model, a second set of parameters giving adifferent temperature dependency is also investigated;W3. Takayama and Muratas 17 wear rate model, including afunctional dependence of absolute temperature;W4. Modified Usui wear rate model, by adding an exponent onthe relative velocity;W5. Vibration-adjusted Usui model, where a constant term isadded to the relative velocity to account for vibrations, whichare not included in the chip formation model.1.1.2. FrictionF1. Coulomb friction model, which states that the friction forceis proportional to the contact pressure;F2. Shear friction model, which states that the friction force is afraction of the equivalent stress;F3.Coulombfrictionmodelwithtwodifferentfrictioncoefficients, a reduced one around the tool tip and at adistance up on the rake face.2. Tool wear modelThe tool wear model consists of a FE chip formation model anda wear model implemented as subroutines to calculate the wearrate at contact points, modifying the tool geometry accordingly.2.1. Chip formation modelThe FE chip formation model was created using the commer-cial software MSC. Marc, which uses an updated Lagrangeformulation. This means that the material is attached to themesh, with periodic remeshing to avoid element distortion. Thecutting process requires a coupled thermo-mechanical analysis,because mechanical work is converted into heat, causing thermalstrains and influencing the material properties. Two types ofthermal assumptions are commonly used for simulation ofmechanical cutting, namely adiabatic heating and fully coupledthermalmechanical calculations. In this work a coupled, stag-gered, model has been used. This means that for each timeincrement the heat transfer analysis is made first, followed by thestress analysis. The time increment was set to 1.5ms in allanalyses. Quasi-static analyses were used, which means that theheat analysis is transient, while the mechanical analysis is staticwith inertial forces neglected.2.1.1. DimensionsThe dimensions of the workpiece used in the simulation modelare 5mm length by 0.5mm height, and the tool used in thesimulation model is 2mm long and 2mm high, see Fig. 1. Thecutting-edgeradiuswassetto16mminagreementwithmeasurement (see Fig. 1), the clearance angle 61 and the rakeangle 01; the feed was 0.1mm and the cutting speed was 0.75m/s.2.1.2. MeshThe meshed workpiece can be seen in Fig. 1. The remeshingtechnique used was the advancing front quad. This meshgenerator starts by creating elements along the boundary of thegiven outline boundary and mesh creation continues inward untilthe entire region has been meshed. The number of elements usedwas about 6000, with the minimum element size set at 2mm. Asseen in Fig. 2a, finer mesh was used where the material separatesaround the tool tip. The tool was meshed with approximately5000 elements, with minimum element size being 2mm.2.1.3. Material propertiesGenerally, the strain magnitude, the strain rate, and thetemperature each have a strong influence on the material flowstress. Thus, it is necessary to capture these dependencies in thematerial model used, in order to correctly predict the chipformation. Here, neglecting a slight (about 10% between 1/s andARTICLE IN PRESSFig. 1. (a) Dimension of the chip formation model, scaled in mm. The start of therake face is marked, as it will serve as a reference point in the wear profiles. (b) Themeasured cutting-edge shape, with the radius indicated; the measurementmethod is presented in Section 4.2.J. Lorentzon, N. Ja rvstra t / International Journal of Machine Tools & Manufacture 48 (2008) 107210801073104/s at room temperature according to 18 and nearly zerobetween 102/s and 105/s at 3001C according to 19) strain ratedependency, a rate-independent piecewise linear plasticity modelwas used. Instead, the flow stress curve after 18 for high strainrate (104/s) was used, see Fig. 2. The temperature trend of the flowstress is taken from 20. The other work-piece material properties21 used can be seen in Fig. 3.The material properties of the uncoated cemented carbide toolwere considered independent of temperature, and are listed inTable 1.2.1.4. Friction at the toolchip interfaceIn this work, three different friction descriptions have beenused. In each case the friction coefficient was calibrated tocorrelate within 5% on the simulated and measured feed force.The feed force is the sum of the ploughing force and the frictionforce. However, in our case the cutting edge radius is smallcompared to the feed rate (see Fig. 1), limiting the ploughingeffect, and consequently friction provides a considerable part ofthe feed force. The models used are:F1: The Coulomb friction model states that the friction force isproportional to the contact pressure through a friction coefficient,m, Eq. (1). The friction coefficient, m, was set to 1.0:st ?msn(1)F2: A shear friction model, which states that the friction force isa fraction of the equivalent stress, Eq. (2). The friction coefficient,m, was set to 1.1:sfr mseqvffiffiffi3p(2)F3: The Coulomb friction model as for F1, but here with twodifferent friction coefficients, m, over the toolchip interface. Aroundthe tool tip and at a distance up on the rake face, where the contactpressure is extremely high (above 1000MPa), the friction coefficientis set to 0.75. Elsewhere the friction coefficient is set to 1.1.A principle sketch of this is seen in Fig. 4. The model is a simplifiedrepresentation of the physical behaviour observed by Zorev 23,that there is a cap on the friction stress at high normal stress.2.1.5. Heat generationIn the machining process heat is generated by friction andplastic deformation. The rate of specific volumetric flux due toplastic work is given by_q f_Wpr(3)Here,_Wpis the rate of plastic work, r is the density and f is thefraction of plastic work converted into heat, which is set to 1.Strictly speaking, this is not correct since some plastic work isstored in the material, but the relative fraction stored is unknown,and since the deformations are so large the fraction of plasticwork stored is neglected. The rate of heat generated due to frictionis given by_Q Ffrvr(4)Here, Ffris the friction force and vris the relative slidingvelocity. The heat generated due to friction is equally distributedARTICLE IN PRESSFig. 2. Flow stress curves (curve at room temp from 18 and thermal softeningfrom 20).Fig. 3. Youngs modulus, E, specific heat, Cp, thermal conductivity, K, and thermalexpansion, a, from 21.Table 1Tool material properties for the cemented carbides 4,5,22Density (Kg/m3)11,900 4Youngs modulus (GPa)630 22Poissons ratio0.26 5Yield limit (MPa)4250 22Thermal expansion5.4?10?65Specific heat (J/KgK)334 4Thermal conductivity (W/mK)100 22Fig. 4. Pressure along toolchip interface, with regions for the different frictioncoefficients marked.J. Lorentzon, N. Ja rvstra t / International Journal of Machine Tools & Manufacture 48 (2008) 107210801074into the two contact bodies. This heat is transferred from theworkpiece, due to convection to the environment and conductionto the tool. Radiation has been neglected. The heat transfercoefficient at the contact between the tool and the workpiecewas set to 1000kW/m2K, which according to Filice et al. 24permits a satisfactory agreement between numerical data andthe experimental evidence, although it should be noted thatthis was utilised for another material combination. The tempera-ture at the outer boundaries of the tool was fixed at roomtemperature.2.2. Wear modelThere are few wear rate models for cutting available inliterature. Two of the more important have been used in thiswork, and a further two modified versions of one have beentested:W1: Usuis 1416 empirical wear rate model Eq. (5) modelsthe wear rate as a function of contact pressure, o0n, relativevelocity, vreland absolute temperature, T:dwdt Asnvrele?B=T(5)W2: A different parameter set was also tested in order toinvestigate the impact of the temperature dependency.W3: Takeyama and Muratas 17 wear rate model Eq. (6) isable to account for diffusion wear dominating at higher tempera-ture. The model is a function of the absolute temperature, T, andthe constants are D, which is a material constant, E, the activationenergy and R (8.314kJ/molK), Boltzmanns constant:dwdt De?E=RT(6)W4: Modified Usui wear rate model by adding an exponent onthe relative velocity Eq. (4):dwdt A0snv0:5rele?B=T(7)W5: Vibration-adjusted Usuis wear rate equation Eq. (4); aconstant term is added to the relative velocity to account forvibrations not included in the chip formation model:dwdt A00snvrel 10e?B=T(8)2.2.1. Wear model constantsConstants for Usuis model (W1) were determined by Lor-entzon and Ja rvstra t 11 by calibrating machining simulationswith measured wear rates: First, tool wear machining tests for theselected material were performed; then FE simulations weremade under the same conditions; and finally the constants of thewear rate model were calculated by regression analysis, giving theconstants B 8900 and A 1.82?10?12. This value of the Bparameter is also used here, although the friction coefficient in thechip formation model differs because it is now calibrated withrespect to feed force. For this reason, the A parameter wasadjusted to give the same crater depth as in the experiments. Thesame methodology was used to calibrate A, D, A0and A00for thewear models W1, W2, W3, W4 and W5. The calibrated parametersare presented in Tables 2 and 3. The activation energy in W3Eq. (6), E, was set to 75.35kJ/mol 25.3. Analysis stepsIn a turning operation, a stationary condition with respect totemperature and forces will generally be reached almost im-mediately after the tool has penetrated the workpiece andsubsequently the initial transient of the chip formation has beenneglected in predictions of the tool wear progress. Instead, toolwear predictions are made on stationary chip formation condi-tions, and the first step in tool wear predictions is therefore tocalculate the stationary chip condition. Finally, the wear model isactivated in the chip formation analysis and the progress of toolwear is calculated.3.1. Chip formationIn order to reach stationary conditions in FE chip formationsimulations using the Lagrangian method, the entire object, onwhich chip formation simulation is to be performed, must bepresent and meshed from the beginning of the simulation.Consequentially a transient analysis for reaching steady-stateconditions would be computationally prohibitive 26. Fortu-nately, by lowering the thermal capacity of the tool, it is possibleto reach equilibrium faster; in our case this was obtained afterabout 1500 increments, see Fig. 5.The reason for this is that lowering the thermal capacity hasthe same effect as taking proportionally longer time increments inthe thermal calculations compared to the mechanical increment,as can be seen in Eq. (5). Note that the left-hand side vanishesat steady state, while an increased Cpincreases the rate ofchange and correspondingly accelerates, reaching the steady-statecondition:rCpqTqt kq2Tqx2q2Tqy2q2Tqz2 !(9)Here, T is the temperature, k is the thermal conductivity, r is thedensity, and Cpis the thermal capacity.3.2. Tool wearThe tool wear model consists of a FE chip formation model anda wear model implemented as subroutines calculating the wearrate at contact points, modifying the tool geometry accordingly.The wear rate is calculated using Usuis empirical wear model forevery node of the tool in contact with the base material. In orderARTICLE IN PRESSTable 2Wear model parameters for friction model F1W1W2W3W4W5A 1.25?10?12A 5.48?10?15D 1.02?10?9A0 5.42?10?13A00 1.08?10?15B 8900B 2000E 75350B 8900B 8900Table 3Wear model parameters for W1 for the different friction modelsF1 (Coulomb)F2 (Shear)F3 (Adjusted)W1A 1.25?10?12A 1.52?10?12A 1.08?10?12B 8900B 8900B 8900J. Lorentzon, N. Ja rvstra t / International Journal of Machine Tools & Manufacture 48 (2008) 107210801075to do this, the temperature, relative velocity, and contact stress arecalculated in the FE chip formation simulation for all nodes of thetool in contact with the workpiece. The calculated values are thenemployed by a user subroutine to calculate the wear rate, seeFig. 6. Based on the calculated wear rate, the geometry of the toolis then updated by moving specific nodes of the tool in the FE chipformation simulation, see 5 for a more comprehensive descrip-tion. The direction a node is moved is based on the direction of thecontact pressure at that node. After moving the node, allintegration point data are mapped to the new integration pointpositions and the chip formation simulation continues, with thetoolpenetratingthroughtheworkmaterial.Updatingthegeometry distorts the elements of the tool. To avoid this, the toolmesh is automatically remeshed using the advancing front quadremeshing technique, at a prescribed frequency.The wear calculations are started at increment 1800, see Fig. 5,with the tool at steady state with respect to both force andtemperature. The wear calculation is subdivided into about 1200increments, each with tool geometry updating. Using fewerincrements would cause convergence problems and numericalerrors; using more increments, however, would unnecessarilyincrease the computation time. The wear calculation correspondsto approximately 15s of dry machining, resulting in about 65mmflank wear land and about 5.3mm deep crater at rake face. Hence,the wear process is accelerated by about 10,000 times in thesimulation model.4. ExperimentsTurning experiments were conducted for calibration of frictionand wear parameters and for comparison of the simulated andmeasured wear profiles.4.1. Experimental conditionsThe turning experiments were carried out in a CNC lathe underdry cutting conditions. One cutting speed, vc, 45m/min and onefeed rate, f, 0.1mm/rev were evaluated. The turning lengthmachined during each experiment was 12mm. The experimentwas conducted with 3 replicates. The workpiece was a bar of agedand forged Inconel 718 that was predrilled at its end face toachieve pipe geometry in order to accomplish near