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    (热与质量转化学报)一个三维模型去预测磨削和磨削硬化期间表层热冶金的影响.pdf

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    (热与质量转化学报)一个三维模型去预测磨削和磨削硬化期间表层热冶金的影响.pdf

    predict the thermo-metallurgical effectsandAvailable online 27 October 2012KeywordsTriangular heat source modelTemperature fieldinputBecause of the used simplifications, for example two-dimensionality, existing approaches to calculatecallyhigh energyAn innovative approach to use the heat generated within thecontact zone area is the grind-hardening process. The target-oriented heat input enables a short time austenitization withinthe surface layer of the machined workpiece [7]. Subsequently,self-quenching effects [8] and the usage of coolant lead to a mar-tensitic surface layer hardening [9–11]. The examination anddevelopment of different process variants, such as straight surface2. State of the artMost of the analytical calculations of the temperature fieldwithin the workpiece during grinding, such as Outwater and Shaw[24] and Hahn [25], are based upon the approach of Carslaw andJaeger [26,27], which describes the effect of a heat source with aconstant heat flux density moving along an adiabatic surface of asemi-infinite solid with a constant velocity. Thereby, the heatsource is assumed as infinitely extensive perpendicular to thedirection of motion leading to a steady-state two-dimensionaltemperature field within the solid. The approach is extended by⇑Corresponding author. Tel. 49 89 289 15534; fax 49 89 289 15555.International Journal of Heat and Mass Transfer 56 2013 223–237Contents lists available atHeatE-mail address tobias.foeckereriwb.tum.de T. Foeckerer.the material. This can be explained by the process-specific effectsof friction, shearing, deformation and separation due to the inter-action of the abrasive grains and the workpiece within the contactzone area [1–3]. Approximately, all of the used energy dissipates asheat leading to high temperatures within the surface layer of theworkpiece, which can damage the structure of the processed sur-face. Thermal damages, such as burning, softening, cracks, reducedfatigue strength and distortion due to residual tensile stresses[4,5], reduce the quality of the machined workpiece and limit theachievable material removal rates [6].thermal damage of the workpiece during grinding and the controlof the metallurgical phase transformation during grind-hardeningrequire the knowledge of the transient temperature field withinthe workpiece as well as the resulting thermo-metallurgical ef-fects. This paper presents a method, which allows for the predic-tion of the three-dimensional thermo-metallurgical effects withinthe surface layer during grinding and grind-hardening using ana-lytical models.Wet grindingSurface layer hardeningHardened layer thickness1. IntroductionMachining processes with geometriedges, such as grinding, require a0017-9310/ - see front matter C211 2012 Elsevier Ltd. Allhttp//dx.doi.org/10.1016/j.ijheatmasstransfer.2012.09.029the temperature fields during wet grinding cannot be successfully utilized to predict the phase transfor-mations and the resulting hardened surface layer due to grind-hardening.This paper presents an analytical model, which enables to calculate a three-dimensional temperaturefield due to grinding and grind-hardening using a triangular heat source and considering the effect of thegrinding fluid. Based on the transient temperature distribution, the phase transformation within the sur-face layer and the resulting hardened layer thickness are determined also using analytical models. Theanalytical method is validated and analyzed comparing the results with measured ones and with thosecalculated using the finite element analysis. Thereby, the presented approach allows for the efficient pre-diction of the thermo-metallurgical effects within the surface layer during grinding and grind-hardening.C211 2012 Elsevier Ltd. All rights reserved.undefined cuttinginput to removegrind-hardening [7,12,13] and cylindrical grind-hardening [14–16], coolant setups [17,18,12,19] and machined materials [20–23] have been subjects of several previous investigations.This previous research illustrates, that both the avoidance of2012Accepted 17 September 2012softening for instance. An approach to use the heat generated during grinding is the grind-hardening pro-cess, which allows for the process-integrated martensitic surface layer hardening of the workpiece.A three-dimensional analytical model towithin the surface layer during grindingT. Foeckerer⇑, M.F. Zaeh, O.B. ZhangInstitute for Machine Tools and Industrial Management iwb, Technische Universitaet Muenchenarticle infoArticle historyReceived 10 February 2012Received in revised form 17 SeptemberabstractThe high amount of energyedges, such as grinding, requiressurface to avoid thermal damaInternational Journal ofjournal homepage www.elserights reserved.grind-hardeningTUM, Boltzmannstr. 15, 85748 Garching, Germanyduring machining processes with geometrically undefined cuttingthe knowledge of the transient temperature field within the machinedges of the workpiece due to thermal-induced residual tensile stresses orSciVerse ScienceDirectand Mass Transfervier.com/locate/ijhmt_Q heat flux represented by the heat source, W_Qchheat flux to the chips, W_Qfheat flux to the grinding fluid, W_Qsheat flux to the grinding wheel, W_Qtotaltotal heat flux, WQwmaterial removal rate, mm3sC01_Qwheat flux to the workpiece, Wt time, st0time when the heat source acts, sT temperature, K or C176C_T;_T1;_T2heating rates, K sC01or C176CsC01T1ambient temperature, K or C176CTchchip temperature, K or C176CTsurfacesurface temperature, K or C176Cvccutting speed, m sC01vfttangential feed rate, mm sC01Heat and Mass Transfer 56 2013 223–237DesRuisseaux and Zerkle [28,29] taking the effect of the surfaceNomenclaturea thermal diffusivity, mm2sC01aedepth of cut, mmbswidth of cut or heat source width, mmB dimensionless heat source width, –c specific heat capacity, J kgC01KC01dsgrinding wheel diameter, mmechspecific inner energy of the chips, J mmC03Fttangential grinding force, Nh heat transfer coefficient, W mmC02KC01H dimensionless heat transfer coefficient, –Hmhardness of martensite, HVHphardness of perlite, HVHrahardness of retained austenite, HVHtotaltotal hardness, HVk thermal conductivity, W mmC01KC01lgcontact length or heat source length, mmL dimensionless heat source length, –Paproportion of austenite, –Pcgrinding power, WPeqproportion at phase equilibrium, –Pmproportion of martensite, –Ppproportion of perlite, –Praproportion of retained austenite, –_q0averaged heat flux density, W mmC02_qx0 triangular heat flux density, W mmC02Q heat quantity, J224 T. Foeckerer et al./International Journal ofcooling due to the usage of grinding fluid into account. To avoidthe integration required to solve the approach of Carslaw andJaeger [26,27], [30] presents a one-dimensional approximationmodel to calculate the maximum temperatures within the contactzone and the workpiece neglecting coolant effects.Liao et al. [31] and Maksoud [32] developed analytical modelsdescribing wet grinding processes to calculate the temperaturesbased on the generated heat due to the interaction of grain, work-piece, chips and coolant. Liao et al. [31] present a two-dimensionalmodel to predict the surface temperatures within the contact zonearea considering the thermal effects within the shear plane and thegrain workpiece interface as well as the grinding fluid. Maksoud[32] describes the thermal effects of creep-feed grinding usingmoving heat sources to model the heat generation at the contactof the grains with the machined material. Therefore, the effectsof energy partition as well as film and nucleate boiling of the cool-ant are taken into account.As shown by Snoeys et al. [4] for grinding as well as by Zaehet al. [12] for grind-hardening, the best approximation of the heatflux density along the contact zone can be accomplished using atriangular heat distribution considering that the largest contactload occurs within the area of the maximum chip thickness. Jinand Cai [33], Jin et al. [34], Rowe [3] and Rowe and Jin [35]extended the basic approach of Carslaw and Jaeger [26,27] usinga triangular heat source. Regarding the contact ratio between thegrinding wheel and the workpiece during high efficiency deepgrinding, the triangular heat source is thereby moving on an in-clined workpiece surface.The mostly used two-dimensional models neglect the heat con-duction perpendicular to the direction of motion. Analytical mod-els with square heat sources [36] and with rectangular heatsources [37] enable to calculate a three-dimensional temperaturefield beneath the contact zone area. Both approaches are basedon a constant heat flux density neglecting coolant effects.Amongst others, the analytical calculations of the temperaturex,y,z cartesian coordinates, mmX,Y,Z dimensionless cartesian coordinates, –x0,y0cartesian coordinates of the heat source, mmz transformed cartesian coordinate, mmq density, kg mmC03s delay time, ss dimensionless time, –p mathematical constant1 sign for infinityfields due to the grinding processes can be used to predict thermaldamages within the machined surface layer [4–6]. Fricker et al.[38] utilize the approach of Carslaw and Jaeger [26,27] to estimatea parameter window concerning the grind-hardening process.3. Analytical model3.1. BasicsThe three-dimensional analytical approach, presented withinthis paper, allows for the calculation of temperatures duringstraight surface grinding and grind-hardening of rectangularFig. 1. Definition of the three-dimensional thermal model with a triangular heatsource and a moving semi-infinite solid.Heatworkpieces. Thereby, the workpiece is machined by a grindingwheel, which moves with a constant tangential feed rate vftandthe depth of cut aeover the workpiece surface. Using the Euler ap-proach within the analytical model, the workpiece, represented asa semi-infinite solid, moves with the negative tangential feed ratevftbeneath a fixed heat source. The heat input within the contactzone area is approximated using a heat source with a triangulardistribution Fig. 1. Defined by the geometrical contact conditionsbetween the workpiece and the grinding wheel, the width of theheat source is equal to the grinding wheel width bsand for thelength the contact length lgis used, which can be calculated usingthe grinding wheel diameter dsand the depth of cut aelgffiffiffiffiffiffiffiffiffidsaep1Due to the assumption of moderate depths of cut ae, the inclinationof the contact zone area is neglected within the analytical model.The utilized grinding wheel has a diameter of 400 mm and a widthof 10 mm. Furthermore, the following analyses were done using thematerial data of the soft-annealed bearing steel 100Cr6 AISI52100. The material properties are homogeneous, isotropic, tem-perature-independent and phase-independent. All analytical mod-els, described in the following, are implemented using thesoftware tool MATLAB of MathWorks.3.2. Heat distribution during grindingTo calculate the temperature field using an analytical model,the heat flux into the workpiece, represented by the heat source,must be known. Assuming that all of the used energy is dissipatedas heat, the total heat flux within the contact zone area can be cal-culated by_Qtotal Pc Ftvc2where Ftis the tangential grinding force and vcis the cutting speed,which is kept constant at the value of 35 m/s within this paper. Theinfluence of the tangential feed rate vftcan be neglected due to thetypical small values compared to the cutting speeds. The total heatflux partitions into heat fluxes to the workpiece_Qw, the grindingwheel_Qs, the grinding fluid_Qfand the chips_Qch[39,3] and there-with can be expressed as_Qtotal_Qw_Qs_Qf_Qch3Based on the analysis of Stephenson and Jin [40] and due to theusage of a vitrified bonded grinding wheel with corundum abrasivegrains at moderate depth of cuts, the heat flux to the grinding wheelcan be assumed to be 10 of the total heat flux. The heat flux to thechips can be calculated by the multiplication of the specific innerenergy of the chips echand the material removal rate Qw[3]_Qch echQw qcTchbsaevft4where q is the density and c is the specific heat capacity of the ma-chined material. In terms of the presented method, the temperatureof the removed chips Tchis defined as the average surface tempera-ture of the contact zone area and calculated iteratively using bothEqs. 4 and 16.As the influence of heat flux to the grinding fluid is consideredby the analytical model, the heat flux_Q, represented by the heatsource, can be expressed by_Q _Qw_Qf_QtotalC0_QsC0_Qch 09FtvcC0qcTchbsaevft5Regarding the heat flux_Q calculated using Eq. 5, the heat flux den-sity of the triangular heat source model Fig. 1 is described byT. Foeckerer et al./International Journal of_qx0_q012lgx0C18C19_Qlgbs1 2lgx0C18C196where_q0is the averaged heat flux density and x0is the x-coordinatedescribing the heat source condition along the contact length.Thereby, the center of gravity of the contact zone area is definedas the point of origin.3.3. Three-dimensional temperature distributionIn consideration of the basic conditions defined in Section 3.1,the nonsteady-state three-dimensional heat conduction in a mov-ing solid is specified by the differential equationk2Tx22Ty22Tz2 qcTtC0vftTxC18C197in which T Tx,y,z,t describes the temperature field depending onthe cartesian coordinates x, y, z and the time t. k is the thermal con-ductivity of the solid material. The generation of latent heat is notconsidered.The initial conditions are set asTx;y;z;tjt0 T1 0C14C 8Regarding a semi-infinite solid with a diabatic surface and a trian-gular heat source Fig. 1, two boundary conditions are definedC0kTzC12C12C12C12z0;jxjlg2;jyjbs2C0hTjz0C0 T19outside of the heat source area andC0kTzC12C12C12C12z0;jxj6lg2;jyj6bs2_qx0C0hTjz0C0 T110inside of the heat source area.Based on the work of DesRuisseaux and Zerkle [28,29], the solu-tion of the differential equation Eq. 7 for an instantaneous pointheat source considering the diabatic surface of the semi-infinitesolid is determined byTx;y;z;x0;y0;t;t0aQk24patC0t0C13832eC0xC0x0vfttC0t0C1382yC0y02z24atC0t0C0h4paktC0t0erfcz2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiatC0t0p hkffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiatC0t0qC1ezhkatC0t0hk2eC0xC0x0vfttC0t0C1382yC0y024atC0t011where a kqcis the thermal diffusivity. Eq. 11 allows for the calcu-lation of the temperature of a point Px,y,z at a time t due to apunctual heat input Q at a point Px0,y0 and a time t0. For a pointheat source with the heat flux density_qx0 featuring differentialdimensions and acting in a differential time step, the heat quantitycan be calculated asQ _qx0dx0dy0dt012Inserting Eq. 12 into Eq. 11 leads to a differential temperaturechangedTx;y;z;x0;y0;t;t0a_qx0k24pat C0 t0C13832eC0xC0x0vfttC0t0C1382yC0y02z24atC0t0C0h4pakt C0 t0erfcz2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiat C0 t0p hkffiffiffi

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