# Identification of heat partition in grinding related to process parameters, using the inverse heat flux conduction model.pdf

condaDpt. Mechanical Engineering, UPV/EHU, Almeda de UrkijobTEMPO EA 4542 Laboratory, UVHC, Carnot Arts Institute,partitiobaseis useded to grindmeasurement:Accepted 21 January 2014Available online 6 February 2014products. The study of thermal damage requires understanding the mechanisms of heat partition be-which strengthens the validity of the results.All rights reserved.dustries (aerospace, energy, tooling.) in terms of tight dimen-sional tolerances and smooth surface roughness. By contrast,grinding is also characterized by requiring a high amount of energyinput per unit volume of material removed. This energy is turnedve heating of the[1]. Thus, thethe limiting con-Increasing material removal rate is limited by the apparition ofworkpiece burn. The classic solution for burning problems is theuse of cooling ﬂuids but their effect is limited. Hence researches tryto improve cooling effect by refrigerating the coolant [2] orimproving their convective effect [3]. However, these advances arenot enough for avoiding burning in some cases. Therefore, under-standing the mechanisms that govern workpiece temperature in-creaseandrelatingthemtoindustrialprocessparametersbecomeakey factor for grinding process control and optimization.* Corresponding author. Tel.: þ34 94 601 73 47.E-mail addresses: eduardojose.garcia@ehu.es, edugarcia.g@gmail.comContents lists availableApplied ThermalApplied Thermal Engineering 66 (2014) 122e130(E. García).C211 2014 Elsevier Ltd.1. IntroductionGrinding is an abrasive machining process characterized byproducing high quality components for high added-value in-into heat in the contact zone and can cause excessiworkpiece leading to thermal damage on its surfaceoccurrence of thermal damage becomes one ofstraints of productivity in grinding technology.Speciﬁc energyCutting mechanismstime-dependant Rwdeﬁnition which had not been previously proposed in literature, and they haveallowed as well relating variations in Rwvalues to physical removing mechanisms of grinding. Resultshave been validated by means of an indirect parameter: workpiece hardness variation during the tests,Keywords:GrindingThermalHeat partition to the workpieceInverse methodtween wheel and workpiece. In this work and original methodology and experimental set-up for thestudy the inﬂuence of grinding variables on the heat partition tothe workpiece, Rw, is presented. The newmethodology avoids errors related to the steep thermal gradients typical of grinding operations. Inaddition, uncertainty related to the actual area of contact is suppressed thanks to a rigid and controlledexperimental conﬁguration. An inverse model based on LevenbergeMarquardt algorithm and a ﬁniteelement model has been used for heat partition to the workpiece identiﬁcation. Results have lead to ahighlightsC15 A methodology for obtaining the heatC15 The methodology used inverse calculationC15 An alternative experimental approachC15 A time-dependant heat partition relatC15 Results validated by means of indirectarticle infoArticle history:Received 9 October 2013http://dx.doi.org/10.1016/j.applthermaleng.2014.01.041359-4311/C211 2014 Elsevier Ltd. All rights reserved.s/n, 48013 Bilbao, Spain59300 Valenciennes, Francen to workpiece in grinding is proposed.d on LevenbergeMarquardt algorithm.to reduce uncertainties.ing chip thickness has been found.workpiece hardness evolution.abstractGrinding is an abrasive machining process characterized by producing high quality components for highadded-value industries. Thermal damage is an undesired phenomenon that may ruin nearly ﬁnishedJose Antonio SánchezaEduardo Garcíaa,*, Damien Méresseb, Iñigo Pomboa, Souad Harmandb,Identiﬁcation of heat partition in grindingparameters, using the inverse heat ﬂuxjournal homepage: www.elsevi8related to processuction modelat ScienceDirectEngineeringer.com/locate/apthermengEngineeringIt is assumed that the power consumed by the grinding wheelspindle is transformed into heat in the contact zone. This heat isevacuated through four ways: workpiece, wheel, ground chips andcooling ﬂuid. The partition of this heat that goes into the work-piece, Rw, is the cause of workpiece temperature increase andthermal damage [4]. Therefore its determination is very importantfor process optimization. However, it is a parameter difﬁcult toassess since it depends on a large number of parameters: tribo-logical, mechanical and geometrical. In fact, on shallow grindingwith Al2O3wheels scientiﬁc literature give values between 0.25and 0.85.Usually, authors have identiﬁed Rwby matching temperaturedata experimentally obtained with calculated temperature fromtheoretical models. One of the main limitations of this methodol-ogy, and one of the causes of thewide dispersion of Rwabove, is thesteepthermal gradients found in the contact zone (upto 10,000 K/s[5]), that limit the reliability of the measured temperatures.Nomenclatureaedepth of cut, mmAccontact area, m2A1attempt frequency, sC01b workpiece thickness, mmh convective heat transfer coefﬁcient, W/m2Kheqequivalent chip thickness, mmh1reaction constant (Arrhenius law), W/m2kgH ﬁnal material hardness, HVH1hardness of the fully-tempered material, HVH3hardness fully quenched material, HVlccontact length, mmP grinding power, WQ0wspeciﬁc material removal rate, mm3/mm sqchheat ﬂux to the chips, W/mm3qﬂheat ﬂux to the ﬂuid, W/mm3qttotal heat ﬂux generated, W/mm3E. García et al. / Applied ThermalFor obtaining the theoretical temperature modelization of theprocess is necessary. Initially, the grinding wheel heating wasmodeled as a rectangular moving heat source along a semi-inﬁnitebody [5]. Analytical models focused their efforts in simulating heatgeneration. This way [7] found that a triangular distribution of theheat source gave as a result temperature distributions closer to thereality. The model developed in Ref. [8] agreed with this conclusionand added that while for shallow grinding heat generation can bemodeled by a band heat source that slides in a plain, in deepgrindinganinclinedsourceisnecessary.InRef.[9]anexactsolutionfor an analytical model accounting for heat generation at shearplanes, coupled with the heat transfer at wear ﬂats is developed.This model is used to assess the inﬂuence of the heat generation(shear planes or wear ﬂats) in the process. Analytical models wereprogressivelyreplacedbynumericalmodelswiththerapidincreaseof calculation power. As it is gathered in Refs. [10], numericalmodels are used following similar approaches: workpiece dis-cretization, effect of grinding wheel as a moving heat source andconsideration of the convective effect of cooling ﬂuid; but differ infour main aspects: geometry of heat source (rectangular vs trian-gular), contact length estimation, material properties (constant ornot with temperatures), and 2D or 3D models. This way, Brosse [11]usedﬁnite element methods and thermography to characterize thedistribution of Rwin the contact zone ﬁnding the triangular or theparabolic shape of the heat ﬂuxes provided more accurate results.Following the approach above described, Kohli found values inthe range 0.6e0.75 for shallow grinding with Alumina wheels [5].He used the Jaegers [6] solution with a triangular heat ﬂux shape.Hadad studied grinding with Minimum Quantity of Lubrication-MQL [12]. Based on analytical models found in Refs. [9], his ex-periments concluded that Rwvaries between 0.73 and 0.77 forgrinding with MQL, 0.82 for dry grinding and the use of coolingﬂuid reduced Rwto 0.36.Inversemethodsarenumerousandwidelyusedtostudyvariousheat transfer phenomena [13]. Recently, the function speciﬁcationmethodwasusedbyMeressetogetheatﬂuxrepartitiononadiscinbraking conditions [14]. Ludowski used the LevenbergeMarquardtmethod [15] to get the thermal boundary conditions in heat ex-changers [16]. The conjugated gradient method with adjointproblem has been used by Luchesi to identify a moving heat sourcein machining conditions [17].Inverse methodology has already been used in machining toqsheat ﬂux to the grinding wheel, W/mm3qwheat ﬂux to the workpiece, W/mm3R molar gas constant, m2kg/s2K molRchheat partition to the chips, eRsheat partition to the grinding wheel, eRﬂheat partition to the grinding ﬂuid, eRwheat partition ratio to the workpiece, eTMabsolute workpiece temperature, KTambabsolute ambient temperature, KU1activation energy for tempering, J/molvfinfeed speed, mm/minvsgrinding wheel speed, m/sV0wspeciﬁc volume of part material removed, mm3/mmε emissivity, ek thermal conductivityj probability of tempering, es StefaneBoltzmann constant, W/m2K466 (2014) 122e130 123identify thermal parameters of the process. In milling of hardenedsteels, the steepest descent method was used in Ref. [18] toinversely estimate the amount of energy directed to the workpieceand the convection coefﬁcient, hf. The LevenbergeMarquardtmethod [15] has also been used for characterizing the thermalproblem in drilling [19]. In this case, authors measured workpiecetemperature in drilling tests and compared it to that obtained froma one dimensional moving heat source analytical model and usedthe minimization of the quadratic error to obtain their results.In grinding this methodology is widely used to determine Rwbymatching experimental temperature with an output numericaldata, the nodal temperature at the sensor location, and minimizingthe error. Three inverses analyses are used in Ref. [20] to obtain Rw,the geometry of the heat source, and the convection coefﬁcient hffrom temperature data. Experiments are described in Ref. [21] andauthors have found Rwvalues in the range 0.70 and 0.74 forgrinding with Al2O3wheels using hardened steel and plain carbonsteel. More recently, Hong has presented the assessment of Rwusing a ﬁnite element method as direct model but results have notbeen validated by experimental data [22]. In Ref. [25] Andersonet al. performed this work for shallow and deep grinding. For theassessment of workpiece temperature distribution they used theﬁnite elements method, and took into account the materialremoved by deleting elements in the model for the case of deepgrinding. They estimated heat partition ratios to the workpiece byheating of it, so that high temporal thermal gradients are avoidedand temperature can be accurately measured with thermocouples.A Power meterdevice Load ControlsInc. UPC-FRinstalled onthewheel spindle and a Kistler 9257B dynamometer are also used forpower and force measurement. Here experimental tests are per-formed with AISI 4140 hardened steel (630HV). The workpiece is arectangular prism of 100 mm length C2 5 mm width C2 45 mmheight.AholeismachinedbyEDMonthesideoftheworkpieceanda K-type thermocouple of 200 mm diameter (each wire) is weldedinside by capacitive discharge to track the temperature evolution.The hole is 1 mm in diameter and is placed 3.5 mm far from theedge of the workpiece, and 2.5 mm in depth. The thermocouple iswelded manually into the hole, a process that leads to weldingalignmenterrors.The positioningof the thermocoupleis submittedto an uncertainty that have been estimated to be under 0.4 mm. Forthe determination this incertitude authors have considered boththe hole machining deviation and the uncertainty of the weldingprocess. The former is in the order of 0.01 mm or lower thanks tothe accuracy of EDM. For the latter, since the thermocouple wiresarewelded manually ithas beenconsideredthat theycan beplacedat any place inside the hole, which would lead to an uncertainty inits position of C60.3 mm (see ﬁgure). The conjunction of both un-certainties will be under C60.4 mm.2.1.2. Test methodologyExperimental tests and then Rwparameter estimations wereperformed in the described experimental conﬁguration for twoEngineeringmatching numerical results to those obtained with an infraredcamera measurements obtaining Rwin the range 0.8e0.85. Resultsmatch those obtained by the model developed by Rowe [9].Theobjectiveof thispaperistoprovideanoriginalmethodologyand experimental set-up that contribute to a better understandingof the inﬂuence of grinding variables on the heat partition ratio Rw.With respect to existing literature, the new methodology elimi-nates the errors induced by the steep thermal gradients that occurin grinding operations. Uncertainty related to the actual area ofcontact between both bodies (wheel and workpiece) is also sup-pressed by using a rigid and controlled geometrical conﬁguration.Assessment of Rwin shallow grinding of hardened steel with Al2O3wheels, and its relation with actual grinding parameters is pre-sented in this paper using an inverse heat conduction model.Grinding tests are developed in the so-called On-Machine TestBench, an alternative experimental set-up that allows reproducinggrinding conditions while accurate temperature measurementsand control of contact area are possible. The transient heat con-duction problem is solved by a ﬁnite element model which takesinto account the workpiece material removal during the process.The heat partition to the workpiece is identiﬁed by matchingtemperature data from thermocouple measurement to nodaltemperature of the ﬁnite element model. The Rwparameter isidentiﬁed with the LevenbergeMarquardt algorithm. Validation oftemperature measurements is indirectly carried out by metallur-gical analyses, which consists of measuring the micro-hardness ofthe tested samples and comparing it to the analytical model pro-posed in Ref. [23]. Results have led to a time-dependent deﬁnitionof Rwwhich had not been previously proposed in literature; inaddition it has been possible to relate the observed variations of Rwto the physical material removing mechanisms of grinding.2. Grinding processAs it has been mentioned, in grinding, for practical issues it isaccepted that all the energy consumed in the grinding wheelspindle is transformed into heat in the contact zone. Therefore, thetotal heat ﬂux generated in the contact zone, qt, can be obtainedfrom Equation (1), where P is the power consumption in thegrinding wheel spindle. The partition of this heat that is evacuatedthrough the workpiece, Rw, and the heat ﬂux directed to theworkpiece can be obtained from Equation (2).qt¼Pb$ae(1)qw¼Rw$Pb$ae(2)An experimental test bench is developed to reproduce thismachining process and to get temperature data close to the contactzone. A thermal ﬁnite element model describing the heat conduc-tion through the workpiece is then deﬁned to allow the identiﬁ-cation of the heat ﬂux boundary condition by an inverse method.2.1. Experimental test bench2.1.1. Test bench descriptionThe experimental work was developed in the new test benchconﬁguration shown in Fig. 1. A horizontal-spindle CNC surfacegrinding machine is used for the study. A cup grinding wheel, withaconstantspinningspeed,carriesoutgrindingofastaticworkpieceplate. The wheel removes material by moving towards the work-piece at a constant infeed speed, v . Insulating PTFE (Teﬂon) platesE. García et al. / Applied Thermal124fare placed at both sides o