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Simulation of the local kinematics in rotational grindingE. Ahearne*, G. Byrne (1)The Advanced Manufacturing Science (AMS) Research Centre, School of Electrical, Electronic and Mechanical Engineering, University College Dublin, Dublin, Ireland1. IntroductionThe rotational grinding process is regarded as the optimumprocess configuration for assuring levels of global surface planaritytomeettheextremespecificationsforproductionoflargediameter(200 mm) silicon substrates 1. The term rotational grindinggenerally refers to a configuration comprising parallel and offsetaxes of rotation of work and grinding tool as shown in Fig. 1 wherethe basic control parameters are also indicated (f: infeed, df/dt:infeed rate, Nc: tool speed and Nw: work speed). The infeed andinfeed rate is controlled in one axis only as shown. The basicprinciples of this configuration have been realised on bothproduction and research machine tools 13 invariably relatedto the production of semiconductor substrates.The basic premise for the present research is that the processcapability may be ultimately limited by the inherently varyinglocal kinematics of the process configuration. The varying localkinematics imply varying meso-scale kinematics and kinema-tical parameters accordingly. The proposed approach is to describethe varying local kinematics by simulation based on principlesdelineated previously in reference 4. The derived kinematicalparameters will then be correlated with test results that includelocalnormalforcemeasurementsfromanintegratedpiezo-electricforce sensor 5.2. Process simulationThe simulation approach has been based on models, assump-tions and algorithms developed for simulating the peripheralgrinding configuration including models of the particular struc-tural parameters of super-abrasive tools 610. The approachproposed for simulating the meso-scale kinematics of rotationalgrinding is to consider a point on the work surface and itskinematical relationship to the simulated tool topography on itslocus under the tool as indicated in Fig. 2. The defined curvilinearcoordinate system, with the origin as shown, provides a basis forexact kinematical relationships and a modular simulation. Thisenables the determination of local meso-scale parameters for therange of practical global parametersThesimulationengendersassumptionsthatmustbeconsideredcritically:?rigid-plastic material response;?infinite machine loop stiffness;?spherical abrasive particle shape.The assumption of a spherical particle shape has a basis inmodels of the fundamental mechanisms in grinding 7,11 and thefinite global stiffness system can be simulated by modification ofinput parameters. The assumption of a rigid-plastic materialresponse is based on the premise that it will provide an upper-bounddeterminationofthegeometricalinterferencebetweenthework and tool abrasive particles 12, and local meso-scaleparameters that will correlate with local measurements (force andsurface roughness) even in brittle-mode grinding.The simulation software comprises the main subroutinesshown in Fig. 3. It is based on the synthesis approach in references8,9 whereby the grinding tool matrix is simulated initially(subroutine#2)byassigningnormallydistributedparticlediameters to uniformly distributed positions within defineddimensional limits in the indicated coordinate system, until thespecified bond concentration is realised. A corresponding array,representing the particles attributes, is then reduced (subroutine#3) to an array representing the surface topography after definingan arbitrary Z-axis plane and particle selection criteria (forexample a pull-out criterion).Having defined the origin in subroutine #1, determined by theselectedradialdistance(r)fromtheworkcentreofrotationandtheouter diameter of the grinding tool (abrasive section) as shown inCIRP Annals - Manufacturing Technology 57 (2008) 333336A R T I C L EI N F OKeywords:GrindingSimulationRotational grindingA B S T R A C TThe rotational grinding process enables production of substrates for the semiconductor industry by asingular capacity to meet planarity and total thickness variation (TTV) requirements. However, thesimple configuration is characterised by varying local kinematics. An upper-bound simulation of themeso-scale engagement kinematics has been developed with analysis algorithms that provide estimatesof local kinematical parameters. These have been correlated with local measurements for typical brittle-mode microgrinding parameters including measurements of the local normal force. The results generallycorrelated for surface roughness but not for local normal force where equilibration was attributed tosystem local and bending stiffness components.? 2008 CIRP.* Corresponding author.Contents lists available at ScienceDirectCIRP Annals - Manufacturing Technologyjournal homepage: /cirp/default.asp0007-8506/$ see front matter ? 2008 CIRP.doi:10.1016/j.cirp.2008.03.080Fig. 2, subroutine #4 either generates a work surface topographyarray ab initio or reads in an array representing the output of aprevious pass under the grinding tool. The definable parametersinclude the number of points (Np), the sample surface arc length(Sws), the initial or continuous depth of cut per revolution (ae) andstochastic positions of the points in the Z direction (Zj) relative tothe reference tool surface as shown in Fig. 4.The main simulation subroutine #5 basically involves thedetermination of each abrasive particles position relative to thedesignated surface point when the centre of the particle is on itslocus. Thus the temporal and spatial colocation of a point andparticle can be determined and rigid-plastic displacement (h)calculated given the assumption of a spherical particle shape. Asindicated, the selection of the coordinate system results in exacttransformation equations and therefore high temporal and spatialresolutions. An output array is generated for each work surfacepoint recording calculated parameters for each qualifying event ateach position and time on the locus. This array is then sorted andanalysed (subroutine #6) to generate the required mapping of theactual rigid-plastic displacement (h) for that surface point and theposition on the locus.Arrays for all the surface points are analysed in the finalsubroutine #7 to provide the required machining unit or meso-scale parameters for that pass including; surface roughnessparameters (Rafor example), mean undeformed chip thickness(ha), the number of kinematical engagements per unit length ofwork surface arc (Nkin) and the rate of kinematical engagements(Nkin).Furtherprocessingofthearraywillalsogenerateundeformed chip area distribution statistics (for example, themean undeformed chip area, am), relate kinematical engagementsto the grinding tool segments and generate graphics indicating andanalysing the distribution of kinematical events on the locus underthe grinding tool.The above subroutines represent a single pass of a samplesurfaceprofile.Multiplepassesaresimulatedbymultipleiterations where the input surface profile array from one pass isthe output of the previous pass. The array is also offset by thepreset depth of cut per pass (or depth of cut revolution, ae, inrotational grinding) determined by the infeed rate (df/dt) and thework rotation speed (Nw). An initial surface profile may also beused in the first pass representing a surface generated by aprevious operation. However, for the present purpose, a surface ofzero initial roughness is assumed and the number of passes isdetermined with reference to the onset of constant movingaverage mean undeformed chip thickness (ha) and requirementsfor statistical significance.3. Simulation resultsThere is significant scope for simulating the process using thedevised algorithms so it is necessary to define specific objectives,assumptions and limitations. The specific objective here is to reportresults comparing local meso-scale kinematical parameters or,specifically, parameters for radial distances of 20, 40, 60, 80 and95 mm from the work centre of rotation. The global parameters, asshown in Table 1, were determined by the constraints imposed bythe experimental system, its specifications and capability. Fig. 5shows the simulation results for that set of parameters. Theindicated meso-scale parameters include: the surface roughness(Ra),themeanundeformedchipthickness(ha),themeanundeformedchiparea(am),thenumberofkinematicalengagementsFig. 1. Rotational grinding configuration.Fig. 2. Defined curvilinear coordinate system.Fig. 3. Simulation subroutines.Fig. 4. Simulation parameters.E. Ahearne, G. Byrne/CIRP Annals - Manufacturing Technology 57 (2008) 333336334(orparticles)perunitlengthofworksurfacearc(Nkin)andtherateofkinematical engagements or particles (Nkin).4. Experimental resultsA Hembrug ultraprecision CNC turning centre was used as amachine tool platform to realise the rotational grinding systemshowninFig.6.Theprocessandtoolparameterswere generallysetup or specifiedto conform with the simulation parameters given inTable 1; other than parameter #7, the tool segment length andinter-segment gap, which were ?8 mm and 18 mm, respectively.Parameters otherwise not common to both simulation andexperiment are shown in Table 2.The work material for the experiments was 200 mm ? 2 mmthick soda-lime glass disks selected as a model brittle materialwithout the anisotropic properties of semiconductor materials.The grinding tool was well-conditioned following recommendeddressing procedures. Procedures were also developed to ensurethatthe initialworksurfaceformwas parallelto theinfinitelystiffform for the given alignment settings of the axes (parameter #15).The indicated alignments were determined to ensure engagementon the tool leading edge only in order to emulate the simulationwithout a significant error.The machine instrumentation includes an integrated miniaturepiezo-electric force sensor to measure the locally varying forces inrotational grinding; the sensor is mounted in the force flux of asingle segment. The force sensing and monitoring system has alevel of resolution and frequency response exceeding the func-tional requirements for the indicated application 4,5. The derivedparameters from the simulation are to be related to the measuredlocalparametersspecifically;forceandsurfaceroughness.Statistically significant differences could not be discerned in localmeasurements of depth of cut in these experiments.Profiles of the normal force on the sensor-integrated toolsegment, as a function of the radial distance at different levels ofinfeed,areshowninFig.7.Attheinfeedlevelsof20and 25mm,thenormal force is nearly constant over 70% of the radial distance.The constant normal force characteristic also develops clearly asthe infeed advances and approaches a limit. Fig. 8 compares thelocal surface roughness (Ra) profile levels obtained by experimentand simulation. The experimental measurements shown weremade on samples at the indicated radial distances by a stylusinstrument (cut-off length of 0.8 mm, 5 mm traverse distance) in atangential direction to conform with the simulation results. Thesamples were removed at the end of the machine infeed so that thesurface was produced at the maximum normal force levels.5. DiscussionOn the basis of the increase in the kinematical parameters (ha,Nkinand am) with radial distance, an increase in the normal forcewould be expected. Pa hler et al. demonstrated an increase in area-related normal force with radial distance in reference 13 (notingthe differences in process parameters). Clearly, the normal forceprofiles shown in Fig. 7 do not conform with the results of Pa hleret al. 13 or the inference from the simulation results. It has beenshown 14 that machine loop stiffness has a significant effect onthe normal force-infeed characteristic and this has been estimatedhere as about 5 N/mm by regression of the normal force-infeedcharacteristic. This is further supported by an analysis of theTable 1Simulation fixed parameters#Simulation parametersValueTool Parameters1Micron particle size, dg(mm)462Upper limit, du(mm)473Lower limit, dl(mm)384Concentration (C)755Tool outer diameter, Ds(mm)2006Tool segment width, Bs(mm)27Tool segment gap (mm)0Work parameters8Sample surface length, Sws(mm)1.09Number of points, Np(#)250Process parameters10Infeed rate, df/dt (mm/s)211Centre distances, Cd(mm)10012Work speed, Nw(rpm)20013Tool speed, Nc(rpm)2900Axis alignment15tana12?10?5tanb5?10?5Fig. 5. Simulation results: variation of kinematical parameters with radial distance.Table 2Experimental fixed parameters#Experiemental parametersDescription1Tool bond materialMetal bond (proprietary)2CoolantProcess water3Coolant flowTwo nozzles directed as shown4Coolant flow rates4 l/min each nozzle5Total infeed25mm6Spark-out timeZeroFig. 6. (a) Rotational grinding set-up on Hembrug ultraprecision turning centre and (b) schematic.E. Ahearne, G. Byrne/CIRP Annals - Manufacturing Technology 57 (2008) 333336335effective series stiffness of the elements shown in Fig. 6(b)(components 1 to 5). It is therefore proposed that equilibration ofthe local normal forces is due in part to both the local stiffnesscomponents and uniaxial bending stiffness about the main spindleaxis in this configuration, as remarked in reference 1. The localstiffnesscomponentsincludethesegmentstiffnessand,ata micro-level, the particle-work and particle-bond components (1, 2, 3 inFig. 6). The proposed effect of uniaxial stiffness is to reduce theinitial set misalignment (a) as the load increases during infeed.Clearly, simulation and experiment show a similar (statisticallysignificant) increase in average surface roughness (Ra) level withradial distance from the work centre of rotation. The resultconforms with the model and reported measurements of Zhouet al. 2,3 for ductile mode grinding of silicon, not withstandingthe equilibration of forces. The model of Zhou et al. is based on amodel of line density variation with radial distance for a singlepoint cutting edge in continuous engagement. Thus, it may beinferred that the local kinematics, with superposed meso-scalekinematics, significantly determines the local surface finishvariation.6. Summary and future workA simulation approach and algorithms have been described forrotational grinding. Specific results of a simulation based onparameters for brittle-mode microgrinding have been reportedand compared with experimental results that included measure-ments ofthe local normalforce. Theresultsgenerallycorrelatedforsurface roughness while equilibration of the local normal forcewas attributed to system local and uniaxial bending stiffness.There is significant potential for further application anddevelopment of both the simulation and the three-componentintegrated force sensor system. The simulation can be applied topredict the effect of a range of process parameters on rigid-plasticsurface finish and machining unit parameters. The modelsderivedbysimulationcanbe dulytestedwithreferencetothelocalforceandsurfacefinishmeasurements.Themediumtermobjective is to apply the simulation and experimental facility formodeling and optimisation of silicon grinding in both brittle andductile grinding modes.AcknowledgmentsWe would like to thank our sponsors Enterprise Ireland andcollaborators Kistler GmbH and Atlantic Diamond for theirsupport.References1 Toenshoff HK, Schmieden Wv, Inasaki I, Koenig W, Spur G (1990) AbrasiveMachining of Silicon. Annals of the CIRP 39(2):621635.2 Eda H, Zhou L, Nakano H, Kondo R (2001) Development of Single Step GrindingSystem for Large Scale 300 Si Wafer. Annals of the CIRP 50(1):225228.3 ZhouLB, Eda H, ShimzuJ(2002) State-of-the-art Technologies and KinematicalAnalysis for One-Stop Finishing of 300 mm Si Wafer. Journal of MaterialsProcessing Technologies 129:3440.4 Ahearne E, Byrne G (2005) Modelling and Simulation of the Rotational Grind-ing Process. Proceedings of the 8th International CIRP Conference on Modelling ofMachining Operations, Chemnitz, Germany, 2005, May 1011, 335341.5 Gangawane M, Ahearne E, Byrne G (2006) Measurement of Lo
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