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Simulation of the local kinematics in rotational grinding E Ahearne G Byrne 1 The Advanced Manufacturing Science AMS Research Centre School of Electrical Electronic and Mechanical Engineering University College Dublin Dublin Ireland 1 Introduction The rotational grinding process is regarded as the optimum process confi guration for assuring levels of global surface planarity tomeettheextremespecifi cationsforproductionoflargediameter 200 mm silicon substrates 1 The term rotational grinding generally refers to a confi guration comprising parallel and offset axes of rotation of work and grinding tool as shown in Fig 1 where the basic control parameters are also indicated f infeed df dt infeed rate Nc tool speed and Nw work speed The infeed and infeed rate is controlled in one axis only as shown The basic principles of this confi guration have been realised on both production and research machine tools 1 3 invariably related to the production of semiconductor substrates The basic premise for the present research is that the process capability may be ultimately limited by the inherently varying local kinematics of the process confi guration The varying local kinematics imply varying meso scale kinematics and kinema tical parameters accordingly The proposed approach is to describe the varying local kinematics by simulation based on principles delineated previously in reference 4 The derived kinematical parameters will then be correlated with test results that include localnormalforcemeasurementsfromanintegratedpiezo electric force sensor 5 2 Process simulation The simulation approach has been based on models assump tions and algorithms developed for simulating the peripheral grinding confi guration including models of the particular struc tural parameters of super abrasive tools 6 10 The approach proposed for simulating the meso scale kinematics of rotational grinding is to consider a point on the work surface and its kinematical relationship to the simulated tool topography on its locus under the tool as indicated in Fig 2 The defi ned curvilinear coordinate system with the origin as shown provides a basis for exact kinematical relationships and a modular simulation This enables the determination of local meso scale parameters for the range of practical global parameters Thesimulationengendersassumptionsthatmustbeconsidered critically rigid plastic material response infi nite machine loop stiffness spherical abrasive particle shape The assumption of a spherical particle shape has a basis in models of the fundamental mechanisms in grinding 7 11 and the fi nite global stiffness system can be simulated by modifi cation of input parameters The assumption of a rigid plastic material response is based on the premise that it will provide an upper bounddeterminationofthe geometricalinterferencebetweenthe work and tool abrasive particles 12 and local meso scale parameters that will correlate with local measurements force and surface roughness even in brittle mode grinding The simulation software comprises the main subroutines shown in Fig 3 It is based on the synthesis approach in references 8 9 whereby the grinding tool matrix is simulated initially subroutine 2 byassigningnormallydistributedparticle diameters to uniformly distributed positions within defi ned dimensional limits in the indicated coordinate system until the specifi ed bond concentration is realised A corresponding array representing the particles attributes is then reduced subroutine 3 to an array representing the surface topography after defi ning an arbitrary Z axis plane and particle selection criteria for example a pull out criterion Having defi ned the origin in subroutine 1 determined by the selectedradialdistance r fromtheworkcentreofrotationandthe outer diameter of the grinding tool abrasive section as shown in CIRP Annals Manufacturing Technology 57 2008 333 336 A R T I C L EI N F O Keywords Grinding Simulation Rotational grinding A B S T R A C T The rotational grinding process enables production of substrates for the semiconductor industry by a singular capacity to meet planarity and total thickness variation TTV requirements However the simple confi guration is characterised by varying local kinematics An upper bound simulation of the meso scale engagement kinematics has been developed with analysis algorithms that provide estimates of 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 generally correlated for surface roughness but not for local normal force where equilibration was attributed to system local and bending stiffness components 2008 CIRP Corresponding author Contents lists available at ScienceDirect CIRP Annals Manufacturing Technology journal homepage 0007 8506 see front matter 2008 CIRP doi 10 1016 j cirp 2008 03 080 Fig 2 subroutine 4 either generates a work surface topography array ab initio or reads in an array representing the output of a previous pass under the grinding tool The defi nable parameters include the number of points Np the sample surface arc length Sws the initial or continuous depth of cut per revolution ae and stochastic positions of the points in the Z direction Zj relative to the reference tool surface as shown in Fig 4 The main simulation subroutine 5 basically involves the determination of each abrasive particle s position relative to the designated surface point when the centre of the particle is on its locus Thus the temporal and spatial colocation of a point and particle can be determined and rigid plastic displacement h calculated given the assumption of a spherical particle shape As indicated the selection of the coordinate system results in exact transformation equations and therefore high temporal and spatial resolutions An output array is generated for each work surface point recording calculated parameters for each qualifying event at each position and time on the locus This array is then sorted and analysed subroutine 6 to generate the required mapping of the actual rigid plastic displacement h for that surface point and the position on the locus Arrays for all the surface points are analysed in the fi nal subroutine 7 to provide the required machining unit or meso scale parameters for that pass including surface roughness parameters Rafor example mean undeformed chip thickness ha the number of kinematical engagements per unit length of work surface arc Nkin and the rate of kinematical engagements Nkin Furtherprocessingofthearraywillalsogenerate undeformed chip area distribution statistics for example the mean undeformed chip area am relate kinematical engagements to the grinding tool segments and generate graphics indicating and analysing the distribution of kinematical events on the locus under the grinding tool The above subroutines represent a single pass of a sample surface profi le Multiplepassesaresimulatedbymultiple iterations where the input surface profi le array from one pass is the output of the previous pass The array is also offset by the preset depth of cut per pass or depth of cut revolution ae in rotational grinding determined by the infeed rate df dt and the work rotation speed Nw An initial surface profi le may also be used in the fi rst pass representing a surface generated by a previous operation However for the present purpose a surface of zero initial roughness is assumed and the number of passes is determined with reference to the onset of constant moving average mean undeformed chip thickness ha and requirements for statistical signifi cance 3 Simulation results There is signifi cant scope for simulating the process using the devised algorithms so it is necessary to defi ne specifi c objectives assumptions and limitations The specifi c objective here is to report results comparing local meso scale kinematical parameters or specifi cally parameters for radial distances of 20 40 60 80 and 95 mm from the work centre of rotation The global parameters as shown in Table 1 were determined by the constraints imposed by the experimental system its specifi cations and capability Fig 5 shows the simulation results for that set of parameters The indicated meso scale parameters include the surface roughness Ra themeanundeformedchipthickness ha themean undeformedchiparea am thenumberofkinematicalengagements Fig 1 Rotational grinding confi guration Fig 2 Defi ned curvilinear coordinate system Fig 3 Simulation subroutines Fig 4 Simulation parameters E Ahearne G Byrne CIRP Annals Manufacturing Technology 57 2008 333 336334 orparticles perunitlengthofworksurfacearc Nkin andtherateof kinematical engagements or particles Nkin 4 Experimental results A Hembrug ultraprecision CNC turning centre was used as a machine tool platform to realise the rotational grinding system showninFig 6 Theprocessandtoolparameterswere generallyset up or specifi edto conform with the simulation parameters given in Table 1 other than parameter 7 the tool segment length and inter segment gap which were 8 mm and 18 mm respectively Parameters otherwise not common to both simulation and experiment are shown in Table 2 The work material for the experiments was 200 mm 2 mm thick soda lime glass disks selected as a model brittle material without the anisotropic properties of semiconductor materials The grinding tool was well conditioned following recommended dressing procedures Procedures were also developed to ensure thatthe initialworksurfaceformwas parallelto the infi nitelystiff form for the given alignment settings of the axes parameter 15 The indicated alignments were determined to ensure engagement on the tool leading edge only in order to emulate the simulation without a signifi cant error The machine instrumentation includes an integrated miniature piezo electric force sensor to measure the locally varying forces in rotational grinding the sensor is mounted in the force fl ux of a single segment The force sensing and monitoring system has a level of resolution and frequency response exceeding the func tional requirements for the indicated application 4 5 The derived parameters from the simulation are to be related to the measured localparameters specifi cally forceandsurfaceroughness Statistically signifi cant differences could not be discerned in local measurements of depth of cut in these experiments Profi les of the normal force on the sensor integrated tool segment as a function of the radial distance at different levels of infeed areshowninFig 7 Attheinfeedlevelsof20and 25mm the normal force is nearly constant over 70 of the radial distance The constant normal force characteristic also develops clearly as the infeed advances and approaches a limit Fig 8 compares the local surface roughness Ra profi le levels obtained by experiment and simulation The experimental measurements shown were made on samples at the indicated radial distances by a stylus instrument cut off length of 0 8 mm 5 mm traverse distance in a tangential direction to conform with the simulation results The samples were removed at the end of the machine infeed so that the surface was produced at the maximum normal force levels 5 Discussion On the basis of the increase in the kinematical parameters ha Nkinand am with radial distance an increase in the normal force would be expected Pa hler et al demonstrated an increase in area related normal force with radial distance in reference 13 noting the differences in process parameters Clearly the normal force profi les shown in Fig 7 do not conform with the results of Pa hler et al 13 or the inference from the simulation results It has been shown 14 that machine loop stiffness has a signifi cant effect on the normal force infeed characteristic and this has been estimated here as about 5 N mm by regression of the normal force infeed characteristic This is further supported by an analysis of the Table 1 Simulation fi xed parameters Simulation parametersValue Tool Parameters 1Micron particle size dg mm 46 2Upper limit du mm 47 3Lower limit dl mm 38 4Concentration C 75 5Tool outer diameter Ds mm 200 6Tool segment width Bs mm 2 7Tool segment gap mm 0 Work parameters 8Sample surface length Sws mm 1 0 9Number of points Np 250 Process parameters 10Infeed rate df dt mm s 2 11Centre distances Cd mm 100 12Work speed Nw rpm 200 13Tool speed Nc rpm 2900 Axis alignment 15tana12 10 5 tanb5 10 5 Fig 5 Simulation results variation of kinematical parameters with radial distance Table 2 Experimental fi xed parameters Experiemental parametersDescription 1Tool bond materialMetal bond proprietary 2CoolantProcess water 3 Coolant fl owTwo nozzles directed as shown 4 Coolant fl ow rates4 l min each nozzle 5Total infeed25mm 6Spark out timeZero Fig 6 a Rotational grinding set up on Hembrug ultraprecision turning centre and b schematic E Ahearne G Byrne CIRP Annals Manufacturing Technology 57 2008 333 336335 effective series stiffness of the elements shown in Fig 6 b components 1 to 5 It is therefore proposed that equilibration of the local normal forces is due in part to both the local stiffness components and uniaxial bending stiffness about the main spindle axis in this confi guration as remarked in reference 1 The local stiffnesscomponentsincludethesegmentstiffnessand ata micro level the particle work and particle bond components 1 2 3 in Fig 6 The proposed effect of uniaxial stiffness is to reduce the initial set misalignment a as the load increases during infeed Clearly simulation and experiment show a similar statistically signifi cant increase in average surface roughness Ra level with radial distance from the work centre of rotation The result conforms with the model and reported measurements of Zhou et al 2 3 for ductile mode grinding of silicon not withstanding the equilibration of forces The model of Zhou et al is based on a model of line density variation with radial distance for a single point cutting edge in continuous engagement Thus it may be inferred that the local kinematics with superposed meso scale kinematics signifi cantly determines the local surface fi nish variation 6 Summary and future work A simulation approach and algorithms have been described for rotational grinding Specifi c results of a simulation based on parameters for brittle mode microgrinding have been reported and compared with experimental results that included measure ments ofthe local normalforce Theresultsgenerallycorrelatedfor surface roughness while equilibration of the local normal force was attributed to system local and uniaxial bending stiffness There is signifi cant potential for further application and development of both the simulation and the three component integrated force sensor system The simulation can be applied to predict the effect of a range of process parameters on rigid plastic surface fi nish and machining unit parameters The models derivedbysimulationcanbe dulytestedwithreferencetothelocal forceandsurface fi nishmeasurements Themediumterm objective is to apply the simulation and experimental facility for modeling and optimisation of silicon grinding in both brittle and ductile grinding modes Acknowledgments We would like to thank our sponsors Enterprise Ireland and collaborators Kistler GmbH and Atlantic Diamond for their support References 1 Toenshoff HK Schmieden Wv Inasaki I Koenig W Spur G 1990 Abrasive Machining of Silicon Annals of the CIRP 39 2 621 635 2 Eda H Zhou L Nakano H Kondo R 2001 Development of Single Step Grinding System for Large Scale 300 Si Wafer Annals of the CIRP 50 1 225 228 3 ZhouLB Eda H ShimzuJ 2002 State of the art Technologies and Kinematical Analysis for One Stop Finishing of 300 mm Si Wafer Journal of Materials Processing Technologies 129 34 40 4 Ahearne E Byrne G 2005 Modelling and Simulation of the Rotational Grind ing Process Proceedings of the 8th International CIRP Conference on Modelling of Machining Operations Chemnitz Germany 2005 May 10 11 335 341 5 Gangawan