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An ideal fixture design maximises locating accuracyand workpiece stability, while minimising displacements.The purpose of this research is to develop a method for mod-elling workpiece boundary conditions and applied loads duringa machining process, analyse modular fixture tool contact areadeformation and optimise support locations, using finite elementanalysis (FEA). The workpiece boundary conditions are definedby locators and clamps. The locators are placed in a 3-2-1 fixtureconfiguration, constraining all degrees of freedom of the work-piece and are modelled using linear spring-gap elements. Theclamps are modelled as point loads. The workpiece is loadedto model cutting forces during drilling and milling machiningoperations.Fixture design integrity is verified. ANSYS parametric de-sign language code is used to develop an algorithm to auto-matically optimise fixture support and clamp locations, andclamping forces, to minimise workpiece deformation, subse-quently increasing machining accuracy. By implementing FEAin a computer-aided-fixture-design environment, unnecessaryand uneconomical “trial and error” experimentation on the shopfloor is eliminated.Keywords FEA Finite Element Analysis Fixture OptimisationN. Amaral (u)V-Engine Manufacturing Engineering,Ford Motor Company, Powertrain Operations,21500 Oakwood Boulevard, Dearborn, MI 48124-4091 USAE-mail: Fax: +1-313-2486734J.J. Rencis Y. RongWorcester Polytechnic Institute,100 Institute Road, Worcester, MA, 01609-2280 USA1 IntroductionMachining fixtures are used to locate and constrain a work-piece during a machining operation. To ensure that the work-piece is manufactured according to specified dimensions andtolerances, it must be appropriately located and clamped. Pro-duction quality depends considerably on the relative position ofthe workpiece and machine tools. Minimising workpiece and fix-ture tooling deflections due to clamping and cutting forces inmachining is critical to machining accuracy. The workpiece de-formation during machining is directly related to the workpiece-fixture system stiffness. An ideal fixture design maximises locat-ing accuracy, workpiece stability, andstiffness, while minimisingdisplacements.Traditionally, fixtures were designed by trial and error, whichis expensive and time consuming. Research in flexible fixtur-ing and computer-aided-fixture-design (CAFD) has significantlyreduced manufacturing lead-time and cost. The purpose of thisresearch is to develop a computer-aided tool to model workpieceboundary conditions and applied loads in machining.The majority of finite element analysis (FEA) research con-ducted in fixture design considers workpiece boundary condi-tions to be rigid and applied loads to be concentrated. In all caseswhere friction is considered, rigid Coulomb friction is assumed.Cutting tool torque, which results in a trend of workpiece ro-tation, is not considered. Clamping forces are considered to beconstant point loads.This study acknowledges that workpiece boundary condi-tions are deformable and influence the global stiffness of theworkpiece-fixture system. The boundary conditions of the work-piece, the locators, are modelled as multiple springs in parallelattached to the actual workpiece-fixture contact area on the sur-face of the workpiece. Also, tangential and normal stiffness com-ponents of the boundary conditions are not assumed to be equalas in rigid Coulomb friction, but are assigned independently. Inapplying loads representative of the machining operation, torque,axial and transverse loads due to feeding are considered. An in-410depth discussion of the work presented herein can be found inAmaral 1.In this study, both the finite element analysis and optimisa-tion are conducted in ANSYS. Within the analysis, a workpieceis imported in initial graphics exchange specification (IGES) for-mat. Material properties, element type, and real constants aredefined. The workpiece is meshed and boundary conditions andloads are applied. The model is then solved and results are re-trieved parametrically, and support locations, clamp locations,and clamping forces are optimised tominimise workpiece deflec-tion 1. The advantage of the method developed herein is that anexternal software package for optimisation is not required, thuscompatibility between two packages is not a concern.2 Literature reviewPrinciples of fixture design and preceding FEA research in fix-ture design are discussed. Although some research has been con-ducted in fixture design, a comprehensive finite element modelthat accurately represent applied boundary conditions and loadshas not been developed. Tables 1 and 2 summarise the precedentresearch conducted on FEA and fixture design.Table1. Literature survey of workpiece modelsReferenceWorkpiece modelMaterialElement typeTypeE (Pa)Lee and Haynes 2Steel homogeneous6.91080.3U/A*3-D solid 8-node brickIsotropic linear elasticPong et al. 3Aluminium homogeneous6.910100.3U/A3-D solid 10-node tetrahedral;Isotropic linear elasticANSYS SOLID92Trappey et al. 5Aluminium homogeneous6.910100.30.3U/AIsotropic linear elasticCai et al. 6Steel2.110110.3U/A2-D 4-node rectangular element;Isotropic linear elasticMSC NASTRAN QUAD4Kashyap and DeVries 7Aluminium homogeneous6.910100.3U/A3-D solid tetrahedral elementsIsotropic linear elastic*U/A: unavailableTable2. Literature survey of boundary conditions and loadingReferenceFixture component modelSteady-state load modelLocatorsClampsDrillingMillingLee and Haynes 2Rigid area constrain,U/A*U/ANormal and shear point loadsRigid coulomb frictionPong et al. 33-D spring-gap interface element,N/A*Normal point loadsN/ARigid coulomb frictionTrappey et al. 53-D solid deformable constraintsPoint loadsNormal point loadsNormal and shear point loadsCai et al. 6Rigid point constraintsN/ANormal point loadsNormal and shear point loadsKashyap and DeVries 7Rigid point constraintsPoint loadsNormal point loadsNormal and shear point loads*U/A: unavailable*N/A: not applicableLee and Haynes 2 used FEA to minimise workpiece deflec-tion. Their workpiece was modelled as linear elastic, howeverfixture tooling was modelled as rigid. Their objective functionincluded the maximum work done by clamping and machiningforces, the deformation index, and the maximum stress on theworkpiece. Their study considers the importance of part defor-mation with respect to the necessary number of fixturing elem-ents and the magnitude of claming forces 3. Coulombs law offriction was used to calculate the frictional forces the workpiece-fixture contact points. The machining forces were applied atnodal points. Manassa and DeVries 4 conducted similar re-search to that of Lee and Haynes 2, but modelled fixturingelements as linear elastic springs.Pong et al. 3 used spring-gap elements with stiffness, sep-aration, and friction capabilities to model elastic workpieceboundary conditions. Three-dimensional tetrahedral elementswere used to mesh the finite element model of the solid work-piece. All contacts between the workpiece and the fixture wereconsidered to be point contacts and machining forces were ap-plied sequentially as point loads. The positions of locators andclamps, and clamping forces were considered design variablesfor optimisation. Trappey et al. 5 developed a procedure forthe verification of fixtures. FEA was used to analyse the stress-strain behaviour of the workpiece when machining and clamping411forces were applied. A mathematical optimisation model wasformulated to minimise workpiece deformation with a feasiblefixture configuration.Cai et al. 6 used FEA to analyse sheet metal deforma-tion and optimised support locations to minimise resultantdisplacements. Kashyap and DeVries 7 used FEA to modelworkpiece and fixture tool deformation, and developed an op-timisation algorithm to minimise deflections at selected nodalpoints by considering the support and tool locations as designvariables.A summary of research on FEA and fixture design optimi-sation is shown in Table 3. The majority of research conductedin finite element analysis and fixture design optimisation, re-sulted in the development of a mathematical algorithm. Pong etal. 3 used the ellipsoid method to optimise support locationsand minimise nodal deflection. Trappey et al. 5 used an exter-nal software package, GINO 8, to optimise support locationsand clamping forces. Cai et al. 6 used a sequential quadraticprogramming algorithm in an external FORTRAN based soft-ware package, VMCON, to perform a quasi-Newton non-linearconstrained optimisation of N-2-1 support locations to minimisesheet metal deflection. Kashyap and DeVries 7 developed a dis-crete mathematical algorithm for optimisation.Table3. Literature survey of optimisation analysisReferenceOptimization analysisMethodObjective functionSoftware packagePong et al. 3Ellipsoid methodNodal deflectionN/A*Trappey et al. 5Non-linear mathematical algorithmNodal deflectionGINO 8Cai et al. 6Sequential quadratic programming algorithmNodal deflection normal to sheet metal surfaceVMCON 9Kashyap and DeVries 7Discrete mathematical algorithmNodal deflectionN/A*N/A: not applicableFig.1.Fixturedesignanalysismethodology3 Fixture design analysis methodologyThe flowchart in Fig. 1 is a summary of the fixture design analy-sis methodology developed and used in this work. In summary,workpiece IGES geometry is imported from the solid modellingpackage, the workpiece model is meshed, boundary conditionsare applied, the model is loaded, representative of a machiningoperation, the model is solved, and then boundary conditions areoptimised to minimise workpiece deflections.3.1 Workpiece modelThe workpiece model is the starting point of the analysis. Thisresearch currently limits the workpiece geometry to solids withplanar locating surfaces. Some workpiece geometry may containthin-walls and non-planar locating surfaces, which are not con-sidered in this study.GeometryTheworkpiecemodel,createdinPro/ENGINEERor other solid modelling software is exported to ANSYS in IGESformat with all wireframes and surfaces. IGES is a neutral stan-dard format used to exchange models between CAD/CAM/CAEsystems. ANSYS provides two options for importing IGES412Table4. Workpiece and locator material propertiesMaterialE (Pa) (kg/m3)y(Pa)WorkpieceAISI 12122.0101178610.2952.3108LocatorsAISI 11442.0101178610.2956.7108files, DEFAULT and ALTERNATE. The DEFAULT option al-lows file conversion without user intervention. The conversionincludes automatic merging and creation of volumes to pre-pare the model for meshing. The ALTERNATE option usesthe standard ANSYS geometry database, and is provided forbackward compatibility with the previous ANSYS import op-tion. The ALTERNATE option has no capabilities for automat-ically creating volumes and modes imported through this trans-lator require manual repair through the PREP7 geometry tools.To select the options for importing an IGES file, the IOPTNis used. See Appendix A in 1 for a detailed description ofimplementation.Material properties The workpiece material in this studyis homogenous, isotropic, linear elastic and ductile; this is con-sistent with the material properties of most metal workpieces.The material selected is SAE/AISI 1212 free-machining grade(a)carbon steel with Youngs modulus, E = 30106psi Poissonsratio, = 0.295, and density, = 0.283 lb/in3, and hardness of175 HB. Although SAE1212 steel was selected for use in thisstudy because it is commonly used and is a benchmark materialfor machinability, any material could be used for the workpieceby simply changing the isotropic material properties in ANSYS.Table 4 lists the material properties selected in this study for theworkpiece and locators.3.2 Meshed workpiece modelAn 8-node hexahedral element (SOLID45), with three degreesof freedom at each node, and linear displacement behaviouris selected to mesh the workpiece. SOLID45 is used for thethree-dimensional modelling of solid structures. The elementis defined by eight nodes having three degrees of freedom ateach node: translations in the nodal X, Y, and Z directions. TheSOLID45 element degenerates to a 4-node tetrahedral configu-ration with three degrees of freedom per node. The tetrahedralconfiguration is more suitable for meshing non-prismatic geom-etry, but is less accurate than the hex configuration. ANSYSrecommends that no more than 10% of the mesh be comprisedof SOLID45 elements in the tetrahedral configuration. For a de-tailed description of the element type selection process, referto 1.3.3 Boundary conditionsLocators and clamps define the boundary conditions of the work-piece model. The locators can be modelled as point or areacontact and clamps are modelled as point forces.LocatorsPoint contact. The simplest boundary condition is a pointconstraint on a single node. A local coordinate system (LCS),referenced from the global coordinate system origin, is createdat the centre of each locator contact area, such that the z-axisnormal to the workpiece locating surface. The node closest tothe centre of the local coordinate system origin is selected andall three translational degrees of freedom (ux, uy, and uz) areconstrained. The point constraint models a rigid locator with aninfinitesimally small contact area.Tomodellocatorstiffnessandfrictionatthecontactpoint,a3-D interface spring-gap element is placed at the centre of the LCS.The element is connected to existing nodes on the surface of theworkpiece and to a fully constrained copied node offset from theworkpiece surface in the z-direction of the local coordinate sys-tem, i.e., perpendicular to the surface. Figure 2 is a model of theCONTAC52element usedtorepresent a linearelastic locator.Area contact. To model a rigid locator with a contact area,multiple nodes are fixed within the contact area. An LCS is cre-ated on the workpiece surface at the centre of the locator contactarea. For a circular contact area, a cylindrical LCS is created andnodes are selected at 0 r rL. For a rectangular contact area,a Cartesian LCS is created and nodes are selected at 0 x xLand 0 y yL. All three translational degrees of freedom (ux,uy, and uz) of each of the nodes are constrained. This model as-sumes rigid constraints, however in reality locators are elastic.A more accurate representation of the elastic locators con-sists of multiple ANSYS CONTAC52 elements in parallel.Nodes are selected within the locator contact area and are copiedoffset perpendicular to the locating surface. Each selectednode isconnected to the copied node sequentially with the CONTAC52element. Figure 3 shows the contact area model with multiplespring-gap elements in parallel used to represent a linear elasticlocator. It is important to note, that the user is constrained to thenumber of nodes within the specified contact area, when attach-ing the CONTAC52 elements. It is possible that there could bea different number of elements modelling each locator, becauseof the number of associated nodes within the contact area. Thus,the element normal and tangential stiffness, which is specifiedin the real constant set would vary. For this reason, multiple realconstant sets must be created for the CONTAC52 element, andthen assigned accordingly when creating elements in a specifiedlocal coordinate system.In Fig. 4, the method for obtaining the normal and tangentialstiffness for a locator is shown. The stiffness divided by the totalFig.2. CONTAC52 element used to model point contact for locators 10413Fig.3. CONTAC52 elements in parallel, used to model area contact forlocators 10Fig.4. Normal and tangential stiffness for locatornumber of springs is assigned accordingly to each spring-gapelement, in the real constant set. A point load is applied to thethree-dimensional finite element model of the real locator, nor-mal to the contact area to determine the normal stiffness. A pointload is applied tangent to the contact area of the real locator todetermine the tangential or “sticking” stiffnessof the locator. Thestiffness values are then assigned to the CONTAC52 elements.Clamps The clamps are used to fully constrain the work-piece once it is located. It is common to use multiple clamps andclamping forces that are generally constant for each clamp. Theclamping force, Fclis applied through either a toggle mechan-ism or a bolt mechanism, which lowers a strap that comes intocontact with the workpiece. Although friction is just as import-ant in clamping as it is in locating, it is not modelled at theclamp contact area due to limitations in ANSYS. In order tomodel friction, a comprehensive three-dimensional model of theentire workpiece-fixture system is required, with contact and tar-get surfaces defined at the fixture-workpiece contact areas. Theclamping forces are modelled in ANSYS as point loads on nodesselectedeither within a rectangular area for a clamp strap or a cir-cular area on the workpiece surface for a toggle clamp. Bothclamps may also be modelled with a single point load at the cen-tre of the clamp contact area.3.4 LoadingThe two machining operations, milling and drilling, are dis-cussed. The purpose of this research is not to accurately modelthe machining process, but to apply the torque and forces that aretransferred through the workpiece in machining, to determine thereactions at the boundary conditions of the workpiece. The de-sired result of the load model is the trend of rotation from theapplied torque of the cutting tool, and translation, due to axialfeeding of the workpiece and transverse motion of the table inmilling.Drilling The forces in a drilling operation include a torque,T, to generate tool rotation, shear force, V, created by tool rota-tion at the cutting edge contact for chip removal, and an axialload, P, due to feeding. The forces in drilling are time and pos-ition dependent and oscillatory due to cutter rotation, since thecutting edge of the tool is not in constant contact with the work-piece at a particular location. The cutting force increases mono-tonically during tool entry and then approaches steady-state.Fluctuations in the cutting force are due to cutting tool toothdistribution during rotation. In this study, the torque and thrustforces in feeding are applied as steady-state loads, since initialtool entry is not considered. In previous FEA fixture design re-search, loads were applied as a steady-state. Also neglected wascutting tool torque and subsequently the workpiece deflectionsdue to the trend of rotation in the fixture. An initial attemptto model the distributed loading using a number of point loadsapplied at key points was unsuccessful, due to limitations inANSYS. The model consisted of placing key points on a localcoordinate system created on the machining surface of the work-piece. The key points were located at exact R, , and Z positionson the cutting tool perimeter. At each key point forces were ap-plied to model a drilling operation. The torque was modelledwith tangential forces placed at the outer radius of the cuttingtool contact area. The tangential couple forces were decomposedinto global X and Y components. The axial load was modelledby applying forces at each key point in the global Z direction.The reason this model failed is that the key points created onthe workpiece surface are g