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DOI 10.1007/s00170-003-1796-6 ORIGINAL ARTICLE Int J Adv Manuf Technol (2005) 25: 409419 Nicholas Amaral Joseph J. Rencis Yiming (Kevin) Rong Development of a finite element analysis tool for fixture design integrity verification and optimisation Received: 15 March 2003 / Accepted: 11 May 2003 / Published online: 25 August 2004 Springer-Verlag London Limited 2004 Abstract Machining fixtures are used to locate and constrain a workpiece during a machining operation. To ensure that the workpiece is manufactured according to specified dimensions and tolerances, it must be appropriately located and clamped. Minimising workpiece and fixture tooling deflections due to clamping and cutting forces in machining is critical to machining accuracy. An ideal fixture design maximises locating accuracy and workpiece stability, while minimising displacements. The purpose of this research is to develop a method for mod- elling workpiece boundary conditions and applied loads during a machining process, analyse modular fixture tool contact area deformation and optimise support locations, using finite element analysis (FEA). The workpiece boundary conditions are defined by locators and clamps. The locators are placed in a 3-2-1 fixture configuration, constraining all degrees of freedom of the work- piece and are modelled using linear spring-gap elements. The clamps are modelled as point loads. The workpiece is loaded to model cutting forces during drilling and milling machining operations. 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, and clamping forces, to minimise workpiece deformation, subse- quently increasing machining accuracy. By implementing FEA in a computer-aided-fixture-design environment, unnecessary and uneconomical “trial and error” experimentation on the shop floor is eliminated. Keywords FEA Finite Element Analysis Fixture Optimisation N. Amaral (a117) V-Engine Manufacturing Engineering, Ford Motor Company, Powertrain Operations, 21500 Oakwood Boulevard, Dearborn, MI 48124-4091 USA E-mail: Fax: +1-313-2486734 J.J. Rencis Y. Rong Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA, 01609-2280 USA 1 Introduction Machining 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 and tolerances, it must be appropriately located and clamped. Pro- duction quality depends considerably on the relative position of the workpiece and machine tools. Minimising workpiece and fix- ture tooling deflections due to clamping and cutting forces in machining 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, and stiffness, while minimising displacements. Traditionally, fixtures were designed by trial and error, which is expensive and time consuming. Research in flexible fixtur- ing and computer-aided-fixture-design (CAFD) has significantly reduced manufacturing lead-time and cost. The purpose of this research is to develop a computer-aided tool to model workpiece boundary 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 cases where 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 be constant point loads. This study acknowledges that workpiece boundary condi- tions are deformable and influence the global stiffness of the workpiece-fixture system. The boundary conditions of the work- piece, the locators, are modelled as multiple springs in parallel attached 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 equal as in rigid Coulomb friction, but are assigned independently. In applying loads representative of the machining operation, torque, axial and transverse loads due to feeding are considered. An in- 410 depth discussion of the work presented herein can be found in Amaral 1. In this study, both the finite element analysis and optimisa- tion are conducted in ANSYS. Within the analysis, a workpiece is imported in initial graphics exchange specification (IGES) for- mat. Material properties, element type, and real constants are defined. The workpiece is meshed and boundary conditions and loads are applied. The model is then solved and results are re- trieved parametrically, and support locations, clamp locations, and clamping forces are optimised to minimise workpiece deflec- tion 1. The advantage of the method developed herein is that an external software package for optimisation is not required, thus compatibility between two packages is not a concern. 2 Literature review Principles 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 model that accurately represent applied boundary conditions and loads has not been developed. Tables 1 and 2 summarise the precedent research conducted on FEA and fixture design. Table 1. Literature survey of workpiece models Reference Workpiece model Material Element type Type E (Pa) Lee and Haynes 2 Steel homogeneous 6.910 8 0.3 U/A* 3-D solid 8-node brick Isotropic linear elastic Pong et al. 3 Aluminium homogeneous 6.910 10 0.3 U/A 3-D solid 10-node tetrahedral; Isotropic linear elastic ANSYS SOLID92 Trappey et al. 5 Aluminium homogeneous 6.910 10 0.3 0.3 U/A Isotropic linear elastic Cai et al. 6 Steel 2.110 11 0.3 U/A 2-D 4-node rectangular element; Isotropic linear elastic MSC NASTRAN QUAD4 Kashyap and DeVries 7 Aluminium homogeneous 6.910 10 0.3 U/A 3-D solid tetrahedral elements Isotropic linear elastic *U/A: unavailable Table 2. Literature survey of boundary conditions and loading Reference Fixture component model Steady-state load model Locators Clamps Drilling Milling Lee and Haynes 2 Rigid area constrain, U/A* U/A Normal and shear point loads Rigid coulomb friction Pong et al. 3 3-D spring-gap interface element, N/A* Normal point loads N/A Rigid coulomb friction Trappey et al. 5 3-D solid deformable constraints Point loads Normal point loads Normal and shear point loads Cai et al. 6 Rigid point constraints N/A Normal point loads Normal and shear point loads Kashyap and DeVries 7 Rigid point constraints Point loads Normal point loads Normal and shear point loads *U/A: unavailable *N/A: not applicable Lee and Haynes 2 used FEA to minimise workpiece deflec- tion. Their workpiece was modelled as linear elastic, however fixture tooling was modelled as rigid. Their objective function included the maximum work done by clamping and machining forces, the deformation index, and the maximum stress on the workpiece. 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 of friction was used to calculate the frictional forces the workpiece- fixture contact points. The machining forces were applied at nodal points. Manassa and DeVries 4 conducted similar re- search to that of Lee and Haynes 2, but modelled fixturing elements as linear elastic springs. Pong et al. 3 used spring-gap elements with stiffness, sep- aration, and friction capabilities to model elastic workpiece boundary conditions. Three-dimensional tetrahedral elements were used to mesh the finite element model of the solid work- piece. All contacts between the workpiece and the fixture were considered to be point contacts and machining forces were ap- plied sequentially as point loads. The positions of locators and clamps, and clamping forces were considered design variables for optimisation. Trappey et al. 5 developed a procedure for the verification of fixtures. FEA was used to analyse the stress- strain behaviour of the workpiece when machining and clamping 411 forces were applied. A mathematical optimisation model was formulated to minimise workpiece deformation with a feasible fixture configuration. Cai et al. 6 used FEA to analyse sheet metal deforma- tion and optimised support locations to minimise resultant displacements. Kashyap and DeVries 7 used FEA to model workpiece and fixture tool deformation, and developed an op- timisation algorithm to minimise deflections at selected nodal points by considering the support and tool locations as design variables. A summary of research on FEA and fixture design optimi- sation is shown in Table 3. The majority of research conducted in finite element analysis and fixture design optimisation, re- sulted in the development of a mathematical algorithm. Pong et al. 3 used the ellipsoid method to optimise support locations and minimise nodal deflection. Trappey et al. 5 used an exter- nal software package, GINO 8, to optimise support locations and clamping forces. Cai et al. 6 used a sequential quadratic programming algorithm in an external FORTRAN based soft- ware package, VMCON, to perform a quasi-Newton non-linear constrained optimisation of N-2-1 support locations to minimise sheet metal deflection. Kashyap and DeVries 7 developed a dis- crete mathematical algorithm for optimisation. Table 3. Literature survey of optimisation analysis Reference Optimization analysis Method Objective function Software package Pong et al. 3 Ellipsoid method Nodal deflection N/A* Trappey et al. 5 Non-linear mathematical algorithm Nodal deflection GINO 8 Cai et al. 6 Sequential quadratic programming algorithm Nodal deflection normal to sheet metal surface VMCON 9 Kashyap and DeVries 7 Discrete mathematical algorithm Nodal deflection N/A *N/A: not applicable Fig.1. Fixture design analysis methodology 3 Fixture design analysis methodology The 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 modelling package, the workpiece model is meshed, boundary conditions are applied, the model is loaded, representative of a machining operation, the model is solved, and then boundary conditions are optimised to minimise workpiece deflections. 3.1 Workpiece model The workpiece model is the starting point of the analysis. This research currently limits the workpiece geometry to solids with planar locating surfaces. Some workpiece geometry may contain thin-walls and non-planar locating surfaces, which are not con- sidered in this study. Geometry The workpiece model, created in Pro/ENGINEER or other solid modelling software is exported to ANSYS in IGES format with all wireframes and surfaces. IGES is a neutral stan- dard format used to exchange models between CAD/CAM/CAE systems. ANSYS provides two options for importing IGES 412 Table 4. Workpiece and locator material properties Material E (Pa) (kg/m 3 ) y (Pa) Workpiece AISI 1212 2.010 11 7861 0.295 2.310 8 Locators AISI 1144 2.010 11 7861 0.295 6.710 8 files, DEFAULT and ALTERNATE. The DEFAULT option al- lows file conversion without user intervention. The conversion includes automatic merging and creation of volumes to pre- pare the model for meshing. The ALTERNATE option uses the standard ANSYS geometry database, and is provided for backward 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 IOPTN is used. See Appendix A in 1 for a detailed description of implementation. Material properties The workpiece material in this study is 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 = 3010 6 psi Poissons ratio, = 0.295, and density, = 0.283 lb/in 3 , and hardness of 175 HB. Although SAE1212 steel was selected for use in this study because it is commonly used and is a benchmark material for machinability, any material could be used for the workpiece by simply changing the isotropic material properties in ANSYS. Table 4 lists the material properties selected in this study for the workpiece and locators. 3.2 Meshed workpiece model An 8-node hexahedral element (SOLID45), with three degrees of freedom at each node, and linear displacement behaviour is selected to mesh the workpiece. SOLID45 is used for the three-dimensional modelling of solid structures. The element is defined by eight nodes having three degrees of freedom at each node: translations in the nodal X, Y, and Z directions. The SOLID45 element degenerates to a 4-node tetrahedral configu- ration with three degrees of freedom per node. The tetrahedral configuration is more suitable for meshing non-prismatic geom- etry, but is less accurate than the hex configuration. ANSYS recommends that no more than 10% of the mesh be comprised of SOLID45 elements in the tetrahedral configuration. For a de- tailed description of the element type selection process, refer to 1. 3.3 Boundary conditions Locators and clamps define the boundary conditions of the work- piece model. The locators can be modelled as point or area contact and clamps are modelled as point forces. Locators Point contact. The simplest boundary condition is a point constraint on a single node. A local coordinate system (LCS), referenced from the global coordinate system origin, is created at the centre of each locator contact area, such that the z-axis normal to the workpiece locating surface. The node closest to the centre of the local coordinate system origin is selected and all three translational degrees of freedom (u x ,u y ,andu z )are constrained. The point constraint models a rigid locator with an infinitesimally small contact area. To model locator stiffness and friction at the contact point, a 3- D interface spring-gap element is placed at the centre of the LCS. The element is connected to existing nodes on the surface of the workpiece and to a fully constrained copied node offset from the workpiece surface in the z-direction of the local coordinate sys- tem, i.e., perpendicular to the surface. Figure 2 is a model of the CONTAC52 element used to represent a linear elastic 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 contact area. For a circular contact area, a cylindrical LCS is created and nodes are selected at 0 r r L . For a rectangular contact area, a Cartesian LCS is created and nodes are selected at 0 x x L and 0 y y L . All three translational degrees of freedom (u x , u y ,andu z ) 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 copied offset perpendicular to the locating surface. Each selected node is connected to the copied node sequentially with the CONTAC52 element. Figure 3 shows the contact area model with multiple spring-gap elements in parallel used to represent a linear elastic locator. It is important to note, that the user is constrained to the number of nodes within the specified contact area, when attach- ing the CONTAC52 elements. It is possible that there could be a different number of elements modelling each locator, because of the number of associated nodes within the contact area. Thus, the element normal and tangential stiffness, which is specified in the real constant set would vary. For this reason, multiple real constant sets must be created for the CONTAC52 element, and then assigned accordingly when creating elements in a specified local coordinate system. In Fig. 4, the method for obtaining the normal and tangential stiffness for a locator is shown. The stiffness divided by the total Fig.2. CONTAC52 element used to model point contact for locators 10 413 Fig.3. CONTAC52 elements in parallel, used to model area contact for locators 10 Fig.4. Normal and tangential stiffness for locator number of springs is assigned accordingly to each spring-gap element, in the real constant set. A point load is applied to the three-dimensional finite element model of the real locator, nor- mal to the contact area to determine the normal stiffness. A point load is applied tangent to the contact area of the real locator to determine the tangential or “sticking” stiffness of the locator. The stiffness 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 and clamping forces that are generally constant for each clamp. The clamping force, F cl is applied through either a toggle mechan- ism or a bolt mechanism, which lowers a strap that comes into contact with the workpiece. Although friction is just as import- ant in clamping as it is in locating, it is not modelled at the clamp contact area due to limitations in ANSYS. In order to model friction, a comprehensive three-dimensional model of the entire workpiece-fixture system is required, with contact and tar- get surfaces defined at the fixture-workpiece contact areas. The clamping forces are modelled in ANSYS as point loads on nodes selected either within a rectangular area for a clamp strap or a cir- cular area on the workpiece surface for a toggle clamp. Both clamps may also be modelled with a single point load at the cen- tre of the clamp contact area. 3.4 Loading The two machining operations, milling and drilling, are dis- cussed. The purpose of this research is not to accurately model the machining process, but to apply the torque and forces that are transferred through the workpiece in machining, to determine the reactions at the boundary conditions of the workpiece. The de- sired result of the load model is the trend of rotation from the applied torque of the cutting tool, and translation, due to axial feeding of the workpiece and transverse motion of the table in milling. 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 axial load, P, due to feeding. The forces in drilling are time and pos- ition dependent and oscillatory due to cutter rotation, since the cutting 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 tooth distribution during rotation. In this study, the torque and thrust forces in feeding are applied as steady-state loads, since initial tool entry is not considered. In previous FEA fixture design re- search, loads were applied as a steady-state. Also neglected was cutting tool torque and subsequently the workpiece deflections due to the trend of rotation in the fixture. An initial attempt to model the distributed loading using a number of point loads applied at key points was unsuccessful, due to limitations in ANSYS. The model consisted of placing key points on a local coordinate system created on the machining surface of the work- piece. The key points w