夹具设计完整性验证和优化的有限元分析工具的开发.pdf

1、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 fi nite element analysis tool for fi xturedesign integrity verifi cation and optimisation Received: 15 March 2003 / Accepted: 11 May 2003 / P

2、ublished online: 25 August 2004 Springer-Verlag London Limited 2004 Abstract Machining fi xtures are used to locate and constrain a workpiece during a machining operation. To ensure that the workpiece is manufactured according to specifi ed dimensions and tolerances, it must be appropriately located

3、 and clamped. Minimising workpiece and fi xture tooling defl ections due to clamping and cutting forces in machining is critical to machining accuracy. An ideal fi xture design maximises locating accuracy and workpiece stability, while minimising displacements. The purpose of this research is to dev

4、elop a method for mod- elling workpiece boundary conditions and applied loads during a machining process, analyse modular fi xture tool contact area deformation and optimise support locations, using fi nite element analysis (FEA). The workpiece boundary conditions are defi ned by locators and clamps

5、. The locators are placed in a 3-2-1 fi xture confi guration, 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 operat

6、ions. Fixture design integrity is verifi ed. ANSYS parametric de- sign language code is used to develop an algorithm to auto- matically optimise fi xture support and clamp locations, and clamping forces, to minimise workpiece deformation, subse- quently increasing machining accuracy. By implementing

7、 FEA in a computer-aided-fi xture-design environment, unnecessary and uneconomical “trial and error” experimentation on the shop fl oor is eliminated. Keywords FEA Finite Element Analysis Fixture Optimisation N. Amaral (u) V-Engine Manufacturing Engineering, Ford Motor Company, Powertrain Operations

8、, 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 fi xtures are used to locate and constrain a work- piece during a machining operation. To

9、 ensure that the work- piece is manufactured according to specifi ed 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 fi x- ture tooling defl ection

10、s 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- fi xture system stiffness. An ideal fi xture design maximises locat- ing accuracy, workpiece stability, andstiffness, while minimisi

11、ng displacements. Traditionally, fi xtures were designed by trial and error, which is expensive and time consuming. Research in fl exible fi xtur- ing and computer-aided-fi xture-design (CAFD) has signifi cantly reduced manufacturing lead-time and cost. The purpose of this research is to develop a c

12、omputer-aided tool to model workpiece boundary conditions and applied loads in machining. The majority of fi nite element analysis (FEA) research con- ducted in fi xture design considers workpiece boundary condi- tions to be rigid and applied loads to be concentrated. In all cases where friction is

13、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 infl uence the global st

14、iffness of the workpiece-fi xture system. The boundary conditions of the work- piece, the locators, are modelled as multiple springs in parallel attached to the actual workpiece-fi xture contact area on the sur- face of the workpiece. Also, tangential and normal stiffness com- ponents of the boundar

15、y 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

16、in Amaral 1. In this study, both the fi nite element analysis and optimisa- tion are conducted in ANSYS. Within the analysis, a workpiece is imported in initial graphics exchange specifi cation (IGES) for- mat. Material properties, element type, and real constants are defi ned. The workpiece is mesh

17、ed 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 tominimise workpiece defl ec- tion 1. The advantage of the method developed herein is that an external soft

18、ware package for optimisation is not required, thus compatibility between two packages is not a concern. 2 Literature review Principles of fi xture design and preceding FEA research in fi x- ture design are discussed. Although some research has been con- ducted in fi xture design, a comprehensive fi

19、 nite 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 fi xture design. Table1. Literature survey of workpiece models ReferenceWorkpiece model MaterialElement type TypeE (Pa) Lee

20、 and Haynes 2Steel homogeneous6.91080.3U/A*3-D solid 8-node brick Isotropic linear elastic Pong et al. 3Aluminium homogeneous6.910100.3U/A3-D solid 10-node tetrahedral; Isotropic linear elasticANSYS SOLID92 Trappey et al. 5Aluminium homogeneous6.910100.30.3U/A Isotropic linear elastic Cai et al. 6St

21、eel2.110110.3U/A2-D 4-node rectangular element; Isotropic linear elasticMSC NASTRAN QUAD4 Kashyap and DeVries 7Aluminium homogeneous6.910100.3U/A3-D solid tetrahedral elements Isotropic linear elastic *U/A: unavailable Table2. Literature survey of boundary conditions and loading ReferenceFixture com

22、ponent modelSteady-state load model LocatorsClampsDrillingMilling Lee and Haynes 2Rigid area constrain,U/A*U/ANormal and shear point loads Rigid coulomb friction Pong et al. 33-D spring-gap interface element,N/A*Normal point loadsN/A Rigid coulomb friction Trappey et al. 53-D solid deformable constr

23、aintsPoint loadsNormal point loadsNormal and shear point loads Cai et al. 6Rigid point constraintsN/ANormal point loadsNormal and shear point loads Kashyap and DeVries 7Rigid point constraintsPoint loadsNormal point loadsNormal and shear point loads *U/A: unavailable *N/A: not applicable Lee and Hay

24、nes 2 used FEA to minimise workpiece defl ec- tion. Their workpiece was modelled as linear elastic, however fi xture 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

25、. Their study considers the importance of part defor- mation with respect to the necessary number of fi xturing elem- ents and the magnitude of claming forces 3. Coulombs law of friction was used to calculate the frictional forces the workpiece- fi xture contact points. The machining forces were app

26、lied at nodal points. Manassa and DeVries 4 conducted similar re- search to that of Lee and Haynes 2, but modelled fi xturing 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 conditi

27、ons. Three-dimensional tetrahedral elements were used to mesh the fi nite element model of the solid work- piece. All contacts between the workpiece and the fi xture were considered to be point contacts and machining forces were ap- plied sequentially as point loads. The positions of locators and cl

28、amps, and clamping forces were considered design variables for optimisation. Trappey et al. 5 developed a procedure for the verifi cation of fi xtures. FEA was used to analyse the stress- strain behaviour of the workpiece when machining and clamping 411 forces were applied. A mathematical optimisati

29、on model was formulated to minimise workpiece deformation with a feasible fi xture confi guration. 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 fi xture tool defor

30、mation, and developed an op- timisation algorithm to minimise defl ections at selected nodal points by considering the support and tool locations as design variables. A summary of research on FEA and fi xture design optimi- sation is shown in Table 3. The majority of research conducted in fi nite el

31、ement analysis and fi xture 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 defl ection. Trappey et al. 5 used an exter- nal software package, GINO 8, to optimise support location

32、s 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 defl ection. Kashyap and DeVries 7 developed

33、a dis- crete mathematical algorithm for optimisation. Table3. Literature survey of optimisation analysis ReferenceOptimization analysis MethodObjective functionSoftware package Pong et al. 3Ellipsoid method Nodal defl ectionN/A* Trappey et al. 5Non-linear mathematical algorithm Nodal defl ectionGINO

34、 8 Cai et al. 6Sequential quadratic programming algorithm Nodal defl ection normal to sheet metal surfaceVMCON 9 Kashyap and DeVries 7Discrete mathematical algorithm Nodal defl ectionN/A *N/A: not applicable Fig.1.Fixturedesignanalysis methodology 3 Fixture design analysis methodology The fl owchart

35、 in Fig. 1 is a summary of the fi xture 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

36、operation, the model is solved, and then boundary conditions are optimised to minimise workpiece defl ections. 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

37、geometry may contain thin-walls and non-planar locating surfaces, which are not con- sidered in this study. GeometryTheworkpiecemodel,createdinPro/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

38、 to exchange models between CAD/CAM/CAE systems. ANSYS provides two options for importing IGES 412 Table4. Workpiece and locator material properties MaterialE (Pa) (kg/m3)y(Pa) WorkpieceAISI 12122.0101178610.2952.3108 LocatorsAISI 11442.0101178610.2956.7108 fi les, DEFAULT and ALTERNATE. The DEFAULT

39、 option al- lows fi le 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

40、 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 fi le, the IOPTN is used. See Appendix A in 1 for a detailed descr

41、iption 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

42、 modulus, E = 30106psi Poissons ratio, = 0.295, and density, = 0.283 lb/in3, 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 th

43、e 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

44、the workpiece. SOLID45 is used for the three-dimensional modelling of solid structures. The element is defi ned 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 confi gu- ration with

45、 three degrees of freedom per node. The tetrahedral confi guration is more suitable for meshing non-prismatic geom- etry, but is less accurate than the hex confi guration. ANSYS recommends that no more than 10% of the mesh be comprised of SOLID45 elements in the tetrahedral confi guration. For a de-

46、 tailed description of the element type selection process, refer to 1. 3.3 Boundary conditions Locators and clamps defi ne 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 simp

47、lest 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 o

48、f the local coordinate system origin is selected and all three translational degrees of freedom (ux, uy, and uz) are constrained. The point constraint models a rigid locator with an infi nitesimally small contact area. Tomodellocatorstiffnessandfrictionatthecontactpoint,a3- D interface spring-gap el

49、ement 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 o

50、f the CONTAC52element usedtorepresent a linearelastic locator. Area contact. To model a rigid locator with a contact area, multiple nodes are fi xed 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 cylindr

51、ical LCS is created and nodes are selected at 0 r rL. For a rectangular contact area, a Cartesian LCS is created and nodes are selected at 0 x xL and 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, howe

52、ver 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 selectednode is connected to th

53、e 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 specifi ed contact area, when

54、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 specifi ed in the real constant set would vary.

55、For this reason, multiple real constant sets must be created for the CONTAC52 element, and then assigned accordingly when creating elements in a specifi ed local coordinate system. In Fig. 4, the method for obtaining the normal and tangential stiffness for a locator is shown. The stiffness divided b

56、y 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 co

57、nstant set. A point load is applied to the three-dimensional fi nite 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” stiffnessof the lo

58、cator. 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, Fclis applied through eith

59、er 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-fi xture system is required, with contact and tar- get surfaces defi ned at the fi xture-workpiece contact areas. The clamping forces are modelled in ANSYS as point loads on nodes selectedeither within a rectangular area for