6 th BETA CAE Internatonal Conference MULTISTAGE OPTIMIZATION OF AUTOMOTIVE CONTROL ARM THROUGH TOPOLOGY AND SHAPE OPTIMIZATION. 1 Duane Detwler, 2 Emly Nutwell*, 2 Deepak Lokesha 1 Honda R&D Amercas, USA, 2 Oho State Unversty SIMCenter, USA, 2 BETA CAE Systems USA Inc., USA, KEYWORDS Optmzaton, Topology, Shape, Mult-stage, Morphng ABSTRACT The ever-evolvng nature of the global automotve ndustry brngs about exctng challenges for the new age desgners. The trends n the overall producton costs, fuel costs and the awareness of envronmental effects are some of the many factors that drve today s automotve desgn strateges. Use of optmzaton methodologes early on n desgn process has been adopted wdely to acheve low cost and effcent component desgns. Ths paper dscusses a mult-stage optmzaton methodology to reduce the tme requred n dentfyng an optmzed concept desgn for a chasss component. As a frst stage, a topology optmzaton s performed on a vehcle control arm desgn usng LS-TaSC (LSTC). The loadng condton appled to the desgn space represents a hghly nonlnear load scenaro smlar to that seen durng a crash event n the vehcle. The topology-optmzed desgn s then subjected to a shape optmzaton. ANSA s (BETA CAE) morphng technology s used to defne the shape change parameters on an LS-DYNA load case model. An ANSA LS-OPT lnk s then created through the ANSA Task Manager. Ths allows for easy creaton of lnkages between the LS-OPT desgn varables and ANSA morphng parameters. A mnmzaton objectve s selected for overall reducton n mass whle mantanng necessary performance targets. The paper wll present results and hghlght the benefts of a multstage optmzaton strategy. 1. INTRODUCTION The use of commercally avalable optmzaton tools has expanded greatly n ndustry n the past few years, partcularly n the feld of automotve desgn. Several optmzaton tools are now readly avalable to the engneer such as topology and shape optmzaton. These tools lend themselves to dfferent stages of the desgn process. In partcular, topology optmzaton s appled early n the desgn process n order to determne the optmum layout of the materal for a defned desgn space and loadng condton(s). In contrast, shape optmzaton s appled to a well-developed structure and s well suted to fndng an optmum of ths structure for a defned loadng condton and constrants. Used n conjuncton wth each other, the structure can be developed from very early stages n whch the engneer defnes a desgn space and requred loadng condtons, to a fne-tunng of the structure, whch results n a mature desgn. Ths process, whch mplements multple optmzaton technques, wll lead to a more effcent structure for the defned loadng condtons. For ths nvestgaton, a vehcle control arm subjected to a nonlnear loadng scenaro s studed. A topology optmzaton s performed on the desgn space for ths control arm usng LS-TaSC. LS-TaSC s a topology optmzaton software avalable through LSTC whch works wth LS-DYNA as the fnte element solver. LS-TaSC provdes a user nterface for the HCA algorthm (Hybrd Cellular Automata) whch effcently handles nonlnear loadng durng topology optmzaton. Ths structure s then the bass for a shape optmzaton where several morph boxes are defned n ANSA. These parameters are then lnked to LS-OPT where constrants and mass mnmzaton s defned. The fnal structure shows that applyng shape optmzaton to the topology results n greater mass reducton whle mantanng desgn requrements. A descrpton of the topology optmzaton methodology s descrbed n the followng secton. The control arm model and loadng condton are then detaled. Topology results and an nterpretaton of the results are dscussed. The shape optmzaton where ANSA and LS-OPT are used jontly s explaned n the followng secton. A dscusson of the results and the challenges encountered durng ths project wll follow. The paper wll then conclude wth a summary.
6 th BETA CAE Internatonal Conference 2. TOPOLOGY OPTIMIZATION METHOD Hstorcally, topology optmzaton n the feld of crashworthness has been a dffcult challenge. Typcally, topology optmzaton solves problems wth elastc materals and statc loadng condtons usng a mnmzaton objectve such as mnmum complance. However, ths approach wll not adequately solve for a structure that s effcent for crashworthness. In ths case, n addton to structural ntegrty, energy absorpton s a desred characterstc. Wth ths n mnd, calculatng the nternal energy densty (IED) of a structure can be expressed as U U e U p ef de (1) 0 where the stress s ntegrated from the undeformed state to the fnal state due to loadng. For a nonlnear problem where energy-absorbng characterstcs are an mportant consderaton of the structure, the dea s to maxmze the area under the force-dsplacement curve for a defned loadng hence maxmzng the energy absorbed by the structure. Fg.1: The area under the force stroke curve represents energy absorpton. Densty based methodologes are often appled for topology optmzaton. The desgn space s represented wth a fnte element mesh and a desgn varable s assgned to each element. For ths methodology, the relatve denstes s the desgn varable ( x ) x 0 x 1 (2) 0 where 0 s the densty of the base materal. Snce nonlnear materal propertes must be consdered, a pecewse lnear materal model s needed to represent the behavor of the alumnum materal. The fnte element analyss model s nonlnear; therefore, the desgn varable not only controls the densty of the materal, but also the elastc modulus (E), the yeld stress ( y ) and the stran hardenng modulus (E h ). E ( x ) x E (3) 0 ( x ) x (4) 0 E (5) h ( x ) xeh 0 In order to avod ntermedate materal propertes, a power law approach, the Sold Isotropc Materal wth Penalzaton (SIMP) approach s mplemented. The materal propertes of the materal, such as the Young s modulus, s nterpolated as E ( x ) x E p 0 (6) where p s a penalzaton parameter whch drves away ntermedate denstes from the topology soluton.
6 th BETA CAE Internatonal Conference The topology results are calculated usng the Hybrd Cellular Automaton Method (HCA). Ths method s not explctly an optmzaton technque; however, by usng the local rules, an optmzed soluton s derved. The local rules operate accordng to local nformaton collected n the neghbourhood of each cell of the CA (Celluar Automaton) lattce so that the average structural performance of the element tself as well as ts neghbours s measured [3]. The HCA method strves to acheve a unform dstrbuton of a feld varable. Here, the feld varable s the nternal energy densty (IED) of the structure. Ths s acheved by mnmzng the devaton from a set pont x new * x K ( S S ) (7) p where K p s a scalng parameter, S s the feld varable and S * s the feld varable set pont. When the change of the structure s approxmatng zero, the feld varable, whch s the IED of the structure, s more unformly dstrbuted. In ths way, the energy absorbed by the structure defned by the desgn space s maxmzed, generatng an optmzed structure for nonlnear loadng scenaros. 3. MODEL OF VEHICLE CONTROL ARM In ths work we consder the optmzaton of a vehcle control arm structure. The load case defned for the topology optmzaton results n yeldng of the part. For ths loadcase, the desred topology optmzaton objectve s to maxmze the energy absorbed by the structure. Fg.2: The LS-Dyna control arm model (left) and the desgn space for the optmzaton (rght). The control arm has a total mass of 4.025 kg of whch the full densty desgn space s 3.506 kg. There s one nonlnear load case defned (Fg. 3) where the control arm s subjected to a prescrbed dsplacement n the x-drecton from 0 to 110mm wthn 200ms. The volume connectng the bushng mounts of the control arm s defned as the desgn space for the topology optmzaton. The volume of the entre control arm structure ncludng the desgn space s meshed usng tetrahedral elements wth a mesh sze of 3 mm nomnal. The materal of the control arm desgn space as well as the suspenson and chasss at the ends are modelled wth a pecewse lnear elastc-plastc alumnum materal model represented wth *MAT24. Ths model represents a laboratory test desgned to ensure that the suspenson components meet a mnmum load requrement. Ths laboratory test s nspred by extreme loadng condtons to the suspenson system of the vehcle. A test fxture s mounted to the wheel hub, and a chan attaches the test fxture to a loadng actuator whch then apples the load. The relevant suspenson components (damper, te rod, knuckles) are modelled usng a smplfed beam representaton n order to model realstc boundary condtons. The rubber bushngs of the model are represented wth sold elements usng *MAT_181_SIMPLIFIED_RUBBER/FOAM. Although ths controlled laboratory test s not nspred by any crash requrement, t provdes a smple but deal load case for the objectve of maxmzng energy absorpton. Ths model s analyzed usng LS-DYNA explct.
6 th BETA CAE Internatonal Conference Fg.3: The LS-Dyna model of the nonlnear load case of the control arm. A prescrbed dsplacement s appled to the chan. The rghtmost fgure shows the deformed structure when the load s appled to the full desgn space. 4. TOPOLOGY OPTIMIZATION The objectve for the topology optmzaton for the defned load case s maxmzng energy absorpton. The topology optmzaton s conducted usng LS-TaSC whch s the topology software desgned to work wth LS-DYNA. LS-TaSC provdes a user nterface for the HCA algorthm descrbed n Secton 2. A volume fracton of 0.49 s defned for the desgn space to acheve a mass target of 1.718 kg. Intally, the topology evolved too quckly allowng for large changes n the structure between teratons. Ths s a concern because f too much materal s removed too quckly, nstabltes can occur whch can results n unwanted contact behavor, large changes n deformaton modes, and possble error termnaton of the fnte element model. In ths case, large dfferences n the structure are noted between the fourth and ffth teraton wth the defned mass fracton as shown n Fgure 4. Fg.4: The topology structure at Iteraton 4 and Iteraton 5 wth default move lmt = 0.1. Contact penetraton s noted n teraton 5. The amount of materal removed n teraton 5 results n a remarkably dfferent deformaton mode and contact nstabltes were noted. The ntermedate densty elements have a very low stffness resultng n challengng contact ssues, and penetraton s noted whch s nonphyscal. Ths can lead to nstabltes, or topology results that are evolved based on nonphyscal deformaton modes. In order to account for ths, LSTC mplemented a feature n LS-TaSC where the move lmt can be adjusted. In the prevous result, nstabltes arose because the materal changed too quckly between teratons. The update rule can be expressed as: ( k) *( k) x max{ 0.1, mn{ K ( S S ),0.1}}. (8) p ( k) Therefore, the maxmum allowable change n relatve densty s 0.1. However, n ths case, 0.1 proved to be too large to develop a stable topology result; therefore, the move lmt s changed from 0.1 to 0.02. Ths wll result n the topology soluton evolvng more slowly requrng more teratons to converge. Ths computatonal cost must be weghed aganst the stablty of the topology results. The settngs LS-TaSC are called out n Table 1.
6 th BETA CAE Internatonal Conference HCA Parameter (LS-TaSC Settng) Parameter Value Mass Fracton 0.49 Mnmum Length Scale (Neghbor Radus) 9mm Move Lmt 0.02 Convergence tolerance 0.002 Table 1: Appled LS-TaSC Parameters The objectve of energy absorpton s calculated by measurng the force n the chan and ntegratng t over the stroke. The loadng and results of the topology s shown n Fgure 5. Fg.5: The topology loadng and results. 4.1 TOPOLOGY RESULTS FOR SHAPE OPTIMIZATION In order to apply the topology results for a shape optmzaton, post processng of the topology results s necessary so that the results are represented by a unform densty structure. Ths post processng was done manually n an teratve fashon, whch was very tme consumng; therefore, the process wll not be detaled here. A smooth shape s nterpreted from the topology results, and the force stroke curves are compared to ensure that the smooth arm s an equvalent structure to the topology results wth respect to the topology objectve of energy absorpton. Snce ths s measured by ntegratng the force stroke curves, ths data s the metrc used to compare the two structures as shown n Fgure 6. Fg.6: The topology results compared to the smooth arm structure as a result of manual post processng. The comparson of the force strokes curves s shown to the rght. The deformed shape of the topology result and the smooth arm s also compared to ensure adequate smlartes between the structures. Ths comparson s shown n Fgure 7.
6 th BETA CAE Internatonal Conference Fg.7: The topology results compared to the smooth arm structure as a result of manual post processng: deformed shapes are smlar. The post processng of the topology results shows comparable performance to the topology results. Therefore, the smooth structure s a good representaton of the topology results and wll be used for further optmzaton usng shape optmzaton technques. 5. SHAPE OPTIMIZATION PARAMETERIZATION IN ANSA Once the topology results are avalable, further mprovements can be made to the desgn by the applcaton of shape optmzaton. Addtonally, as a result of the post processng necessary to represent the topology results as a smooth, unform densty model, there tends to be a shft away from the optmzed pont n the desgn space. The shape optmzaton stage s necessary to mnmze the effects of such shfts and to mprove upon the topology results n order to acheve a truly optmzed desgn. To create the model for shape optmzaton, some areas of the model are dentfed for shape changes (morphng) usng the ANSA pre processor s morphng technology. The areas ntended for morphng are contaned n morphng boxes. Fgure 8 shows the structure of morphng boxes constructed to encompass the desred areas of nterest. Fg.8: The morphng boxes created to nclude areas for shape changes. Each of these hexagonal boxes ncludes handles defned for movements (morphng) whch are referred to as control ponts. The movements of these control ponts n 3-D space affect the shape of the boxes and n turn the enttes contaned wthn them. Ths nduces local changes n the shape for the control arm.
6 th BETA CAE Internatonal Conference Fg.9: Undrectonal morphng parameter to change thckness of a regon. These morphng operatons are parameterzed usng the ANSA morph parameters. A few such examples are shown n Fgure 9 & 10 to showcase the ntended effects brought about on the control arm wth the change n values of the morph parameters. Fg.10: Multdrectonal morphng parameter to change thckness of a regon. In ths model, a total of 31 such morphng parameters (Appendx A) are created to provde very specfc control over the shape change operatons. An optmzaton task created n the ANSA Task Manager tool s used to lnk these parameters to the LS-OPT optmzer code as desgn varables. The Task Manager s also used to assgn ndvdual constrant space for each desgn varable. There are tasks n place to manage the mesh qualty n cases where the morphng operaton creates dstortons n orgnal model. A meshng task s ncluded to automatcally generate sold meshes for each model status. The output from the ANSA Task Manager s a completely defned LS-DYNA model. Optmzaton Task Desgn Varable Card Fg.11: ANSA Task Manager wth Optmzaton task to lnk morph parameters to LS-OPT desgn varables. Based on the parameterzed model, a desgn of experments (DOE) study s conducted. A smple Space Fllng method s used to create 50 samples. Ths ensures a good representaton of the desgn space whle lmtng the need for a large number of samples. Partcular consderaton s placed on reducng the overall computatonal resources and human tme requred to generate a response surface. Pror to executng the LS-DYNA runs, the smulate functon n the ANSA Task Manager s used to determne potental falure samples. If necessary, the morphng boxes are adjusted such that each sample wll result n a runnng LS-DYNA fle n order to elmnate erroneous results. Ths crtcal step s necessary to make ths process economcally vable whle beng techncally relevant.
6 th BETA CAE Internatonal Conference 6. SHAPE OPTIMIZATION: LS-OPT The LS-OPT optmzaton setup s created as shown n Fgure 12. LS-OPT s programmed to call n an ANSA module to lnk the ANSA fle contanng the morphed model. It s also able to decpher the ANSA generated DV (Desgn Varable) fle and auto load the desgn varables nto LS-OPT. LS-OPT then updates the DV fle based on the samplng data to execute the ANSA module and create the desgn of experment models and submt them to LS-DYNA for soluton. The responses and constrants are defned usng LS-DYNA output. The objectve for the shape optmzaton s defned to mnmze the mass of the structure. In order to mantan structural ntegrty, a mnmum load n the chan s defned as a constrant. Also, a maxmum plastc stran s defned n order for the shape optmzaton to generate a robust structure. Fg.12: The LS-OPT Database for shape optmzaton. The LS-DYNA parameters and the constrants are detaled. The accuracy plots show that although the force and mnmum mass values are well predcted by the meta model defned, the plastc stran show sgnfcant nose. Ths can be traced back to several ssues ncludng the manual post processng that was used to generate the smooth model of the lower arm needed for the shape optmzaton. Ths problem s hghlghted when the confrmaton run volates the plastc stran constrant resultng n the computed optmum not meetng the plastc stran requrement. Fg.13: The calculated optmum arm shows volatons of the plastc stran constrant. The accuracy plots ndcate that although the mass objectve and force constrant are well predcted; the plastc stran constrant s not. The arrow n the mass plot ndcates the best feasble smulaton run (lowest mass and all constrants satsfed). For purposes of ths nvestgaton, the best smulaton pont (.e. lowest mass) whch s feasble wll be used as the result of the shape optmzaton rather than the calculated optmum whch volates the plastc stran constrant. Ths pont s ndcated n the mass plot n Fgure 13. Although ths s not a true
6 th BETA CAE Internatonal Conference optmum, t s suffcent to valdate the process of usng topology and shape optmzaton n tandem wth each other. Fgure 14 shows the results of the shape optmzaton compared to the smooth arm that s derved from the topology optmzaton. Overall, the shape optmzaton results n an 11% reducton n mass of the desgn space. Fg.14: The results of the arm derved from topology optmzaton only and topology + shape optmzaton. The shape optmzaton results n an 11% reducton n mass whle achevng all constrants defned for the control arm performance as shown n the force-stroke curves. 7. CONCLUSIONS In ths paper, a process s outlned to combne topology optmzaton wth shape optmzaton n order to evolve a desgn of a suspenson control arm wth mnmzed weght whle achevng performance targets. Topology optmzaton s conducted on a desgn space whch would be avalable early n the development flow. Post processng of the topology results s necessary n order to apply shape optmzaton to ths desgn. Ths s a potental area of future research snce ths was done manually and was not an effcent process. Ths manual process also results n dffcultes for the morphng durng the shape optmzaton. Combnng shape optmzaton wth topology optmzaton results n an 11% reducton n mass over applcaton of topology optmzaton alone. Therefore, ths nvestgaton successfully showcases the applcaton of topology and shape optmzaton to generate an optmal structure whch meets defned desgn requrements. 7. ACKOWLEDGEMENTS We thank Wllem Roux from LSTC for hs contnung support, partcularly wth regard to the mplementaton of the varable move lmt functonalty n LS-TaSC. We also thank Imtaz Gandkota from LSTC for hs support wth LS-OPT. REFERENCES (1) ANSA verson 12.1.5 User s Gude, BETA CAE Systems S.A., July 2008 (2) Patel, N. M.: Crashworthness desgn usng topology optmzaton, Ph. D. thess, Unversty of Notre Dame, 2007. (3) Patel, N. M., Kang, B.-S., Renaud, J. E. and Tovar, A.: Crashworthness desgn usng topology optmzaton, Journal of Mechancal Desgn 131, 2009, 061013. (4) Lvermore Software Technology Corporaton: The LS-TaSC TM Software, Topology and Shape Computatons Usng the LS-Dyna Software, User s Manual, Verson 3.0, from: www.lspoptsupport.com, 2013. (5) Lvermore Software Technology Corporaton: The LS-OPT TM User s Manual A Desgn Optmzaton and Probablstc Analyss Tool for the Engneerng Analyst, Verson 5.0, from: www.lspoptsupport.com, 2013. (6) Aulg, N., Nutwell, E., Menzel, S., Detwler, D.: Towards mult-objectve topology optmzaton of structures subject to crash and statc load cases, Engneerng Optmzaton 2014, CRC Press, 2014, 847-852.
6 th BETA CAE Internatonal Conference (7) Olason, A., Tdman D.: Methodology for Topology and Shape Optmzaton n the Desgn Process, Master s Thess, Chamlers Unversty of Technology, 2010. (8) Bendsøe, M.: Optmzaton of Structural Topology, Shape, and Materal, Sprnger Verlag Berln Hedelberg New York, 1995. (9) Roux, W.: Topology desgn usng LS-TaSC TM verson 2 and LS-DYNA, 8th European LS-DYNA Users Conference, 2011. (10) Lvermore Software Technology Corporaton: The LS-DYNA TM Keyword User s Manual Vol I and II, LS-DYNA R7.1, from: www.lstc.com/download/manuals, 2014. (11) ETA PostProcessor verson 6.2.0. User s Gude, BETA CAE Systems S.A., June 2008
6 th BETA CAE Internatonal Conference APPENDIX A: Table A: Desgn Varables and constrants space