MULTI-DISCIPLINARY SYSTEM DESIGN OPTIMIZATION OF THE F-350 REAR SUSPENSION *

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1 AIAA-00-xxxx MULTI-DISCIPLINARY SYSTEM DESIGN OPTIMIZATION OF THE F-350 REAR SUSPENSION * Jcob Wronki Mter of Science Cndidte Deprtment of Mechnicl Engineering MIT CADlb J. Michel Gry Mter of Science Cndidte Deprtment of Mechnicl Engineering MIT CIPD ABSTRACT Thi pper preent how Multi-Diciplinry Sytem Deign Optimiztion (MSDO) pproch cn be implemented to optimize the performnce of the F 350 Ford truck rer upenion ubytem. The MSDO pproch encompe five phe: problem nd ytem definition phe, numericl imultion phe, deign pce explortion phe, ingle objective optimiztion phe, nd multi-objective optimiztion phe. Ech of thee phe i preented within the pecific context of the deign nd performnce of the F-350 Ford truck rer upenion. The upenion ytem w defined uing even deign vrible, twelve fixed prmeter, ix contrint nd two objective. The overll objective, to mximize upenion performnce, w meured in term of penger comfort which w in turn bed primrily on the mximum ccelertion experienced by the penger cbin. For multi-objective optimiztion, the ettling time of the penger cbin w dded econd meure of penger comfort. Uing thi ytem definition, numericl imultion of the upenion w creted in Mtlb. An orthogonl rry w ued to determine n initil trting point for full optimiztion. Both grdient-bed nd heuriticbed optimiztion technique re employed well weighted multi-objective technique. The reult of thee effort re preented nd ome concluion re drwn. Motivtion INTRODUCTION When cutomer buy vehicle, there re mny fctor he/he conider. Among thee re cot, g milege, fety, nd the moothne of the ride. It i well known tht the deign of the upenion ffect ll of thee fctor. To illutrte, poorly deigned upenion my reult in ny of the following itution tht directly relte to the fctor bove: rough ride over certin rod condition, cttrophic filure of the xle under certin loding condition, fuel inefficiency due to exce weight, nd increed ticker price due to the ue of unnecerily expenive component. A good deign theoreticlly would void ll thee itution. However, thi cn be difficult to chieve in prctice. Approch In n effort to reduce the difficulty ocited with upenion deign, Multidiciplinry Deign Optimiztion (MSDO) pproch w ued. Specificlly, it w pplied to the deign of the rer upenion of the F-350 Ford truck. Figure 1 how the rchitecture of thi upenion. * In Collbortion with Ford Motor Compny. Copyright 00 by J. Michel Gry nd Jcob Wronki of the Mchuett Intitute of Technology. Publihed by the Americn Intitute of Aeronutic nd Atronutic, Inc. nd the Americn Society of Mechnicl Engineer with permiion. 1

2 K Spring Stiffne N/m None The deciion w lo motivted by the fct tht the deign vrible motly repreent the geometry of the upenion deign, nd chnge in thi geometry re n ey thing to viulize nd undertnd. Pper Outline Figure 1. CAD Model of the F-350 Rer Supenion. The reminder of thi pper proceed follow. Firt, forml definition both the ytem nd the problem re preented. Second, the numericl imultion of the phyicl ytem i dicued. Next follow dicuion of the initil deign pce explortion proce. Fourth, the etup nd reult of ingle objective optimiztion re preented for both grdient-bed nd heuritic-bed erch method. Next, the reult from multi-objective optimiztion technique re explored. Finlly, concluion drwn from the reult re mentioned with brief dicuion of future work. PROBLEM AND SYSTEM DEFINITION The deign problem being ddreed i relted to the optimiztion of the performnce of the F-350 Ford truck rer upenion. Thi upenion ytem w defined in four wy. Firt, it w defined by everl deign vrible. Thee re deign chrcteritic tht cn be chnged by the deigner within certin bound. Second, it w defined by et of fixed prmeter. Thee re thoe deign chrcteritic tht cnnot be chnged by the deigner. Third, contrint were ued to define the ytem. Thee re limittion tht the upenion deign i ubject to or minimum performnce criteri tht the deign mut meet. Finlly, ytem objective were defined. Thee re chrcteritic by which the performnce of the upenion w meured. Ech of thee four re of ytem definition i now ddreed. Deign Vrible The choen deign vrible re ll rel, continuou, bounded number nd re hown in Tble 1. Alo, only the dmping coefficient of the hock borber, C, i not geometric chrcteritic. Thee chrcteritic were choen deign vrible becue it w felt tht upenion deigner would hve liberty to chnge them within certin bound. Fixed Prmeter The fixed prmeter for the upenion re hown in Tble. Thee include mteril propertie, overll vehicle nd tire dimenion, rod urfce prmeter nd phyicl contnt. Thee were chrcteritic of the ytem tht were umed to be out of control of the deigner. Tble 1. Deign Vrible. L Tble 1. Deig n Vrible Lower/Upper Symbol Decription Unit Nominl Vlue Bound length of lef pring m 1 1 <= L <= 1.5 h thickne of lef pring m <= h <=.05 b width of lef pring m <= b <=.15 t thickne of xle tube m <= t <=.015 d outer dimeter of xle tube m <= d <=.150 L bending length of xle m <= L <= 0.7 C dmping coefficient of hock borber N/m <= C <= 5000 Tble Tble. Fixed. Prmeter. Symbol Decription Unit Vlue E Modulu of Elticity, teel P 06x10 9 ω i Rod bump frequency rd/ 1.57 m c M of penger cbin kg 1800 g grvity contnt m/ 9.81 d w dimeter of the wheel meter 0.5 u tire on cement liding friction coeffient Unitle 0.6 F t Rod bump height meter 0.1 K t Stiffne of Tire N/m ρ denity of teel kg/m S f Stre fety fctor Unitle L hlf length of xle meter 0.9 m t M of the tire kg 18 Contrint Tble 3 lit the intermedite vrible of the upenion deign tht were either ubject to contrint or were needed for the clcultion of the objective. Note tht while the ettling time, S t, i lited here being ubject to contrint, it i lter treted econd objective in the multi-objective optimiztion phe of MSDO. There re lo contrint on cot, g milege, internl xle tre, nd the nturl frequency rtio of the m of the upenion nd the m of the penger cbin. Tble 3. Intermedite T ble 3. Intermedite or Contrined Vrible Vrible. Symbol Decription Unit Contrint m M of Supenion Prt kg None

3 Objective Tble how the objective for ingle objective optimiztion. The overll objective of thi optimiztion deign i to mximize the penger comfort inide the utomobile cbin. After creful conidertion it w decided tht penger comfort would be defined in numericl term the verticl ccelertion of the penger cbin cued by the vehicle driving over rod bump. The ingle objective optimiztion problem w to minimize thi ccelertion. The Dynmic Module The dynmic behvior of the F-350 rer upenion w modeled uing th order qurter-cr upenion model coniting of pring, me, nd dmper (ee Figure ) [1]. To imulte the rod diturbnce, tep input function, F t, of 0.1 meter w ued to imulte lrge bump []. Criticl model input re: (i) the penger cbin nd upenion m, m c nd m, (ii) the lef pring nd tire tiffne, K nd K t, nd (iii) the dmping coefficient of the upenion dmper, C. Since the dmping coefficient of the tire, C t, w negligible in reltion to the ret of the ytem it w not included in thi nlyi. The output of thi model re the ettling time, S t, the mximum cbin ccelertion mx, nd the nturl frequency rtio, ω rtio between the two me. Tble. Single T ble Optimiztion. Objec ve Objective. Symbol Decription Unit Minimize mximum Min [ mx ] ccelertion experienced by m/ penger cbin In the lt phe of MSDO econd objective w introduced, nmely the ettling time, S t. Settling time i lo n importnt meure of overll comfort in the penger cbin it repreent how long the cbin ocillte fter rod diturbnce h been clered. A long ocilltion period my be very uncomfortble to the penger inide jut high ccelertion re. For thi reon it w choen the econd objective. NUMERICAL SIMULATION In order to ue the MSDO methodology, numericl imultion of the behvior of the phyicl ytem mut be creted. Thi w done uing the ytem definition decribed bove to crete et of linked multidiciplinry module tht imulte the behvior of the ytem. In thi ce, there were ix module, one for ech of the following pect of the deign: the dynmic, the tiffne of the lef pring, the xle internl tree, the upenion m, the cot, nd the g milege. Ech of thee module will now be dicued. 3 To vlidte the dynmic module, the verticl diplcement repone of m when ubject to 0.1 meter tep rod diturbnce, F t, w compred to the reult found in [1] for n identicl itution. The two repone mtched to within bout 5%. The Lef Spring Stiffne Module The lef pring w modeled teel primtic br obeying Hooke lw [3]. The boundry condition were imple upport on ech end with ingle centered point lod F (ee Figure 3). Input for thi module re the dimenion of the lef pring, L, h, nd b, nd E, the modulu of elticity of teel. The output of thi module i the lef pring tiffne, K, which i found from the following eqution: F 8EI Eb h K = = = δ L 3 L 3 3 E = m o dulu o f e l tic ity o f te e l 3 b h I = 1 h b L (1) A F

4 ytem i ntive to I-DEAS Verion 8 nd i hown in Figure 5. Thi output i ued in everl other module. The phyicl upenion i compoed of three-piece lef pring nd dmper ttched to hollow xle. To obtin the upenion m, the I-DEAS model w prmetriclly driven uing five deign vrible nd one fixed prmeter: (i) the lef pring length, L, (ii) the lef pring width, b, (iii) the lef pring thickne, h, (iv) the hft dimeter, d, (v) the hft The Axle Internl Stre Module The xle w modeled tubulr bem with imple upport t ech end [3]. The penger comprtment reting on the xle w modeled two equl nd ymmetriclly locted point lod F (ee Figure ). The input for thi module re the loction of the lod from the end of the bem, F, nd the dimenion of the xle, t nd d. The output of thi module i the mximum internl tre, Ω mx. To find Ω mx, the bending, her, nd torion tree due to the combintion of the weight of the penger cbin nd the dynmic loding were clculted from the following eqution repectively: mx d 8 m c ( g + mx ) d I π ( d ( d T M = = () σ mx ) ) V m c( g + mx ) (b) ν mx = = A c πd Td m c ( g + mx ) d w µ (c) τ mx = = J π ( d ( d T ) ) wll thickne, t, nd (vi) the denity of teel, ρ. DOME, progrm tht link CAD model to other imultion code uch Mtlb nd w developed t the MIT CADlb, w ued to link thi module to the other module. Penger Cbin A L F D B F L T Then, uing Mohr circle [3] nd the tree bove, mximum internl tre of the xle, Ω mx, cn be found from the following eqution: Ω = mx[ Z, Z ] (3) mx 1 L C Figure. A) Rer view of truck, B) xle cro ection, nd C) front view of xle. mx where Z = σ mx 1 + σ mx +τ (3b) nd Z = τ +ν (3c) mx mx The Supenion M Module Thi imple but importnt module i ued to clculte the m of the upenion, m, bed on the prt dimenion nd mteril denitie obtined directly from the CAD geometry of the upenion. The CAD model repreenttion of the F-350 upenion

5 Figure 5. CAD model of F-350 rer upenion. DESIGN SPACE EXPLORATION G Milege Module The g milege module i plceholder module bed on dt of other vehicle in the me cl. G milege, GM, i given by the following eqution uing the m of the upenion, m, input: GM = ( m ) () Thi model clculte the energy conumption of the propoed upenion deign nd uch introduce environmentl libility in thi multi-diciplinry optimiztion problem. Cot Module Since the ctul cot of the F-350 rer upenion ytem w not known, imple polynomil expreion w ued to etimte reonble cot in thi tudy. Input re the me of the cr nd upenion, m c nd m, the bending length of the xle nd lef pring, m c nd m, nd the dmping coefficient of the hock borber. The cot, C, of the upenion i given by: C = y ( m + m )+ y c C + L where y 1 3 L y 3 3 The complete numericl imultion of the upenion w creted by the input nd output of ll ix module hown in Figure 6. It i intereting to note tht there re no feedbck loop in the imultion. Figure 6. The Completed Simultion with Six Linked Module. (5) Before beginning ny rigorou optimiztion, n L 18 orthogonl rry of even deign vrible with three level w ued to explore the deign pce. From thi rry of experiment, n initil deign vector X o, w choen tht hd the lowet objective vlue, mx, without violting ny of the contrint. Thi initil deign vector pper in the left ide of Figure 7. Then, by clculting the digonl entrie of the Hein, X o w cled o tht ll the deign vrible were roughly on the me order of mgnitude. Thi cled deign vector i hown in Figure 7 on the right X o. L 1.00 h. 005 b. 100 X o = t =. 010 d. 15 L. 5 C 1500 Before X o L 1.5 h 0.5 b 1.0 = t = 1.0 d 1.5 L. 6 C 1. 5 After Figure 7. The Deign Vector Before nd After Ccling. SINGLE OBJECTIVE OPTIMIZATION Grdient-Bed Serch With the MSDO frmework etblihed nd n initil deign vector choen, forml optimiztion cn now be executed. Initilly, the Qui-Newton, SQP grdient erch embodied in the fmincon function in Mtlb w ued to optimize the deign. The erch w executed by trting with both the cled nd uncled initil deign vector nd the reult re hown in Tble 5. Mtlb reported tht both run converged uccefully. Thi men tht the Kruh- Kuhn-Tucker (KKT) condition re tified within the defult tolernce of t the optimum olution. It i cler from Tble 5 tht lthough both run converged to the me objective vlue of mx, J(X*), the erch converged much quicker (more thn.5 time) when trting with the cled initil deign vector. Tble 5. Effect of Scling on J(X*) nd Elped Time. 5 Run Decription J(X*) (m/ ) Elped Time () Uncled, (X o ) Scled, (X o )

6 Compring the deign vector before nd fter optimiztion (uing the cled initil deign vector), everl thing cn be noted (ee Tble 6). Firt, L, remin unchnged. Thi i becue L only ffect the internl tre in the xle nd while it i not pprent now, we will ee lter tht the contrint on the internl tre i not ctive t the optiml olution. Second, t the optiml olution, t nd d re ner their upper bound thu reulting in bigger xle nd hevier upenion. Thi i mot likely due to the fct tht hevier upenion reult in lower cbin ccelertion nd lower internl tree, both deirble effect in thi ce. Of coure, hevier upenion lo men lower g milege rting. We will ee lter tht the g milege contrint i ctive t the optimum. Third, h i ner it lower bound. Thi probbly due to the fct tht thinner lef pring will hve mller lower tiffne thereby reducing penger cbin ccelertion. Finlly, mx, w reduced by 3%, ignificnt improvement. Of coure, there i no gurntee tht thi erch found the globlly optiml olution, but it h clerly found locl optimum (ince the KKT condition re met) nd Tble it repreent 6. Optimiztion modet Reult: improvement Deign Vrible over & Objective the bet olution Deign (cled) found wit L h hth e b orthogonl t d Lrry. C J(x)= For mx Before viul Optimiztion1.00 repreent n of 1.00 thi improv emen t, 1.5 Figure After how Optimiztion the verticl cc 1.16 elertion of the penger cbin,, function of time, both before nd fter optimiztion. mx occur fter bout.05 econd t the pek of the firt ocilltion. Tble 6. The Initil nd Optimum Deign Vector. Deign L h b t d L C J(X), mx Initil, (X o ) Optimum, (X*) / ) Accelertion (m = Before Optimiztion = After Optimiztion Heuritic-Bed Serch In ddition to uing Qui-Newton grdient erch, two heuritic technique were executed for comprion: Simulted Anneling lgorithm (SA), nd Genetic Algorithm (GA). Both of thee heuritic method were executed in isight uing the me initil cled deign vector, X o, hown in Figure 7. The reult of thee optimiztion run re hown in Tble 7 nd 8. The reult from the grdient erch re lo hown in thee tble for comprion. The SA w et to converge when the erch reulted in five conecutive identicl deign. Convergence for the GA w bed on the number of genertion, which w et to 50 in thi ce. Tble 7. The Optimum Deign Vector Obtined by All Three Serch Method. Run Type L h b t d L C J(X*), mx SA, (X*) GA, (X*) SQP, (X*) Tble 8. The Contrined Module Output nd Elped Time for the Three Serch Method. Run Type Ω mx (MP) GM (mpg) S t () ω rtio C ($) xc mx (m) Elped Time () SA GA SQP Looking t Tble 7, it cn be een tht the grdient erch found better olution thn either of the two heuritic technique lthough ll three found deign with imilr performnce. The mot triking difference between the three erch method i in the elped time. The SA took 70 time long nd the GA took 10 time long the SQP method. It i cler tht for t let thi deign problem, the grdient technique w both fter nd more ucceful. Objective Senitivity Anlyi Once the optiml deign vector, X*, w clculted, the enitivity of the objective function with repect to the deign vrible round the optiml point w invetigted. Time () Figure 8. The Verticl Accelertion of the Penger Cbin Before nd After Optimiztion. 6

7 Normlized enitivitie of the objective function with repect to ech deign vrible were obtined uing the finite difference pproch. The clculted enitivitie re hown in Figure 9. It i cler from Figure 9 tht the objective function w mot enitive to the dmping coefficient of the hock borber, C. Since the objective w to minimize the mximum verticl ccelertion of the penger cbin, mx, ny incree in the dmping coefficient would hve reulted in wore deign. Thoe with knowledge of upenion deign my hve been ble to nticipte thi reult. It cn lo be een from Figure 9 tht ny incree in the outer dimeter of the xle, d, the thickne of the xle tube, t, nd the length of the lef pring, L, would improve the objective. Thi i to be expected ince they ll incree the weight of the upenion nd hevier upenion re not enitive to rod condition. However, thee chnge come with price. Increing the weight of the upenion lo h ome undeirble ide effect. More on thi trde off between performnce nd weight will be highlighted lter. From Figure 9, it cn lo be een tht objective function i inenitive to the loction of the ttch point of the penger cbin to the xle, L, Thi i due to the fct tht L, only ffect the internl tree of the xle nd not the weight or dynmic propertie of the upenion. Deign Vrible Dmping Coefficient Width of Lef Spring Ditnce To "Attch Point" Outer Dimeter of Axle Tube Thickne of Axle Tube Thickne of Lef Spring Length of Lef Spring Figure 9. Senitivity of J(X* ) With Repect to the Deign Vrible. Prmeter Senitivity Anlyi The enitivity of the optimum deign vector X* w invetigted with repect to the following fixed prmeter: the mteril denity, ρ, the m of the cr, m c, nd the cr tire tiffne, K t. A forwrd difference pproximtion w ued to clculte δp/δx for ech of the even deign vrible. Thi w 7 ccomplihed by clculting p/ X for 1 different perturbtion tep ize, p, rnging from 0.1%-10% of the nominl vlue of ech fixed prmeter. Thi dt w ued to determine the perturbtion rnge over which the liner pproximtion mde when uing finite differencing method i vlid. The bet tep ize w choen for ech ce nd the reult re ummrized in Tble 9. Tble 9. Senitivity of X* With Repect to Three of the Fixed Prmeter. Deign Vrible Prmeter L / p b / p h / p t / p d / p L / p C / p ρ (Mteril Denity) -6.0E-0 -.0E E E E m c (M of Cr).00E E E-0 K t (Tire Stiffne) 1.50E E It cn be een from Tble 9 tht n incree in the mteril denity will reult in decree in ll but of the deign vrible. Thi i becue thee two deign vrible, L nd C, re not relted to the mteril denity in ny of the module in the imultion nd therefore their enitivitie with repect to the mteril denitie re both zero. From Figure 9 it i lo evident tht L, h, nd C re enitive to chnge in the m of the cr (penger cbin). Thi i becue chnge in the m of the cr ffect the dynmic propertie of the ytem nd the pring dimenion nd hock borber dmping propertie mut compente. Similrly, when K t i chnged, the pring dimenion mut chnge to ccommodte. Contrint Senitivity Anlyi Clcultion reveled tht three of the 6 contrint re ctive t X*. They re the lower limit on GM (g milege), nd the upper limit on ω rtio (nturl frequency rtio) nd S t (ettling time). Notice tht the mximum internl tre, Ω mx, i not ctive t the optimum. The Lgrnge multiplier, λ, for the ctive contrint repreent the enitivity of J(X*) to thee contrint. Tble 10 how the Lgrnge multiplier for the three ctive contrint. It cn bee een tht Settling time i the mot importnt ctive contrint. Tble 10. Lgrnge multiplier of the Three Active Contrint t X*. Active Contrint λ GM (g milege) 1.3 S t (ettling time) ω rtio (nturl frequency rtio) 1.551

8 In fct, moving the minimum ettling time contrint from vlue of.5 to 5.0 econd llow the objective function to chnge from m/ to 6.87 m/. Thi ignificnt improvement confirm the importnce of thi contrint to the minimiztion of the mximum verticl ccelertion of the penger cbin. For the lt phe of MSDO, thi contrint w lifted nd ettling time w treted econd objective. MULTI-OBJECTIVE OPTIMIZATION In the previou phe, the focu w on deign optimiztion reltive to ingle objective. Since mximizing penger comfort when trveling over rough terrin w the overll gol, minimizing mx w uitble objective. However, nother fctor tht i importnt to penger comfort relting to the upenion i the mount of time tht the penger cbin continue to ocillte fter the rough terrin h been ped. Thi i often clled ettling time. A upenion tht optimize overll penger comfort would relly tke thi into ccount in ddition the verticl ccelertion. Thu ettling time, S t, w choen econd objective. Preto Front Cretion To crete Preto front for the multi-objective problem decribed bove, weighted um pproch w ued. The new objective h the following form: min[j ( X )] (6) i where J i ( X ) = (1 w i ) ( mx ) + w i (S t ) 0 < w i < 1 w i +1 w i = 0. 1 Since mx nd S t re poitive quntitie, there i no dnger of the two cnceling ech other out in the compoite objective. In ddition to the nine weighting fctor lited in the formultion bove (0.1, 0.,, 0.9),.01,.99, nd.85 were lo included to mke the Preto front more complete. The Preto front i hown in Figure 10 below. The dt i hown in Tble 11 (ll vlue re cled). Tble 11. The Preto Front Dt. w i mx S t L h b t d L C By looking t the Preto front, everl thing cn be noted. Firt, the only deign vrible tht undergoe ignificnt chnge one move up nd down the Preto front i, C, the dmping coefficient of the hock borber. Thi men tht thi deign vrible i the one tht hould be djuted to convert upenion with high ccelertion but hort ettling time to one with low ccelertion but high ettling time. Second, for weighting fctor between.01 nd.3, there w no chnge in the vlue of the individul objective function. Thi i becue the dmping coefficient, C, reched it lower bound of.5 (or 500 N/m when not cled From the Preto front we cn lo ee tht initil deign vector found by uing the orthogonl rry w cloe to Preto-optiml. Alo, the deign found uing ingle objective optimiztion i lo on the Preto front nd i cloe to the initil deign vector. Thi my be reon tht the SQP method w o effective nd the runtime w hort. Figure 11 nd 1 how the verticl ccelertion nd diplcement of the penger cbin for two deign: one generted by minimizing the ettling time, S t (hown in red), nd one creted by minimizing the ) ime ( Preto Front Initi l De ign Vector 8

9 t verticl ccelertion, mx (hown in blue). It i cler tht the two deign hve very different behvior. When minimizing the ettling time i the dominnt objective, the reult i deign tht top ocillting in le thn one econd fter climbing the 0.1 meter rod diturbnce, but lo experience n ccelertion of over 0 m/ (ee Figure 11). When minimizing the ccelertion i the dominnt objective, the reult i deign tht ocillte for more thn ix econd but only experience n ccelertion of 5.7 m/ (ee Figure 1). imultion to find the deign with the optiml performnce. It w found tht hevier upenion with low tiffne reulted in lower verticl cbin ccelertion. Settling time cn lo be reduced by increing the dmping coefficient of the hock borber (i.e. uing more vicou oil). However, thi reduction come t the expene of increed verticl ccelertion of the penger cbin. In the future, the uthor hope to look cloer t the trdeoff between the mximum ccelertion nd other potentil objective uch cot or g milege. It i nticipted tht more of the deign vrible will chnge ignificntly when mking trding-off between thee diimilr objective. Verticl Diplcem ent (m ) ) Accelertion (m/ ) = Min [Mx Accelertion] = Min[Settling Time] Time () Figure 11. The Penger Cbin Accelertion Function of Time. = Min [Mx Accelertion] = Min[Settling Time] Time () Figure 1. The Penger Cbin Diplcement Function of Time. CONCLUSIONS AND FUTURE WORK In thi pper, n MSDO pproch h been ued to optimize the performnce of the F-350 rer truck upenion. Single- nd multi-objective optimiztion method were ued in conjunction with numericl We lo hope to continue to improve the fidelity of the numericl imultion o tht it cpture more of the behvior of the ctul F-350 truck rer upenion. A prt of thi, we hope to include more rod condition in ddition to the 0.1 meter tep input. Another re of future work involve the imultion linking oftwre DOME. The uthor foreee tht with DOME, ech module of the imultion could be chrcterized in different oftwre pckge tht i mot uitble for the prticulr dicipline. For exmple, n FEA oftwre pckge could be ued in to meure the tiffne of the lef pring nd the internl tree in the xle more ccurtely thn the imple Mtlb code ued for the imultion in thi pper. Cot nd g milege module could be put into Excel. Then, DOME could be ued to emlely link ll thee module together. DOME lo would mke it ey for more module to be dded lter, uch module for noie, hndling, nd lignment. REFERENCES [1] Wong, Jo Yung, Theory of Ground Vehicle, New York, John Wiley, 001. [] Hyniov, Kterin, A. Stribrky, nd J. Honcu, Fuzzy Control of Mechnicl Vibrting Sytem, Proceeding of Interntionl Crpthin Control Conference, [3] Norton, Robert L., Mchine Deign: An Integrted Approch, New Jerey, Prentice-Hll,