OPTIMIZATION OF CAR FRONTAL PROTECTION SYSTEMS

Transcription

1 6th Internatonal DAAAM Baltc Conference INDUSTRIAL ENGINEERING Aprl 2008, Tallnn, Estona OPTIMIZATION OF CAR FRONTAL PROTECTION SYSTEMS Pohlak, M.; Majak, J. & Eerme, M. Abstract: Desgn of car frontal protecton system s performed by use of artfcal neural networks and genetc algorthm. Man attenton s pad to optmal desgn of brackets. An analyss of car-pedestran collson stuaton s performed by use of explct FEA solver and the stffness analyss wth mplct FEA solver. Multcrtera optmal desgn problem s formulated and the necessary optmalty condtons are derved. The obtaned numercal results are valdated aganst expermental test results and alternatve numercal approach realzed by use of software package LS-OPT. Key words: Energy Absorpton, Neural Networks; Genetc Algorthm, Fnte Element Analyss, Engneerng Optmzaton 1 INTRODUCTION A large number of papers coverng varous problems related to mpact energy absorbers can be found n lterature [ 1, 2 ]. Alghamd revewed common shapes of collapsble energy absorbers ncludng crcular tubes, square tubes, frusta, struts, honeycombs, and sandwch plates [ 1 ]. Testng and numercal smulaton of multmateral energy absorbers s performed by de Kanter [ 2 ]. The propertes of the metallc and fbre renforced plastc (FRP) cylnders n the crushng behavour are dscussed. It s stated that mult-materal elements demonstrate both, metallc and composte characterstcs n crushng behavour. Employment of varous optmzaton technques s one of the trends n car frontal protecton system desgn. In [ 3 ] a cylnder mpact on rgd wall s consdered as an example. The am of the current study s to desgn the extra frontal protecton system of vehcle consstng of tubular parts and the brackets. The possbltes to ncrease the safety of the car frontal protecton system n accdents wth pedestrans are studed. The frontal protecton system, consstng of tubular parts and the brackets, s smply added by bolts to a standard motor vehcle wthout major modfcatons of the vehcle. It s mportant that the orgnal energy absorbng structures of the vehcle wll reman n place wthout alteraton. Man attenton s pad to the desgn of brackets. The stffness of the brackets s lmted by pedestran safety and requred structural stffness of the car accessores. On one hand, the stffness of the accessores mounted on the car frontal protecton system (e.g. extra lghts) must be hgh enough to wthstand the vbratons and acceleratons of the car. On the other hand, the stffness must not be too hgh n order to avod excessve acceleratons of human body n case of accdent. In order to obtan maxmum energy absorpton that s smooth enough, search for optmal confguraton of support components of the structure s performed. The refned algorthms are proposed for desgn mprovement (two stage genetc algorthm (GA) and hybrd GA), snce n standard formulaton the GA may converge close to optmal soluton (not to the optmal soluton). The optmzaton procedures proposed n the current paper and n [ 4 ] are compared and valdated aganst expermental test results.

2 2 PROBLEM FORMULATION In the current study, t s assumed that the heght of the car frontal protecton system desgned s less than 500 mm and man attenton s pad to the safety requrements proceedng from lower legform test requred by drectve of the European Parlament and the Councl 2005/66/EC [ 5 ] (see Fgure 1). the reacton force ncreased steadly to some predefned level and remans constant on ths level [ 6 ]. In order to decrease the acceleraton, optmal desgn of tubular parts and fastenng components has to be addressed. Current study s focused on desgn of brackets. The man energy absorbng component s shown n Fgure 2. Intal desgn of the energy absorbng component depcted n Fgure 2 s gven by manufacturer. Thus, the topology s predefned n certan extent by manufacturer and man task s search for optmal set of desgn varables a, b, c, d and e (see Fgure 2). However, some correctons n topology are avalable. The propertes of the tubes are selected as approprate as technologcally possble (lght structure, thn walls, etc), detaled optmzaton of tubes s omtted. Fg. 1. Lower legform mpact testng (a Legform mpactor, b Frontal protecton system, V velocty of mpactor) In the test, the mpactor (a n Fgure 1) s shot at the speed of 11.1 m/s at the frontal protecton system of the vehcle. There are three types of sensors mounted nsde the mpactor: acceleraton sensor, bendng angle sensor and shear dsplacement sensor. Accordng to the drectve 2005/66/EC [ 5 ]: - the maxmum dynamc knee bendng angle shall not exceed 21.0 ; - the maxmum dynamc knee shearng dsplacement shall not exceed 6.0 mm; - the acceleraton measured at the upper end of the tba shall not exceed 200g (g=9.81 m/s 2 ). It s assumed above that the total permssble mass of the vehcle s less than 2500kg. Unfortunately, most of structures absorb energy n unstable manner. There wll be a hgh peak of reacton force when mpact loadng starts followed by smaller peaks or more constant level of reacton forces. More desrable stuaton would be f Fg. 2. Energy absorbng component (a, b, c, d and e are desgn varables) 3 FE ANALYSIS The stress-stran behavor s modeled wth mult-lnear approxmaton. In order to consder plastc ansotropy the Hll s second order yeld crteron s employed. The FEA s performed separately for crash smulaton and stffness analyss. The total number of smulatons depends on the number of desgn varables and on grd densty, fxed n the stage of smulaton data desgn. The dynamc and statc analyss s performed wth the same sets of the smulaton data n order to get complete

3 set of output data. The output data used n further optmzaton procedure contans extreme values of the frontal force component and dsplacements n y-z plane. The expermental valdaton of the computer smulaton s ncluded n algorthm n order to descrbe full desgn process. Compresson tests of the brackets were performed n Laboratory of Mechancal Testng and Metrology of Tallnn Unversty of Technology. Proceedng from the test results obtaned, some modfcatons to the desgn data and topology of the fastenng component were made. 4 RESPONSE SURFACE MODELING In the current paper, the generalzed regresson neural networks (NN) are used for the response surface modelng (RSM). The surface constructed by use of NN do not normally contan the gven response values (smlarty wth least-squares method n ths respect). An approach proposed s based on the use of the MATLAB neural network toolbox. In MATLAB NN toolbox a two-layer network s generated by use of functon newgrnn. The frst layer has radbas neurons and the second layer has pureln neurons. The response surfaces are generated smultaneously (wth one call to newgrnn) for all response quanttes (frontal force component and y-z dsplacement). 5 OPTIMIZATION PROBLEM The mult-crtera optmzaton problem s formulated as subjected to [ f w f ] mn w + (1) 1 1 g j ( x ) 0, j = 1,..., m, (2) h k ( x ) = 0, k = 1,..., l. (3) 2 2 The constrants (2)-(3) are gven n terms of desgn varables x1,x2,...xn. Both, the peak force f 1 and dfference between maxmal and mnmal force values f 2 are subjected to mnmzaton. The proportons of the functons f 1 and f 2 n objectve functon are determned by weght coeffcents w 1 and w 2. The constrants lad on desgn varables depend on structure and topology of the car frontal protecton system consdered. In general form the lnear constrants can be wrtten as x x, x, ( = 1,..n ), (4) x where x and x stand for upper and lower bounds of the desgn varable, respectvely. As mentoned above, the stffness of the components of the car frontal protecton system s lmted by pedestran safety and requred structural stffness of the car accessores. The constrant provdng the requred stffness of the car frontal protecton system can be expressed n terms of dsplacements as u 2 2 c = u y + uz u, (5) where u y and u z stand for the dsplacements n y and z drecton, respectvely and u s a gven lmt value determned expermentally. The extended functonal J s ntroduced as J = 2 λ T w1 f1( x ) + w2 f ( x ) + g( x ), (6) where λ stand for the Lagrange multpler vector and all constrants are ncluded n nequalty constrant vector g ( x ). In order to obtan the necessary optmalty condtons, the total varaton of the functonal J s equalzed to zero ( δ J = 0 ).

4 6 NN AND GA BASED DESIGN Global optmzaton s performed by use of the two stage GA and hybrd GA algorthms. 6.1 Search for optmal soluton In order to determne the mnmal value of the objectve functon (1) the MATLAB functon ga has been utlzed (Genetc algorthm and Drect Search Toolbox). The response surfaces for frontal force component F and y-z dsplacement u c are treated as objectve and constrants functons, respectvely. In order to acheve hgher accuracy, the real-coded approach of genetc algorthm s consdered. An alternatve soluton s realzed by use of LS-OPT software. Latter soluton s based on use of leap-frog algorthm. As t can be expected, optmzaton va genetc algorthms utlzes natural selecton as a means of fndng the optmal soluton n the global doman, the computed soluton s not global extreme, but close value to t. Thus, further refnement of the desgn s stll necessary. 6.2 Desgn mprovement In the case of two stage GA, both global and local search s performed va GA. The doman for local search s taken as x g δ <= x <= x + δ, ( = 1,... n), (7) g g where x stands for the value of the desgn varable obtaned from global search and δ s a gven devaton for the -th varable. In the case of hybrd approach, the global search s performed by GA, but the steepest descent method s appled for local search usng the same doman (7) for desgn varables. Use of the two stage GA s justfed n cases when several extreme values of the objectve functon are expected n local search doman. Otherwse, the hybrd approach s preferred, snce t s assumed to converge faster and exactly to extreme value (not close to extreme value as GA). Snce GA s a stochastc search based method, whch converges close to global extreme value n better case, the results obtaned n dfferent subsequent runs of the algorthm may dffer slghtly. Furthermore, f there exst several equal or close extreme values of the objectve functon n global search doman, then the results obtaned n dfferent subsequent runs of the algorthm may dffer sgnfcantly. 7 RESULTS AND DISCUSSION As mentoned above, the lmtaton on acceleraton (or correspondng force component) appears to be the most crtcal. For that reason f 1 s consdered as domnatng term n optmalty crteron (3). As result of desgn process, the maxmal value of the frontal force component F( t,x ) s reduced more than 4 tmes n comparson wth ntal desgn. In Fgure 3 the frontal force component F ( t,x ), correspondng to ntal and optmal sets of desgn varables, s gven, respectvely. All constrants are fulflled n the case of both desgns. Note that energy absorpton s twce hgher n the case of ntal desgn. Latter fact can be explaned wth reduced dmensons of the component. Force, N Intal desgn Optmal desgn 0 0,0000 0,0003 0,0005 0,0008 0,0010 0,0013 0,0015 0,0018 Tme, s Fg. 3. Force Tme dagram: ntal desgn and the optmal desgn

5 In Table 1 the optmal values of the frontal force component obtaned by use of dfferent optmzaton algorthms are compared. Table 1. Frontal force components obtaned by dfferent optmzaton algorthms Opt. alg. GA Two st. GA Hybrd GA LS- OPT F ( t,x ) (N) The two stage GA and hybrd GA algorthms are dscussed above; let us descrbe brefly an algorthm used n LS- OPT. The LS-OPT verson 3.1 features Monte Carlo based pont selecton schemes. The sub-problem s optmzed by the dynamc leap-frog method. The gradent vectors of general compostes based on mathematcal expressons of the basc response surfaces are computed usng numercal dfferentaton. In the current study, the neural network based metamodel s employed due to hgher accuracy acheved n comparson wth polynomal model. It can be seen from Table 1, that the results obtaned by use of GA, two stage GA and hybrd GA are close to each other, but dffer to a certan extent from the result obtaned by use of LS-OPT software (less than 10%). Latter fact can be explaned wth dfferent approaches used for response surface (RS) modelng. In the frst case (GA, two stage GA and hybrd GA) the RS s modeled as a statc - t s composed once and used for global and local search. In LS-OPT based soluton the RS s updated n each global teraton step ( dynamc RS). The data set s modfed by performng FE computng wth LS- DYNA explct and mplct solvers. Such an approach s not complcated due to compatblty of the FE software LS- DYNA and LS-OPT. Dynamc data exchange between MATLAB and LS-OPT, also handlng the FE solvers and MATLAB processes together are much more complcated tasks (several restrctons exsts on what knd of standalone executable MATLAB code can be compled wth MATLAB compler). Note, that applyng non-lnear constrant (5) causes some complcatons n the case of MATLAB based soluton. In some cases the convergence to the soluton, where u c s sgnfcantly less than u has been observed. Latter fact s not contradcton tself, but the frontal force component F ( t,x ), correspondng to such soluton appears to be far from optmal value. In order to avod such results the followng possbltes are consdered: - replacng nequalty n (5) wth equalty, - replacng condton (5) wth more strct condton: u 2 2 ε u2 + u3 u, (8) where ε s gven constant n nterval ε [ u /100, u /1000]. The condton (8) s satsfed when u c s close to u and ts applcaton n MATLAB optmzaton functons ga and fmncon appears less complcated than strct equalty constrant u c = u. In order to valdate the FEA models the expermental study was carred out. Several versons of component shown n Fgure 2 were tested. The forces and deformaton modes were found to be reasonably close to that calculated by FEA. It follows from the numercal smulatons and expermental tests done that the optmal desgn s most senstve wth respect to the thckness of the fastenng component. 8 CONCLUSIONS General concluson s that the car frontal protecton system satsfyng the requrements of drectve 2005/66/EC can be manufactured by use of exstng

6 equpment and materals. As a result, the EU patent applcaton number Mountng bracket for frontal protecton system, has been appled for. At the moment nne products have been passed through the type test. Desgn optmzaton of the car frontal protecton system was performed. Man attenton was pad to the optmal desgn of the fastenng components. The desgn procedure proposed contans an analyss wth dynamc loadng for car-pedestran collson stuaton by use of LS-DYNA explct solver, stffness analyss wth LS- DYNA mplct solver, response surface modelng (Neural Networks) and search for optmal desgn (MATLAB Optmzaton Toolbox, Genetc Algorthm and Drect Search Toolbox). The desgn mprovement was performed. The two stage GA and hybrd GA algorthms were developed for posed optmzaton problem. The obtaned results were compared wth the results of an alternatve soluton realzed by use of LS- OPT software. The advantages of the LS- OPT based soluton are compatblty wth LS-DYNA solvers (flexble RS modelng, data exchange) and specalzaton to partcular optmzaton problem consdered. The advantages of the GA based approach are ts generalty and flexblty. The algorthm developed has been used by authors wthout sgnfcant modfcatons for solvng dfferent optmzaton problems (materal parameters dentfcaton, modelng of the new composte from recycled GFP, etc.). The obtaned results from smulatons (LS- DYNA and MATLAB) were found to be close to correspondng expermental results. The nfluence of the dfferent desgn parameters on fnal result was estmated. 9 ACKNOWLEDGEMENTS The work has been supported by Estonan Scence Foundaton grant G REFERENCES 1. Alghamd, A. A. A. Collapsble mpact energy absorbers: an overvew. Thn- Walled Structures, 2001, 39, De Kanter, J. Energy absorpton of monolthc and fbre renforced alumnum cylnders. Delft Unversty of Technology, In PhD Thess, Hörmann, M., Schulz, A., Rust, W. Structural Optmzaton usng LS-OPT: Bascs and Examples. In Proceedngs of 21st CAD-FEM Users Meetng, Potsdam Pohlak, M., Majak, J., Eerme, M. Optmzaton study of car frontal protecton system. In Proceedngs of the Frst Internatonal Conference on Multdscplnary Optmzaton and Applcatons (Bassr, D.H., ed). Besancon, Drectve 2005/66/Ec Of The European Parlament And Of The Councl, Avalable from: ste/en/oj/2005/l_309/l_ en pdf, Accessed: Lu, G., Yu, T. X. Energy absorpton of structures and materals. Woodhead Publshng Lmted, Cambrdge, ADDITIONAL DATA ABOUT AUTHORS Meels Pohlak, PhD. Tallnn Unversty of Technology, Dept. of Machnery. Address: Ehtajate tee 5, Tallnn, Estona. Phone: , E-mal: meelsp@staff.ttu.ee Jür Majak, PhD. Tallnn Unversty of Technology, Dept. of Machnery. Address: Ehtajate tee 5, Tallnn, Estona. Phone: , E-mal: jmajak@staff.ttu.ee Martn Eerme, Prof., PhD. Tallnn Unversty of Technology, Dept. of Machnery. Address: Ehtajate tee 5, Tallnn, Estona. Phone: , E-mal: eerme@staff.ttu.ee