Acceleration-Diplacement Crah Pule Optimiation A New Methodology to Optimie Vehicle Repone for Multiple Impact Speed D. Gildfind 1 and D. Ree 2 1 RMIT Univerity, Department of Aeropace Engineering 2 Holden Ltd, Vehicle Synthei, Analyi and Simulation Previou crah pule optimiation tudie have involved optimiation of a vehicle crah pule at a ingle impact peed. Whilt the reult of uch a tudy may lead to ignificantly improved crah performance at the peed conidered, deign for vehicle afety require atifactory performance acro a range of impact peed. A method of optimiing vehicle repone acro a range of impact peed i required, balancing afety requirement acro each potential impact cenario. Thi paper decribe a new methodology developed to achieve thi aim. It wa propoed that the front tructure of the vehicle which cruhe during impact, thereby decelerating the remaining tructure could be modelled a a non-linear pring. Auming that the force-diplacement curve of thi pring wa independent of impact peed, it followed that the deceleration of the remaining vehicle tructure wa alo a function of cruh diplacement. Hence, uing a vehicle unique acceleration-diplacement profile during a crah event, the dynamic repone of the vehicle could be derived for any impact peed. Optimiation of an acceleration-diplacement curve wa performed uing a Simulated Annealing algorithm. At each iteration, acceleration-time crah pule were derived for the tandard crah tet peed of 28, 48 and 56 km/hr. Occupant repone wa imulated in MADYMO, and a harm metric wa ued to etimate injury cot at each peed. A function weighting harm acro all three peed wa ued a the optimiation objective function. Comparing optimied reult with reult from a et of real vehicle crah pule, it wa found that occupant harm wa ignificantly reduced for each impact peed. A expected, improvement were not a great a thoe achieved for crah pule optimied for a ingle impact peed only, highlighting the trade-off required for optimied performance acro multiple peed. However, the methodology demontrated that a et of ignificantly improved acceleration-time crah pule could be generated, each being conitent with a ingle vehicle acceleration-diplacement profile, and therefore a ingle tructural deign. NOTATION vehicle cruh diplacement (m) v,max maximum deign impact velocity (m/), non-dimenional diplacement (-) a vehicle acceleration (m/ 2 ) initial cruh diplacement (m) a,a non-dimenional acceleration (-) f final cruh diplacement (m) a SF acceleration caling factor (m/ 2 ) max maximum cruh diplacement (m) SF diplacement caling factor (m) v vehicle velocity (m/) t time () v initial vehicle impact velocity (m/) kk, ( ) vehicle front tructure tiffne (N/m) v f final vehicle impact velocity (m/) F () vehicle front tructure reaction force (N) v,i any impact velocity, i (m/) m RB ma of tructure aft of front firewall (kg) INTRODUCTION Applied to full frontal colliion, the crah pule decribe the forward deceleration of the vehicle occupant compartment a it cruhe into a barrier during a colliion. Uually defined - 1 -
by a deceleration-time plot, the hape of the crah pule ha a direct effect on the reulting interaction of occupant within the vehicle, and therefore directly affect occupant injury rik during a colliion. A uch, everal tudie have previouly been conducted to tudy the effect of crah pule hape on occupant injury rik. Previou tudie have focued on crah pule optimiation at a ingle impact peed. Whilt uch tudie have yielded variou degree of improved occupant repone, they are ubject to a evere limitation a vehicle mut protect it occupant acro a range of impact peed. Several author have uggeted olution to thi problem. Complex adaptive tructure have been propoed which would permit optimal deceleration repone at any peed [1], however their complexity and expene will diallow uch deign in the foreeeable future. Other have propoed non-adaptive tructure which aim to produce crah pule which are deirable acro a range of peed [2]. Certainly, thi i the only viable alternative available at preent. The problem i identifying what the optimal tiffne ditribution of uch tructure hould be. Thi paper decribe a new methodology to optimie vehicle repone for multiple impact peed, through optimiation of the vehicle acceleration-diplacement curve. Preliminary reult ugget that unlike previou tudie, thi new methodology can be ued to lower injury rik of a non-adaptive tructure acro everal impact peed. Thi reearch i part of a broader crah pule optimiation tudy. Another paper ha been written on optimiation of vehicle crah pule for ingle impact peed [3]. Reference to thi paper will provide more detailed decription of ome of the concept and methodology common to both tudie. THEORY Acceleration-diplacement crah pule Conidering the vehicle during a full frontal crah, prior to the crah the vehicle i travelling with initial velocity, v, toward a rigid barrier. A the vehicle plough into the barrier, the front tructure cruhe, tranforming the vehicle kinetic energy primarily into train energy within the vehicle deforming front tructure, thereby bringing the vehicle to ret. The diplacement of the vehicle during the crah i not contant acro the tructure. The front of the vehicle low down immediately a it hit the barrier, whilt the ret of the tructure decelerate at a lower rate. Modern vehicle are generally deigned o that the front of the tructure, forward of the front firewall, will aborb the colliion energy of a full frontal crah. The remaining rearward tructure generally remain tructurally intact. Conequently, thi rearward tructure diplace approximately a a whole ytem. A ueful definition of the vehicle cruh diplacement during a crah, denoted by, may therefore be taken to be the diplacement of the vehicle rearward of the front firewall, a illutrated in Figure 1. t = = v k( ) = max = Figure 1. Meaurement of cruh diplacement. Idealiation of front tructure. - 2 -
Referring to Figure 1, tructure rearward of the front firewall i conidered to act like a rigid body during a full frontal crah. A the front tructure cruhe, it applie a decelerating force to the ret of the vehicle, which varie with cruh diplacement. The vehicle frontal tructure can be likened to a nonlinear pring, with tiffne k, which varie with pring compreion (the cruh diplacement, ). Thi concept i illutrated in Figure 1. A the vehicle cruhe, the pring produce a reiting force, F(), which decelerate the rigid body portion of the vehicle (with ma denoted by m RB ). Figure 2 below illutrate thi rigid body approximation at the initiation of the colliion event. At any given impact peed, a force-diplacement curve may be ued to decribe the variation of thi force a the vehicle front tructure cruhe. An example of uch a curve i illutrated in Figure 2 below: t = = v F( ) Vehicle i at ret F( ) m RB Figure 2. Force of deforming front tructure.. Example of a force-diplacement curve In order to proceed, an important implifying aumption i made about the forcediplacement characteritic of the vehicle front tructure. It i aumed that the forcediplacement behaviour of the front tructure i a contant property of the ytem, independent of colliion velocity, or any other factor. Thi aumption implie that for any colliion peed, at a given cruh diplacement, the applied force on the rigid body portion of the vehicle i the ame. Thi aumption i only approximately true to varying degree, rate of deformation doe affect the tiffne repone of a tructure. The validity of thi aumption i conidered later in the dicuion ection of thi paper. Referring to Figure 2, F() act on rigid body ma, m RB. Summing force in the direction of initial motion, v : F () = mrb a [1] where a i the longitudinal acceleration of the rigid body ma during the colliion event. Equation [1] may be rearranged a follow: F () a = [2] m Oberving Equation [2], if the rigid body ma remain contant during the colliion, and if the force i a function of diplacement only, then it mut follow that vehicle acceleration i alo a function of diplacement only: a= a() [3] Equation [3] preent a ignificant propoition, with implication a follow: 1. Any given tructural configuration will have a unique acceleration-diplacement function, a(). 2. a() i a contant property of the ytem, independent of impact peed or any other conideration. RB max - 3 -
3. Given any initial impact peed, v,i, a() may be ued to derive the deceleration repone (crah pule) of the ytem. 4. There i a maximum impact velocity, v,max, for which a given a() will produce a complete deceleration of the vehicle. If thi impact velocity i exceeded, the vehicle will till have velocity once all of the available cruh pace ha been ued. Crah pule requirement Some contraint were impoed on the crah pule variable generated by the optimier. At each iteration of the optimiation, the following crah pule characteritic were enforced: 1. The change in velocity acro the acceleration-diplacement crah pule wa et equal to the maximum allowable impact peed, v,max. 2. The total cruh diplacement available wa et equal to a maximum length, max. 3. The acceleration wa forced to be negative or zero for the duration of the impact. 4. The initial acceleration wa et equal to zero. Thee requirement are outlined in Figure 3 and below. a () Requirement: f = a, ( ) = f = max a ( ) = a ( ) for all max v ad= () 2 2,max Figure 3. General crah pule model. Crah pule requirement Crah pule generation The variable crah pule had to be expreed in term of a dicrete et of optimiation variable. A et of n dicrete control point variable wa ued to define a non-dimenional acceleration-diplacement crah pule hape. The coordinate of thee control point were defined in term of non-dimenional acceleration, a, and non-dimenional diplacement, : ( a, a,... a ) T a = n [4] = (,,... ) T n [5] 1 2 1 2 The et of non-dimenional diplacement control point,, wa kept contant for any given optimiation tak. The et of non-dimenional acceleration control point, a, wa defined a the et of optimiation variable. A cubic pline wa interpolated through the control point, reulting in a et of data point defining an approximately mooth function: a ( ) a ( ) [6] Thi interpolated function repreented the non-dimenional crah pule hape, and required caling o that diplacement and velocity criteria were met. The continuou non-dimenional - 4 -
crah pule hape wa therefore caled to meet the requirement outlined in Figure 3. Two caling factor were derived to cale a ( ) into a fully dimenional crah pule: {} SF { } = [7] {} a = a { a } [8] SF Referring to Equation [7] and [8], it can be hown that: SF = [9] max f a SF 2 v,max = max 2 a d Hence, a methodology wa developed to generate an acceleration-diplacement crah pule which atifie maximum cruh diplacement and maximum impact velocity criteria. For any impact peed v, i < v,max, the acceleration-time repone of the vehicle may then be derived. OPTIMISATION PROCESS An optimiation proce wa developed to optimie an acceleration-diplacement crah pule acro the three indutry tandard and regulatory impact velocitie: 28 km/hr (ADR), 48 km/hr (ADR) and 56 km/hr (NCAP). The acceleration-diplacement crah pule wa caled to atify a maximum impact peed of 56 km/hr, and a maximum cruh diplacement of 6 mm. Occupant repone wa imulated uing a generic driver-ide MADYMO retraint model upplied by Holden Ltd. The optimiation wa performed with the robut Simulated Annealing global earch algorithm, via the commercial optimiation code isight. Occupant injury wa etimated uing a harm metric of the following form: Harm = Probability of injury cot of injury = HIC, N, CTI, Femur [11] all injurie conidered ( ) f ( ij ) The harm metric ued injury criteria from MADYMO to predict the probable cot aociated with thee injurie. The derivation of thi harm metric i dicued in another paper [4]. Harm wa calculated for each impact peed, and weighted by the relative frequency of crahe at each given velocity. Weighting value were derived from MUARC [5]. A total weighted harm wa then calculated, incorporating all three impact peed. Thi total weighted harm wa ued a the optimiation objective function: [1] Harm =.43 Harm28 km/hr +.377 Harm48 km/hr +.193 Harm56 km/hr [12] Figure 4 below how an illutration of the driver-ide retraint ytem ued for the analyi. The general optimiation model ued in the analyi i preented in Figure 4. It i noted that the proce hown i a implified chematic of the more complex ytem developed: Crah pule a () 56 km/hr at () 28 km/hr at () 48 km/hr at () 56 km/hr MADYMO MADYMO MADYMO isight Optimier Harm 28 km/hr Harm48 km/hr Harm56 km/hr Weighted Harm ($) Figure 4. MADYMO driver-ide retraint model. Optimiation proce - 5 -
OPTIMISATION RESULTS An acceleration-diplacement crah pule, defined by 21 control point, wa optimied for minimum weighted occupant harm, acro the three impact velocitie of 28, 48 and 56 km/hr. The optimied harm reult were compared to harm reult calculated for a et of real-life crah pule repreentative of a mid-ized edan crah, provided by Holden Ltd for comparative purpoe. It wa found that optimiation approximately halved the weighted occupant harm compared to the repreentative crah pule. Figure 5 below how the harm calculated at each individual velocity, and the total weighted harm, for both the repreentative and optimied crah pule. Figure 5 provide a correponding ummary of calculated injury criteria for repreentative and optimied crah pule. It i clear that optimiation of the acceleration-diplacement crah pule acro the three velocitie produced reduction in occupant injury rik at each velocity. Figure 5 demontrate that ignificant reduction in harm correpond to ignificant reduction in mot of the injury criteria: Harm ($AUD) $1, $75, $5, $25, $ $9,989 $11,935 $21,265 $47,91 $42,63 $82,343 $2,43 $38,777 28 km/hr 48 km/hr 56 km/hr Weighted Harm Optimied Crah Pule Repreentative Pule HIC (-) Nij (-) CTI (-) Femur (N) Harm ($AUD) 28 km/hr 48 km/hr 56 km/hr Opt. Pule Repr. Pule Opt. Pule Repr. Pule Repr. Pule Opt. Pule 127 97 462 197 686 435.379.31.41.49.484.374.591.589.918.765 1.83.874 1841 1655 236 1945 1878 1967 11,935 9,989 47,91 21,265 82,343 42,63 Figure 5. Reult for harm optimied v. repreentative crah pule. Comparion of etimated occupant harm. Comparion of injury criteria Figure 6 below compare optimied and repreentative acceleration-diplacement curve. The three acceleration-time crah pule derived from the optimied accelerationdiplacement curve are hown in Figure 6(b-d), for each of the three velocitie. Thee are compared to each of the correponding repreentative crah pule for each peed. 3 3 Acceleration (m/ 2 ) -3-6 -9 2 4 6 8 Cruh Diplacement (mm) Optimied Pule Repreentative Pule 3 Acceleration (m/ 2 ) -3-6 -9 3 2 4 6 8 1 Time (m) Optimied Pule Repreentative Pule Acceleration (m/ 2 ) -3-6 -9 2 4 6 8 1 Time (m) Optimied Pule Repreentative Pule Acceleration (m/ 2 ) -3-6 -9 2 4 6 8 1 Time (m) Optimied Pule Repreentative Pule (c) (d) Figure 6. Optimied v. repreentative vehicle crah pule. Acceleration-diplacement crah pule. 56 km/hr acceleration-time crah pule. (c) 48 km/hr acceleration-time crah pule. (d) 28 km/hr acceleration-time crah pule. - 6 -
The occupant repone were analyed at each impact peed, for both repreentative and optimied crah pule. Figure 7 how the reultant eatbelt load for the repreentative crah pule. Figure 7 how the reultant eatbelt load for crah pule derived from the optimied acceleration-diplacement curve. 8 8 Belt Load (N) 6 4 2 Belt Load (N) 6 4 2 DISCUSSION 4 8 12 16 Time (m) 56 km/hr 48 km/hr 28 km/hr The reult demontrate that the acceleration-diplacement crah pule optimiation methodology can be ued to produce a et of vehicle crah pule which outperform the reallife crah pule provided by Holden Ltd. However, unlike previou crah pule optimiation tudie, thi new methodology enure that thee optimied crah pule are compatible with one another, both in term of tructural deign, and the ue of vehicle cruh diplacement. Oberving the reult, it i clear that reduction in injury are ignificant, particularly at higher peed. Referring to Figure 7(a,b), it appear that the common trend between optimied crah pule i that occupant are loaded up fater, courtey of the high initial deceleration pike oberved in each of the crah pule (Figure 6). The balanced reduction in injury level at each peed alo validate the harm metric ued. The abolute value of the harm etimate are not of great relevance what i important i that the dollar cot allocated to different et of injurie i properly weighted o that an automated optimiation proce will be effective. It i upected that the three localied deceleration pike oberved in Figure 6 have evolved during the optimiation routine in order to provide pecific performance advantage at the three impact velocitie conidered. It i poible that the equence of thee pike i important, and that at other impact velocitie thee deceleration pike may actually be harmful to the occupant. In term of improving performance in indutry crah tet, the crah pule only ha to be optimied for the peed which the vehicle will be teted at. However, thi pragmatic option doe not reponibly addre real world deign requirement. In reality, a whole pectrum of velocitie hould be conidered in order to obtain a true overall optimied acceleration-diplacement pule. It i expected that a the number of impact velocitie conidered i increaed, the performance of the optimied pule for any of thee individual peed may uffer, but will till provide a tangible improvement over current deign. Finally, the proper value of thee reult depend upon the validity of the key aumption underpinning the methodology: that vehicle tructural tiffne doe not vary with impact velocity. The proper verification of thee reult would be achieved via tructural imulation and crah teting. However, at thi conceptual tage, everal factor are noted. Firtly, it i noted that train-rate change the tiffne of tructural material. For example, high train rate increae the trength and energy aborption of mild teel [6]. However, train rate effect uually only vary ignificantly over everal order of magnitude of train rate. Seriou vehicle impact occur over a comparatively narrow range of impact velocitie (conidering thi analyi, the difference between maximum and minimum velocitie i 5%). Further, an 4 8 12 16 Time (m) 56 km/hr 48 km/hr 28 km/hr Figure 7. Reultant eatbelt load. Repreentative crah pule. Optimied crah pule. - 7 -
increaingly popular automotive tructural material, aluminium, ha been hown to have mechanical propertie which are relatively inenitive to train rate effect [6, 7]. Secondly, material mechanical propertie are not the only tructural propertie which are enitive to loading rate. The dynamic repone of the tructure (i.e. the reulting vibration and ocillation which reult after impact) i not independent of the loading rate. Thirdly, current numerical imulation of vehicle colliion do not model train rate phenomena with much accuracy, often under-predicting the dynamic tiffne of vehicle. Depite thi inadequacy, current numerical imulation are capable of producing meaningful prediction of the tructural repone. Hence, the aumption made in thi analyi hould nonethele provide meaningful and relevant reult. However, it i expected that thi methodology would have le value a a detailed deign tool. It i more likely to have ue a a mean of identifying an approximately optimal tructural repone, which can then be ued to guide deciion about tructural layout and deign at the preliminary deign tage. CONCLUSION Baed on the aumption that the vehicle force-diplacement curve i independent of impact velocity, the methodology introduced in thi paper allow the vehicle tructural repone to be optimied acro multiple peed. Thi analyi ha hown that the methodology i viable that it can be uccefully implemented and optimied uing commercially available oftware package. The methodology yield ufficient improvement in occupant repone to jutify further invetigation. Key factor which require addreing include: Verification of the aumption via tructural teting and computer imulation; Conideration of a greater number of impact peed. ACKNOWLEDGEMENTS Sincere appreciation i extended to Holden Ltd for upplying the reource neceary to carry out thi project. Thank are due to the member of the VSAS Safety Group at Holden Ltd., under the uperviion of M Suzannah Hanie epecially to Mr Lincoln Budiman for hi continual aitance with the analyi oftware, and to the other for their regular aitance, upport and valuable advice. Thank are due to the RMIT Univerity Department of Aeropace Engineering, for coordinating thi indutry-baed final year thei project. Finally, thank you to Dr. Nick Bardell and Mr David Hughe for aitance in proof reading thi paper. REFERENCES [1] Witteman, W. J., 'The neceity of an adaptive vehicle tructure to optimize deceleration pule for different crah velocitie', 17th International Conference on the Enhanced Safety of Vehicle, Amterdam, 21. [2] Sparke, L. J., 'Optimiation of Crah Pule Through Frontal Structure Deign', 1996, Holden Paper No. 96-S4-W-21. [3] Gildfind, D., Ree, D., 'Crah Pule Optimiation for Minimum Occupant Harm - A New Methodology to Calculate Fully Optimied Crah Pule', Young Automotive and Tranport Executive Conference, Melbourne, Autralia, 29-3 October, 22. [4] Gildfind, D., Ree, D., 'Development of a Harm Metric for Crah Pule Optimiation', Young Automotive and Tranport Executive Conference, Melbourne, Autralia, 29-3 October, 22. [5] Monah Univerity Accident Reearch Centre, 'Frontal Crah Performance and Occupant Injury Outcome', 1993-21 (on-going). [6] Chatfield, D. A., Rote, R. R., 'Strain Rate Effect on the Propertie of High Strength, Low Alloy Steel', 1974, SAE Paper No. 74177. [7] Lin, C. H., 'Strain Rate Effect in Vehicle Frontal Impact', Proceeding of the 1999 GM CAE Conference, Pontiac, Michigan, September 16-17, 1999. - 8 -