A simplified model for analysis of Side-impact Velocity Based on Energy Method

Transcription

1 IOP Conference Seres: Maerals Scence and Engneerng PAPER OPEN ACCESS A smplfed model for analyss of Sde-mpac Velocy Based on Energy Mehod To ce hs arcle: Tao we e al 08 IOP Conf. Ser.: Maer. Sc. Eng Vew he arcle onlne for updaes and enhancemens. Relaed conen - Traffc accden nesgaon: A suable heme for eachng mechancs P K Tao - The energy mehod. Applcaon o PDEs of hydrodynamcs wh nonsandard growh S N Anonse and S I Shmare - Can physcs help wn he case? A realworld applcaon of an unusual wodmensonalprojecle moon suaon Lawrence H Day Ths conen was downloaded from IP address on 8/09/08 a :5

2 IOP Conf. Seres: Maerals Scence and Engneerng (08) 066 do:0.088/ x/39/6/066 A smplfed model for analyss of Sde-mpac Velocy Based on Energy Mehod Tao we,, Lu Zh-qang, Zhang A-hong 3, J Lang School of Auomoble & Traffc Engneerng, Jangsu Unersy, Zhenjang Jangsu 03,Chna Jangsu Jaoong College, Zhenjang Jangsu 08, Chna 3 Traffc Managemen research nsue of he Mnsry of Publc Secury, Wux Jangsu, 45, Chna Emal: @qq.com Absrac. Wh he ncreasng number of auomoble, he frequency of road raffc accden ncreases n he same way. Therefore, accden reconsrucon s requred as effece mehod o make confrmaon of lables. Ths paper se up an energy mehod based car-car sde mpac elocy compung model. In hs model, frsly, Pc-crash was used as a smulaon plaform, usng he message leaed by car-car sde collson accden such as sop poson, sop angle and collson rajecory. Nex he relaonshp beween oal deformaon energy and pre-mpac elocy was also analyzed n he model. Then pre-mpac elocy was consruced n he compung model based on he prncple of energy conseraon and momenum conseraon. Fnally, a numercal smulaon was proded o es he aldy of he resuls. I s shown ha he car-car sde mpac elocy calculaon model was effece for he accden analyss and could be used n praccal cases.. Inroducon The handle of raffc accdens always ncludes feld nesgaon of an accden, accden analyss and confrmaon on he lably of raffc accden. And he accden process analyss s manly bass of confrmaon on lably. Obously s a grea sgnfcance o hae he accden reconsruced for he analyss on he cause of he accden and rulng he responsbly fas and farly. Table. daa sascs daa sascs for dfferen ypes of collson accdens [](0) number of accden (%) number of njury (%) drec propery loss (%) fron mpac sde-mpac rear-mpac oppose drecon collson Same drecon collson oal Conen from hs work may be used under he erms of he Creae Commons Arbuon 3.0 lcence. Any furher dsrbuon of hs work mus manan arbuon o he auhor(s) and he le of he work, journal caon and DOI. Publshed under lcence by Ld

3 IOP Conf. Seres: Maerals Scence and Engneerng (08) 066 do:0.088/ x/39/6/066 In fac, he number of boh he raffc accden and he njury caused by collson s much larger han he ohers. Among he collson accden, sde-mpac akes oer a grea majory. Table shows a sasc daa ndcang a bg proporon by sde-mpac of Chnese car accdens n 0. In he process of deermnaon of raffc accden lables, was ery dffcul o deermne he pre-mpac speed []. Mc Lunde e al. apply fne elemen mehod o esablsh he model of ehcle and bcycle and explore he possbly of fne elemen mehod for he smulaon of wo wheeled ehcle accden[3]. Ln Qngfeng e al. make a quanae analyss on he accden of he car and he wo rounds accordng o a large number of bcycle accden daa and crash es, whch manly research he rder hrowng model, debrs hrowng model and bcycle hrowng model ec[4]. Yang Bo e al. apply he mage measuremen and deo mehod on he accden reconsrucon, and combne hem and he fne elemen mehod o smulae he model of accden[5]. Howeer, n case of nal daa s mssng or parameer s uncerany, smplfed model sll can be used. In hs paper, smplfed model for calculang ehcle collson speed was esablshed fnally accordng o energy conseraon mehods combne wh he conseraon of momenum and sofware smulaon. Ths model presens he relaonshp beween energy loss and elocy hrough sofware smulaon, calculaes wh hgh accuracy by seeral smple parameers. Collson moon. Theorecal analyss and Compuaon of Collson No maer whch par of collson process: pre-crash, crash or pos-crash, he analyss of energy and force noled n he collson sages s complex, for faclang he analyss and assumng ha: () Durng he collson he locaon n earh s axs keeps sable,he change of dsplacemen n he nsan of collson s gnored; () The force lke Gray, ground frcon force, drng force, ar drag and he ny change of energy loss s negleced; (3) The energy before and afer he collson comples wh energy conseraon prncple; (4) Parameers would no change n he collson such as qualy, cenrod poson, momen of nera, wheel rack.. Knemac Equaon Accordng o aboe assumpons, n hs paper, he prncple of energy conseraon was ulzed, neglecng he loss of he oal deformaon energy. Formula can be gen as: ( m m I ) ( m I m I ) E. () Where , represens he ranslaon elocy and roae elocy of ehcle and ehcle before and afer mpac respecely. E s he loss of energy. Consderng ha he work done by four wheel frconal forces s along he wheel-rack L, hen he alue of he work s equals o araon of knec energy, accordng o: mgfl E m I c. () Where f s he frcon coeffcen beween locked wheels and he ground, assumng ha all he roae and ranslaon speed hae a lnear behaor and boh moon fnsh a he same me (hs can be erfed easly when all wheel are locked), parameer se as: k 0. (a) g. (b) 0

4 IOP Conf. Seres: Maerals Scence and Engneerng (08) 066 do:0.088/ x/39/6/066 a ( 0 ) 0 x ( 0 ) 0 Accordng o equaons aboe, 0 herefore:. (c) a. (3) x Subsuon equaon (3) no () we can ge: a E c ( m I ). (4) x Combnng equaon (), (3) and (4), s possble o oban he pos-mpac elocy as: mgfl. m I( a x ) (5) a. x (6) Accordng o he prncple of energy conseraon and momenum conseraon, formula can be wren as: ( m k I m I ) f m gl f m gl E. (7) m 0n m 0 m m 0n 0 m n m m. n m. (8) Fg. The sde mpac wh he collson angle θ Fg. Rgh - angle sde mpac As Fgure, he longudnal drecon of ehcle before mpac was aken as -axs and he laeral as n-axs. 0 n 0, 0 0. (9) When he angle beween -axs and longudnal of pos-mpac of ehcle s, where he pos-mpac speed s, we can oban: cos. (0) sn. n 3

5 IOP Conf. Seres: Maerals Scence and Engneerng (08) 066 do:0.088/ x/39/6/066 In he smlar way, he angle of ehcle s β and elocy s, we can ge: cosβ. n snβ. and can be obaned a Eqs (5). Now pre-elocy 0 0 can be calculaed based on E qs (7) (8) (9) (0) (). The resolng sll exss wo unknown parameers, whch s he dsance coered by he yre n he process of collson (L), and he energy loss ( E ).. The dsance L Consdered he collson of wheel lock, he adheson coeffcen of he four wheels n each drecon s consan. Alhough n realy all wheel lockng s no common, hs assumpon can coer mos of he accdens for a suable ressance facor. In he case of all-wheel lock, adheson coeffcen of he four wheels s consan n all drecons. Afer collson, he ehcle s roaed and ranslaed around s cenrod. One wheel rajecory s a crcle and s radus s r. In order o smplfy he calculaon, he X d r was selec he medum alue. The cenrod rajecory dsance s X ( ), where he angle of roaon afer he collson s α and he radus of he cener of mass of he ehcle s d. In road accdens, d s usually greaer han r, whch s beleed ha ranslaon s more mporan han roaon. Because d approaches nfny, he moon s close o he real ranslaon and he wheel rael dsance L wll approach he cenrod dsance X. Conersely, f he ehcle s prmarly roang, he rajecory of each wheel s sgnfcanly longer relae o he cener of mass. The rao of he locus of he wheel o he cener-of-mass locus s close o r/d. Approxmae formula for L can be deduced as: r L X( 0.4 ). () d The formula was erfed wh hgh precson and calculaed faser han he negral[6]..3 Toal deformaon energy E Accordng o he hypohess, deformaon energy s he domnaed loss. In order o analyze he relaonshp beween oal deformaon energy and collson speed, We used he popular accden reconsrucon sofware pc-crash o do smulaon expermen. In smulaon, ehcle-was aken as he one crashed car under he range of 40km/h-80km/h, and a he same me ehcle- was he collson-car under 0-40km/h. Vehcle- h ehcle- n dfferen () collson angle θ( θ 45, as shown n Fgure ). Collson occurred n 4 8 of sde of ehcle-. In order o keep oher parameers consans n smulaon, we obsered ha he oal deformaon energy s proporonal o he mpac elocy of ehcle-, whch presens he endency of a lnear funcon or he quadrac funcon. The cure fng could be made on he maxmum and mnmum of cure seres, as shown n Fgure 3. 4

6 IOP Conf. Seres: Maerals Scence and Engneerng (08) 066 do:0.088/ x/39/6/066 Fg. 3 he relaonshp beween elocy and energy loss based on pc-crash Sofware smulaon es I s can be seen from Fgure 3 ha he change area of oal deformaon s relaely concenraon. When ncden angle s greaer han 45, he maxmum of oal deformaon manly focus on he cure of he /4 collson pon wh 45 ncden angle and he speed of ehcle- s 30km/h. The mnmum of oal deformaon s manly concenraed on he cure of he / collson pon wh 0 ncden angle and he speed of ehcle- s 30km/h. The rend lne s used o f he oal deformaon energy wh he ncrease of collson speed, and he wo rend lnes are obaned. The upper and lower boundary cure equaons are as follows: E K max (3) E K mn (4) A mdlne s fed beween he upper and lower boundares o characerze he aerage change n oal deformaon energy wh he mpac elocy. E K (5) The oal deformaon energy n Eq. (5) s relaed only o he elocy before collson of he wo ehcles. Subsung hs equaon no Eq. (), he elocy before collson can be soled. The parameers requred for hs equaon can be obaned from a measuremen or from an exsng model, whch s erfed below. 3. Case sudy 3. Case descrpon and calculaon Two same ype car sop afer rgh-angle sde-collson. Through nesgaon n accden scene, he poson of wo cars shows n Fgure 4. The arrow means he drecon of elocy. All nformaon of hs case can be found n able : Car Car Forward Fg.4 Vehcle n he mpac confguraon 5

7 IOP Conf. Seres: Maerals Scence and Engneerng (08) 066 do:0.088/ x/39/6/066 Table. The parameers of he accden measured n scene parameers ehcle- ehcle- mass(kg) lengh (m) wdh (m).7.7 Angle wh X drecon before collson(deg) 0 90 Angle wh X drecon afer collson(deg) 6 70 he dsance coered by he cenral of mass of he ehcle afer mpac(m) Frcon coeffcen beween yre and ground wheel rack(fron/rear)(m).44/.4.44/.4 Accordng o formula (Eq.), L can be calculaed as: L X 0.4 r. ( = ) Where X 9. 8, 6, r. 5, X 6., 0, r. 5, L 0.0, L 6. 7, I 0.478m l 4.8% ( = ) Now momen of nera I can be obaned as aboe : I 373, I 373 and pos-mpac elocy can be calculaed a formula (5) as : mgfl 0.79m / s m I ( a x ) m gfl 8.3m / s m I ( a x ) The momenum conseraon n x-axs as shown n Fgure 3: m 0 cos 0 m 0 cos 90 m cos 6 m cos m / s 9.9km / h can be obaned. 0 ( m0 0 m 0 0 ) fm gl fm gl E k Where E k ,combne wh aboe formula, 8.05m / s 64.95km / h model aldaon Generally deformaon energy can be calculaed by some mehods lke energy grd and sffness coeffcen mehod, where energy grd has a wdely applcaon. I dded he fron of ehcle no seeral pars and calculaed he energy absorbed by each par, whch can be used n unceran damage mode or complex relaonshp beween he force and resdual deformaon energy. Howeer, hose mehods obaned by collson expermen need ceran fnancal and power [7], and herefore can 6

8 IOP Conf. Seres: Maerals Scence and Engneerng (08) 066 do:0.088/ x/39/6/066 be wdely applcae. Accordng o he area coered by he energy grd and he deformaon cure n hs case, he oal energy loss of he collson deformaon absorpon s 34704J. The oal deformaon energy obaned by he aboe model s 40956J. 3.. Sffness coeffcen mehod Accordng o a lo of pose walls collson es, Campbell [8] proded he lnear relaon beween he resdual deformaons and collson elocy, and consequenly deformaon energy can be calculaed by followng formula. E [ B C R A C R A /( B )] d. (7) 0 A =Force per un wdh wh zero resdual deformaon (N/m); B =Sffness coeffcen per un wdh(n/m); C =Resdual deformaon(m); R =Wdh of ehcle damaged(m). Fg.5 Deformable conours The measuremen daa of deformaon on car body n hs case can be found as follows: For car-, C=0.0m, C=0.m, C3=0.3m, C4=0.3m, C5=0.5m, C6=0.0m, =3.0m. For car-, C=0.37m, C=0.4m, C3=0.35m, C4=0.4m, C5=0.4m, C6=0.35, =.70m. The Naonal Hghway Traffc Safey Admnsraon (NHTSA) dded ehcle no seen caegores on he bass of he wheelbase lengh [8], and reference alue of parameers lke A, B, G was gen. Accordng o hs case, parameer alue seleced as follows: A=303N/cm and B=39.3N/cm for sffness reference coeffcen of car-; A=555.N/cm B=38.6N/cm for car-, now he oal plasc deformaon energy loss n he case can be obaned based on Eqs (7),whch s J Smulaon on Pc-crash Fg.6 Parameer npu nerface Fg.7 Resul of smulaon 7

9 IOP Conf. Seres: Maerals Scence and Engneerng (08) 066 do:0.088/ x/39/6/066 Table.3 Vehcle parameers before he collson on smulaon No. Smulaon elocy Angle wh X-axs Vehcle- 8km/h 86.5 Vehcle- 69km/h 3 Table.4 The comparson of sop locaon beween smulaon and real accden No. Vehcle- Vehcle- X-axs Accden scene measuremen Smulaon on pc-crash Y-axs Accden scene measuremen Smulaon on pc-crash Roaon angel Accden scene measuremen -0 6 Smulaon on pc-crash Fgure 6 shows ha he es resul n he pc-crash smulaon s approxmaely equal o he acual measured alue, whch means smulaon resuls s effece. The ehcle mpac speed n Fgure 4 s close o he elocy goen by model aboe, and fnally he alue of he deformaon energy by he smulaon s J. Toal deformaon energy Table.5 The alue of deformaon energy calculaed by four mehods Smulaon Sffness coeffcen(e3 Energy grd( E) Model(Ek) (E) ) J J J J Error rae ( E - E )/ E k 6.30%.80% 4.60% 3..3 Velocy resul comparson of wo mehods Formula for car-car sde collson elocy based on he speed echncal ealuaon for ehcles noled n represenae road accdens (n hs case he longudnal adheson correcon coeffcen k k ake.0) as: m ( gks snβ gks cos ) km / h m m ( gks sn gks cosβ) km / h m Table.6 Pre-mpac elocy he conras of pre-collson elocy calculaed n hree mehods analogue smulaon Sandard formulas. Model 0 a 0 a 0 b 0 b 0 0 b 8km/h 69km/h 9.43km/h 64.84km/h 9.9km/h 64.95km/h Error rae ( - 0) / 4.60% 5.90% 0.40% 0.0% 8

10 IOP Conf. Seres: Maerals Scence and Engneerng (08) 066 do:0.088/ x/39/6/066 Through he comparson resul n able 5, s easy o found ha he model presened n hs sudy ges modes dfferences n comparson wh he oher mehods, snce errors n he pre-elocy are less han 6%, and hose dfferences are consdered accepable, whch can be appled o he real case and calculang he deformaon effecely. Alhough rgdy coeffcen and deformaon energy grd fgure mehods are common mehods o mos knds of collson accdens, hey all need dfferen coeffcen o parcular car whch s obously unrealsc. The smple model we suded here can calculae pre-elocy and he oal deformaon wh hgh precson, and brng conenence for he analyss of he accden. 4. Concluson In hs research, he calculaon model of sde-mpac speed based on mehods of energy s esablshed. Accordng o he fed cure from he desgned expermens on Pc-crash smulaon sofware on he relaonshp beween plasc deformaon wh he pre-elocy speed, and combnng wh he prncple of conseraon of momenum and conseraon of energy, hs model can be appled boh n he case when wheel parally locked or all locked when hae an approprae drag facor. Smplfed model was aldaed hrough a case hrough comparng he resul wh Pc-crash sofware smulaon, sffness coeffcen mehod, he energy grd mehod and he sandard speed calculaon formula, he errors are been hough consderable. The model has a grea adanage ha, he only necessary nal daa for he model are he angle and dsance changed, he dsance beween he conac area of wheels he cener of mass,and he frcon coeffcen beween he road and yre wh locked wheels, hose parameers can be found n he feld measuremen. Howeer hs model s no applcable o specal crcumsances, specal weaher, bu sll has a wde scope of applcaon. Reference [] Wang X J. Research on Smulaon and Reconsrucon of ehcle Collsons Traffc Accden. Chang an Unersy, 0. [] Road raffc accden sascs repor of he People's Republc of Chna, Wux. Traffc Managemen Research Insude of he Mnsry of Publc Secury, 0. [3] Mclunde W M. Smulaon of -wheeled rder o car accden scenaros, usng an adaped LS-DYNA pedesran humanod[j]. Proceedngs of he 8h Inernaonal Conference on he Enhanced Safey of Vehcle (ESV), Nagoya, Japan, 003. [4] Ln Q F, Xu H, Cheng B. Traffc accden pedesran, cycls and bcycle hrow dsance model. Transporaon sysems engneerng and nformaon, 006,6(6): [5] Yang B, Jn H, Zhang X Y. Traffc accden nformaon collecon and process reconsrucon based on Dgal Phoogrammery. Auomoe Engneerng, 00,3(6): [6] Macmllan R H. Dynamcs of Vehcle Collsons, S Heler, Jersey: Inderscence Enerprses, 983, 4 9. [7] Vang D. A smplfed model for analyss of he pos-mpac moon of ehcles, Auomoble Engneerng, 03, 7(6): [8] Wang J G, Zhu X C, L H G. Energy squares of ehcle collson and s applcaon n raffc accden analyss, Journal of Hghway and Transporaon Research and Deelopmen, 00. 9