32 4 2013 8 JournalofLanzhouJiaotongUniversity Vol32No4 Aug2013 :1001-4373(2013)04-0132-07 DOI:103969/ jissn1001-4373201304029 * - 聂 宇, 张金敏 (, 730070) : 利用多体系统运动学理论以及多体动力学软件 SIMPACK 精确的建立国内某主型动车与轨道系统的耦合 动力学模型, 通过在 SIMPACK 软件中仿真车辆在不同速度下的运动状态, 对该型车的垂动加速度, 横向振动加速 度 轮轨垂向力 轮轨横向力 车体垂向位移 车体横向位移等数据进行分析, 得到振动响应随速度的变化 进一步 分析根轨迹值得出自然阻尼与振动频率的分布曲线图, 判断车辆振动与速度的关系以及在该速度下车辆是否失 稳, 为轨道 车辆结构设计提供一定的参考 : 车辆 ; 速度 ; 振动 ; 频率 :U2701 :A 11 ( ),, [1] nh, 300km h -1 Φ K (q)= [Φ 1 K (q),φ 2 K (q),,φ nh(q)] K T =0 (1) [2] nh nc SIMPACK,, hc>nh, nh, DOF =nc-nh, (nc-nh) : 1 Φ D (q,t)=0 (2) (1) (2), : (q,t) Φ(q,t)= [ ΦK Φ D (q,t ] =0 (3) ),, (3) (3), [3-4], q(t) [ 3?4], 12 (3) * :2013-03-26 : (1988-), E-mail:412188106@qqcom
4 :? 133 : Φ (q, q,t)=φq ( q,t) q+φt (q,t)=0 (4) ν=-φt(q,t) Φ (q, q,t)=φq ( q,t) q-ν=0 (5) q,t) q+φt (q,t)=0 (6) η=-(φq q) qq-2φqt q-φt Φ(q, q, q,t)=φq ( q,t) q-η (q, q,t)=0(7) r p = r+ As p = r+ φbs p (12) (12) : rp = r+ φbs p + φ Bs p = r+ φbs p - φ 2 As p Φq, (5) (13) q (4) : Φ(q, q, q,t)=φq ( q,t) q+ (Φq ( q,t) q ) q+2φqt ( Φq (7) q 1 (5) (7) Φq Fig1 Two-dimensionalspatialcoordinatetransformation, Φ m,q n, Φq m n (Φq ) i,j = Φi/ qj Φq nc 13, xoy x io iy i s 烄 s= [sx,s y ] T, 烅 (8) 烆 s = [sx,s y ] T xoy P 1 2 x io iy i P Fig2 Three-dimensionalspatialcoordinatetransformation 2, : r p =r+s p =r+as p (9) 2 - SIMPACK :r p P ;r O ;s p s 21 ;s p s ;A 4 A =A( φ )= cos φ -sinφ [ sinφ cos ] φ, 1 (10), A A = d φ dφ =A φ -sin φ -cosφ [ cosφ -sin ] φ = φb(11) (9), [3?5] 3~ 5 (9), :
134 32 1 Tab1 DOFofvehiclesystems 22 - ; xc yc zc φ c β c ψ c, xt yt zt φ t β t ψ t xw yw zw φ w β w ψ w 3 Fig3 Frontviewofvehiclesystemdynamics, 5 320km h -1 ~ Fig5 Topviewofvehiclesystemdynamics 350km h -1 6 - Fig6 Motorcar-trackmodel MBS, [6-8] - 6 3 200km h -1 350km h -1 6 4, Fig4 Sideviewofvehiclesystemdynamics ( 7 ) ( 7 ) 320km h -1, 260km h -1, 320km h -1 350km h -1 350km h -1 ( 8), 350km h -1,
4 :? 135 7 Fig7 Verticalvibrationacceleration 8 Fig8 Lateralvibrationacceleration Fig9 9 1 Wheel/railverticalforceofthefirstwheelset
136 32 9 1 km h -1 ~350km h -1 ( 11 ) 350km h -1 ( 11 ( 10) ), 320 Fig10 10 Wheel/raillateralforceofthefirstwheelset 11 Fig11 Vertical Lateraldeviationofthecarbody,,,?, [9], n, n λ=α+ωi, 4
4 :? 137 12,,, 350km h -1,, ( ), 13 12 Fig12 Rootlocusvalues h -1 ~270km h -1 2) ( 350km h -1 ), 3),, 220km h -1 ~270km h -1 350km h -1, 4), 13 : Fig13 Rootlocusplot [1] ZhaiW M,CaiC BDynamieinteractionbetweena 5 lumpedmassvehicleandadiscretelysupportedcon- tinuousrailtrack[j]computers& Structures,1997, 1) 63(5):987-997 [2] [M] :, 2009 [3] [M] : 320km h -1, 220km,1989
138 32 [4] [M] :,1992 [5] UdwadiaFE,PhohomsiriPExplicitequationsofmo- tem Dynamics,1996,26(l):61-79 [7] - [J],1999,21 tionforconstrainedmechanicalsystemswithsingular massmatricesandapplicationstomulti-bodydynamics 2117 [6] ZhaiW M,CaiCB,GuoSZCouplingmodelofvertical (5):70-74 [8] [D] :,2008 [9],,, SIMPACK ( )[M] :,2010 DynamicCouplingVibrationResponseAnalysisofHigh-SpeedTrain-Track NIE Yu, ZHANGJin-min (SchoolofMechatronicEnguneering,LanzhouJiaotongUniversity,Lanzhou730070,China) [J]ProceedingsoftheRoyalSociety, 2006,462:2097- andlateralvehicle/trackinteractions[j]vehiclesys- Abstract:Themulti-bodysystemkinematicstheoryandmulti-bodydynamicssoftwareSIMPACKareused toestablishthetracksystemdynamicsmodelofonemaintypeofmotorvehicleinchinathemotionstate ofthevehicleatdiferentspeedsissimulatedbysimpacksoftwaretoanalyzethedataoftheverticaldy- namicacceleration,lateralacceleration,wheel-railverticalforce,thewheel-raillateralforce,thebodyverti- caldisplacementandthebodyworkhorizontaldisplacementofthecar,andtoobtainthevibrationresponse withthechangeofspeedmoreover,therootlocusworthisfurtheranalyzedtoobtainthenaturaldamping andvibrationfrequencydistributioncurve,soastodeterminetherelationshipofthevibrationandtojudge whetherthevehicleisinstableatthespeedinordertoprovidesomereferencesforthedesignofthetrack andthevehiclestructure Keywords:vehicle;speed;vibration;frequency