【導讀】fewdecades.E-mailaddress:(M.Bouazara).accidents(Mattesonetal.,2020).Nearly50%ofthesinglevehicle

　　

【正文】 n parallel in the following expression.Fsi188。 Kiei254。 Ci_ei(19)6. Results and discussionThe parisons are evaluated in terms of variations in lateralacceleration, roll angle, yaw rate, lateral load transfer and thevehicle’s path trajectory response with both rigid and liquidcharges. In this study, steady and transient steer manoeuvres, withstep steer inputs (open loop), single lane change manoeuvres anddouble lane change manoeuvres (closed loop) are considered tostudy the steadystate and transient directional performance.Since a partial fill condition in a vehicle tank is most frequentlydue to variations in product density, initial analyses are performedto investigate the dynamic response characteristics of a tankvehicle with 50% fill volume (oil liquid, weight density188。966 kg/m3).The simulationparametersof thetankvehicleare summarizedin Table 1.Specific steeringinputs are applied in openloop control and thevehicle response is observed. Openloop control is used to characterize the vehicle response. A rapid transition from straightlinerunning to constant radius cornering requires a steplike steeringsteer, the vehicle enters a steady turn and follows a circular path ona constant radius. To generate a severe but feasible steplike input,thesteeringanglewasrampedfromzerotothemaximumvalueovera period of 1 s (Sampson and Cebon, 2020) as shown in Fig. closedloop control, a desired vehicle motion or trajectory, such asfollowingapreciselyprescribedpathinalanechangemanoeuvre,isachieved by continuously monitoring the vehicle response (longitudinal and lateral position in the lane change) and adjustingfor estimating rearward amplification and several other safetyrelated performance measures as shown in Fig. 4. In closedloopcontrol the driver is actively involved in the control processthroughout the manoeuvre. A double lane change manoeuvre isoften used to avoid an obstacle in an emergency. The double lanesince it can be used to measure rearward amplification.02468104,03,02,01,00,01,02,03,04,0(Rigid)(Liquid)Time (s)ay(m/s2)0 3 56789106420246Roll angle (deg)Time (s)(Rigid)(Liquid)468(Rigid)(Liquid)2468(Rigid)(Liquid)12 4M. Toumi et al. / European Journal of Mechanics A/Solids 28 (2020) 1026–1034 1033Time (s)01 10864202Yaw rate (deg/s)Lateral rear load transfert048100,000,050,100,150,200,250,30(Rigid)(Liquid)Time (s)2345678926Fig. 11. Vehicle response to doubleRoll rate (deg)Time (s)035 1086420048100,000,020,040,060,080,100,120,14(Rigid)(Liquid)Time (s)Lateral front load transfert124678926lane change manoeuvre.Figs. 9–11 illustrate the time histories of the roll angle, thelateral acceleration and roll rate response of the sprung mass, thelateral load transfer ratio (LTR) and the yaw rate of the vehicle toa steady steer. The maximum values of the vehicle responseparameters tend to increase considerably with an increase indirection angle input. The results show that the magnitude of thesprung mass roll angle increases. This increase is attributed toa higher lateral acceleration response caused by the larger steerinput.The roll dynamics of heavy vehicles when cornering are muchmore relevant to vehicle safety than those of automobiles (Fancherimplemented in a general puter program easy to use witha positive error control. This new algorithm presented here for theanalysis of liquid cargo does not require the calculation of the firstandsecondordergradient. It hasperformedwell inmanyexamplesand promises good results in treating plex fluid systems inmotion with a large number of design variables. The selfformulating nature of the method allows the designer to analyze andscrutinize the effect of various influential parameters to ultimatelydesign a more stable liquid cargo vehicle.ReferencesM. Toumi et al. / European Journal of Mechanics A/Solids 28 (2020) 1026–10341034et al., 1986). Heavy vehicles feature relatively high centres of massand narrow track widths and can lose roll stability at moderatelevels of lateral acceleration. Whereas the performance limit of anautomobile is characterized by a loss of yaw stability (Sampson,2020), the performance limit of a heavy vehicle is typically characterized by a loss of roll stability. However, an examination of theresults shows that for a vehicle equipped with a liquid charge, themagnitude of the response is more significant than that with arigidcharge. Conversely, nonlinearities in the directional behaviour ofheavyvehiclesaredominatedbythesensitivityof theslipangletothe lateral force relationship to changes in vertical load. Heavyvehicles typically feature elevated payloads and parativelynarrow track widths。 so lateral load transfer is significant even atmodest levels of lateral acceleration. This difference is moresignificant for the vehicle with a liquid charge than with a rigidcharge.7. ConclusionThe results achieved in this study clearly demonstrate theperformance of this simplified analytical algorithm to characterizethe sloshing liquid in a road tanker. The parison between thisand a plex numerical model shows a good correlation for casesof difficult movement such as steadystate turning and both singleand double lane change manoeuvres. The small difference betweenthe two models is probably due to the assumption of linearity andthe iterative calculation used to capture the form of the freesurfacefor the analytical model pared to the numerical model. In thesecond simulation, the analytical model is coupled with a fullnonlinear unit vehicle. The parison with a vehicle transportinga rigid load shows that the forces and moments arising froma directional manoeuvre yield a considerable dynamic load shift inthe roll and pitch planes due to the slo