| With the development of society and the improvement of traffic regulations,car-trailer combinations(CTC)are quite popular in transportation.Different with single-unit vehicle,CTC involve kinematic and dynamic coupling of multiple vehicles.At high speed,the system may suffer from jack-knifing or lateral instability under even minor disturbance.Eventually,it may lead to the occurrence of accidents and endanger the safety of lives and properties.In this paper,a 5-DOFs extended single-track model with suspension system is established for the CTC system,and the influence mechanism of suspension system characteristics on body sway of CTC is studied sufficiently.The main tasks of this paper are shown as follows:(1)An extended single-track model(ESTM)and virtual prototype model based on the commercial software Trucksim for CTC are established.Considering the nonlinear characteristics of tires and shock absorbers,a 5-DOFs ESTM describing the lateral,yaw and roll motions of CTC is established.In addition,the coefficient of determination r~2 is proposed as the model evaluation criterion.According to the coefficient of determination of CTC’s various motion states(such as towing car/trailer yaw rate,hitch angle,etc.)between the ESTM and Trucksim model,the correctness of ESTM is verified.(2)The influence mechanism of suspension system characteristics on the body sway of CTC is systematically analyzed.Spring stiffness,shock absorber damping characteristics and damper failure behavior are focus of suspension characteristics.The effects of different damper characteristics and spring stiffness on the dynamic stability of CTC are analyzed.Then,the main factors affecting the body sway of CTC can be summarized.Both system dynamic response and global stability of the CTC are affected by the nonlinear characteristics of the shock absorber.In addition,the damper failure model is used to study the influence mechanism of the damper failure phenomenon on the body sway of CTC.(3)The dynamic stability and instability mechanism of CTC system are analyzed by qualitative and quantitative methods.The dynamic critical speed of CTC system can be obtained by the Hurwitz criterion.Then,according to Hopf theorem,it is confirmed that the dynamic critical speed is the Hopf bifurcation point of CTC.At this speed,the phenomena of Hopf bifurcation and limit-cycle vibration of the system are generated.In addition,through the research on eigenvalues of the system,the influence of dominant pole on the dynamic response of CTC is investigated.Finally,the bifurcation characteristics,instability mechanism and global stability of CTC system are analyzed sufficiently.(4)The influence of system parameters on body sway of CTC is studied.Results show that the parameters(such as friction coefficient,yaw moment of inertia of trailer,distance from front axle to hitch point of trailer,etc.)have great influence on the dynamic critical speed of the CTC system.This results provide theoretical basis for the design of CTC system.(5)A quantitative analysis of the CTC with the incremental harmonic balance method(IHB)is proposed,and an analytical approximate solution of the nonlinear system state equation is obtained.The IHB method can directly solve the response frequency of the system,which facilitates the frequency domain analysis of the system.Further,an error analysis is performed between the IHB and the Runge-Kutta method.It is very clear that the IHB method has better performance in analyzing the body sway of CTC system. |
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