Research On The Shimmy Of Electric Vehicle And The Coupling Effects Of Body's Motions

Shimmy is a kind of self-excited vibration that may occur on the steering mechanism of wheeled transport equipment such as motorcycles,automobiles,airplanes,trailers and trolleys,and is also a quality defect that affects the normal operation of transport equipment.Vehicle shimmy shows as the continuous swing of a steering wheel around its kingpin,which is essentially a bifurcation phenomenon of a nonlinear mechanical vibration system.Vehicle shimmy only occurs in a range of velocity.Shimmy may occur when the vehicle velocity enters the shimmy's range of velocity,and it will disappear after leaving this range of velocity.When the varity of vehicle velocity cause the appearance or disappear of shimmy,the system has a Hopf bifurcation,so the shimmy belongs to Hopf bifurcation.In recent decades,many scholars paid attention to the problem of shimmy,and carried out a lot of theoretical research and experimental exploration,then fruitful research results are achieved.However,these studies can't commendably explain the mechanism of shimmy,and the studies about various factors causing shimmy is not complete.Therefore,the problem of vehicle shimmy is still not completely solved at present.The existing researches related to shimmy mainly consider the influence of steering wheel's dynamics model,steering system's structure parameters,front wheels' positioning parameters,gaps between kinematic pairs,and the parameters of suspension on shimmy,but the shimmy problem of electric vehicle equiped electric driving system and the influence of body motions on shimmy were not covered.For the electric vehicles,the physical mechanisms of its front wheels' shimmy problem is still exist,and the factors causing front wheels' shimmy such as tire elasticity,road excitation,and tire imbalance are also exist.At the same time,some new problems such as the increase of the unsprung mass of the vehicle,the change of the vehicle's center of gravity,and the electromechanical coupling in drive system are introduced.The force generated by the body's movement can be transmitted to the tires through the suspensions,and the lateral swing of the front wheel axis generated by front wheels' shimmy is also transmitted to the vehicle body through the suspensions.Thus there are coupling effects between the body's motion and the front wheels' shimmy,and the further researches on this case are urgently needed.Aimed at the above problems,using the Second Lagrange Equation,a 5-DOF electric vehicle shimmy system's model and a 9-DOF vehicle shimmy system's model considering the coupling effect of the vehicle body are established in this paper,The structure and parameters of the front suspensions,the front wheels' positioning parameters,the dynamic characteristics of the tire,and the coupling effect of the body's motion on the shimmy are comprehensively considered.Based on the side-slip and longitudinal-slip mixed conditions of tire during vehicle shimmy,a dynamic model of the tire was established,and a nonholonomic constraint equation between the tire shimmy angle and the slip angle was also established.According to the mathematic model of the 9-DOF shimmy system,the coupling relationship between the body's motion and the front wheels' shimmy is analyzed.Based on the methods of numerical analysis and simulation,the dynamic responses under the initial excitation of two systems with different models are solved,and they are deeply analyzed in terms of the time history dynamic response,power spectrum density diagram,and steady-state phase portrait.Based on the state equation,the state matrix's eigenvalue trajectory of the non-linear shimmy system's linearly derived system varying with the vehicle velocity can be solved.Based on these eigenvalue trajectory,and using the linear system stability theorem and Lyapunov's discriminant theorem for the stability of nonlinear systems,the Hopf bifurcation characteristics and motion stability of two shimmy systems with different models are compared and analyzed.The effects of the change in wheel's mass,body's mass,and vehicle's center of gravity on the Hopf bifurcation characteristics and kinematic stability of the shimmy system are discussed.By calculating the power spectral density of each degree of freedom,the frequencies of each degree of freedom of the shimmy system and the relationship between these frequencies are obtained.At the same time,the effect of the varity of vehicle's velocity on the frequency of the front wheels' shimmy is studied.By comparing with the fuel vehicle,the influence of the increase in mass of electric vehicle's wheels on shimmy is studied.At the same time,the influences of vehicle's front wheels' positioning parameters such as caster angle and kingpin inclination angle on vehicle shimmy are also studied.Using numerical calculation method,the relationship between the amplitude of each DOF in shimmy system and the vehicle velocity,the effects of parameters such as the body mass,the position of the vehicle's center of gravity,and the inclination angle of the front suspension on the amplitude of the respective degree of freedom,and the effect of these parameters on the range of velocity of the vehicle's shimmy are study respectively.Using the test prototypes builted by the laboratory,the shimmy tests of straight-line driving and counterweight driving were carried out.The analysis of the test data verified the accuracy of the model and the correctness of the numerical simulation results.The research results provide a theoretical reference for the design of electric vehicles and the implementation of anti-shimmy measures.