Multiple Limit Cycles Shimmy of the Dual-Front Axle Steering Heavy Truck Based on Bisectional Road

The shimmy problem causes considerable harm to vehicles and is difficult to solve, especially multiple limit cycle shimmy. Moreover, the dynamic behavior of the multiple limit cycle shimmy of vehicles based on a bisectional road is more complex. Shimmy is practically observed in trucks of cooperative factories during utilization. Thus, we take a heavy truck of a cooperative factory as the prototype and establish a dynamic model of the vehicle-road coupling shimmy system, considering the road adhesion coefficient and dry friction between the suspension and steering system. Based on the dynamic model, the Hopf bifurcation theory is used to qualitatively analyze the existence of the limit cycle for the vehicle shimmy system, and the multiple limit cycle shimmy phenomenon is successfully reproduced using a numerical method. Moreover, the effect of the road adhesion coefficient on the multiple limit cycle shimmy characteristic is studied. Results show that the speed interval and amplitude of the multiple limit cycle shimmy decrease with the road adhesion coefficient; when the coefficient is reduced to a certain extent, the multiple limit cycle shimmy phenomenon is not observed. In addition, the adhesion coefficient of the second axle has a stronger effect on the shimmy characteristic than that of the first axle.