Summary
This work presents a new mathematical model of wheel hop for a vehicle with independent suspension, and performs a bifurcation analysis to investigate its nonlinear response under changes in tire inflation pressure and vertical load. Specifically, a three degree-of-freedom (DOF) model of a rear wheel is established that includes the coupling mechanism between longitudinal and vertical modes, along with an extended tire model that considers the influence of inflation pressure and vertical load on tire friction. Numerical continuation is used to study the effect of input speed on the wheel’s hop response. This analysis yields two oscillation modes: wheel hop at 1.86 Hz, with a longitudinal and vertical displacement ratio of 1: 3.1, which may occur over a range of 5~108 rad/s (strongly depending on initial conditions); and a high frequency longitudinal mode identified from 5~231 rad/s. The tire’s stick-slip effect is found to be the cause of wheel hop, and across one period of oscillation the wheel experiences a conversion from sticking to slipping. Finally, the effect of the inflation pressure and vertical load on wheel hop is revealed: the range where wheel hop occurs expands first to maximum and then shrinks to zero at fold bifurcations as the pressure and load are increased. The results of this study can not only provide a theoretical reference for hop attenuation, but also demonstrate the effectiveness of the analyzed model, which can be used in further dynamic analysis of wheel vibrations with suspension geometry considered.
