Bifurcation analysis of wheel hop considering the influence of tyre inflation pressure and vertical load

<p dir="ltr">Wheel hop is an undesirable self-sustaining vibration in the driving wheels of a vehicle. A three degree-of-freedom (DOF) model of a rear wheel is created to investigate how the tyre inflation pressure and vertical load influence the nonlinear dynamic response of wheel hop. This model captures the effects of kinematic coupling between longitudinal and vertical motions and the transient tyre behaviour during oscillations, along with an extended tyre model that considers the influence of pressure and load on longitudinal force generation. The effect of the input angular speed from the shaft on the wheel is first studied, yielding the limit cycle representing wheel hop with a longitudinal and vertical displacement ratio of 1: 3.1. Three areas bounded by Hopf and saddle-node bifurcations are identified, with wheel hop found to occur over a range of 5.83~89.6 rad/s: its occurrence strongly depends on initial conditions. The stick-slip effect is then shown to be the cause of wheel hop, and the critical point for the conversion of the wheel’s behaviour from sticking to slipping motion appears when the longitudinal tyre force peaks. Finally, a three-parameter space reveals that the wheel hop area expands first to maximum and then shrinks to zero at fold bifurcations with increased pressure and load. The key to the influence mechanism is found to be the shape factor in the tyre model, which influences the wheel’s stick-slip behaviour significantly.<br></p>