Vibration Analysis of the Bicycle-Car Model Considering Tire-Road Separation

This article investigates the dynamics of non-smooth and nonlinear oscillations of a bicycle-car model, considering the tire-road separation. Road contact applies a non-holonomic constrain on the dynamics system that makes the equations of motion to be different under in-contact and off-contact conditions. The set of nonlinear equations of the system has been formulated based on nondimensionalization to minimize the number of parameters and generalize the results. To compare the quality of different suspensions in reducing the unpleasant no-contact conditions, we define a contact-free fraction indicator to measure the separation fraction time during a cycle of steady-state oscillation. An observation of frequency responses including vertical displacements, the pitch mode, and the domain of contact-free fraction of time has been investigated to clarify engineering design directions. The separating boundaries have also been identified utilizing implicit function for in-contact dynamics and sensitivity of the separation condition to various dynamics system parameters are simulated and explained. The separation dynamics are numerically solved to determine which values of suspension structures can postpone the occurrence of tire-road separation or the contactless process, which leads to eradicating the potentially undesirable vibration and improving the efficiency of suspension quality.