An Experimentally Validated Model of a Motorcycle Shock Absorber for Studying Suspension Dynamics

Abstract

Nowadays advanced shock absorbers are equipped with hydraulic valves that offer many possibilities of adjustment of orifices and shims. The theoretical force-velocity curve can be accurately designed and modified by means of these adjustments, in order to achieve the desired performance. Actually, compressibility of gas in compensation chamber, compressibility of oil, cavitation and compliance of seals and cylinders can significantly alter the force-velocity diagram. In some working conditions the behavior of the shock absorber may differ from the optimized one, with important consequences on the performance of the vehicle. Therefore there is the need of mathematical models able to predict the behavior of shock absorbers in the presence of large hysteresis phenomena, these models cannot be too complex and cumbersome, because they have to be implemented in multibody models of vehicles. The paper starts showing some experimental data collected by testing in laboratory a motorcycle shock absorber and aims to quantify the effect of hysteresis on performance and tuning. Then a mathematical model of a shock absorber is developed and presented. Valves are modeled with detail taking into account flow through bleed orifices and shim stacks and the effect of adjustments can be predicted. Compressibility of oil and compliances are taken into account by means of an equivalent compressibility coefficient. The model has a little number of parameters and a method is presented for identifying these parameters from laboratory tests. Some simulations show that the model is able to predict the behavior of the shock absorber over a wide range of frequencies. After validation, the shock absorber model is implemented into a two degree of freedom model of a rear suspension of a motorcycle. A MATLAB code is developed to solve the system of differential equations that describe the dynamic response of the suspension and the fluid motion inside the shock absorber. The response of the vehicle to a road bump is simulated. Acceleration of the suspended mass and tire load fluctuations show the effect of hysteresis and of adjustments of shock absorber on the performance of the vehicle.