Stochastic analysis of motorcycle dynamics

Off-road and racing motorcycles require a particular setup of the suspensions to improve the comfort and the safety of the rider, maintaining a continuous contact between the road and the motorcycle (by means of the tires). Further, because of the ground roughness, in the case of offroad motorcycle, suspensions usually experience extreme and erratic excursions (suspension stroke) in performing their function. In this regard, the adoption of nonlinear devices can, perhaps, limit both the acceleration experienced by the sprung mass and the excursions of the suspensions. This leads to the consideration of asymmetric nonlinearly-behaving suspensions. This option, however, induces the difficulty of the need to solve nonlinear differential equations governing the motion of the motorcycle as excited by the stochastic road ground profile. In this paper a “quarter” dynamic model of a motorcycle is considered. The model involves suspension elements with asymmetric behavior. Further, it is assumed that the motorcycle is exposed to loading of a stochastic nature as it moves with a specified speed over a road profile defined by a relevant power spectrum. It is shown that a meaningful analysis of the motorcycle response can be conducted by using the technique of statistical linearization. The validity of the proposed approach is established by comparison with results from pertinent Monte Carlo studies. It is hoped that the proposed approach can be used for a variety of parameter/ride quality studies and as preliminary design tool by the motorcycle industry.