Effect of yaw moment of inertia on vehicle transient behaviour to steer

Abstract

Experienced drivers sometimes explain vehicle transient behavior to steering as "after the front wheels start to turn, the rear wheels start to turn with a delay" or "the rear wheels swing around the front wheels like a pendulum. In this paper, the former is called two-stage motion and the latter is called pendulum motion. In order to realize more fun handling performance, it would be effective to physically understand these motions and to reflect these understanding into vehicle developments. Thus, these motions were studied using equations of motion. In these studies, however, since the yaw moment of inertia has been limited to a special case, the valid ranges to which these studies results can be applied are unknown. Therefore, this paper studies these motions for general cases of yaw moments of inertia. Firstly, this paper yields the equations of motion for two-stage motion by algebraically manipulating the equations for, so-called, bicycle model whose yaw moment of inertia is not limited. These yielded equations mean that the front wheels begin to turn immediately after steering, and then the point a, where one of impact centers locates, begins to turn with a delay. Secondly, these equations are transformed into form of the true pendulum equation, whose one of the variables is the attitude angle at position e, where the attitude angle is zero on steady turn. By interpreting these equations, finally, it is pointed out that the pendulum motion is a phenomenon in which the point a accelerates toward the extension of the speed vector at the point e.