Abstract
This paper presents the formulation of the rigorous and approximate contact condition between the wheel and road for numerical simulations of vehicle motion on uneven terrain. In the rigorous contact condition, the curvature of the road surface is taken into account. The approximate contact condition is formulated on the assumption that the gradient of the road is constant around the contact point between the wheel and road. The rigorous contact condition needs not only two holonomic constraint equations but also a nonholonomic constraint equation using the coordinate of the contact point. The approximate contact condition needs only a holonomic constraint equation as well as a nonholonomic constraint equation. Both conditions are applied to numerical simulations of vehicle motion on uneven terrain. The differential-algebraic equations (DAE) with the rigorous contact conditions are derived from 29 Lagrange equations and 24 constraint equations, while DAE with the approximate contact condition is derived from 25 Lagrange equations and 20 constraint equations. In order to investigate the vehicle motion under both conditions, anti-phase sinusoidal surfaces of the same amplitude are given for the contact surface of the left and right wheels, respectively, and the translational vehicle velocity is assumed to be constant. In the case that the curvatures of the road surfaces are close to that of the wheels, vehicle motion under both conditions are remarkably different from each other. On rigorous condition, the horizontal, vertical and rotational velocities of the wheels show the rapid changes around the bottoms of the road, at which the curvature of the road is maximum. These rapid changes of the wheel motion cause the rapid changes of the vertical and rotational velocities of the car body.
Keywords - Contact, curvature, nonholonomic, multibody, DAE