Features of an elastic wheel motion along a curvilinear and rectilinear trajectory with a slip

Abstract

The results of the study of the motion of an elastic wheel as an integral mechanism along a curvilinear and a rectilinear trajectory with a slip on the ground plane having a high adhesion coefficient are presented. The previous researches analysis has shown that the most complete theory of wheel skidless rolling without slipping on elastic pneumatics was formulated by Keldysh V. M. who proposed the equation for calculating the curvature of the motion trajectory. Due to the difficulty of this equation coefficients determining, its use is currently limited. In this paper, the dependences for determining the components of the equation of the elastic wheel motion trajectory curvature have been proposed.
According to the shimmy theory, during an elastic wheel rolling along a curvilinear trajectory, the rim turn and its lateral displacement relative to the tire-ground contact patch occur simultaneously. The rim turn causes tire body torsion, and the lateral displacement causes the elastic wheel moving with a slip angle. It is established that the absolute value of the tire body torsion angle is equal to the slip angle, and their values depend on the trajectory curvature, on the tire-ground contact patch longitudinal axis, and on the existence of traction there.
The condition, under which the tire body energy distribution on the rim relative rotation and on its lateral displacement during the movement along a curved trajectory is uniform, has been determined. The experimental confirmation of the hypothesis of uniform distribution of the energy supplied to the elastic wheel during its movement along a curvilinear trajectory on the rim relative turning and its lateral displacement has been obtained.
When the elastic wheel moves along a rectilinear trajectory with a slip, only the rim lateral displacement occurs, this displacement is accompanied by a cornering force applied in the center of the tire-ground contact patch and by the tire alining torque relative to the vertical axis passing through the contact patch geometric center. The energy consumption for the rim lateral displacement during the wheel rolling along a rectilinear trajectory with a slip has been also determined.
The results of the research can be useful to professionals improving the wheeled vehicles performance characteristics, including maneuverability, handling, and road stability.