Calculation of the Effective Normal Stiffness of a Deformable Wheel with a Tilted Rotation Axis

Abstract

The study is relevant for design modeling of the trajectory movement of vehicles on deformable support wheels. Purpose of the study: obtaining a theoretical relationship for calculating the effective normal stiffness of a deformable wheel with an inclined axis of rotation. Mathematical relationships between this stiffness and the angle of inclination of the wheel rotation axis have been established. It is determined that the effective normal stiffness changes by a factor of \({{K}_{{\alpha z}}}\) at the specified slope. A theoretical dependence was obtained for calculating the correction factor \({{K}_{{\alpha z}}}\). The dependence is a function of \({{K}_{{\alpha z}}}\) on the design parameters of the wheel and the angle of inclination of the rotation axis α. The dependence is correct at angles \(\alpha \leqslant 10^\circ \). At angles of inclination that are acceptable under wheel wear conditions (up to 5°) the effective normal stiffness is significantly reduced, for example, for the object of study to 25%. The validity of the theoretical dependence was confirmed by laboratory experiments using a specially created installation for measuring the parameters of the elastic properties of a deformable wheel at different positions of its rotation axis. Based on the processing of experimental data, the error in calculating \({{K}_{{\alpha z}}}\) from the obtained theoretical dependence was determined, which does not exceed 6%.