Theoretical determination of the distribution of forces and the size of the boundaries of the contact in the interaction of the deformable drive wheel with the soil

Abstract

The article presents the results of an analytical determination of the forces distribution along the length of the contact curve of the driving deformable wheel on the deformable supporting surface, and also are defined the boundaries of the contact zone. The case in a flat statement of the problem is considered. The supporting surface and the surface of the deformable wheel are represented as a continuous deformable medium. The shape of the wheel in the contact zone is represented by the circle equation, which in the contact zone is expanded in a Macloran-series. By using conditions at the boundaries of the contact zone, a system of equations is obtained from which the sizes of the contact zone are determined. The solution of these equations allows one to find expressions of the sizes of the contact zone of the deformable wheel with the deformable surface, depending on the mechanical properties of the wheel materials and the supporting surface, from the geometric dimensions of the wheel and from the loads applied to it. In addition, the results of the studies allow us to determine the analytical expression of the coefficient of rolling resistance of a deformable wheel over a deformable surface, depending on their mechanical properties, geometric parameters, and the loads applied to it.