Mathematical model of force interactions wheel ground when the machine turns

Abstract

The behavior of the car at the turn is described by the equations of motion into which the reactions from the side of the soil necessarily enter. The scope of applications of the motion model is determined by the description of the force interaction in the contact.

Today, many models are based on empirical dependencies. This limits their wide application. Often the assumptions made when describing the forces in contact lead to a violation of the laws of mechanics. The article examines the main errors most frequently encountered in describing
the force interaction of the wheel with the ground when the machine is turned.

The article proposes a new model of force interaction, based on the laws of mechanics and the mathematical theory of friction. This model describes the ground reaction forces as a function of the coordinates of the instantaneous sliding of the contact spot. This reduces the power problem to the kinematics of the motion of the wheel. Power and kinematic problems are solved
together, which confirms their interconnection and interdependence.

The advantages of the new model is that it describes each wheel individually. This allows you to take into account the mode of motion of the wheel (drive, non-drive or braking), the elastic properties of the pneumatic tire and deformation of the ground, enter different sizes, the shape of the contact and the value of the normal load on the wheel. The model allows to take into account the anisotropic properties of the contact in the future. The model is tested and confirmed
by experiment when turning a small tractor.