Lateral Force Evaluation in Vehicle’s Wheel Interaction with a Rut

The operation of roads under modern conditions associated with high speeds and traffic density results in wear of pavement and formation of a rut. When crossing the ruts, instability can occur when relatively small steering inputs lead to large changes in the trajectory. The lateral force acting on a wheel of a car is of particular importance in the study of stability and controllability. The magnitude of this force is determined by various factors: tire stiffness, speed, change in the angle of rotation of the wheel, the geometry of the transverse profile of the rut.The objective of the study refers to the problem of determining the angles of inclination of side walls of the rut that are safe for movement at different speeds. The paper considers the interaction of a car wheel with the road surface, proposes a mathematical model for interaction of a tire with ruts, considers the angle of the wheel running on the rut wall. To describe the elastic response of a tire in contact with a rut, an elastic foundation model and a plane section method are used. The lateral force was estimated based on equations of motion of the wheel when crossing the rut. The dependences of the ratio of the lateral force to the normal load for various rut depths and angles of inclination of its walls on the angle of rotation of the wheel and the speed of the vehicle were obtained. It is shown that at a rut inclination angle exceeding five degrees, the lateral force begins to increase significantly with an increase in the angle of rotation of the wheel, as well as the speed of the vehicle, and may exceed the applied normal load. According to the condition of vehicle stability against skidding on a wet surface, limiting average angles of inclination of the side walls of the rut are estimated for various values of the vehicle speed and wheel rotation angles.