Rectilinear car motions taking into account the elasticity and deformability of tires

Abstract

In this paper, the problem of developing a mathematical model of rectilinear motion of a car is solved, taking into account the elasticity and deformability of tires, as well as, for the same radii of the wheels of the car, and taking into account plane-parallel motion at a constant speed. The kinetic energy of the rectilinear motion of the car is found in the case of the same rotation of the front wheels around the axis of the pivots. Generalized forces are taken as sum of forces acting on the system and forces due to the deformation of the pneumatics. The forces acting on the system are found by virtual work method. The forces due to the deformation of the pneumatics are found as the generalized forces acting on the system under consideration, in the calculation of which all forces are taken into account, except for the tire deformation forces associated with angles and displacements. Using these kinetic energies and generalized force expressions, Lagrange's equations of the second type were used to obtain the differential equations of the rectilinear motion of the car. From the resulting mathematical model, it is possible to check and analyze the dynamics and stabilities of the system in various specific cases, i.e., under the influence of non-potential forces in the tire materials, and at large values of the tire kinematic parameters, and at high speed movements of the car. As a result of determining the stability field and stability borders at different values of constructive parameters, it will be possible to find the optimal parameters of the system and study its dynamics.