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Car wheel models using the distributions laws of forces on a contact patch with the road surface

It is natural to consider the rolling dynamics of an automobile wheel when it interacts with the road surface. At the same time the most difficult and important task is to determine the force components applied to the wheel, such as the friction driving force, the drag force, the rolling and spinning resistance moments that occur in the contact spot from the side of the roadbed. The paper investigates the aspects of dry friction, rolling and sliding of an automobile wheel presented as a deformable body. In this case, it is of great importance to take into account the treads, which is reflected in the tire models. An important aspect is the study of the laws of distribution of normal stresses in the contact area. To solve practical issues of road transport, approaches based on the Magic Formula of Pacejka and calculation methods based on brush, ribbon and string models, in particular, the Brush model of Svendenius, are highlighted. The conditions of its applicability are obtained and justified.