Analysis of Various Types of Elastic Wheel Radii and Establishing Necessity and Sufficiency of Their Application for Various Problems

The wheel has the following radii types: free \( R_{0} \), static \( R_{st} \), dynamic \( R_{d} \), rolling \( r_{k} \). The difference between them can reach 20% depending on the value of tire radial deformation. It is established that at tire operation deformations the rolling radius decreases by no more than 2%. It is known that a wheel radius has a complex, ambiguous influence on car active safety properties: dynamical stability, manageability, brake dynamics. The purpose of this paper is defining the types of wheel radii necessary for the application at the solution of various problems connected to the car active safety properties. The authors conducted the design analysis of the influence of the type of the used radius at the estimation of longitudinal sliding \( s_{x} \) on the form of the obtained \( \varphi - s_{x} \)-diagrams. The problem of obtaining \( s_{x} \) is encountered at the mathematical simulation of the properties of active safety of wheeled vehicles as well as at their physical simulation on simulator stands and at the manufacture of automatic unmanned vehicles. It is established that at the calculations of \( \varphi - s_{x} \)-diagrams one can apply the close value of free radius instead of a rolling radius value. A more complex problem is providing a rationale of the applied wheel radius in the problems of determining linear deviations, brake way, and car angular orientation. It is connected to complicated and unambiguous interconnections of a wheel radius with the car trajectory parameters. It is determined that at the calculation of car motion trajectory parameters (linear deviations, brake way, angular orientation) one should use the rolling radius value. By the rolling radius value, one should estimate the wheel longitudinal sliding as well as a coupling moment.