Advantages of Using Wheel Rolling Radius for Calculating Friction Characteristics in Wheel-to-Road Contact Patch

Abstract

When improving the design of electronic control devices and car stability control system algorithms based on maximizing the road–tire friction coefficients, one has to evaluate the friction between the elastic wheel and the bearing surface. $\varphi{-}s_{x}$-diagrams are simulated to that end. These are the dependencies of the friction coefficients on the wheel sliding. What they look like depends, aside from external conditions (type of coating, lateral forces, etc.), on the law of contact-patch sliding increase, which in its turn depends on multiple factors including the estimated radius of the wheel. As of today, free radius, dynamic radius, and rolling radius values are used to that end. In this case, the difference between them can reach up to 20%, depending on the value of the tire radial deformation. Despite the large number of studies on the theory of rolling wheels, experts still have not developed a consensus on what radius should be used for these purposes, which, naturally, is accompanied by a difference in the calculations in which these radii are used. The researchers prove the advantages of using the estimated kinematic radius and propose a correlation for calculating it. Herein are presented $\varphi{-}s_{x}$-diagrams for different radii.