The Lateral Flexibility of Pneumatic Tire and Its Application to the Lateral Rolling Contact Problem

The role of the tire in controlling vehicle motion rests mainly upon its ability to generate desired lateral forces and moments when rolling at a “slip angle.” This paper deals with a method of predicting the lateral characteristics of a rolling tire from the detailed knowledge of its lateral flexibility in the contact region and the law of friction. At first, a method of determining the variation of the lateral flexibility is described, using experimentally obtained distributions of lateral force and deformation with a modified “Gough apparatus.” Considering the tire as a running band of a linear structure of high order, Green's Function of lateral flexibility is obtained. Such a function can adequately bring out finer differences due to variation in the constructional parameters and service variables of actual tires. This approach not only enables one to consider the lateral flexibility of actual tires in design calculations, but also seems to be promising in assessing the “lateral-longitudinal” interactions as well as “normal-tangential” interactions by simple extensions of the methods described herein. The two-dimensional contact problem of a tire rolling at a slip angle is then considered after reducing it to a one-dimensional problem with total slip using a “free rolling factor” to superimpose the free rolling slip on the lateral slip. The resulting solution is qualitatively similar to the conventional one assuming a region of adhesion and is probably a more realistic approximation of the conditions arising at the contact. The problem of the nonstationary motion of a tire initially at rest with slip angle, set into motion, is numerically solved using the Green's function of lateral flexibility and the nonlinear distance-dependent part of the law of friction of rubber. The paper intends to show how the Green's function of lateral flexibility may be combined with the law of friction to predict the cornering characteristics affecting vehicle control. Conversely, from the point of view of tire designers, this approach serves as a first step in the synthesis between tire construction service variables and the tread rubber compound so as to realize a desired cornering characteristic on a given road surface with known frictional properties.