On the effect of the anisotropic dry friction and the deformed state of tires on the shimmy initiation

The shimmy theories based on the Keldysh assumption can be easily implemented analytically and are still quite efficient for the preliminary analysis of the stability of steady state rolling regimes with no slip and spin of tires. On the other hand, such a shimmy theory uses the non-holonomic rolling model, therefore it is inconsistent with unsteady rolling regimes characterized by the non-vanishing sliding and spin. The qualitatively different model accounting the dry friction effect on the stability of motion is constructed on the groundwork of the coupled dry friction theory. This model has shown its’ applicability to some practical problems of engineering design even if a wheel is assumed to be rigid. Here the improved model accounting for the tire deforming, the complex contact pressure distribution, an the anisotropy of the dry friction coefficient in case of the combined kinematics is presented