Anisotropic Combined Dry Friction in Problems of Pneumatics’ Dynamics

• DOI: 10.1007/s42417-019-00140-1
• Publication Date: 2019-06-22T13:02:28Z
• Authors: Alexey A. Kireenkov; Sergey I. Zhavoronok
• Keywords: Dry friction; Friction torque; Normal force

Traditionally used shimmy models assume vanishing slip at each point of a roadwheel contact spot, at the same time the observed instable wheel motion observed at unsteady rolling stages with significant sliding could not be described by traditional theories. Thus, a principally new model of the wheel shimmy is required to be consistent with such regimes. A new model of a rolling wheel accounting for the dry friction under the conditions of combined kinematics (i.e. simultaneous sliding, spinning and rolling) as well as for contact pressure distributions in pneumatic tires could become a background for various engineering methods of prediction of the shimmy appearing at unsteady rolling regimes. The proposed model of a pneumatic wheel’s motion is based on the improved dry friction theory accounting for the friction anisotropy; the Coulomb law is assumed for each contact spot’s point where the summary slip velocity is resulted by the simultaneous sliding and spinning, and the contact pressure could be obtained from the finite element simulation of quasistatic tire deforming. The theory of the coupled dry friction is improved by accounting for the anisotropy of the friction factor represented in a form of the second-rank tensor. The general formulation for the resultant vector of dry friction forces, dry friction torque and the rolling friction couple are obtained. The contact pressure for a typical tire is computed numerically, its polynomial interpolation is introduced, and the coefficients of the approximate model of the dry friction are obtained. The constructed model allows an efficient accounting for the dry friction effects on the rolling stability as well as the real contact pressure distribution; thus, it can be interpreted as the second approximation improving the model of the shimmy of quasi-rigid wheel.