The contact problem of in-plane rolling of tires on a flat road

The paper describes an analysis of contact problem of free-rolling of pneumatic tires on a flat road. The tire is modelled as an elastic ring supported on a viscoelastic foundation. Additional elastic spring elements on the outer surface of the ring are included to model the compliance of the tread rubber. The contact problem of a free-rolling tire is formulated for prescribed normal deflection and subjected to constraints of both normal contact and friction. The equations of motion for the treadband displacements are expressed in terms of modal expansion and non-linear boundary conditions of rolling contact are solved numerically to determine the region of contact the distribution of normal and shear tractions and the effective rolling radius of the free-rolling tire. The contributions of tire hysteresis and frictional sliding in the contact region to the rolling resistance are determined. The influence of damping and Coriolis acceleration at higher rolling speeds on the asymmetric distribution of normal and tangential traction in the contact patch is considered. The analysis also considers how some of the typical damping models influence the variation of rolling resistance with the rolling speed.