Rolling resistance of a rigid sphere with viscoelastic coatings

•A 3D boundary-element formulation for a spherical multi-layered coating is presented.•Viscoelastic, inertial and Coriolis effects due to steady-state rotation are included.•A rolling contact solving scheme is proposed and surface friction is discussed.•The model is applied to rolling resistance and verified by comparison to FE simulations.•An example illustrates the dependence of rolling resistance on several parameters.

We present a novel three-dimensional boundary-element formulation that fully characterizes the mechanical behavior of the external boundary of a multi-layered viscoelastic coating attached to a hard rotating spherical core. The proposed formulation incorporates both, the viscoelastic, and the inertial effects of the steady-state rolling motion of the sphere, including the Coriolis effect. The proposed formulation is based on Fourier-domain expressions of all mechanical governing equations. It relates two-dimensional Fourier series expansions of surface displacements and stresses, which results in the formation of a compliance matrix for the outer boundary of the deformable coating, discretized into nodes. The computational cost of building such a compliance matrix is optimized, based on configurational similarities and symmetry. The proposed formulation is applied, in combination with a rolling contact solving strategy, to evaluate the viscoelastic rolling friction of a coated sphere on a rigid plane. Steady-state results generated by the proposed model are verified by comparison to those obtained from running dynamic simulations on a three-dimensional finite element model, beyond the transient. A detailed application example includes a verification of convergence and illustrates the dependence of rolling resistance on the applied load, the thickness of the coating, and the rolling velocity.