Normal vibrations and friction under harmonic loads. Part 1. Hertzian contacts

Nonlinear vibrations at a Hertzian contact are studied by the perturbation technique known as the method of multiple scales. The vibrations are excited by the dynamic component of an externally applied normal load. Solutions are obtained for both the average and instantaneous contact deflections. As a result of the nonlinear Hertzian stiffness, the average normal contact deflection during oscillations is smaller than the static deflection under the same average load. It is shown that this can result in a reduction of the average area of contact and, by implication, the average friction force in the presence of even small dynamic loads. The parametric dependence of the normal motion on the various contact parameters is investigated. It is shown that the maximum average friction reduction without contact loss is approximately ten percent.