Transient Rolling Contact Phenomena

Two cylinders of identical purely elastic materials are pressed together with parallel axes under the action of a normal force so that a contact strip forms. The cylinders are then shifted with respect to each other, which, under the influence of dry friction, gives rise to Cattaneo's (2) traction distribution with two slip areas. Subsequently they are rolled under the influence of a constant couple, reaching eventually Carter's (3) steady state with one slip area. The question arises how the former traction distribution passes into the latter as a function of time. It is answered in the framework of a more general rolling contact problem. The problem is solved numerically under the assumption of vanishing inertial effects, and results are presented. In the problem mentioned above it is found that Carter's (3) distribution is virtually attained when one to two contact widths have been traversed.