Oblique contact of two identical cylinders (Q2760580)

A time-periodic problem of contact of two cylinders is considered in the framework of Hertz theory. Both cylinders are constrained against rotation. The axis of the upper cylinder is non-movable and the axis of the lower one oscillates under some angle to the common normal of cylinders. The length of contact zone is variable in time. Under the contact interaction with friction and adhesion, nonzero tangential stresses in the contact zone arise. An analytic solution for time history of tangential stresses is derived. Typically, intervals of slip, adhesion -- partial counterslip and complete counterslip take place. It is found that resultant of the stresses taken over time of contact is nonzero. Thus, free upper cylinder would rotate. The obtained solution explains principle of operation of the standing wave ultrasonic motor.