COUPLED THERMOELASTIC ANALYSIS OF PERFECT ROLLING CONTACT: SOLUTION BEHAVIOR NEAR YIELD INITIATION

An insulated rigid cylinder of infinite length rolls without slip on a half-space at constant rolling speed. The equations of coupled thermoelasticity in the dynamic steady state hold. The analytical solution for the mixed boundary-value problem is extracted from robust asymptotic versions of exact integral transforms. The solution, in turn, gives contact zone size and location, and temperature change and von Mises yield function on the contact zone. The function exhibits a maximum at the contact zone center, which is above the location of its maximum in the half-space. For some insight into behavior near yield initiation, therefore, contact zone center yield is used to derive expressions for the corresponding contact zone size, compressive load on the cylinder, and zone temperature increase. Calculations for 4340 steel indicate that initiation is multi-axial and that mild temperature increases occur. In addition, the contact zone center, which corresponds to the contact point in the rigid–rigid limit, is found to have a small tangential speed. The rolling speed is allowed to take any value between zero and the thermoelastic Rayleigh speed. This range perhaps exceeds that required in applications, but allows a clearer view of variation with rolling speed.