EFFECTS OF AN OSCILLATING TORSIONAL COUPLE ON THE CONTACT SURFACES OF ELASTIC SPHERES
COLUMBIA UNIV NEW YORK DEPT OF CIVIL ENGINEERING AND ENGINEERING MECHANICS
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The Lubkin solution J. Mech. 18183-187, 1951 for the torsional contact of 2 like elastic spheres in Hertz contact with an allowance for the occurrence of slip was extended to 1 the case in which the normal force is held constant while the torsional couple decreases after having reached a certain value, and 2 the case in which the torsional couple oscillates between fixed amplitudes. In the latter, the curve relating twisting moment to angle of twist forms a closed loop, the area of which represents the frictional energy dissipation per cycle. For small amplitudes, this energy loss varied as the cube of the twisting moment. The solution was considered strictly valid only for small amplitudes of the applied moment because of an approximation. Practically, however, it was believed applicable to a large portion of the permissible range of moment-normal force ratios. An approximate expression was obtained for the torsional compliance. The initial value of the compliance during the first loading process was the same as that obtained by Mindlin J. Appl. Mech. 16259- 268, 1949 in which the tangential traction rose to infinity on the elliptic boundary of contact in the absence of slip.