
TORSIONAL LOADHISTORIES OF ELASTIC SPHERES IN CONTACT
by Juergen Jaeger, Blattwiesenstr. 7, D76227 Karlsruhe, Germany
Contact Mechanics 93, First Int. Conference, eds.:M. H. Aliabadi, C. A. Brebbia, Computational Mechanics Publications, Southampton, UK, pp. 405412
email: j_jaeger@tonline.de
Abstract: The traction, moment and the twisting angle of two geometrically and materially identical elastic spheres in Hertzian contact are computed, acted upon by a varying normal force and a varying torsional couple. It has been found that, in the case of a monotonically increasing couple with constant normal force, the contact area is split into an inner, circular area of adhesion and an outer, annular region of partial slip. The traction distribution for this problem is called a Lubkin function, and it is shown that general loadhistories can be presented as a sum of Lubkin functions. An approximation for the moment and the twisting angle is introduced, which is valid for the entire range of the twisting angle, with an error less than 3%. It is also shown that the number of Lubkin functions, which are necessary to describe the contact problem, depends on the number of points of instantaneous adhesion, where the entire contact area sticks for a short moment. This theory is also a good approximation for geometrically and materially dissimilar spheres.
