by Juergen Jaeger, Blattwiesenstr. 7, D-76227 Karlsruhe, Germany

Contact Mechanics 93, First Int. Conference, eds.:M. H. Aliabadi, C. A. Brebbia, Computational Mechanics Publications, Southampton, UK, pp. 405-412


 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 load-histories 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.