A general solution to the axisymmetric torsion problem is investigated, taking into account partial slips for a known distribution of normal stresses and a known size of the contact zone. Arbitrary contact geometries of bodies are considered. The presented approach differs from the classical solution, which employs Hertz theory. The problem of partial slips is reduced to integral equations solved numerically. The presented results are consistent with the classical solution for the torsional contact of two spheres, and in particular with the relationship between the angle of twist and the size of the adhesion zone in the Lubkin problem.
In classical works concerning the study of partial slips in torsional contact [2], a very important assumption is that the geometry of the bodies is spherical and the normal contact is described within the framework of Hertz theory [1]. Jäger [8] generalized the contact problem taking into account partial slips for arbitrary, yet smooth surfaces of bodies, citing the application of his theory for polynomial geometry, namely, the function x 2 n, n = 1, 2, 3,… was used to describe the profile of the punch base.
In this article, we investigate another general solution to the torsion problem taking into account partial slips, assuming that the distribution of normal stresses and the size of the contact zone are known. At the beginning, we assume that upon the application of a torque, the resulting friction forces are large enough to counteract slip, i.e., we consider the torsion problem with total adhesion, which we solve in section 2.1. (…)
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Source: Logistyka Magazine