The Torsion of Elastic Spheres in Contact

Abstract

A small torsional couple is applied about the axis of symmetry of a system of two elastic spheres (or solids of revolution) which have been pressed together by a force perpendicular to their common tangent plane. This problem may be reduced to a “problem of the plane,” and it has been found that in the absence of slip on the interface, the tangential traction is singular on the bounding circle. Hence the assumption of no slip is physically untenable. In the present solution allowance is made for slip by assuming that the tangential component of traction, for the area over which slip has progressed, is equal to the product of a constant friction coefficient and the normal or Hertzian distribution. A continuous expression for the traction is developed. A formula relating the radial depth of penetration of slip to the magnitude of the applied moment is given, and another relating this moment to the rotation of the contact surface of one of the bodies with respect to remote points in that body.

Numerical Analysis of Partial Slip Contact under a Tangential Force and a Twisting Moment

“…Good agreement is observed between the authors' numerical results and the analytical solutions. Figure 4 shows comparisons of the shear traction q r (q r = √ q x + q y ) with the present results and Lubkin's solutions [17] for a purely torsional contact problem, and also good agreement is observed between the authors' numerical results and the analytical solutions. The traction q r drops to zero at the contact centre if the tangential load contains only a pure torque.…”

“…Lubkin [17] first gave analytical solutions of shear tractions in circular contact under a pure torsional load. The stress fields corresponding to the pressure and twist moment were investigated by Hetenyi and McDonald [18] and Hills and Sackfield [19].…”

A Simple Semi-Analytic Contact Mechanical Model for Tangential and Torsional Fretting Wear of Axisymmetric Contacts

“…For the elementary loading history (constant normal force, subsequently applied increasing torque; sometimes referred to as the "Lubkin [31] problem"), the solution goes as follows [32]: first, a function φ must be determined according to…”

Έξυπνες Υφασμάτινες Κατασκευές

“…Ο Lubkin(1951) υπολόγισε ότι οι διατμητικές τάσεις εντός της επιφάνειας επαφής που δεν περιστρέφεται (stick zone, rc  ) θα δίνονται από την σχέση…”

“…Σχ 3.6. Η στρεπτική ροπή σε συνάρτηση με την γωνία στροφής των νημάτων λόγω του ζεύγους των διατμητικών τάσεων (Lubkin,(1951)). Το πρωτογενές δομικό στοιχείο του υφάσματος είναι η ίνα.…”