A Minimum Principle for the Law of Dry Friction, With Application to Elastic Cylinders in Rolling Contact—Part 1: Fundamentals—Application to Steady Rolling

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Abstract
In Part 1 of the present paper a minimum principle for the Coulomb-Amontons law of friction is derived. This minimum principle is uniform in the sense that no distinction is made between the slip and the no-slip conditions. The principle is applied to the two-dimensional contact problem in which the normal pressure is Hertzian. After discretization, the principle leads to a linear programming problem in the case of steady rolling as considered by Carter [1] and Bentall and Johnson [2]. Good agreement is found with these authors, and the force-creepage law for elastically dissimilar cylinders has been calculated completely. In the case of the nonsteady contact problem, which is treated in Part 2 and in which the traction evolves under the influence of a gross motion and loading program, the principle leads to a time sequence of linear programming problems. Such problems under several restrictions have been treated before by Kalker [3–5], without the aid of minimization techniques. In the present paper these restrictions are all removed. Numerical results are presented.

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