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In many engineering problems involving friction, the friction is treated as Coulomb friction, where the magnitude of the friction force is constant but its direction is always opposite to that of the sliding velocity. In dynamic problems, the direction of the sliding velocity can change quite often. The many changes of the velocity direction cause many discontinuities in the friction force, complicating the process of evaluating the response of systems involving friction. In this paper, it is shown that the discontinuous Coulomb friction force can be represented by at least four different continuous functions. Each of these functions involves one constant that controls the level of accuracy of that function's representation of the friction force. The accuracy of the various representations is verified by comparing the response of a single degree freedom system, obtained through numerical solutions utilizing these representations, with an exact analytical solution. © 1997 by John Wiley & Sons, Ltd.
Mostaghel et al. (Thu,) studied this question.