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Most studies in the literature consider the value of the coefficient of dynamic friction to be constant. We studied the evolution of a dynamic system when the coefficient of friction results in different values depending on the contact surfaces. A system with four balls fixed on an aluminium plate was driven with constant velocity into motion on the coaxial races of two identical outer bearing rings. The assembly presents a motion with periodic variable amplitude between two extremes, a fact that suggests the presence of a periodical excitation. The test was repeated, but this time, new bodies were used, which were two identical bodies made of two balls rigidised via a short cylindrical rod. When the rings were driven into rotational motion, the two bodies performed different motions; if the bodies were inter-changed, the differences between the motions remained. The rings were analysed, and a small region on the race of one ring was observed, where the roughness was considerably greater than the rest of the surface. Then, a mathematical model for the dynamic system with different friction coefficients was proposed and solved. This model is capable of simulating different situations, such as oscillatory motion and circular motion, with or without separation of the contacting bodies. Here, we present a dynamic model with Hertzian contact points in the presence of dry friction, with the coefficient of friction changing suddenly on the contacting surfaces.
Alaci et al. (Thu,) studied this question.