Free oscillations in a self-sustained system with solid friction. (2nd report. Analytical method by piecewise linear approximation and effect of maximum static friction different from kinetic friction without slipping).

Abstract

Following the previous report, the frictional vibrations in a mechanical driving system were treated theoretically in the case of Fs (maximum static friction) different from Fd (kinetic friction without slipping). Friction-velocity characteristic curves were approximated by a polygon having numerous segments and the analytical method was shown for the solutions of steady-state vibrations which occurred in such a piecewise linear system. Lastly, when the friction-velocity curves were of types [A] (a cubic function), [B] (a quintic function) and [C] (combined function of a straight line and a hyperbolic curve) . which were already used in calculation examples in the previous report, except for the condition of Fs≠Fd, the curves of displacement-amplitudes and periods of limit cycles in such a system were obtained versus the speed of a moving surface on which a sliding block was lying.