Self-excited vibrations in machine assemblies with a self-braking device

Abstract

A dynamic analysis is made of the motions of a machine assembly, idealized as a mechanical system of two masses joined by elastic members and a one-way self-braking device or coupling. One example of such a system contains a worm-gear drive (Fig. 3), self-locking on reversal of the transmitting forces, and possibly also with backlash in its mesh, the whole being subject to torsional oscillations due to the torsionally flexible shafts. A non-linear system of differential equations is obtained, which changes when the self-braking coupling locks. Two regimes of operation are identified, characterized by the self-locked or the normal-running state of the coupling; the conditions which determine these states are found. To obtain a solution, the differential equations are linearized, and it is then shown that a condition can exist which allows a self-excited autovibrational motion; its period is found.