Rotational Vibration With Backlash: Part 1

Abstract

This paper considers the problem of dynamic tooth loads on lightly loaded precision class gears running at high speed. It provides theoretical and experimental explanations of the surprising fact that lightly loaded gears may suffer from both pitting and tooth breakage, while the same gear, heavily loaded, is immune from such damage. In the theoretical part, two idealized mathematical models—a two-mass system and a three-mass system—are analyzed. Both models provide for consideration of time-varying backlash (backlash is a function of gear angular position) as well as impact and displacement excitations. Large dynamic tooth load was shown to result from backlash impact, on both drive and nondrive tooth flanks. The motion was termed “rotation vibration” to distinguish it from “torsional vibration” as commonly understood. Rotational vibration includes torsional vibration as well as the “rigid body mode” oscillation of a mathematical form similar to a ball bouncing upon an oscillating table. In the experimental part, a testing rig was specially designed and built. The test results confirm the theory.