The Optimum Modification of Tooth Profile for a Pair of Spur Gears to Make its Rotational Vibration Equal Zero

Abstract

Abstract This paper develops an optimum modification method of tooth profile for a pair of spur gears to make its rotational vibration become zero by using an exact vibration model. By minimizing the equivalent exciting force, which includes the effects of the static load, time-varying stiffness, and relative tooth profile error, each optimum modification curve for each gear pair with different designed contact ratios can be obtained. The magnitude and the shape of the optimum modification curve depend upon the value of the designed contact ratio ε strongly. Especially, the concave modification curve is obtained in case of ε ≤ 1.1. The effect of the optimum modification on eliminating the vibration, is verified by the numerical calculation using an exact equation of vibration. A parameter study is presented to investigate the effect of running condition.