On the stability analysis of gear pairs with tooth profile modification

This paper deals with the stability of loaded gear pairs, considering the effects of tooth profile modification. An analytical method to predict the stability of gear pairs has been developed by transforming their equations of motion to a form similar to the Mathieu equation and employing Floquet theory. The variation of (spur gear pair) teeth meshing stiffness due to tooth profile modification has been introduced, for different amounts of transmitted torque. Stability charts are obtained for different gear pairs, as well as undamped and damped conditions. The simulation results have shown that during operation, the examined gear pairs may cross regimes of unstable behaviour, thus contributing to aggressive oscillations of the gearbox. A holistic transmission design must take the above potential effects into consideration when predicting the durability of machine elements, such as gears and bearings.