On the stability analysis of gear pairs with tooth profile modification. (August 2022)

• Record Type: Journal Article
• Authors: Hajjaj, A.Z.; Corrigan, K.; Mohammadpour, M.; Theodossiades, S.
• Is Part Of: Mechanism and machine theory. Volume 174(2022)
• Publication Date: 2022-08
• Subjects: Spur gear pair -- Teeth meshing stiffness -- Tooth profile modification -- Stability analysis; Machine theory -- Periodicals; Machinery -- Periodicals; Machines -- Périodiques; Génie mécanique -- Périodiques; Machine theory; Machinery; Periodicals; 621.81
• DOI: 10.1016/j.mechmachtheory.2022.104888
• Languages: English
• ISSNs: 0094-114X

Abstract

Highlights: A method to predict stability of gear pairs with modified teeth profile is presented. Floquet theory and the Mathieu equation have been the basis behind this method. The teeth meshing stiffness varies due to loading and modification amount. The stability results depend on the applied load, modification amount and damping. Abstract: 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.