Dynamic Analysis of Thin-Web Helical Gears Systems Based on Various Types of Discretized-Analytical Modelling Methods

In the aerospace industry, thin-web gears are preferred for achieving high power-density transmission. However, thin-webbed structures always lead to out-of-plane resonance during the transmission process, which commonly happens in helical gears, manifesting as severe vibration at a specific rotational speed. To address this, a shaft–web–ring dynamic model is proposed. The shaft, gear web, and gear ring are modelled based on the Timoshenko straight beam, Mindlin plate, and Timoshenko bent beam theory. Simultaneously, the potential energy caused by the time-varying meshing stiffness is coupled to the gear ring. The kinetic and potential energies of each discretized finite element of the components are derived based on elastic deformation theory, and the governing equations of each element are obtained using Hamilton’s principle. The model is verified through a modal experiment. The comparison with traditional rotor-gear models has demonstrated the significance of gear body flexibility in helical gears with thin webs. The effects of the web thickness and helix angle on dynamic response are studied, revealing that gear web elasticity and an appropriately high helix angle can effectively reduce vibrations at the support bearing, prevent excessive vibrations, and contribute to vibration and noise reduction in the transmission system.