A flexible-helical-geared rotor dynamic model based on hybrid beam-shell elements

Considering the flexibility of gear foundations and rotational effects, a geared rotor dynamic model for thin-rimmed helical gears is established. The deformable shafts and gear foundations are modelled by Timoshenko beam elements and Mindlin-Reissner shell elements, respectively. The beam element and the shell element are connected using the ‘interfacial coupling element’. Then the modal superposition method is adopted to improve the computational efficiency. The proposed dynamic model is verified through the comparison between the simulated responses and experimental results in a published literature. Based on the proposed dynamic model, the effects of the web thickness, the rotational effects and the helix angle on the dynamic behaviors are discussed. The results show that the dynamic responses of thin-rimmed gears obtained from the traditional dynamic model and the proposed model are quite different, which emphasizes the significances of the flexible body modeling. Compared to the centrifugal stiffening and the spin softening, the gyroscopic effect has more significant effect on dynamic characteristics. The nodal diameter vibration cannot be excited due to the absence of the axial exciting force when helix angle is zero. The increase of the helix angle will lead to more significant out-of-plane vibration of the gear foundation.