Dynamics of planetary gear trains with consideration of moving force effect and ring flexibility

Abedini Laksar, Mohammad Javad (2023) Dynamics of planetary gear trains with consideration of moving force effect and ring flexibility. Doctoral (PhD) thesis, Memorial University of Newfoundland.

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Abstract

This Ph.D. dissertation focuses on the dynamics of planetary gear trains (PGTs). The direct motivation comes from the wind power industry, where PGT size and load become larger and larger, leading to more complicated dynamic behaviour. The time-varying mesh stiffness in a gear system causes parametric resonances. Additionally, the multiple planet arrangement in a PGT makes the stability more complicated. This dissertation first investigates the instability caused by the time-varying stiffness, with a focus on the instability related to the repeated natural frequencies caused by the multiple planets. The research employs the method of multiple scales, enabling the derivation of an analytical formulation to describe the instability zones. The obtained results are validated against numerical results from Floquet theory. Notably, the research enhances the existing formulation for instability zones by presenting a slightly larger region for the unstable zone compared to what has been reported in earlier literature. To ensure the accuracy of the proposed formulation, the obtained results are validated against the numerical results from Floquet theory. With the growing size and load of PGTs, the ring gear in these systems tends to be designed with a relatively thin wall, which leads to significant deflection when subjected to increased loads. In light of this phenomenon, this dissertation focuses on investigating the free vibration behaviour of the ring gear. Initially, the ring gear is simplified as an elastic ring, and then Euler-Bernoulli and Timoshenko theories are applied based on the ring's thickness. The support is modeled with general elastic boundary conditions to mimic a bolt connection. As a result, the natural frequencies and closed-form mode shapes are derived and analyzed. The obtained results are then compared against Finite Element Method (FEM) results to ensure their validity. In a PGT, the meshing force between the ring gear and planet gear is not stationary. Instead, it moves along the circumference of the ring with the angular speed of the carrier, creating a moving load excitation. The dissertation thoroughly investigates the dynamics of the ring gear subjected to this moving meshing load. By leveraging the obtained mode shapes, the partial differential equation of the ring is transformed into ordinary differential equations, which are solved using the Maple package. Furthermore, the effect of the moving force is analyzed in great detail, and the critical speed that causes resonances is obtained and examined. The results are compared against data from the literature and validated against FEM results.

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