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Time-variant excitations in planetary gear trains can cause excessive noise and vibration and even damage the system on a permanent basis. This paper focuses on the elastic vibrations of a helical planetary ring gear subjected to mesh and planet-pass excitations. Motivated by the structure, excitation and deformation symmetries, this paper proposes dual-frequency superposition and modulation methods to capture the mesh and sideband vibrations. The transition between ring gear tooth and planet is introduced to address the excitations and vibrations. The phasing effect of ring gear tooth and planet on various deformations is formulated. The inherent connections between the two types of vibrations are identified. The vibrations share identical exciting rules and the wavenumber and modulating signal order both equal the linear combination of tooth and planet counts. The results cover in-plane bending and extensional, out-of-plane bending and torsional deformations. Main findings are verified by numerical calculation and comparisons with the open literature. The analytical expressions can be used to determine whether the sideband is caused by component fault or only by elastic vibration. The methods can be extended to other power-transmission systems because little restriction is imposed during the analysis.

Investigation on Mesh and Sideband Vibrations of Helical Planetary Ring Gear Using Structure, Excitation and Deformation Symmetries