Parametric vibrations and instabilities can be induced in an elliptical gear pair. This study examined the effects of basic parameters on vibration instability. Geometric parameters and time-variant mesh stiffness are calculated. A torsional dynamic model is established by introducing the lumped parameter assumption. Based on the model, the parametric vibrations caused by the excitations of eccentricity and time-variant mesh stiffness are investigated, and the additive and difference combination resonances are identified. Comparison between the elliptical and circular gears implies that the vibration amplitude at mesh frequency of the elliptical gears is lower than that of the regular circular gears. The vibrations caused by load torque are also examined. The results show that the vibrations with different frequencies are coupled with each other. The inherent reason behind the coupling is the interaction between the eccentricity, time-variant stiffness, and load.

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. which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.