This article summarizes published journal articles on planetary and epicyclic gear dynamics and vibration. Research in this field has increased dramatically over the past two decades. The wide range of research topics demonstrates the technical challenges of understanding and predicting planetary gear dynamics and vibration. The research in this review includes mathematical models, vibration mode properties, dynamic response predictions including nonlinearities and time-varying mesh stiffness fluctuations, the effects of elastic compliance, and gyroscopic effects, among other topics. Practical aspects are also included, for example, planet load sharing, planet phasing, tooth surface modifications, and characteristics of measured vibration response.

A Review of Planetary and Epicyclic Gear Dynamics and Vibrations Research

The rotordynamics of a double-helical gear transmission system is investigated. The equation of motion of the system with bearing and gyroscopic effect is derived by using the finite element method, in which Timoshenko beam finite element is used to represent the shaft, a rigid mass for the gear. Natural frequencies, mode shapes and Campbell diagrams are illustrated to indicate the effects of gear input speed and time varying mesh stiffness. Besides, effects of mesh stiffness on the critical speed of the gear transmission system are analyzed. The numerical results show that the axial force has significant influence on the natural frequency and the mode shape of the double-helical gear transmission system, for which the mix whirling motion dominates the natural characteristics. There are two higher critical speed curves which increase with the mesh stiffness, but one of them is related to the gyroscopic effect.

Rotordynamics analysis of a double-helical gear transmission system

Dynamic analysis of a planetary gear system with multiple nonlinear parameters

Bifurcation and chaos analysis for multi-freedom gear-bearing system with time-varying stiffness

Coupled torsion–bending dynamic analysis of gear-rotor-bearing system with eccentricity fluctuation

A nonlinear time-varying dynamic model for a multistage planetary gear train, considering time-varying meshing stiffness, nonlinear error excitation, and piece-wise backlash nonlinearities, is formulated. Varying dynamic motions are obtained by solving the dimensionless equations of motion in general coordinates by using the varying-step Gill numerical integration method. The influences of damping coefficient, excitation frequency, and backlash on bifurcation and chaos properties of the system are analyzed through dynamic bifurcation diagram, time history, phase trajectory, Poincare map, and power spectrum. It shows that the multi-stage planetary gear train system has various inner nonlinear dynamic behaviors because of the coupling of gear backlash and time-varying meshing stiffness. As the damping coefficient increases, the dynamic behavior of the system transits to an increasingly stable periodic motion, which demonstrates that a higher damping coefficient can suppress a nonperiodic motion and thereby improve its dynamic response. The motion state of the system changes into chaos in different ways of period doubling bifurcation, and Hopf bifurcation.

Bifurcation and chaos analysis of multistage planetary gear train

To improve the efficiency and design quality of vibro flotation device design, this paper builds a rapid design system based on KBE (Knowledge Based Engineering) for Vibroflotation device, offers a way to implement KPT (Knowledge Processing Technology) and establish the framework of the system. The knowledge base system is embedded into all the design process. Moreover, according to the requirement of automatic design, both the CAD/CAE integration and automatically extraction of mass parameters are realized based on uniform product model and secondary development of 3D modeling software and homogeneous coordinate transformation, respectively. Then the final KBE based vibro flotation device system is built. Our system not only reduces the development cycle and complexity of vibro flotation device but also improves its quality of design, effectively.

Qingming Wu

Papers

Bifurcation and chaos analysis of multistage planetary gear train

Research and Development of Vibroflotation Device Design System Based on Knowledge Based Engineering