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 dynamic behaviour of a double-helical gear system supported by journal bearings is theoretically and experimentally investigated in this study. A bending–torsional–axial coupling model for dyna...

https://journals.sagepub.com/doi/pdf/10.1177/1687814016646977

Theoretical and experimental studies on dynamics of double-helical gear system supported by journal bearings:

This study investigates the dynamics and vibration of high-speed planetary gears, spinning cantilevered beams, and gear pairs. High-speed planetary gear dynamics and vibration are analyzed using a lumped-parameter model. A continuous model is used to study spinning cantilever beam vibration. A finite element/contact mechanics model is used for the dynamics of gear pairs. Chapter 2 investigates the modal property structure of high-speed planetary gears with gyroscopic effects. The vibration modes of these systems are complex-valued and speed-dependent. Equally-spaced and diametrically-opposed planet spacing are considered. Three mode types exist, and these are classified as planet, rotational, and translational modes. The properties of each mode type and that these three types are the only possible types are mathematically proven. Reduced eigenvalue problems are determined for each mode type. The eigenvalues for an example highspeed planetary gear are determined over a wide range of carrier speeds. Divergence and flutter instabilities are observed at extremely high speeds. In Chapter 3, the structured properties of the critical speeds and associated critical speed eigenvectors of high-speed planetary gears are identified and mathematically proven. Planetary gears have only planet, rotational, and translational mode critical speeds. Divergence instability is possible at speeds adjacent to critical speeds, and whether or not it occurs is determined using a perturbation method. Numerical results ii verify the critical speed locations and the stability near these critical speeds. Flutter instabilities occur at extremely high speeds, and these are investigated numerically for each mode type. Chapter 4 demonstrates unusual gyroscopic system eigenvalue behavior observed in a lumped-parameter planetary gear model. While the model has been used for dynamic analyses in industrial applications, the focus is on the eigenvalue phenomena that occur at especially high speeds rather than practical planetary gear behavior. The behaviors include calculation of exact trajectories across critical speeds, uncommon stability features near degenerate critical speeds, and unique stability transitions. These eigenvalue behaviors are not evident in the vast literature on gyroscopic systems. Chapter 5 investigates eigenvalue sensitivity to model parameters and eigenvalue veering in high-speed planetary gears. The eigenvalue perturbation approach is formulated such that the results apply to discrete, continuous, and hybrid discretecontinuous gyroscopic systems. Third-order perturbation approximations for the eigenvalues are determined. From the second-order perturbation approximation an eigenvalue veering parameter is defined and used to analyze veering in high-speed planetary gears. The sensitivity of the eigenvalues to model parameters are written in terms of modal kinetic and potential energies. Eigenvalue veering is prominent in planetary gears that have disrupted cyclic symmetry. In Chapter 6, the single-mode vibrations of high-speed planetary gears are investigated in the rotating carrier-fixed and the stationary inertial reference frames. The properties of the structured planetary gear modes result in gear motions with

High-Speed Dynamics and Vibration of Planetary Gears, Vibration of Spinning Cantilevered Beams, and An Efficient Computational Method for Gear Dynamics

A Study on the Dynamic Characteristics of an Epicyclic Gear Train with Journal Bearing

On the dynamic loading of gear teeth as affected by journal motion in a hydrodynamic bearing-rotor-gear pair system

The dynamic analysis of the journal bearing which supports the planets of an epicyclic gear stage is described. The analysis includes an assessment of the damping characteristics of the bearing, the stability, and the response of the planet to gear mesh interactions between the sun, the planet, and the ring gear. A digital program was developed which provides the numerical solution of the equations of motion by forward integration in time. The full nonlinear expressions have been used for both the hydrodynamic bearing forces and the gear mesh interaction forces. Centrifugal and Coriolis effects due to the planetary motion are taken into account. Numerical results for a PT6 reduction gearbox indicate that the bearing is highly stable and not adversely affected by gear mesh excitations.

J. L. Nikolajsen

Papers

Dynamic Behavior of a Journal Bearing in a Planet Gear