High-speed Planetary Gears Research Articles

Eigenvalue sensitivity and veering in gyroscopic systems with application to high-speed planetary gears

Abstract This study investigates eigenvalue sensitivity to model parameters and veering in gyroscopic systems. The eigenvalue perturbation approach is formulated such that the results apply to discrete, continuous, and hybrid discrete-continuous gyroscopic systems. Third-order perturbation approximations for distinct eigenvalues are determined. Perturbations through second-order are derived for degenerate eigenvalues. The perturbation results are applied to a high-speed planetary gear model, where the results are shown to be accurate over a wide range of rotation speeds. The sensitivity of the eigenvalues to model parameters are written in terms of modal kinetic and potential energies. From the second-order perturbation approximation an eigenvalue veering parameter is defined and used to analyze veering in high-speed planetary gears, which is prominent in planetary gears that have disrupted cyclic symmetry.

Dynamic modeling and analysis of high-speed planetary gear including centrifugal force

The planetary gear in electric vehicles always works at high-speed and variable-speed process. For high speed, the centrifugal force of planets cannot be ignored. Therefore, a dynamic model of the planetary gear for variable-speed process is first proposed which also considers the centrifugal force by deriving the formulae of planet acceleration anew. For the utilization of the model in variable-speed process, the angular displacements are chosen as the generalized coordinates, and the time-variant meshing stiffness and profile error vary with the gear angular displacements directly in this model. Next, the comprehensive influences of profile modification, profile error, and variable-speed process are investigated on the dynamic characteristics of high-speed planetary gear, finding that: the modification can reduce the dynamic meshing forces effectively at low speed, but the reduction disappears at high speed, and profile error excitation is the main reason; profile error excitation is also the main reason of deterioration of the dynamic characteristics of planetary gears at high speed; the dynamic characteristics for variable-speed process are severer than that of steady process at the corresponding same speed.

Dynamic imbalance of high-speed planetary gears

Dynamic imbalance of high-speed planetary gears

Transverse-Torsional Vibrations of the High-Speed Planetary Gear Transmission

The vibration characteristics of a high-speed planetary gear transmission (PGT) are studied in this paper. A transverse-torsional coupling dynamic model is developed using lumped parameter method. In order to ensure the accuracy of the analysis model, the mesh stiffness, support stiffness and the influence of eccentric masses on system are also considered. By solving the eigenvalue of differential equations of motion, the natural frequencies and mode shapes are calculated. According to the vibration modes of this gear transmission, the characteristics of translational mode and torsional mode are described in details. The influence of mesh stiffness, support stiffness and modal modes are discussed by adopting strain and kinetic energy.

Mechanical stability of high-speed planetary gears

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 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.

Unusual gyroscopic system eigenvalue behavior in high-speed planetary gears

This study 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.

Vibration Properties of High-Speed Planetary Gears With Gyroscopic Effects

This study 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 high-speed planetary gear are determined over a wide range of carrier speeds. Divergence and flutter instabilities are observed at extremely high speeds.

A dynamic model to study the influence of planet position errors in planetary gears

An original lumped parameter model of planetary gears is presented which accounts for planet position errors and simulates their contribution to the quasi-static and dynamic load sharing amongst the planets. A unique feature of the model is that instantaneous gear geometry is used which depends on the combination of deflections and errors. The numerical results compare well with experimental evidence from the literature thus validating the modelling methodology. Simulations are then extended to dynamic tooth loads and trajectories for both fixed and rotating carriers. Finally, the advantages and drawbacks of floating members in high-speed planetary gears are illustrated and commented upon.

Finite element analysis of internal gear in high-speed planetary gear units

The stress and the elastic deflection of internal ring gear in high-speed spur planetary gear units are investigated. A rim thickness parameter is defined as the flexibility of internal ring gear. Six evenly spaced linear springs are used to describe the fitting status between internal ring gear and the gearcase. The finite element model of the whole internal ring gear is established by means of Pro/E and ANSYS. The loads on meshing teeth of internal ring gear are applied according to the contact ratio and the load-sharing coefficient. With the finite element analysis (FEA), the influences of flexibility and fitting status on the stress and elastic deflection of internal ring gear are predicted. The simulation reveals that the principal stress and deflection increase with the decrease of rim thickness of internal ring gear. Moreover, larger spring stiffness helps to reduce the stress and deflection of internal ring gear. Therefore, the flexibility of internal ring gear must be considered during the design of high-speed planetary gear transmissions.