Vibration Properties of High-Speed Planetary Gears With Gyroscopic Effects

Abstract

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.

Vibration mode structure and simplified modelling of cyclically symmetric or rotationally periodic systems

“…, N − 2. In planetary gears [6,[19][20][21][22]34] and CPVA systems [23][24][25] In cases like planetary gears [6,[19][20][21][22]34] and CPVA systems [23][24][25] where the substructures do not connect with each other but only connect to the central components, the submatrix A s is block-diagonal. The A i (defined in equations (2.3) and (2.4)) vanish for i = 1.…”

“…The vibration modes when k = 0 in planetary gears [6,[19][20][21][22] and CPVA systems [23][24][25] Therefore, we get a total of L independent equations from the substructure equations.…”

“…Natural frequencies, ω = Im(λ) (rad s −1 ), for the example cyclically symmetric system in figure 2 with N equally spaced, identical substructures at rotating speed Ω = 0 rad s −1 . The system parameters are given in [19,22] for zero speed also gives degenerate translational modes with multiplicity two. For the planet modes (i.e.…”

Modal Analysis of Equal Spacing around Sun Gear Double Power Branch System

“…The mode shapes calculated and summed up three kinds of the system vibration modals: star gear vibration modal, planetary gear vibration modal and modal coupling [7][8][9]. The first stage star gear in planetary gear vibration system, when no vibration, called this mode is the star gear vibration mode [10][11][12].…”

“…In these frequencies, vibration central is component of star gear, star formation rate, with natural frequency Table 3 corresponding to 934.8Hz, 1259.6Hz and 2474.7Hz; and a single frequency, center star gear components is only torsional vibration, gear deformation is the same as in Table 3, and the corresponding frequency is 6638.8Hz. [16][17][18]. The change rules:…”