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Research Papers

Vibration Properties of High-Speed Planetary Gears With Gyroscopic Effects

[+] Author and Article Information
Christopher G. Cooley

The Ohio State University,
Columbus, OH, 43210

Robert G. Parker

The Ohio State University,
Columbus, OH, 43210;
Distinguished Professor Chair,
State Key Laboratory for Mechanical Systems and Vibration,
University of Michigan-Shanghai Jiao Tong University Joint Institute,
Shanghai Jiao Tong University,
Shanghai, China, 200240
e-mail: parker.242@osu.edu

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 17, 2011; final manuscript received March 2, 2012; published online October 29, 2012. Assoc. Editor: Alan Palazzolo.

J. Vib. Acoust 134(6), 061014 (Oct 29, 2012) (11 pages) doi:10.1115/1.4006646 History: Received June 17, 2011; Revised March 02, 2012

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.

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References

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Figures

Grahic Jump Location
Fig. 1

Time evolution of a high-speed planetary gear in single mode, harmonic, free vibration at the natural frequency. Only the response of a single planet is shown. The planet radial motion (ζ) is shown by a solid line, the tangential motion (η) by a dashed line, and the rotational motion (u) by a dash-dotted line.

Grahic Jump Location
Fig. 2

Structured vibration modes of high-speed planetary gears at Ωc=0.3. The real and imaginary parts of the mode shape are shown by a solid (blue) line and a dashed (red) line, respectively. The dotted black line is the gear body nominal position.

Grahic Jump Location
Fig. 3

Imaginary (upper) and real (lower) part of the eigenvalue, λ, for varying carrier speeds for the planetary gear in Table 1 with four equally-spaced planets. Planet eigenvalues are shown by a dashed (red) line, rotational eigenvalues are shown by a dash-dotted (blue) line, and translational eigenvalues are shown by a solid (black) line from Eq. (41) and a dotted (green) line from Eq. (44).

Grahic Jump Location
Fig. 4

Imaginary (upper) and real (lower) part of the eigenvalue, λ, for varying carrier speeds for the planetary gear in Table 1 with four diametrically-opposed planets. Planet eigenvalues are shown by a dashed (red) line, rotational eigenvalues are shown by a dash-dotted (blue) line, translational eigenvalues are shown by a solid (black) line.

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