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.

Copyright © 2012 by ASME
Your Session has timed out. Please sign back in to continue.


Cunliffe, F., Smith, J. D., and Welbourn, D. B., 1974, “Dynamic Tooth Loads in Epicyclic Gears,” J. Eng. Ind., 96(2), pp. 578–584. [CrossRef]
Botman, M., 1976, “Epicyclic Gear Vibrations,” J. Eng. Ind., 98(3), pp. 811–815. [CrossRef]
Kahraman, A., 1994, “Planetary Gear Train Dynamics,” J. Mech. Des., 116(3), pp. 713–720. [CrossRef]
Kahraman, A., 1994, “Natural Modes of Planetary Gear Trains,” J. Sound Vib., 173(1), pp. 125–130. [CrossRef]
Saada, A., and Velex, P., 1995, “An Extended Model for the Analysis of the Dynamic Behavior of Planetary Trains,” J. Mech. Des., 117(2), pp. 241–247. [CrossRef]
Lin, J., and Parker, R. G., 1999, “Analytical Characterization of the Unique Properties of Planetary Gear Free Vibration,” J. Vib. Acoust., 121(3), pp. 316–321. [CrossRef]
Lin, J., and Parker, R. G., 2000, “Structured Vibration Characteristics of Planetary Gears With Unequally Spaced Planets,” J. Sound Vib., 233(5), pp. 921–928. [CrossRef]
Lin, J., and Parker, R. G., 1999, “Sensitivity of Planetary Gear Natural Frequencies and Vibration Modes to Model Parameters,” J. Sound Vib., 228(1), pp. 109–128. [CrossRef]
Lin, J., and Parker, R. G., 2001, “Natural Frequency Veering in Planetary Gears,” Mech. Struct. Mach., 29(4), pp. 411–429. [CrossRef]
Lin, J., and Parker, R. G., 2002, “Planetary Gear Parametric Instability Caused by Mesh Stiffness Variation,” J. Sound Vib., 249(1), pp. 129–145. [CrossRef]
Kiracofe, D. R., and Parker, R. G., 2007, “Structured Vibration Modes of General Compound Planetary Gear Systems,” J. Vib. Acoust., 129(1), pp. 1–16. [CrossRef]
Wu, X., and Parker, R. G., 2008, “Modal Properties of Planetary Gears With an Elastic Continuum Ring Gear,” J. Appl. Mech., 75(3), p. 031014. [CrossRef]
Parker, R., and Wu, X., 2010, “Vibration Modes of Planetary Gears With Unequally Spaced Planets and an Elastic Ring Gear,” J. Sound Vib., 329(11), pp. 2265–2275. [CrossRef]
Eritenel, T., and Parker, R. G., 2009, “Modal Properties of Three-Dimensional Helical Planetary Gears,” J. Sound Vib., 325(1–2), pp. 397–420. [CrossRef]
Guo, Y., and Parker, R., 2010, “Purely Rotational Model and Vibration Modes of Compound Planetary Gears,” Mech. Mach. Theor., 45(3), pp. 365–377. [CrossRef]
Kahraman, A., 2001, “Free Torsional Vibration Characteristics of Compound Planetary Gear Sets,” Mech. Mach. Theor., 36(8), pp. 953–971. [CrossRef]
Bahk, C.-J., and Parker, R. G., 2011, “Analytical Solution for the Nonlinear Dynamics of Planetary Gears,” J. Comput. Nonlinear Dyn., 6(2), p. 021007. [CrossRef]
Abousleiman, V., Velex, P., and Becquerelle, S., 2007, “Modeling of Spur and Helical Gear Planetary Drives With Flexible Ring Gears and Planet Carriers,” J. Mech. Des., 129(1), pp. 95–106. [CrossRef]
Meirovitch, L., 1974, “A New Method of Solution of the Eigenvalue Problem for Gyroscopic Systems,” AIAA J., 12(10), pp. 1337–1342. [CrossRef]
Meirovitch, L., 1975, “A Modal Analysis for the Response of Linear Gyroscopic Systems,” J. Appl. Mech., 42(2), pp. 446–450. [CrossRef]
D’Eleuterio, G., and Hughes, P., 1984, “Dynamics of Gyroelastic Continua,” J. Appl. Mech., 51(2), pp. 415–422. [CrossRef]
Ambarisha, V. K., and Parker, R. G., 2006, “Suppression of Planet Mode Response in Planetary Gear Dynamics Through Mesh Phasing,” J. Vib. Acoust., 128(2), pp. 133–142. [CrossRef]
Han, R. P. S., and Zu, J. W.-Z., 1992, “Modal Analysis of Rotating Shafts: A Body-Fixed Axis Formulation Approach,” J. Sound Vib., 156(1), pp. 1–16. [CrossRef]
Tobias, S. A., and Arnold, R. N., 1957, “The Influence of Dynamical Imperfection on the Vibration of Rotating Disks,” Proc. Inst. Mech. Eng., 171(1), pp. 669–690. [CrossRef]
Mote, C. D., Jr., 1970, “Stability of Circular Plates Subjected to Moving Loads,” J. Franklin Inst., 290(4), pp. 329–344. [CrossRef]
Chen, J. S., and Bogy, D. B., 1992, “Effects of Load Parameters on the Natural Frequencies and Stability of a Flexible Spinning Disk With a Stationary Load System,” J. Appl. Mech., 59(2), pp. S230–S235. [CrossRef]
Parker, R. G., and Sathe, P. J., 1999, “Free Vibration and Stability of a Spinning Disk-Spindle System,” J. Vib. Acoust., 121(3), pp. 391–396. [CrossRef]
Parker, R. G., and Sathe, P. J., 1999, “Exact Solutions for the Free and Forced Vibration of a Rotating Disk-Spindle System,” J. Sound Vib., 223(3), pp. 445–465. [CrossRef]
Leissa, A. W., 1974, “On a Curve Veering Aberration,” J. Appl. Math. Phys. (ZAMP), 25(1), pp. 99–111. [CrossRef]
Kuttler, J. R., and Sigillito, V. G., 1981, “On Curve Veering,” J. Sound Vib., 75(4), pp. 585–588. [CrossRef]
Perkins, N. C., and Mote, C. D., Jr., 1986, “Comments on Curve Veering in Eigenvalue Problems,” J. Sound Vib., 106(3), pp. 451–463. [CrossRef]


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.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In