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TECHNICAL PAPERS

Suppression of Planet Mode Response in Planetary Gear Dynamics Through Mesh Phasing

[+] Author and Article Information
Vijaya Kumar Ambarisha

Department of Mechanical Engineering, Ohio State University, 650 Ackerman Rd., Columbus, OH 43202

Robert G. Parker1

Department of Mechanical Engineering, Ohio State University, 650 Ackerman Rd., Columbus, OH 43202parker.242@osu.edu

1

Corresponding author.

J. Vib. Acoust 128(2), 133-142 (Feb 10, 2005) (10 pages) doi:10.1115/1.2171712 History: Received February 27, 2004; Revised February 10, 2005

This work analytically derives design rules to suppress certain harmonics of planet mode response in planetary gear dynamics through mesh phasing. Planet modes are one of three categories of planetary gear vibration modes. In these modes, only the plantes deflect while the carrier, ring, and sun gears have no motion (Lin, J., and Parker, R. G., 1999, ASME J. Vib. Acoust., 121, pp. 316–321;J. Sound Vib, 233(5), pp. 921–928). The dynamic mesh forces are not explicitly modeled for this study; instead, the symmetry of planetary gear systems and gear tooth mesh periodicity are sufficient to establish rules to suppress planet modes. Thus, the conclusions are independent of the mesh modeling details. Planetary gear systems with equally spaced planets and with diametrically opposed planet pairs are examined. Suppression of degenerate mode response in purely rotational degree-of-freedom models achieved in the limit of infinite bearing stiffness is also investigated. The mesh phasing conclusions are verified by dynamic simulations of various planetary gears using a lumped-parameter analytical model and by comparisons to others’ research.

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Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Planetary gear lumped-parameter analytical model

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Figure 2

Vibration modes of planetary gear system of case I in Table 3: (a) rotational mode at 857Hz, (b) translational mode at 963Hz, and (c) planet mode at 1115Hz. Carrier and ring motions are not shown.

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Figure 3

Convergence of rotational-translational model natural frequencies to purely rotational model natural frequencies as all bearing stiffnesses are increased. The system is that of case I in Table 3. Values in parentheses denote multiplicity of a natural frequency.

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Figure 4

The rms of steady-state planet 1 rotation for different mesh-phasing cases of equally spaced planets in Table 3 for decreasing speeds. Vertical lines indicate possible resonant peaks (lω≈ωn) corresponding to the planet mode with natural frequency 1115Hz.

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Figure 5

Waterfall spectra of steady-state planet-1 rotation of case II in Table 3 for decreasing speeds. Resonant peaks corresponding to the planet mode with natural frequency 1115Hz are not excited by the second and fourth harmonics of the mesh frequency.

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Figure 6

The rms of steady-state planet-1 rotation for different parameter cases of two pairs of diametrically opposed planets in Table 4 for decreasing speeds. Vertical lines indicate possible resonant peaks (lω=ωn) corresponding to the planet mode with natural frequency 1140Hz.

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Figure 7

Waterfall spectra of steady-state planet-1 rotation for case I in Table 4 for decreasing speeds. Resonant peaks corresponding to the planet mode with natural frequency 1140Hz are not excited by the first and third harmonics of the mesh frequency.

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