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TECHNICAL PAPERS

Structured Vibration Modes of General Compound Planetary Gear Systems

[+] Author and Article Information
Daniel R. Kiracofe

Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210kiracofe.8@osu.edu

Robert G. Parker

Department of Mechanical Engineering, The Ohio State University, Columbus, OH 43210parker.242@osu.edu

Note the sign differences between 30 and the corresponding equation in Lin and Parker’s derivation (4). This is a typographical error in (4) that is corrected in this paper.

Some numerical solvers may return coupled eigenvectors for this example degenerate pair. The results will not look like either planet modes or rotational modes. They can be decoupled by an orthogonalization process.

Equation 62 is similar to the result given in (12), but 63 is not given in (12). This is an omission in (12) that is corrected here.

J. Vib. Acoust 129(1), 1-16 (May 08, 2006) (16 pages) doi:10.1115/1.2345680 History: Received August 05, 2005; Revised May 08, 2006

This paper extends previous analytical models of simple, single-stage planetary gears to compound, multi-stage planetary gears. This model is then used to investigate the structured vibration mode and natural frequency properties of compound planetary gears of general description, including those with equally spaced planets and diametrically opposed planet pairs. The well-defined cyclic structure of simple, single-stage planetary gears is shown to be preserved in compound, multi-stage planetary gears. The vibration modes are classified into rotational, translational, and planet modes and the unique properties of each type are examined and proved for general compound planetary gears. All vibration modes fall into one of these three categories. For most cases, both the properties of the modes and the modes themselves are shown to be insensitive to relative planet positions between stages of a multi-stage system.

FIGURES IN THIS ARTICLE
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Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 7

Typical rotational mode for example system of Fig. 6 and Table 1, ω=932.0Hz

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Figure 8

A pair of typical translational modes for example system of Fig. 6 and Table 1, ω=3499.2Hz

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Figure 9

Two typical planet modes for the example system of Fig. 6 and Table 1. (a) A mode in which stage 1 planets have motion and stage 2 has no motion, ω=2382.2Hz (b) A mode in which stage 1 has no motion and stage 2 planets have motion, ω=3890.2Hz.

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Figure 2

Example of a meshed planet compound planetary gear

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Figure 1

Example of a stepped planet compound planetary gear

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Figure 3

Example of a multi-stage compound planetary gear

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Figure 4

A planet-planet mesh modeled by a linear spring and static transmission error

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Figure 5

A sun-planet mesh modeled by a linear spring and static transmission error

Tables

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