Research Papers

Modal Properties of Planetary Gears With an Elastic Continuum Ring Gear

[+] Author and Article Information
Xionghua Wu

Department of Mechanical Engineering,  The Ohio State University, 201 W. 19th Avenue, Columbus, OH 43210

Robert G. Parker1

Department of Mechanical Engineering,  The Ohio State University, 201 W. 19th Avenue, Columbus, OH 43210parker.242@osu.edu


Corresponding author.

J. Appl. Mech 75(3), 031014 (May 01, 2008) (12 pages) doi:10.1115/1.2839892 History: Received May 27, 2006; Revised November 08, 2007; Published May 01, 2008

The distinctive modal properties of equally spaced planetary gears with elastic ring gears are studied through perturbation and a candidate mode method. All eigenfunctions fall into one of four mode types whose structured properties are derived analytically. Two perturbations are used to obtain closed-form expressions of all the eigenfunctions. In the discrete planetary perturbation, the unperturbed system is a discrete planetary gear with a rigid ring. The stiffness of the ring is perturbed from infinite to a finite number. In the elastic ring perturbation, the unperturbed system is an elastic ring supported by the ring-planet mesh springs; the sun, planet and carrier motions are treated as small perturbations. A subsequent candidate mode method analysis proves the perturbation results and removes any reliance on perturbation parameters being small. All vibration modes are classified into rotational, translational, planet, and purely ring modes. The well defined properties of each type of mode are analytically determined. All modal properties are verified numerically.

Copyright © 2008 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

Elastic-discrete model of a planetary gear and corresponding system coordinates. The distributed springs around the ring circumference are not shown.

Grahic Jump Location
Figure 2

Typical modes of a planetary gear. The system parameters are given in Table 1. Distinct planet modes as in (d) only exist for an even number of planets.



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