Technical Briefs

Effect of Ring-Planet Mesh Phasing and Contact Ratio on the Parametric Instabilities of a Planetary Gear Ring

[+] Author and Article Information
Sripathi Vangipuram Canchi

Department of Mechanical Engineering, Ohio State University, 201 West 19th Avenue, Columbus, OH 43210

Robert G. Parker1

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


Corresponding author.

J. Mech. Des 130(1), 014501 (Dec 07, 2007) (6 pages) doi:10.1115/1.2803716 History: Received July 24, 2006; Revised December 22, 2006; Published December 07, 2007

Parametric excitation of a rotating ring subject to moving time-varying stiffnesses has previously been investigated and given as closed-form expressions in the system parameters. These conditions are applied to identify ring gear parametric instabilities in a planetary gear system. Certain mesh phasing and contact ratio conditions suppress parametric instabilities, and these conditions are presented with examples.

Copyright © 2008 by American Society of Mechanical Engineers
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Figure 1

(a) Representation of the planetary gear ring showing a single ring-planet mesh. (b) Spring stiffness variation with time.

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Figure 2

Parametric instability regions for three identical and equally spaced rotating springs with cr=1.7, vr=0, k1j=0, k2j=k, and βj=0deg. (a) In-phase meshes with Zr=9. (b) Sequentially phased meshes with Zr=10. –, analytical solution;  ***, numerical solution.

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Figure 3

Parametric instability regions for two pairs of identical, diametrically opposed springs with cr=1.7, vr=0, k1j=0, k2j=k, βj=0deg, ϕ1=0deg, ϕ2=91.42deg, ϕ3=180deg, and ϕ4=271.42deg. (a) In-phase meshes with Zr=10. (b) Counter-phased meshes with Zr=9. –, analytical solution.

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Figure 4

Effect of contact ratio on parametric instability regions with vr=0. Sequentially phased meshes: two identical and equally spaced radial rotating springs with Zr=9. (a) cr=1.5. (b) cr=1.7. –, analytical solution;  ***, numerical solution.



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