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Structured Eigensolution Properties of Planetary Gears With Elastically Deformable Ring Gears

[+] Author Affiliations
Robert G. Parker, Xionghua Wu

The Ohio State University, Columbus, OH

Paper No. DETC2009-87340, pp. 1423-1439; 17 pages
doi:10.1115/DETC2009-87340
From:
  • ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1: 22nd Biennial Conference on Mechanical Vibration and Noise, Parts A and B
  • San Diego, California, USA, August 30–September 2, 2009
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4898-2 | eISBN: 978-0-7918-3856-3
  • Copyright © 2009 by ASME

abstract

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 (DPP), 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 (ERP), 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 © 2009 by ASME

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