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Sensitivity of General Compound Planetary Gear Natural Frequencies and Vibration Modes to Model Parameters

[+] Author Affiliations
Yichao Guo, Robert G. Parker

Ohio State University, Columbus, OH

Paper No. DETC2007-35802, pp. 647-670; 24 pages
doi:10.1115/DETC2007-35802
From:
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 7: 10th International Power Transmission and Gearing Conference
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4808-6 | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME

abstract

This paper studies sensitivity of general compound planetary gear natural frequencies and vibration modes to all inertia and stiffness parameters. The results are expressed in compact formulae for tuned and mistuned compound planetary gears. Analysis reveals that for tuned (i.e., cyclically symmetric) compound planetary gears, eigenvalue sensitivities to stiffness parameters are directly proportional to modal strain energies, and eigenvalue sensitivities to inertia parameters are proportional to modal kinetic energies. Furthermore, the eigenvalue sensitivities to all model parameters are determined by inspection of the modal strain and kinetic energy distributions for a given mode. For mistuned systems, the results differ for the cases of tuned one mistuned parameter, two or more independent mistuned parameters, and two or more dependent mistuned parameters. For cases of one mistuned parameter, and two or more independent mistuned parameters, compact formulae of eigensensitivities are derived, and they are proportional to modal strain/kinetic energies. For the case of two or more dependent mistuned parameters, however, only general expressions of eigensensitivities are derived. These eigensensitivities depend not only on modal energies, but also on how the dependent mistuned parameters are related. Hence inspection of modal energies alone may fail to locate the parameter that is most effective in tuning natural frequencies.

Copyright © 2007 by ASME

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