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Research Papers

A Dynamic Model for Double-Planet Planetary Gearsets

[+] Author and Article Information
Dylan C. Fyler

Department of Mechanical Engineering,
University of Massachusetts Lowell,
Lowell, MA 01854

Murat Inalpolat

Department of Mechanical Engineering,
University of Massachusetts Lowell,
1 University Avenue,
Lowell, MA 01854
e-mail: Murat_Inalpolat@uml.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 28, 2015; final manuscript received November 25, 2015; published online January 20, 2016. Assoc. Editor: Philippe Velex.

J. Vib. Acoust 138(2), 021006 (Jan 20, 2016) (9 pages) Paper No: VIB-15-1188; doi: 10.1115/1.4032181 History: Received May 28, 2015; Revised November 25, 2015

In this study, a two-dimensional (2D), steady-state, discrete dynamic model of a double-planet planetary gearset is proposed. The dynamic model is generalized such that it can consist of N number of planet branches and can operate under any operating conditions (load and speed). The contact between each external to external and external to internal gear pair is modeled to obtain stiffnesses and mesh displacement excitations using a generalized load distribution model. The natural modes are computed by solving the corresponding eigenvalue problem. The forced vibration response to gear mesh excitations is obtained by applying the modal summation technique. The model is capable of predicting gear mesh dynamic load and dynamic transmission error spectra for each gear mesh, dynamic bearing load spectra for each bearing as well as gear body dynamic displacements. Forced vibration response of an example system that consists of three double-planet branches is studied to demonstrate the influence of some of the key design parameters.

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Figures

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Fig. 1

Illustration of a double-planet planetary gearset

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Fig. 2

Dynamic model of a double-planet planetary gearset (single branch shown for brevity)

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Fig. 3

Dynamic model illustrating the coupling between a representative planet gear branch and the carrier

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Fig. 4

Representative mode shapes: (a) rotational mode at 2386 Hz and (b) translational mode at 5063 Hz

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Fig. 5

Representative mode shapes of a four-branch system: (a) radial planet mode at 5524 Hz and (b) tangential planet mode at 5873 Hz

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Fig. 6

Comparison of dynamic mesh force spectra (Fsp1) for a nonfloating and a floating sun gear

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Fig. 7

Comparison of dynamic mesh force spectra for the example gearset with a nonfloating and a floating carrier

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Fig. 8

Comparison of dynamic mesh force spectra for the gearset with equally spaced planet branches and with the first planet intentionally offset

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Fig. 9

Comparison of dynamic mesh force spectra for sequentially phased and in-phase systems

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Fig. 10

Gearset assembly configurations A and B

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Fig. 11

Comparison of the dynamic mesh force spectra for planet assembly configurations A and B

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Fig. 12

Dynamic system representation of configurations A and B

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Fig. 13

Comparison of dynamic mesh force spectra for alternate numbers of planet teeth

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