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Review Article

A Review of Planetary and Epicyclic Gear Dynamics and Vibrations Research

[+] Author and Article Information
Christopher G. Cooley

University of Michigan–Shanghai Jiao
Tong University Joint Institute,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: cooley.168@osu.edu

Robert G. Parker

L. S. Randolph Professor and Head
Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24061

1Corresponding author.

Manuscript received January 12, 2014; final manuscript received June 2, 2014; published online June 20, 2014. Editor: Harry Dankowicz.

Appl. Mech. Rev 66(4), 040804 (Jun 20, 2014) (15 pages) Paper No: AMR-14-1005; doi: 10.1115/1.4027812 History: Received January 12, 2014; Revised June 02, 2014

This article summarizes published journal articles on planetary and epicyclic gear dynamics and vibration. Research in this field has increased dramatically over the past two decades. The wide range of research topics demonstrates the technical challenges of understanding and predicting planetary gear dynamics and vibration. The research in this review includes mathematical models, vibration mode properties, dynamic response predictions including nonlinearities and time-varying mesh stiffness fluctuations, the effects of elastic compliance, and gyroscopic effects, among other topics. Practical aspects are also included, for example, planet load sharing, planet phasing, tooth surface modifications, and characteristics of measured vibration response.

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Inalpolat, M., and Kahraman, A., 2009, “A Theoretical and Experimental Investigation of Modulation Sidebands of Planetary Gear Sets,” J. Sound Vib., 323(3–5), pp. 677–696. [CrossRef]
Hidaka, T., Terauchi, Y., and Ishioka, K., 1979, “Dynamic Behavior of Planetary Gear (4th Report, Influence of the Transmitted Tooth Load on the Dynamic Increment Load),” Bull. JSME, 22(168), pp. 877–884. [CrossRef]
Hidaka, T., Terauchi, Y., and Nagamura, K., 1979, “Dynamic Behavior of Planetary Gear (5th Report, Dynamic Increment of Torque),” Bull. JSME, 22(169), pp. 1017–1025. [CrossRef]
McFadden, P. D., and Smith, J. D., 1985, “An Explanation for the Asymmetry of the Modulation Sidebands About the Tooth Meshing Frequency in Epicyclic Gear Vibration,” Proc. Inst. Mech. Eng., Part C, 199(1), pp. 65–70. [CrossRef]
Ericson, T. M., and Parker, R. G., 2013, “Experimental Quantification of the Effects of Torque on the Dynamic Behavior and System Parameters of Planetary Gears,” Mech. Mach. Theory 74, pp. 370–389.
McFadden, P. D., and Smith, J. D., 1986, “Effect of Transmission Path on Measured Gear Vibration,” ASME J. Vib. Acoust., 108(3), pp. 377–378. [CrossRef]
Yu, S., and Kaatz, S., 2005, “Asymmetric Gear Noise Sidebands and Application to Planetary Gear Noise Reduction,” SAE Technical Paper Series No. 2005–01–2462.
McFadden, P. D., 1991, “A Technique for Calculating the Time Domain Averages of the Vibration of the Individual Planet Gears and the Sun Gear in an Epicyclic Gearbox,” J. Sound Vib., 144(1), pp. 163–172. [CrossRef]
McFadden, P. D., 1994, “Window Functions for the Calculation of the Time Domain Averages of the Vibration of the Individual Planet Gears and Sun Gear in an Epicyclic Gearbox,” ASME J. Vib. Acoust., 116(2), pp. 179–187. [CrossRef]
McNames, J., 2002, “Fourier Series Analysis of Epicyclic Gearbox Vibration,” ASME J. Vib. Acoust., 124(1), pp. 150–153. [CrossRef]
Blunt, D. M., and Keller, J. A., 2006, “Detection of a Fatigue Crack in a UH-60A Planet Gear Carrier Using Vibration Analysis,” Mech. Syst. Signal Process., 20(8), pp. 2095–2111. [CrossRef]
Patrick, R., Ferri, A., and Vachtsevanos, G., 2012, “Effect of Planetary Gear Carrier-Plate Cracks on Vibration Spectrum,” ASME J. Vib. Acoust., 134(6), p. 061001. [CrossRef]
Chen, Z., and Shao, Y., 2013, “Mesh Stiffness of an Internal Spur Gear Pair With Ring Gear Rim Deformation,” Mech. Mach. Theory, 69, pp. 1–12. [CrossRef]
Litvin, F. L., Vecchiato, D., Demenego, A., Karedes, E., Hansen, B., and Handschuh, R., 2002, “Design of One Stage Planetary Gear Train With Improved Conditions of Load Distribution and Reduced Transmission Errors,” ASME J. Mech. Des., 124(4), pp. 745–752. [CrossRef]
Vecchiato, D., 2006, “Tooth Contact Analysis of a Misaligned Isostatic Planetary Gear Train,” Mech. Mach. Theory, 41(6), pp. 617–631. [CrossRef]

Figures

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Fig. 1

Schematic of a planetary gear with four planets

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Fig. 2

Finite element/contact mechanics model of a planetary gear from a helicopter application using Calyx [6]. The colors show the stress contours and the instantaneous contact pressure at a sun-planet mesh.

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Fig. 3

Histogram of research papers on planetary gear dynamics and vibration

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Fig. 4

Lumped-parameter planetary gear model from Ref. [10]

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Fig. 5

Planetary gear mode types for the lumped-parameter model shown in Fig. 4 from Ref. [10]. The dotted (black) lines denote the gear nominal positions, and the solid (blue) lines are the deflected gear positions. (a) Planet mode at ω = 0.9617, (b) rotational mode at ω = 0.9077, and (c) translational mode at ω = 0.7199.

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Fig. 6

Mode types for a gearbox consisting of a planetary gear and a gear pair. The stages are coupled by a shaft from the sun gear to the output (larger) gear of the parallel-axis stage. Overall mode (upper) and planet mode (lower). The dotted (black) lines denote the gear nominal positions, and the solid (blue) lines are the deflected gear positions.

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