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TECHNICAL PAPERS

Dynamic Response of a Planetary Gear System Using a Finite Element/Contact Mechanics Model

[+] Author and Article Information
Robert G. Parker

Associate Professore-mail: parker.242@osu.edu

Vinayak Agashe

Department of Mechanical Engineering, The Ohio State University, 206 W. 18th Ave., Columbus, OH 43201-1107

Sandeep M. Vijayakar

Advanced Numerical Solutions, 3554 Mark Twain Ct., Hilliard, OH 43026

J. Mech. Des 122(3), 304-310 (May 01, 1999) (7 pages) doi:10.1115/1.1286189 History: Received May 01, 1999
Copyright © 2000 by ASME
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References

Cunliffe,  F., Smith,  J. D., and Welbourn,  D. B., 1974, “Dynamic Tooth Loads in Epicyclic Gears,” ASME J. Eng. Ind., 95, pp. 578–584.
Botman,  M., 1976, “Epicyclic Gear Vibrations,” ASME J. Eng. Ind., 97, pp. 811–815.
Kahraman,  A., 1994, “Natural Modes of Planetary Gear Trains,” J. Sound Vib., 173, pp. 125–130.
Lin,  J., and Parker,  R. G., 1999, “Analytical Characterization of the Unique Properties of Planetary Gear Free Vibration,” J. Vibr. Acoust., 121, pp. 316–321.
Lin,  J., and Parker,  R. G., 2000, “Structured Vibration Properties of Planetary Gears with Unequally Spaced Planets,” J. Sound Vib., 233, pp. 921–928.
Lin,  J., and Parker,  R. G., 1999, “Sensitivity of Planetary Gear Natural Frequencies and Vibration Modes to Model Parameters,” J. Sound Vib., 228, pp. 109–128.
Kahraman,  A., 1994, “Load Sharing Characteristics of Planetary Transmissions,” Mech. Mach. Theory, 29, pp. 1151–1165.
Kahraman,  A., 1994, “Planetary Gear Train Dynamics,” ASME J. Mech. Des., 116, pp. 713–720.
Velex,  P., and Flamand,  L., 1996, “Dynamic Response of Planetary Trains to Mesh Parametric Excitations,” ASME J. Mech. Des., 118, pp. 7–14.
Saada,  A., and Velex,  P., 1995, “An Extended Model for the Analysis of the Dynamic Behavior of Planetary Trains,” ASME J. Mech. Des., 117, pp. 241–247.
Valco, M. J., 1992, “Planetary Gear Train Ring Gear and Support Structure,” Doctoral Dissertation, Cleveland State University.
Gradu, M., Langenbeck, K., and Breunig, B., 1996, “Planetary Gears with Improved Vibrational Behavior in Automatic Transmissions,” VDI BERICHTE NR 1996, pp. 861–879.
Vijayakar,  S., 1991, “A Combined Surface Integral and Finite Element Solution for a Three-Dimensional Contact Problem,” Int. J. Numer. Methods Eng., 31, pp. 525–545.
Vijayakar,  S. M., Busby,  H. R., and Houser,  D. R., 1988, “Linearization of Multibody Frictional Contact Problems,” Comput. Struct., 29, pp. 569–576.
Parker, R. G., Vijayakar, S. M., and Imajo, T., 2000, “Nonlinear Dynamic Response of a Spur Gear Pair: Modeling and Experimental Comparisons,” J. Sound Vib., in press.
Blankenship, G. W., and Kahraman, A., 1996, “Gear Dynamics Experiments, Part-I: Characterization of Forced Response,” Proc. of ASME Power Transmission and Gearing Conference, San Diego.
Krantz, T. L., 1992, “Gear Tooth Stress Measurements of Two Helicopter Planetary Stages,” NASA Technical Memorandum 105651, AVSCOM Technical Report 91-C-038, pp. 1–8.
Seager,  D. L., 1975, “Conditions for the Neutralization of Excitation by the Teeth in Epicyclic Gearing,” J. Mech. Eng. Sci., 17, pp. 293–298.
Kahraman, A., and Blankenship, G. W., 1994, “Planet Mesh Phasing in Epicyclic Gear Sets,” Proc. of International Gearing Conference, Newcastle, UK, pp. 99–104.
Parker,  R. G., 2000, “A Physical Explanation for the Effectiveness of Planet Phasing to Suppress Planetary Gear Vibration,” J. Sound Vib., 236, pp. 561–573.

Figures

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Contact region division into inner and outer regions
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Finite element mesh for the planetary gear system
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Frequency content of the sun translation transients for the three planet gear system impulse test. Force impulses are applied only to the sun and carrier translational degrees of freedom.
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Frequency response amplitude of the planet radial deflection at various speeds for a sun torque of 1130 N-m (10000 lb-in) in a four planet gear system
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Frequency response amplitude of the planet tangential deflection at various speeds for a sun torque of 1130 N-m (10000 lb-in) in a four planet gear system
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Frequency response amplitude of the planet rotational deflection at various speeds for a sun torque of 1130 N-m (10000 lb-in) in a four planet gear system
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Frequency response amplitude of the planet radial deflection at various speeds for a sun torque of 1130 N-m (10000 lb-in) in a four planet gear system. fi denotes the natural frequencies of the system.
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Frequency response amplitude of the planet rotational deflection of Fig. 6 presented such that the individual harmonics are clarified
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Frequency response amplitude of the sun tangential deflection at various speeds for a sun torque of 1130 N-m (10000 lb-in) in a four planet gear system
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Frequency response amplitude of the sun rotational deflection at various speeds for a sun torque of 1130 N-m (10000 lb-in) in a four planet gear system
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Frequency response amplitude of the planet radial deflection at various speeds for a sun torque of 1130 N-m (10000 lb-in) in a three planet gear system
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Comparison of the change in the RMS sun gear rotational and translational deflections as the torque is increased. These are the results of static analyses.
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Comparison of the peak sun gear resonant response for the 1) rotational mode at 1144 Hz, and 2) translational mode at 778 Hz. Solid curves denote sun rotation and dashed curves denote sun translation.
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Comparison of the peak planet gear resonant response for the 1) rotational mode at 1144 Hz, and 2) translational mode at 778 Hz. The curves denote planet radial deflection for both modes.

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