Analysis of planetary gear transmission in non-stationary operations

Abstract

Planetary gearboxes operate usually in non-stationary conditions generated mainly by variable loads applied to these transmissions. In order to understand the dynamic behavior of planetary gearboxes in such conditions, a mathematic model is developed including driving unit, transmission and load. The variability of load induces a variable speed of the transmission which is taken into account when characterizing the main dynamic parameter of the transmission which is the mesh stiffness function. This function is not periodic following the variability of the transmission speed. The computation of the dynamic response shows an intimate relation between the vibration amplitude level and the load value. As the load increase the vibration level increase. A combined amplitude and frequency modulation is observed which is well characterized using Short Time Fourier transform more suited than the spectral analysis.

Keywords

planetary gearbox / non-stationary conditions / variable load / dynamic response / time frequency analysis

References

[1] Randall R B. A new method of modeling gear faults. Journal of Mechanical Design, 1982, 104(2): 259-267

[2] Bartelmus W. Mathematical modeling and computer simulations as an aid to gearbox diagnostics. Mechanical Systems and Signal Processing, 2001, 15(5): 855-871

[3] Bartelmus W. Vibration condition monitoring of gearboxes. Machine Vibration, 1992, 1: 178-189

[4] Bartelmus W, Zimroz R. Vibration condition monitoring of planetary gearbox under varying external load. Mechanical Systems and Signal Processing, 2009, 23(1): 246-257

[5] Bartelmus W, Chaari F, Zimroz R, Haddar M.Modelling of gearbox dynamics under time-varying non stationary load for distributed fault detection and diagnosis. European Journal of Mechanics A/Solids, 2010, 29: 637-646

[6] Zimroz R, Millioz F, Martin N. A procedure of vibration analysis from planetary gearbox under non-stationary cyclic operations for instantaneous frequency estimation in time-frequency domain. In: Proceedings of Conference on Condition Monitoring and Machinery Failure Prevention Technologies (CM and MFPT 2010), Stratford-upon-Avon: United Kingdom, 2010

[7] Zhan Y, Makis V, Jardine A K S. Adaptive state detection of gearboxes under varying load conditions based on parametric modeling. Mechanical Systems and Signal Processing, 2006, 20(1): 188-221

[8] Khabou M T, Bouchaala N, Chaari F, Fakhfakh T, Haddar M. Study of a spur gear dynamic behavior in transient regime. Mechanical Systems and Signal Processing, 2011, 25(8): 3089-3101

[9] Chaari F, Bartelmus W, Zimroz R, Fakhfakh T, Haddar M. Gearbox vibration signal amplitude and frequency modulation. Sh Vibration, 2011, 18: 1-18

[10] Chaari F, Bartelmus W, Zimroz R, Fakhfakh T, Haddar M. Model based investigation on a two stages gearbox dynamics under non-stationary operations. In: Proceedings of the Second International Conference on Condition Monitoring of Machinery in Non Stationary Opertations, 2012

[11] Bouchaala N, Chaari F, Khabou M T, Fakhfakh T, Haddar M. Influence of the nonlinear Hertzian stiffness on the dynamics of a spur gear system under transient regime and tooth defects. International Journal of Vehicle Noise and Vibration, 2011, 7(2): 149-177

[12] Lin J, Parker R G. Analytical characterization of the unique properties of planetary gear free vibration. Journal of Vibration and Acoustics, 1999, 121(3): 316-321

[13] Wright D. Class notes on design and analysis of machine elements . Department of Mechanical and Materials Engineering, The University of Western Australia, 2005

[14] Kahraman A. Planetary gear train dynamics. The ASME Journal of Mechanical Design, 1994, 116(3): 713-720

[15] Saada A, Velex P.An extended model for the analysis of the dynamics of planetary trains. The ASME Journal of Mechanical Design, 1995, 117: 241-247

[16] Qian S, Chen D. Joint Time-Frequency Analysis: Method and Application. Upper Saddle River: Prentice Hall, 1996

Acknowledgements

This paper was financially supported by the Tunisian-Spanish Joint Project No. A1/037038/11.

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg