Experimental Investigation of Parameters Affecting Natural Frequencies of Planetary Gear Systems
Keywords:
Perturbed system, Design parameters, Eigen sensitivities, Natural frequency, Tuned system.Abstract
In the present work, an experimental model of general planetary gear transmission is used to study the sensitivity of the natural frequencies to system parameters in perturbed situations. Design parameters considered are mass of components and their moment of inertia, mesh stiffness and bearing support stiffness. A three-planer degree of freedom model is selected for planets, sun, ring, and carrier. For cyclically symmetric (tuned) planetary gear system well-defined modal properties considering timeinvariant and linear conditions defined modal properties are applied to calculate Eigen sensitivities and indicate them in the form of simple formulae. These formulae are quite efficient to determine the Eigen sensitivities to support and mesh stiffness, mass and inertia of the components in perturbed situations. The effect of these parameters on sensitivity of the natural frequency was verified experimentally and the results so obtained are found in good agreement with those available in literature.
References
[2] Cunliffe F, Smith JD, Welboum DB. Dynamic tooth loads in epicyclic gears. Journal of Engineering for Industry 1974; 94: 578-84.
[3] Botman M. Epicyclic gear vibrations. Journal of Engineering for Industry 1976: 811-15.
[4] Frater JL, August R, Oswald FB. Vibration in planetary gear systems with unequal planet stiffnesses. NASA Technical Memorandum 1983; 83428.
[5] Kahraman A. Planetary gear train dynamics. ASME Journal of Mechanical Design 1994b; 116(3): 713-20.
[6] Kahraman A. Natural modes of planetary gear trains. Journal of Sound and Vibration 1994c; 173(1): 125-30.
[7] Kahraman A. Dynamic analysis of a multi-mesh helical gear train. ASME Journal of Mechanical Design 1994d; 116(3): 706-12.
[8] Kahraman A. Load sharing characteristics of planetary transmissions. Mechanism and Machine Theory 1994a; 29: 1151-65.
[9] Mehrabi M, Singh VP. Analytical modeling of planetary gear and sensitivity of natural frequencies. International Journal of Applied Research in Mechanical Engineering 2013; 3(2).
[10] Yichao G, Parker RG. Sensitivity of general compound planetary gear natural frequencies and vibration modes to modal parameters. Journal of ASME 2010; 132(1).
[11] Parker RG. A physical explanation for the effectiveness of planet phasing to suppress planetary gear vibration. Journal of Sound and Vibration 2000; 236(4): 561-73.
[12] Lin J, Parker RG. Analytical characterization of the unique properties of planetary gear free vibration. Journal of Vibration and Acoustics 1999a; 121: 316-21.
[13] Sun T, Hu HY. Nonlinear dynamics of a planetary gear system with multiple clearances. Mechanism and Machine Theory 2003; 38: 1371-90.
[14] Lin J, Parker RG. Sensitivity of planetary gear natural frequencies and vibration modes to model parameters. Journal of Sound and Vibration 1999b; 228(1): 109-28.
[15] Thareja, Priyavrat and Goyal, Manu, Zero Defect Planning of Case Hardened Transmission Gears-A Case Study. Proceedings of Competitive Product Development, September 29, 2009. Available http://dx.doi.org/10.2139/ssrn. 1541171.
[16] Mehrabi M, Singh VP. Vibration analysis of planetary gear system. International Journal of Engineering & Research Sep 2013; 2(9).
[17] High GD. An iterative method for eigenvector derivatives. The Mac Neal- Schwendler Corporation, Los Angeles, CA, 1990.
[18] Herting DN. Eigenvector derivative with second order terms. MSC Memo DNH- 43. Jul 6, 1984.
