Vibration Behavior of the Planetary Gear System by Considering the Fixed Output

Subject Areas : Mechanical Engineering

Ali  Shahabi ¹ (Department of Mechanical Engineering, University of Sistan and Baluchestan, Zahedan, Iran Nedayedanesh Institute of Higher Education of Hormozgan, Bandar Abbas, Iran)
Amir Hossein  Kazemian ² (Department of Mechanical Engineering, University of Sistan and Baluchestan, Zahedan, Iran)

Received: 2022-04-08 Accepted : 2022-08-07 Published : 2023-06-01

Keywords: Natural frequency, Mesh stiffness, Spur planetary gear, Backlash, Chaotic phenomenon,

Abstract :

This work studies on analytical model of the single–stage spur planetary gear in form of lumped–parameter model. It includes key nonlinear factors of planetary gear vibration such as mesh stiffness and backlash of meshing gears. The planetary gear set is modeled as a set of lumped masses and springs and dynamic model of the planetary gear set is presented. Nonlinear equations of motion are presented for each component and each component has three degrees of freedom in planar motion. We have numerically evaluated a set of linear and nonlinear equations to obtain natural frequencies and analysis of vibration behavior of the system under nonlinear factors and fixed output. In previous researches, natural frequencies of planetary gears were evaluated from two points of view: the first one considered fixed output for planetary gears and the second one consists of free rotational output. In this research, the influence of the output flexibility is evaluated on natural frequencies of the planetary gear. Meanwhile, by considering the fixed output, vibration behavior of the nonlinear system is investigated. Results show that the most important effect of the output flexibility is on the principal natural frequency. Because of chaotic phenomenon, vibration behavior of components in translational directions is different.

References:

• Lin, J., Parker, R., Planetary Gear Parametric Instability Caused by Mesh Stiffness Variation, Journal of Sound and Vibration, Vol. 249, No. 1, 2002, pp. 129-145.


• Shi, J. F., Gou, X. F., and Zhu, L. Y., Modeling and Analysis of a Spur Gear Pair Considering Multi-State Mesh with Time-Varying Parameters and Backlash, Mechanism and Machine Theory, Vol. 134, 2019, pp. 582-603.


• Sun, T., Hu, H., Nonlinear Dynamics of a Planetary Gear System with Multiple Clearances, Mechanism and Machine Theory, Vol. 38, No. 12, 2003, pp. 1371-1390.


• Kahraman, A., Natural Modes of Planetary Gear Trains, Journal of Sound Vibration, Vol. 173, 1994, pp. 125-130.


• Kahraman, A., Load Sharing Characteristics of Planetary Transmissions, Mechanism and Machine Theory, Vol. 29, No. 8, 1994, pp. 1151-1165.


• Ambarisha, V. K., Parker, R. G., Suppression of Planet Mode Response in Planetary Gear Dynamics Through Mesh Phasing, Journal of Vibration and Acoustics, Vol. 128, No. 2, 2006, pp. 133-142.


• Lin, J., Parker, R. G., Analytical Characterization of the Unique Properties of Planetary Gear Free Vibration, Journal of Vibration and Acoustics, Vol. 121, No. 3, 1999, pp. 316-321.


• Parker, R. G., A Physical Explanation for the Effectiveness of Planet Phasing to Suppress Planetary Gear Vibration, Journal of Sound and Vibration, Vol. 236, No. 4, 2000, pp. 561-573.


• Lin, J., Parker, R. G., Natural Frequency Veering in Planetary Gears, Mechanics of Structures and Machines, Vol. 29, No. 4, 2001, pp. 411-429.


• Parker, R. G., Lin, J., Mesh Phasing Relationships in Planetary and Epicyclic Gears, J Mech Des, Vol. 126, No. 2, 2004, pp. 365-370.


• Tatar, A., Schwingshackl, C. W., and Friswell, M. I., Dynamic Behaviour of Three-Dimensional Planetary Geared Rotor Systems, Mechanism and Machine Theory, Vol. 134, 2019, pp. 39-56.


• Shahabi, A., Kazemian, A. H., Analysis of Time–Varying Mesh Stiffness for the Planetary Gear System with Analytical and Finite Element Methods, ADMT Journal, 2021.


• Shahabi, A., Kazemian, A. H., Dynamic and Vibration Analysis for Geometrical Structures of Planetary Gears, Journal of Solid Mechanics, Vol. 13, No. 4, 2021, pp. 384-398.


• Li, C. H., Chiou, H. S., Hung, C., Chang, Y, Y., and Yen, C. C., Integration of Finite Element Analysis and Optimum Design on Gear Systems, Finite Elements in Analysis and Design, Vol. 38, No. 3, 2002, pp. 179-192.


• Chen, Z. G., Shao, Y. M., and Lim, T. C., Non-Linear Dynamic Simulation of Gear Response Under the Idling Condition, International Journal of Automotive Technology, Vol. 13, No. 4, 2012, pp. 541-552.


• Masoumi, A., Pellicano, F., Samani, F. S., and Barbieri, M., Symmetry Breaking and Chaos-Induced Imbalance in Planetary Gears, Nonlinear Dynamics, Vol. 80, No. 1-2, 2015, pp. 561-582.


• Sainsot, P., Velex, P., and Duverger, O., Contribution of Gear Body to Tooth Deflections—A New Bidimensional Analytical Formula, J. Mech. Des., Vol. 126, No. 4, 2004, pp. 748-752.


• Kahraman, A., Free Torsional Vibration Characteristics of Compound Planetary Gear Sets, Mechanism and Machine Theory, Vol. 36, No. 8, 2001, pp. 953-971.


• Kiracofe, D. R., Parker, R. G., Structured Vibration Modes of General Compound Planetary Gear Systems, Journal of Vibration and Acoustics, Vol. 129, No. 1, 2006, pp. 1-16.


• Mabrouk, I, B., El Hami, A., Walha, L., Zghal, B., and Haddar, M., Dynamic Response Analysis of Vertical Axis Wind Turbine Geared Transmission System with Uncertainty, Engineering Structures, Vol. 139, 2017, pp. 170-179.


• Shahabi, A., Kazemian, A. H., Farahat, S., and Sarhaddi, F., The Influence of Engine Gyroscopic Moments on Vehicle Transient Handling, Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, Vol. 235, No. 9, 2021, pp. 2425-2441.


• Shahabi, A., Kazemian, A. H., Farahat, S., and Sarhaddi, F., Dynamic Behavior of the Full-Car Model in the J-Turn Maneuver by Considering the Engine Gyroscopic Effects, Communications-Scientific letters of the University of Zilina, Vol. 23, No. 3, 2021, pp. B237-B249.


• Shahabi, A., Kazemian, A. H., Farahat, S., and Sarhaddi, F., Vehicle’s Dynamic Behavior in Fishhook Maneuver by Considering the Engine Dynamics. ADMT Journal, Vol. 14, No. 2, 2021, 23-35.


• Shahabi, A., Kazemian, A. H., Farahat, S., and Sarhaddi, F, Wheel Slip Ratio Regulation for Investigating the Vehicle's Dynamic Behavior During Braking and Steering Input, Mechanics & Industry, Vol. 22, No. 17, 2021.


• Eritenel, T., Parker, R. G., Modal Properties of Three-Dimensional Helical Planetary Gears, Journal of Sound and Vibration, Vol. 325, No. 1-2, 2009, pp. 397-420.


• Bahk, C. J., Parker, R. G., Analytical Solution for the Nonlinear Dynamics of Planetary Gears, Journal of Computational and Nonlinear Dynamics, Vol. 6, No. 2, 2011.


• Orzechowski, G., Frączek, J., Integration of the Equations of Motion of Multibody Systems Using Absolute Nodal Coordinate Formulation, Acta Mechanica Et Automatic, Vol. 6, 2012, pp. 75-83.


• Wang, J., Rodriguez, J., and Keribar, R., Integration of Flexible Multibody Systems Using Radau IIA Algorithms, Journal of Computational and Nonlinear Dynamics, Vol. 5, No. 4, 2010.