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Analytical Rotordynamic Study of a High-Speed Gear Transmission System for Race Applications
ISSN: 0148-7191, e-ISSN: 2688-3627
Published September 30, 2020 by SAE International in United States
This content contains downloadable datasetsAnnotation ability available
Event: 11th International Styrian Noise, Vibration & Harshness Congress: The European Automotive Noise Conference
In motorsport power transmission systems, high-speed operation can be associated with significant rotordynamic effects. Changes in the natural frequencies of lateral (bending) vibrational modes as a function of spin speed are brought about by gyroscopic action linked to flexible shafts and mounted gear components. In the investigation of high-speed systems, it is important that these effects are included in the analysis in order to accurately predict the critical speeds encountered due to the action of the gear mesh and other sources of excitation.
The rotordynamic behaviour of the system can interact with crucial physical parameters of the transmission, such as the stiffnesses of the gear mesh and rolling element-to-raceway contact in the bearings. In addition, the presence of the gear mesh acts to couple the lateral and torsional vibration modes of a dual-shaft transmission through which a torque flows. The relative interactions and effects of bearing and gear components can be captured in the form of modal analysis with parametric studies of key stiffness elements, such as mean value as a linear representation of stiffness.
In the presented study, an analytical finite element method is followed in order to construct the mass, stiffness and gyroscopic terms of a high-speed transmission system. In this method, the shafts comprise flexible elements with distributed mass, the gears are represented by disks of lumped mass and inertia, and the bearings are elements of multi-directional stiffness and negligible mass. The lateral, torsional and coupled vibrational modes of the system are solved and studied parametrically.
CitationFriskney, B., Theodossiades, S., and Mohammadpour, M., "Analytical Rotordynamic Study of a High-Speed Gear Transmission System for Race Applications," SAE Technical Paper 2020-01-1502, 2020, https://doi.org/10.4271/2020-01-1502.
Data Sets - Support Documents
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- Swanson, E., Powell, C.D., and Weissman, S. , “A Practical Review of Rotating Machinery Critical Speeds and Modes,” Sound Vib. 39(5):10-17, 2005.
- Rao, J.S. , Rotor Dynamics Third Edition (Delhi: New Age International Ltd., 1996).
- Ozguven, H.N. , “A Non-Linear Mathematical Model for Dynamic Analysis of Spur Gears Including Shaft and Bearing Dynamics,” J. of Sound Vib. 145(2):239-260, 1991.
- Kubur, M., Kahraman, A., Zini, D.M., and Kienzle, K. , “Dynamic Analysis of a Multi-Shaft Helical Gear Transmission by Finite Elements: Model and Experiment,” J. Vib. Acoust. 126(3):398, 2004.
- Kahraman, A., Ozguven, H.N., Houser, D.R., and Zakrajsek, J.J. , “Dynamic Analysis of Geared Rotors by Finite Elements,” J. Mech. Des. 114(3):507, 2008.
- Maatar, M., and Velex, P. , “Quasi-Static and Dynamic Analysis of Narrow-Faced Helical Gears with Profile and Lead Modifications,” J. Mech. Des. 119(4):474, 1997.
- Özgüven, H.N., and Özkan, Z.L. , “Whirl Speeds and Unbalance Response of Multibearing Rotors Using Finite Elements,” Journal of Vibration Acoustics Stress and Reliability in Design 106(1):72, 1984.
- Zorzi, E.S., and Nelson, H.D. , “Finite Element Simulation of Rotor-Bearing Systems with Internal Damping,” J. Eng. Power 99(1):71-76, 1977.
- Rajan, M., Rajan, S.D., Nelson, H.D., and Chen, W.J. , “Optimal Placement of Critical Speeds in Rotor-Bearing Systems,” J. Vib. Acoust. Stress Reliab. Des. 109(2):152-157, 1987.
- Rajan, M., Nelson, H.D., and Chen, W.J. , “Parameter Sensitivity in the Dynamics of Rotor-Bearing Systems,” J. Vib. Acoust. Stress Reliab. Des. 108(2):197-206, 1986.
- Nelson, H.D. , “A Finite Rotating Shaft Element Using Timoshenko Beam Theory,” J. Mech. Des. 102(4):793, 1980.
- Nelson, H.D. , “Rotordynamic Modelling and Analysis Procedures: A Review,” JSME Int. J. 41(1), 1998.
- Rao, J.S., Shiau, T.N., and Chang, J.R. , “Theoretical Analysis of Lateral Response due to Torsional Excitation of Geared Rotors,” Mech. Mach. Theory 33(6):761-783, 1998.
- Choi, S.-T., and Mau, S.-Y. , “Dynamic Analysis of Geared Rotor-Bearing Systems by the Transfer Matrix Method,” J. Mech. Des. 123(4):562, 2002.
- Iida, H., Tamura, A., Kikuch, K., and Agata, H. , “Coupled Torsional-Flexural Vibration of a Shaft in a Geared System of Rotors (1st Report),” Bull. JSME 23(186):2111, 1980.
- Chen, S., Tang, J., and Li, Y. , “Rotordynamics Analysis of a Double-Helical Gear Transmission System,” Meccanica 51(1):251-268, 2016.
- Hu, Z., Tang, J., and Chen, S. , “Analysis of Coupled Lateral-Torsional Vibration Response of a Geared Shaft Rotor System with and without Gyroscopic Effect,” Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci. 232(24):4550-4563, 2018.
- Meirovitch, L. , Analytical Methods in Vibrations (New York: The Macmillan Company, 1967).
- Nelson, H.D., and McVaugh, J.M. , “The Dynamics of Rotor-Bearing Systems Using Finite Elements,” J. Eng. Ind. 98(2):593, 1976.
- Rao, S.S. , Mechanical Vibrations Fifth Edition (Upper Saddle River, NJ: Pearson Education, Inc, 2011).