Comparative study of vibration analysis in rotary shafts between Rayleigh's and Dunkerley's methods
The importance of vibrations in rotating rotors in engineering applications has been examined, as has the best approach to interpreting vibration data. The most extensively used analytical approaches for rotating shaft vibration analysis have been investigated. In this research, a detailed study was made of the Rayleigh and Dunkerley methods due to their importance in the special calculations to find the amplitude of vibrations in the rotation system. The multi-node method was used to calculate both Dunkerley's and Rayleigh's methods. An experimental platform was built to study the vibrations that occur in the rotating shafts, and the results were compared with theoretical calculations and with different distances of the bearings. It proved that there is very little error between the experimental and theoretical results. The vibration signal from the sensors was analyzed using the LABVIEW program. Rayleigh's method was compared to the exact method, and it was considered the most accurate method. It was found that it made very little difference, up to about 0.06%. As for the Dunkerley method, the difference between it and the proper method is about 4%, which is acceptable. Then a comparison was made between Rayleigh's and Dunkerley's methods, and it was found that Dunkerley's method is the most appropriate in the calculations.
J. M. Vance, F. Y. Zeidan, and B. G. Murphy, Machinery vibration and rotordynamics. John Wiley & Sons, 2010.
F. M. A. El-Saeidy and F. Sticher, "Dynamics of a Rigid Rotor Linear/Nonlinear Bearings System Subject to Rotating Unbalance and Base Excitations," Journal of Vibration and Control, vol. 16, no. 3, pp. 403-438, 2009, doi: 10.1177/1077546309103565.
A. H. Haslam, C. W. Schwingshackl, and A. I. J. Rix, "A parametric study of an unbalanced Jeffcott rotor supported by a rolling-element bearing," Nonlinear Dynamics, vol. 99, no. 4, pp. 2571-2604, 2020, doi: 10.1007/s11071-020-05470-4.
A. Khadersab and S. Shivakumar, "Vibration analysis techniques for rotating machinery and its effect on bearing faults," Procedia Manufacturing, vol. 20, pp. 247-252, 2018.
J. Heikkinen, B. Ghalamchi, J. Sopanen, and A. Mikkola, "Twice-Running-Speed Resonances of a Paper Machine Tube Roll Supported by Spherical Roller Bearings: Analysis and Comparison With Experiments," in ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2014: American Society of Mechanical Engineers Digital Collection.
R. V. Daniel, S. A. Siddhappa, S. B. Gajanan, S. V. Philip, and P. S. Paul, "Effect of Bearings on Vibration in Rotating Machinery," presented at the IOP Conference Series: Materials Science and Engineering, Karunya University, Coimbatore 641114, Tamil Nadu, India., 2017.
G. Chandrashekar, W. Raj, C. Godwin, and P. S. Paul, "Study On The Influence Of Shaft Material On Vibration In Rotating Machinery," Materials Today: Proceedings, vol. 5, no. 5, pp. 12071-12076, 2018, doi: 10.1016/j.matpr.2018.02.182.
R. Tiwari, "Conditioning of regression matrices for simultaneous estimation of the residual unbalance and bearing dynamic parameters," Mechanical Systems and Signal Processing, vol. 19, no. 5, pp. 1082-1095, 2005/09/01/ 2005, doi: https://doi.org/10.1016/j.ymssp.2004.09.005
M. R. Reddy and J. Srinivas, "Vibration Analysis of a Support Excited Rotor System with Hydrodynamic Journal Bearings," Procedia Engineering, vol. 144, pp. 825-832, 2016, doi: 10.1016/j.proeng.2016.05.093.
A. Wang, W. Yao, K. He, G. Meng, X. Cheng, and J. Yang, "Analytical modelling and numerical experiment for simultaneous identification of unbalance and rolling-bearing coefficients of the continuous single-disc and single-span rotor-bearing system with Rayleigh beam model," Mechanical Systems and Signal Processing, vol. 116, pp. 322-346, 2019, doi: 10.1016/j.ymssp.2018.06.039.
S. Yang et al., "Dynamic modeling and analysis of an axially moving and spinning Rayleigh beam based on a time-varying element," Applied Mathematical Modelling, vol. 95, pp. 409-434, 2021.
K. Zhu and J. Chung, "Vibration and stability analysis of a simply-supported Rayleigh beam with spinning and axial motions," Applied Mathematical Modelling, vol. 66, pp. 362-382, 2019.
R. Farshbaf Zinati, M. Rezaee, and S. Lotfan, "Nonlinear vibration and stability analysis of viscoelastic rayleigh beams axially moving on a flexible intermediate support," Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, vol. 44, no. 4, pp. 865-879, 2020.
M. A. Aouadi and F. Lakrad, "Linear flexural natural frequencies and stability analysis of spinning Rayleigh beams: application to clamped-clamped beams," in MATEC Web of Conferences, 2018, vol. 241: EDP Sciences, p. 01002.
M. Faraji Mahyari, K. Faraji Mahyari, and S. Fardpour, "New Approach to Instability Threshold of a Simply Supported Rayleigh Shaft," Journal of Solid Mechanics, vol. 6, no. 2, pp. 150-157, 2014.
K. Zhu and J. Chung, "Dynamic modeling and analysis of a spinning Rayleigh beam under deployment," International Journal of Mechanical Sciences, vol. 115-116, pp. 392-405, 2016, doi: 10.1016/j.ijmecsci.2016.07.029.
R. Tamrakar and N. Mittal, "Experimental Investigation of Shaft Whirl Carrying 3 Rotors," Trends in Mechanical Engineering & Technology, vol. 5, no. 2, pp. 17-21, 2015.
C. Levy, "An iterative technique based on the Dunkerley method for determining the natural frequencies of vibrating systems," Journal of sound and vibration, vol. 150, no. 1, pp. 111-118, 1991.
K. Low, "A modified Dunkerley formula for eigenfrequencies of beams carrying concentrated masses," International Journal of Mechanical Sciences, vol. 42, no. 7, pp. 1287-1305, 2000.
S. S. Rao, Mechanical Vibrations in SI Units, Global Edition, Sixth ed. Pearson, 2017.
J. Metsebo, N. Upadhyay, P. Kankar, and B. N. Nbendjo, "Modelling of a rotor-ball bearings system using Timoshenko beam and effects of rotating shaft on their dynamics," Journal of Mechanical Science and Technology, vol. 30, no. 12, pp. 5339-5350, 2016.
N. Wang, D. Jiang, and H. Xu, "Dynamic characteristics analysis of a dual-rotor system with inter-shaft bearing," Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 233, no. 3, pp. 1147-1158, 2019.
W. T. Thomson, Theory of vibration with applications. CrC Press, 2018.
How to Cite
Copyright: Open Access authors retain the copyrights of their papers, and all open access articles are distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution and reproduction in any medium, provided that the original work is properly cited. The use of general descriptive names, trade names, trademarks, and so forth in this publication, even if not specifically identified, does not imply that these names are not protected by the relevant laws and regulations. While the advice and information in this journal are believed to be true and accurate on the date of its going to press, neither the authors, the editors, nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.