Abstract
Blade-rotor systems frequently encounter the problem of blade-to-case rubbing, which affects their safety and stability. Numerical simulation can be used to predict the steady-state response of these systems. However, such simulation is frequently computationally expensive because of the high dimensions of the dynamic model of a blade-rotor system. To overcome this problem, a new method that combines the receptance-based dimension-reduction approach with the incremental harmonic balance (IHB) method is presented in this study. First, a dynamic model of a blade-rotor system is developed using the finite element method, and the number of dimensions of the model is reduced by the receptance method. Subsequently, the steady-state response is obtained by the improved IHB method to conveniently manage the large number of super-harmonic components of the local rubbing system. Finally, the precision and efficiency of the proposed method is verified by comparing its results with those obtained by the Newmark-β method. The proposed method is found to be efficient in analyzing local rubbing blade-rotor systems with high dimensions, local nonlinearities, and rich super-harmonics.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A. Muszynska, Rotor-to-stationary part rubbing contact in rotating machinery, Rotordynamics, CRC Press (2005) 555–710 (Chapter 5).
S. Bouaziz et al., Transient response of a rotor-AMBs system connected by a flexible mechanical coupling, Mechatronics, 23 (6) (2013) 573–580.
M. Legrand et al., Two-dimensional modeling of an aircraft engine structural bladed disk-casing modal interaction, Journal of Sound and Vibration, 319 (1–2) (2009) 527–546.
F. L. Chu and Z. S. Zhang, Periodic, quasi-periodic and chaotic vibrations of a rub-impact rotor system supported on oil film bearings, International Journal of Engineering Science, 35 (10–11) (1997) 963–973.
S. Kawamura et al., Analysis of nonlinear steady state vibration of a multi-degree-of-freedom system using component mode synthesis method, Applied Acoustics, 69 (7) (2008) 624–633.
T. S. Zheng and N. Hasebe, An efficient analysis of highorder dynamical system with local nonlinearity, Journal of Vibration and Acoustics-Transactions of the ASME, 121 (3) (1999) 408–416.
D. H. Bae, C. H. Lee and D. S. Bae, Non-linear flexible body analysis for mechanical systems, Journal of Mechanical Science and Technology, 26 (7) (2012) 2159–2162.
F. Wei and G. T. Zheng, Multi-harmonic response analysis of systems with local nonlinearities based on describing functions and linear receptance, Journal of Vibration and Acoustics-Transactions of the ASME, 132 (2010) 031004–1-031004-6.
Y. Ren and C. F. Beards, A new receptance-based perturbative multi-harmonic balance method for the calculation of the steady state response of non-linear systems, Journal of Sound and Vibration, 172 (5) (1994) 593–604.
P. Bonello and H. P. Minh, A receptance harmonic balance technique for the computation of the vibration of a whole aero-engine model with nonlinear bearings, Journal of Sound and Vibration, 324 (1) (2009) 221–242.
M. Guskov, J. Sinou and F. Thouverez, Multi-dimensional harmonic balance applied to rotor dynamics, Mechanics Research Communications, 35 (8) (2008) 537–545.
A. Gelb and W. E. V. Velde, Multi-input describing functions and nonlinear system design, McGraw-Hill, New York (1968).
P. Bonello and P. M. Hai, A receptance harmonic balance technique for the computation of the vibration of a whole aero-engine model with nonlinear bearings, Journal of Sound and Vibration, 324 (1–2) (2009) 221–242.
P. Bonello, M. J. Brennan and R. Holmes, Non-linear modeling of rotor dynamic systems with squeeze film dampersan efficient integrated approach, Journal of Sound and Vibration, 249 (4) (2002) 743–773.
P. Bonello, M. J. Brennan and R. Holmes, The prediction of the non-linear dynamics of a squeeze film damped aeroengine rotor housed in a flexible support structure, Proceedings of the IMechE Part G Journal of Aerospace Engineering, 218 (3) (2004) 213–230.
Y. Ren and C. F. Beards, A new receptance-based perturbative multi-harmonic balance method for the calculation of the steady state response of non-linear systems, Journal of Sound and Vibration, 172 (1994) 593–604.
H. L. Yao et al., Detection of rubbing location in rotor system by super-harmonic responses, Journal of Mechanical Science and Technology, 26 (8) (2012) 2431–2437.
S. L. Lau, Y. K. Cheung and S. Y. Wu, A variable parameter incremental method for dynamic instability of linear and nonlinear elastic systems, Journal of Applied Mechanics of the ASME, 49 (1982) 849–853.
Y. Shen, S. Yang and X. Liu, Nonlinear dynamics of a spur gear pair with time-varying stiffness and backlash based on incremental harmonic balance method, International Journal of Mechanical Sciences, 48 (11) (2006) 1256–1263.
J. X. Zhou and L. Zhang, Incremental harmonic balance method for predicting amplitudes of a multi-d.o.f. non-linear wheel shimmy system with combined Coulomb and quadratic damping, Journal of Sound and Vibration, 279 (2005) 403–416.
A. Raghothama and S. Narayanan, Non-linear dynamics of a two-dimensional airfoil by incremental harmonic balance method, Journal of Sound and Vibration, 226 (3) (1999) 493–517.
L. Xu, M. W. Lu and Q. Cao, Nonlinear vibrations of dynamical systems with a general form of piecewise linear viscous damping by incremental harmonic balance method, Physics Letters A, 301 (2002) 65–73.
K. Y. Sze, S. H. Chen and J. L. Huang, The incremental harmonic balance method for nonlinear vibration of axially moving beams, Journal of Sound and Vibration, 281 (2005) 611–626.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Editor Yeon June Kang
Qian Zhao is currently a doctoral candidate at Northeastern University, China. She obtained her B.S. in Mechanical Manufacturing from Hebei Normal University, China in 2011, and her M.S. degree in Mechanical Engineering from Northeastern University, China in 2013. Her research interests include rotor dynamics and nonlinear vibration.
Hongliang Yao is currently an associate professor at Northeastern University, China. He obtained his B.S. degree in 2000 from the Hebei Institute of Technology, China, and his M.S. and Ph.D. degrees in 2003 and 2006, respectively, from Northeastern University, China. His research interests include rotor dynamics and rotating machinery fault diagnosis.
Rights and permissions
About this article
Cite this article
Zhao, Q., Yao, H., Xu, Q. et al. Prediction method for steady-state response of local rubbing blade-rotor systems. J Mech Sci Technol 29, 1537–1545 (2015). https://doi.org/10.1007/s12206-015-0326-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-015-0326-4