Abstract
A dynamic model is established for an offset-disc rotor system with a mechanical gear coupling, which takes into consideration the nonlinear restoring force of rotor support and the effect of coupling misalignment. Periodic solutions are obtained through harmonic balance method with alternating frequency/time domain (HB-AFT) technique, and then compared with the results of numerical simulation. Good agreement confirms the feasibility of HB-AFT scheme. Moreover, the Floquet theory is adopted to analyze motion stability of the system when rotor runs at different speed intervals. A simple strategy to determine the monodromy matrix is introduced and two ways towards unstability are found for periodic solutions: the period doubling bifurcation and the secondary Hopf bifurcation. The results obtained will contribute to the global response analysis and dynamic optimal design of rotor systems.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Dewell D L, Mitchell L D. Detection of a misaligned disk coupling using spectrum analysis. ASME J Vib Acoust, 1984, 106: 9–16
Sekhar A S, Prabhu B S. Effects of coupling misalignment on vibrations of rotating machinery. J Sound Vib, 1995, 185: 655–671
Xu M, Marangoni R D. Vibration analysis of a motor-flexible coupling-rotor system subject to misalignment and unbalance, Part I: theoretical model and analysis. J Sound Vib, 1994, 176: 663–679
Xu M, Marangoni R D. Vibration analysis of a motor-flexible coupling-rotor system subject to misalignment and unbalance, Part II: experimental validation. J Sound Vib, 1994, 176: 681–691
Lee Y S, Lee C W. Modelling and vibration analysis of misaligned rotor-ball bearing systems. J Sound Vib, 1999, 224: 17–32
Li M, Yu L. Analysis of the coupled lateral torsional vibration of a rotor-bearing system with a misaligned gear coupling. J Sound Vib, 2001, 243: 283–300
Al-Hussain K M, Redmond I. Dynamic response of two rotors connected by rigid mechanical coupling with parallel misalignment. J Sound Vib, 2002, 249: 483–498
Al-Hussain K M. Dynamic stability of two rigid rotors connected by a flexible coupling with angular misalignment. J Sound Vib, 2003, 266: 217–234
Sinha J K, Lees A W, Friswell M I. Estimating unbalance and misalignment of a flexible rotating machine from a single run-down. J Sound Vib, 2004, 272: 967–989
Lees A W. Misalignment in rigidly coupled rotors. J Sound Vib, 2007, 305: 261–271
Bouaziz S, Attia H M, Mataar M, et al. Dynamic behaviour of hydrodynamic journal bearings in presence of rotor spatial angular misalignment. Mech Mach Theory, 2009, 44: 1548–1559
Bouaziz S, Messaoud N B, Mataar M, et al. A theoretical model for analyzing the dynamic behavior of a misaligned rotor with active magnetic bearings. Mechatronics, 2011, 21: 899–907
Bouaziz S, Messaoud N B, Choley J Y, et al. Transient response of a rotor-AMBs system connected by a flexible mechanical coupling. Mechatronics, 2013, 23: 573–580
Patel T H, Darpe A K. Vibration response of misaligned rotors. J Sound Vib, 2009, 325: 609–628
Patel T H, Darpe A K. Experimental investigations on vibration response of misaligned rotors. Mech Syst Signal Pr, 2009, 23: 2236–2252
Jalan A K, Mohanty A R. Model based fault diagnosis of a rotorbearing system for misalignment and unbalance under steady-state condition. J Sound Vib, 2009, 327: 604–622
Redmond I. Study of a misaligned flexibly coupled shaft system having nonlinear bearings and cyclic coupling stiffness—theoretical model and analysis. J Sound Vib, 2010, 329: 700–720
Rybczynski J. The possibility of evaluating turbo-set bearing misalignment defects on the basis of bearing trajectory features. Mech Syst Signal Pr, 2011, 25: 521–536
Lal M, Tiwari R. Multi-fault identification in simple rotor-bearingcoupling systems based on forced response measurements. Mech Mach Theory, 2012, 51: 87–109
Lal M, Tiwari R. Quantification of multiple fault parameters in flexible turbo-generator systems with incomplete rundown vibration data. Mech Syst Signal Pr, 2013, 41: 546–563
Lü J H, Chen G R. A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE T Autom Control, 2005, 50: 841–846
Li Y, Wu X Q, Lu J A, et al. Synchronizability of duplex networks. IEEE T Circuits-II, 2016, 63: 206–210
Liu K X, Zhu H H, Lü J H. Bridging the gap between transmission noise and sampled data for robust consensus of multi-agent systems. IEEE T Circuits-I, 2015, 62: 1836–1844
Liu K X, Wu L L, Lü J H, et al. Finite-time adaptive consensus of a class of multi-agent systems. Sci China Tech Sci, 2016, 59: 22–32
Hou L, Chen Y S. Analysis of 1/2 sub-harmonic resonance in a maneuvering rotor system. Sci China Tech Sci, 2014, 57: 203–209
Hou L, Chen Y S. Super-harmonic responses analysis for a cracked rotor system considering inertial excitation. Sci China Tech Sci, 2015, 58: 1924–1934
Li D C, Xiang J W. Nonlinear aeroelastic analysis of airfoil using quasi-analytical approach (in Chinese). Acta Aeronaut Astronaut Sin, 2007, 28: 1080–1084
Niu Y B, Wang Z W. Flutter analysis of 2-D airfoil with nonlinearities using elliptic harmonic balance method (in Chinese). Eng Mech, 2013, 30: 461–465
Atadan A S, Huseyin K. An intrinsic method of harmonic analysis for nonlinear oscillations (a perturbation technique). J Sound Vib, 1984, 95: 525–530
Huseyin K, Lin R. An intrinsic multiple-scale harmonic balance method for nonlinear vibration and bifurcation problems. Int J Nonlinear Mech, 1991, 26: 727–740
Yuste S B. Comments on the method of harmonic balance in which Jacobi elliptic functions are used. J Sound Vib, 1991, 145: 381–390
Lau S L, Cheung Y K. Amplitude incremental variational principle for nonlinear vibration of elastic systems. ASME J Appl Mech, 1981, 48: 959–964
Liang F, Yang X D, Wen B C. Parametric resonances of clampedclamped pipes conveying fluid by incremental harmonic balance method (in Chinese). J Mech Eng, 2009, 45: 126–130
Yan Z T, Zhang H F, Li Z L. Galloping analysis of iced transmission lines based on incremental harmonic balance method (in Chinese). J Vib Eng, 2012, 25: 161–166
Raghothama A, Narayanan S. Bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method. J Sound Vib, 1999, 226: 469–492
Yang S P, Shen Y J, Liu X D. Nonlinear dynamics of gear system based on incremental harmonic balance method (in Chinese). J Vib Shock, 2005, 24: 40–42
Wang W, Song Y L, Li G X. Nonlinear dynamics of automobile steering using incremental harmonic balance method (in Chinese). J Vib Eng, 2010, 23: 355–360
Zhang J, Liu R Q, Guo H W, et al. Nonlinear dynamic characteristics of deployable structures with joints and cables based on incremental harmonic balance method (in Chinese). J Vib Shock, 2014, 33: 4–10
Cameron T M, Griffin J H. An alternating frequency/time domain method for calculating the steady-state response of nonlinear dynamic systems. ASME J Appl Mech, 1989, 56: 149–154
Yamauchi S. The nonlinear vibration of flexible rotors, 1st Report, Development of a new analysis technique. Trans JSME C, 1983, 49: 1862–1868
Kim Y B, Noah S T. Stability and bifurcation analysis of oscillators with piecewise-linear characteristics: A general approach. ASME J Appl Mech, 1991, 58: 545–553
Kim Y B, Noah S T. Response and bifurcation analysis of an MDOF rotor system with a strong nonlinearity. Nonlinear Dyn, 1991, 2: 215–234
Kim Y B, Noah S T. Quasi-periodic response and stability analysis for a non-linear Jeffcott rotor. J Sound Vib, 1996, 190: 239–253
Groll G V, Ewins D J. The harmonic balance method with arc-length continuation in rotor/stator contact problems. J Sound Vib, 2001, 241: 223–233
Tiwari M, Gupta K. Effect of radial internal clearance of a ball bearing on the dynamics of a balanced horizontal rotor. J Sound Vib, 2000, 238: 723–756
Villa C, Sinou J J, Thouverez F. Stability and vibration analysis of a complex flexible rotor bearing system. Commun Nonlinear Sci Numer Simulat, 2008, 13: 804–821
Zhang Z Y, Chen Y S, Li Z G. Influencing factors of the dynamic hysteresis in varying compliance vibrations of a ball bearing. Sci China Tech Sci, 2015, 58: 775–782
Zhang Z Y, Chen Y S, Cao Q J. Bifurcations and hysteresis of varying compliance vibrations in the primary parametric resonance for a ball bearing. J Sound Vib, 2015, 350: 171–184
Han J. Study on kinematic mechanism of misalignment fault of rotor system connected by gear coupling (in Chinese). J Vib Eng, 2004, 17: 416–420
Harsha S P, Sandeep K, Prakash R. Nonlinear dynamic response of a rotor bearing system due to surface waviness. Nonlinear Dyn, 2004, 37: 91–114
Saito S. Calculation of nonlinear unbalance response of horizontal Jeffcott rotors supported by ball bearings with radial clearances. ASME J Vib Acoust, 1985, 107: 416–420
Shen J H, Lin K C, Chen S H, et al. Bifurcation and route-to-chaos analyses for Mathieu-Duffing oscillator by the incremental harmonic balance method. Nonlinear Dyn, 2008, 52: 403–414
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, H., Chen, Y., Hou, L. et al. Periodic response analysis of a misaligned rotor system by harmonic balance method with alternating frequency/time domain technique. Sci. China Technol. Sci. 59, 1717–1729 (2016). https://doi.org/10.1007/s11431-016-6101-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11431-016-6101-7