Modeling unbalanced rotor system with continuous viscoelastic shaft by frequency-dependent shape function

Abstract

A reduced-order dynamic model for an unbalanced rotor system is developed, taking the coupling between torsional and lateral vibrations into account. It is assumed that a shaft is regarded as a continuous viscoelastic shaft with unbalanced and small deformation properties. The equations of motion for the torsional and lateral vibrations are derived using Lagrange’s approach with the frequency-dependent shape function. The rotor torsional vibration is coupled with the lateral vibrations by unbalance elements in a way of excitations. Simulation and experiment results show clearly that the torsional vibration has strong impact on the rotor lateral vibrations, and it causes subharmonic and superharmonic excitations through unbalance elements, which leads to the superharmonic resonances in the lateral vibrations. This model with low-order and high accuracy is suitable for rotor dynamic analysis in real time simulation as well as for active vibration control syntheses.

Keywords

rotor dynamics / distributed unbalance rotor / shape function / torsional and lateral vibrations coupling

References

[1] RuhlR L, BookerJ F. A finite element modell for distributed parameter turborotor systems, transactions of ASME [J]. Journal of Engineering for Industry, 1972, 94: 126-132

[2] GuoR, JangS-h, ChoiY-hyu. Torsional vibration analysis of lathe spindle system with unbalanced workpiece [J]. Journal of Central South University of Technology, 2011, 18(1): 171-176

[3] ChenR-l, ZengQ-y, ZhangJ-yan. New algorithm applied to vibration equations of time-varying system [J]. Journal of Central South University of Technology, 2008, 15(S1): 57-60

[4] YuanZ-w, ChuF-l, LinY-li. External and internal coupling effects of rotor’s bending and torsional vibrations under unbalances [J]. Journal of Sound and Vibration, 2007, 299(1/2): 339-347

[5] HuangD G. Characteristics of torsional vibrations of a shaft with unbalance [J]. Journal of Sound and Vibration, 2007, 308(3/4/5): 692-698

[6] PatelT H, DarpeA K. Experimental investigations on vibration response of misaligned rotors [J]. Mechanical Systems and Signal Processing, 2009, 23(7): 2236-2252

[7] GuyanR J. Reduction of Stiffness and Mass Matrices [J]. AIAA Journal, 1965, 3(2): 380

[8] ShiauT N, HwangJ L. A new approach to the dynamic characteristic of undamped rotor-bearing systems [J]. ASME Transactions, Journal of Vibration, Acoustics, Stress and Reliability in Design, 1989, 111: 379-385

[9] AlthausJ. An active hydraulic bearing for rotor system [C]. Proceedings Reviews VDI Duesseldorf: VDI-Publish, 1991154

[10] NelsonW J, ChenH D. Undamped critical speeds of rotor systems using assumed modes [J]. ASME Transactions, Journal of Vibration and Acoustics, 1993, 115: 367-369

[11] LiW, EngeH. Investigation on a suitable reduced-order rotor system model for active vibration control [C]. Synergies between Information Processing and Automation, Technische Universitaet Ilmenau, 200455-61

[12] LiW, MaisserP, EngeH. Self-learning control applied to vibration control of a rotating spindle by piezopusher bearings [J]. Proceedings of the I MECH E Part I: Journal of Systems and Control, 2004, 218(3): 185-196

[13] Al-bedoorB. Modeling the coupled torsional and lateral vibrations of unbalanced rotors [J]. Computer Methods in Applied Mechanics and Engineering, 2001, 190(45): 5999-6008

[14] MaisserP. Analytical dynamics of multibody system [J]. ZAMM, 1988, 68(10): 463-481

[15] RitzW. Theory of transverse vibrations [J]. Annals of Physics, 1909, 333(4): 737-786

[16] BremerHDynamic and control of mechanical system [M], 1988StuttgartTeubner Study Book

[17] OrtegaRPassivity-based control of Euler-Lagrange systems: Mechanical, electrical and electromechanical applications [M], 1998BerlinSpringer

[18] BremerH. Kinetic rigid-elastic multi-body system [C]. Proceedings Reviews VDI, 1983DuesseldorfVDI-Publish53