Unbalance in magnetically levitated rotor (MLR) can cause undesirable synchronous vibrations and lead to the saturation of the magnetic actuator. Dynamic balancing is an important way to solve these problems. However, the traditional balancing methods, using rotor displacement to estimate a rotor’s unbalance, requiring several trial-runs, are neither precise nor efficient. This paper presents a new balancing method for an MLR without trial weights. In this method, the rotor is forced to rotate around its geometric axis. The coil currents of magnetic bearing, rather than rotor displacement, are employed to calculate the correction masses. This method provides two benefits when the MLR’s rotation axis coincides with the geometric axis: one is that unbalanced centrifugal force/torque equals the synchronous magnetic force/torque, and the other is that the magnetic force is proportional to the control current. These make calculation of the correction masses by measuring coil current with only a single start-up precise. An unbalance compensation control (UCC) method, using a general band-pass filter (GPF) to make the MLR spin around its geometric axis is also discussed. Experimental results show that the novel balancing method can remove more than 92.7% of the rotor unbalance and a balancing accuracy of 0.024 g mm kg ？1 is achieved.
References
[1]
Schweitzer, G.; Maslen, E.H. Magnetic Bearing Theory: Design, and Application to Rotating Machinery; Springer: New York, NY, USA, 2009.
[2]
Fang, J.C.; Wen, T. A wide linear range eddy current displacement sensor equipped with dual-coil probe applied in the magnetic suspension flywheel. Sensors 2012, 12, 10694–10706.
[3]
Wowk, V. Machinery Vibration: Balancing; McGraw-Hill: New York, NY, USA, 1995.
[4]
Pang, D.C. Magnetic Bearing System Design for Enhanced Stability. Ph.D. Thesis, University of Maryland, Baltimore, MD, USA, 1994.
[5]
Li, G.X.; Lin, Z.L.; Allaire, P.E. Robust optimal balancing of high-speed machinery using convex optimization. J. Vib. Acoust. 2008, 130, 031008:1–031008:11.
[6]
Jugo, J.; Lizarraga, I.; Arredondo, I. Nonlinear modelling and analysis of active magnetic bearing systems in the harmonic domain: A case study. IET Control Theory Aplica. 2008, 21, 61–71.
[7]
Habermann, H.; Maurice, B. The Active Magnetic Bearing Enables Optimum Damping of Flexible Rotors. Proceedings of 1984 ASME International Gas Turbine Conference, Amsterdam, NL, USA, 4–7 June 1984.
[8]
Herzog, R.; Buhler, P.; Ghler, C. Unbalance compensation using generalized notch filters in the multivariable feedback of magnetic bearings. IEEE Trans. Contr. Syst. T. 1996, 45, 580–586.
[9]
Shi, J.; Zmood, R.; Qin, L. Synchronous disturbance attenuation in magnetic bearing systems using adaptive compensating signals. Control Eng. Pract. 2004, 12, 283–290.
[10]
Li, L.; Shinshi, T.; Lijima, C. Compensation of rotor imbalance for precision rotation of a planar magnetic bearing rotor. Precis. Eng. 2003, 27, 140–150.
[11]
Tang, J.Q.; Liu, B.; Fang, J.C.; Ge, S.Z. Suppression of vibration caused by residual unbalance of rotor for magnetically suspended flywheel. J. Vib. Control. 2012. org/10.1016/j.jvc.
[12]
Sekhar, A.S.; Sarangi, D. On-line Balancing of Rotors. Proceedings of the 11th National Conference on Machines and Mechanisms, Delhi, India, 18–19 December 2003; pp. 437–443.
[13]
Everett, L.J. Optimal two-plane balance of rigid rotors. J. Sound Vib. 1997, 208, 656–663.
[14]
Garvey, E.J.; Williams, E.J.; Cotter, G.; Davies, C.; Grum, N. Reduction of noise effects for in situ balancing of rotors. J. Vib. Acoust. 2005, 127, 234–246.
Kang, Y.; Liu, C.P.; Sheen, G.J. A modified influence coefficient method for balancing unsymmetrical rotor-bearing systems. J. Sound Vib. 1996, 194, 199–218.
[17]
Yu, J.J. Relationship of influence coefficients between static-couple and multiplane methods on two-plane balancing. J. Eng. Gas Turb. Power 2009, 13, 012508.
[18]
Ling, J.; Cao, Y. Improving traditional balancing methods for high-speed rotors. J. Eng. Gas Turb. Power 1996, 118, 95–99.
[19]
Shafei, A.; Kabbany, A.S.; Younan, A.A. Rotor balancing without trial weights. J. Eng. Gas Turb. Power 2004, 126, 604–609.
[20]
Li, H.W.; Xu, Y.; Gu, H.D.; Zhao, L. Field Dynamic Balance Method Study for the AMB-flexible Rotor System. Proceedings of Transactions of the 19th International Conference on Structural Mechanics in Reactor Technology, Toronto, Canada, 12–17 August 2007.
[21]
Zhang, K.; Zhang, X.Z. Rotor Dynamic Balance Making Use of Adaptive Unbalance Control of Active Magnetic Bearings. Proceedings of 2010 International Conference on Intelligent System Design and Engineering Application, Changsha, China, 13–14 October 2010; pp. 347–350.
[22]
Han, F.J.; Fang, J.C. Field balancing method for rotor system of a magnetic suspending flywheel. ACTA Aeron. Astron. Sinica. 2010, 311, 184–190.
[23]
Lum, K.Y.; Coppla, V.T.; Bernstein, D.S. Adaptive virtual autobalancing for a rigid rotor with unknown mass imbalance supported by magnetic bearings. J. Vib. Acoust. 1998, 120, 557–570.
[24]
Zhou, S.Y.; Shi, J.J. Active balancing and vibration control of rotating machinery: A survey. Shock Vib. Digest. 2001, 334, 361–371.
[25]
Zhou, K.M.; John, C.D. Essentials of Robust Control; Prentice Hall: Upper Saddle River, NJ, USA, 1999.
[26]
Muller, L.; Ernst, R.R. Coherence transfer in the rotating frame: Application to heteronuclear cross-correlation spectroscopy. Mol. Phys. Taylor Fr. 1979, 383, 963–992.
[27]
Federn, K. Multi-plane balancing of elastic rotors: Fundamental theories and practical application; General Electric Technical Information Series. No. 85GL121; General Electric Corporationp: Fairfield, CT, USA, 1968.
[28]
(ISO) International Organization for Standardization 1940–1. Mechanical vibration—Balance quality requirements for rotors in a constant (rigid) state—Part 1: Specification and verification of balance tolerances. 2003.
[29]
Kim, C.S.; Lee, C.W. In situ runout identification in active magnetic bearing system by extended influence coefficient method. IEEE/ASME Trans. Mech. 1997, 21, 51–57.
