Active Magnetic Bearing Rotor Model Updating Using Resonance and MAC Error

Modern control techniques can improve the performance and robustness of a rotor active magnetic bearing (AMB) system. Since those control methods usually rely on system models, it is important to obtain a precise rotor AMB analytical model. However, the interference fits and shrink effects of rotor AMB cause inaccuracy to the final system model. In this paper, an experiment based model updating method is proposed to improve the accuracy of the finite element (FE) model used in a rotor AMB system. Modelling error is minimized by applying a numerical optimization Nelder-Mead simplex algorithm to properly adjust FE model parameters. Both the error resonance frequencies and modal assurance criterion (MAC) values are minimized simultaneously to account for the rotor natural frequencies as well as for the mode shapes. Verification of the updated rotor model is performed by comparing the experimental and analytical frequency response. The close agreements demonstrate the effectiveness of the proposed model updating methodology.

[1]  John E. Mottershead,et al.  Finite Element Model Updating in Structural Dynamics , 1995 .

[2]  Nuno M. M. Maia,et al.  Modal analysis identification techniques , 2001, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[3]  Boris A. Zárate,et al.  Finite element model updating: Multiple alternatives , 2008 .

[4]  John Yen,et al.  A hybrid approach to modeling metabolic systems using a genetic algorithm and simplex method , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[5]  John E. Mottershead,et al.  Model Updating In Structural Dynamics: A Survey , 1993 .

[6]  J. K. Dutt,et al.  Model updating of rotors supported on journal bearings , 2014 .

[7]  Randall J. Allemang,et al.  THE MODAL ASSURANCE CRITERION–TWENTY YEARS OF USE AND ABUSE , 2003 .

[8]  Panagiotis Tsiotras,et al.  A combined application of H/sub /spl infin// loop shaping and /spl mu/-synthesis to control high-speed flywheels , 2005, IEEE Transactions on Control Systems Technology.

[9]  Alexander H. Pesch,et al.  Rotor Model Updating and Validation for an Active Magnetic Bearing Based High-Speed Machining Spindle , 2012 .

[10]  Zongli Lin,et al.  Control of a flexible rotor active magnetic bearing test rig: a characteristic model based all-coefficient adaptive control approach , 2014 .

[11]  Miroslav Pástor,et al.  Modal Assurance Criterion , 2012 .

[12]  Garnett C. Horner,et al.  The Riccati Transfer Matrix Method , 1978 .

[13]  G. Schweitzer,et al.  Magnetic bearings : theory, design, and application to rotating machinery , 2009 .

[14]  Alex Berman,et al.  Theory of Incomplete Models of Dynamic Structures , 1971 .

[15]  HighWire Press Philosophical Transactions of the Royal Society of London , 1781, The London Medical Journal.

[16]  S. Dasgupta Computation of Rayleigh Damping Coefficients for Large Systems , 2003 .

[17]  John M. Vance,et al.  Machinery Vibration and Rotordynamics , 2010 .

[18]  Jeffrey C. Lagarias,et al.  Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions , 1998, SIAM J. Optim..

[19]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[20]  Zongli Lin,et al.  Modeling of a High Speed Rotor Test Rig With Active Magnetic Bearings , 2006 .