A new model of electrodynamic bearings is presented in this paper. The model takes into account the dynamics of the eddy currents on which this type of bearing is based, making it valid for both quasistatic and dynamic analyses. In the quasistatic case, the model is used to obtain the force generated by an off-centered shaft rotating at a fixed speed in a constant magnetic field. The model is then used to analyze the dynamic stability of a Jeffcott rotor supported by electrodynamic bearings. The essential role played by nonrotating damping in ensuring a stable operating range to the rotor is studied by means of root loci. Comparison with literature results is finally used to validate the model.
Issue Section:
Research Papers
1.
Post
, R. F.
, and Ryutov
, D. D.
, 2000, “The Inductrack: A Simpler Approach to Magnetic Levitation
,” IEEE Trans. Appl. Supercond.
1051-8223, 10
, pp. 901
–904
.2.
Thornton
, R. D.
, and Thompson
, M. T.
, 1997, “Magnetically Based Ride Quality Control for an Electrodynamic Maglev Suspension
,” Proceedings of the Fourth International Symposium on Magnetic Suspension Technology
, Gifu City
, Japan
, Oct. 30–Nov. 1, pp. 303
–311
.3.
Basore
, P. A.
, 1980, “Passive Stabilization on Flywheel Magnetic Bearings
,” MS thesis, Massachusetts Institute of Technology, Cambridge, MA.4.
Post
, R. F.
, and Ryutov
, D. D.
, 1998, “Ambient-Temperature Passive Magnetic Bearings: Theory and Design Equations
,” Proceedings of the Sixth International Symposium on Magnetic Bearings
, Massachusetts Institute of Technology
, Cambridge, MA
, Aug. 5–7, pp. 109
–122
.5.
Bender
, D. A.
, and Post
, R. F.
, 2000, “Ambient-Temperature Passive Magnetic Bearings for Flywheel Energy Storage Systems
,” Proceedings of the Seventh International Symposium on Magnetic Bearings
, ETH Zurich
, Switzerland
, Aug. 23–25, pp. 153
–158
.6.
Lembke
, T. A.
, 2003, “Induction Bearings, a Homopolar Concept for High Speed Machines
,” Ph.D. thesis, Royal Institute of Technology, Stockholm, Sweden.7.
Lembke
, T. A.
, 2004, “3D-FEM Analysis of a Low Loss Homopolar Induction Bearing
,” Proceedings of the Ninth International Symposium on Magnetic Bearings
, Lexington, KY
, Aug. 3–6.8.
Murakami
, C.
, and Satoh
, I.
, 2000, “Experiments of a Very Simple Radial-Passive Magnetic Bearing Based on Eddy Currents
,” Proceedings of the Seventh International Symposium on Magnetic Bearings
, ETH Zurich
, Switzerland
, Aug. 23–25, pp. 141
–146
.9.
Filatov
, A.
, and Maslen
, E. H.
, 2001, “Passive Magnetic Bearing for Flywheel Energy Storage Systems
,” IEEE Trans. Magn.
0018-9464, 37
, pp. 3913
–3924
.10.
Filatov
, A.
, 2002, “Null-E Magnetic Bearings
,” Ph.D. thesis, University of Virginia, Charlottesville, VA.11.
Filatov
, A.
, 2006, “Flywheel Energy Storage System With Homopolar Electrodynamic Magnetic Bearing
,” Proceedings of the Tenth International Symposium on Magnetic Bearings
, Martigny, Switzerland
, Aug. 21–23.12.
Moser
, R.
, Regamey
, Y.-J.
, Sandtner
, J.
, and Bleuler
, H.
, 2002, “Passive Diamagnetic Levitation for Flywheels
,” Proceedings of the Eighth International Symposium of Magnetic Bearings
, Mito, Japan
, Aug. 26–28, pp. 599
–603
.13.
Sandtner
, J.
, and Bleuler
, H.
, 2004, “Electrodynamic Passive Magnetic Bearing With Planar Halbach Arrays
,” Proceedings of the Ninth International Symposium on Magnetic Bearings
, Lexington, KY
, Aug. 3–6.14.
Sandtner
, J.
, and Bleuler
, H.
, 2006, “Passive Electrodynamic Magnetic Thrust Bearing Especially Designed for Constant Speed Applications
,” Proceedings of the Tenth International Symposium on Magnetic Bearings
, Martigny, Switzerland
, Aug. 21–23.15.
Sodano
, H. A.
, Bae
, J.-S.
, Inman
, D. J.
, and Belvin
, W. K.
, 2006, “Improved Concept and Model of Eddy Current Damper
,” ASME J. Vibr. Acoust.
0739-3717, 128
, pp. 294
–302
.16.
Nagaya
, K.
, and Kojima
, H.
, 1984, “On a Magnetic Damper Consisting of a Circular Magnetic Flux and a Conductor of Arbitrary Shape. Part I: Derivation of the Damping Coefficients
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 106
, pp. 46
–51
.17.
Nagaya
, K.
, Kojima
, H.
, 1984, “On a Magnetic Damper Consisting of a Circular Magnetic Flux and a Conductor of Arbitrary Shape. Part II: Applications and Numerical Results
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 106
, pp. 52
–55
.18.
Nagaya
, K.
, and Karube
, Y.
, 1989, “A Rotary Magnetic Damper or Brake Consisting of a Number of Sector Magnets and a Circular Conductor
,” ASME J. Dyn. Syst., Meas., Control
0022-0434, 111
, pp. 97
–104
.19.
Graves
, K. E.
, Toncich
, K. E.
, and Ioveniti
, P. G.
, 2000, “Theoretical Comparison of Motional and Transformer emf Device Damping Efficiency
,” J. Sound Vib.
0022-460X, 233
(3
), pp. 441
–453
.20.
Tonoli
, A.
, 2007, “Dynamic Characteristics of Eddy Current Dampers and Couplers
,” J. Sound Vib.
0022-460X, 301
, pp. 576
–591
.21.
Genta
, G.
, Macchi
, P.
, Carabelli
, S.
, Tonoli
, A.
, Silvagni
, M.
, Amati
, N.
, and Visconti
, M.
, 2006, “Semi-Active Electromagnetic Dampers for the Dynamic Control of Rotors
,” Proceedings of the Seventh IFToMM—Conference on Rotordynamics
, Vienna, Austria
, Aug. 23–25, pp. 1
–10
.22.
Tonoli
, A.
, and Amati
, N.
, 2008, “Dynamic Modeling and Experimental Validation of Eddy Current Dampers and Couplers
,” ASME J. Vibr. Acoust.
0739-3717, 130
, pp. 021011
–021011
.23.
Crandall
, S. H.
, Karnopp
, D. C.
, Kurtz
, E. F.
, and Pridmore-Brown
, E. C.
, 1968, Dynamics of Mechanical and Electromechanical Systems
, McGraw-Hill
, New York
.24.
Karnopp
, D.
, 1989, “Permanent Magnets Linear Motors Used as Variable Mechanical Dampers for Vehicle Suspensions
,” Veh. Syst. Dyn.
0042-3114, 18
, pp. 187
–200
.25.
Genta
, G.
, 2005, Dynamics of Rotating Systems
, Springer
, New York
.Copyright © 2008
by American Society of Mechanical Engineers
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