MEASURED FORCE/CURRENT RELATIONS IN SOLID MAGNETIC THRUST BEARINGS

Transcription

1 THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 343 E. 47th St., New York, N.Y The Society shall not be responsible for statements or opinions advanced in papers or discussion at meetings of the Society or Of ita Divisions or Sections, or printed In Its publications. Discussion is printed only it the paper Is published In an ASME Journal. Authorization to photocopy material for Internal or personal use under circumstance not falling within the fair use provisions of the Copyright Act is granted by ASME to libraries and other users registered with the Copyright Clearance Center (CCC) Transactional Reporting Service provided that the base fee of S0.30 per page Is paid directly to the CCC, 27 Congress Street Salem MA Requests for special permission or bulk reproduction should be erased to the ASME Technical Rd:fishing Department Copyright C 1995 by ASME All Rights Reserved Printed In U.S.A. 956T-400 MEASURED FORCE/CURRENT RELATIONS IN SOLID MAGNETIC THRUST BEARINGS P.E. Allaire R.L. Fittro E.H. Maslen Mechanical, Aerospace and Nuclear Engineering Department University of Virginia, Charlottesville, Virginia W.C. Wakefield Proctor & Gamble Hunt Valley, Maryland III I MILO ME Th ABSTRACT When magnetic bearings are employed in a pump, compressor, turbine or other rotating machine, measurement of the current in the bearing coils provides knowledge of the forces imposed on the bearings. This can be a significant indicator of machine problems. Additionally, magnetic bearings can be utilized as a load cell for measuring impeller forces in test rigs. The forces supported by magnetic bearings are directly related to the currents, air gaps and other parameters in the bearings. This paper discusses the current/force relation for magnetic thrust bearings. Force vs. current measurements were made on a particular magnetic bearing in a test rig as the bearing coil currents were cycled at various time rates of change. The quasi-static force vs. current relations were measured for a variety of air gaps and currents. The thrust bearing exhibits a hysteresis effect which creates a significant difference between the measured force when the current is increasing as compared to that when the current is decreasing. For design current loops, 0.95 A to 2.55 A, at the time rate of change of 0.1 A/sec, the difference between increasing and decreasing current curves due to hysteresis ranged from 4% to 8%. If the bearing is operated in small trajectories about a fixed (non-zero) operation point on the F/I (force/current) curve, the scatter in the measurement error could be expected to be on the order of 4 percent. A quasi-static non-linear current/force equation was developed to model the data and curve fit parameters established for the measured data. The effect of coercive force and iron reluctance, obtained from conventional magnetic materials tests, were included to improve the model but theoretically calculated values from simple magnetic circuit theory do not produce accurate results. Magnetic fringing, leakage and other effects must be included. A sinusoidal perturbation current was also imposed on the thrust bearing. Force/current magnitude and phase angle values vs. frequency were obtained for the bearing. The magnitude was relatively constant up to 2 Hz but then decreased with frequency. The phase lag was determined to increase with frequency with value of 16 degrees at 40 Hz. This effect is due to eddy currents which are induced in the solid thrust bearing components. NOMENCLATURE Symbol _s_g Mea lin A, Pole Cross Sectional Area (One Pole) b, Hysteresis Offset b, Equivalent Iron Gap Offset Magnetic Flux Density Bearing Inner Diameter Coil Inner Diameter Coil Outer Diameter Bearing Outer Diameter Force Nominal Force Air Gap (One) Nominal Air Gap Coercive Force (Field Intensity) Current Effective Current Nominal Current Total Axial Stator Length - + L, Thrust Collar Length Length of Magnetic Path in hem Number of Turns Air Gap Reluctance - 2,/(ti oad Iron Reluctance a L,A1) Force Proportionality Constant Permeability of Free Space Relative Permeability Presented at the International Gas Turbine and Aeroengine Congress Re Exposition Houston, Texas - June 54, 1995 This paper has been accepted for publication in the Transactions of the ASME Discussion of it will be accepted at ASME Headquarters until September 30, 1995

2 INTRODUCTION Magnetic bearings have been used in supporting shaft forces in compressors, pumps, turbines and other rotating machines. Normally a magnetic thrust bearing is employed to provide an axial load capacity in a rotating machine [Allaire, 1989 a,b]. 1 shows the geometry of a magnetic thrust bearing. Proper design of the bearing requires detailed knowledge of the force which results when a current is applied. Simple magnetic circuit analysis is often employed for preliminary thrust bearing design [Allaire, 1994a]. This paper discusses measurements of the current/force relation in a magnetic thrust bearing and an extension of simple circuit analysis to account for other effects. In recent years, magnetic bearings have begun to be used for the measurement of forces as well, including load cells in impeller test rigs, excitation for system identification and monitoring. The use of a magnetic bearing as an excitation force has been described by Ulbrich [1988]. Wagner and Pietruszlca [1988] developed a magnetic bearing to be used for the measurement of fluid forces in turbocompressor applications. Imlach et al. [1991] described the use of magnetic bearings to measure force, stiffness and damping in a canned motor pump. Hawkins et al. [1991] have also employed magnetic bearings as a known force input device for the identification of rotor dynamic coefficients in a test stand. Humphris [1992] described the use of magnetic bearings as a diagnostic tool for rotating shafts. Feng et al. [1982] and Verhoeven et at [1993] employed magnetic bearings in two test rigs for the identification of long seals and impeller/casing interactions. Hawkins and Imlach [1993] described an experimental method for the measurement of the freqnenry dependent force displacement transfer function of a magnetic bearing/controller system. Test rigs have been developed for measuring thrust and radial forces by several investigators. A review of journal articles related to pump impeller forces up to 1984 is given in Flack and Allaire [1984]. Several works have appeared in the literature since that time. An example is Jery et al. [1985] reporting on a strain gage based test rig. Rigs of this type require very careful construction to minimize structural interactions which contribute to uncertainties in the measurements. Testing has also been limited to impellers with relatively large clearances compared to industrial practice. The current/force relation is an important topic for magnetic bearings. However, there have been few studies reported on accurately determining the characteristics of this relation for specific magnetic bearing configurations and comparing this to a theoretical model. Some preliminary results on this topic were reported in Allaire [1994b]. Many effects such as nonlinearities, eddy currents, hysteresis, fringing, leakage, and frequency effects are not included in these simple models. Hysteresis and eddy current effects are important in magnetic bearing characterization. The B-H curve of any magnetic material exhibits hysteresis which affects the current/force relation. A hysteresis curve for a typical magnetic material is shown in Fig. 2. The increasing H values follow a different curve than the decreasing H values. The area between the curves represents the energy loss during the cycle. Eddy current effects also degrade magnetic bearing performance [Zmood, 1987]. Williams and Trumper [1993] have investigated material/air gap hysteresis effects in a laminated stack similar to 16 FIGURE 1. SIDE VIEW OF THRUST BEARINGS H magnetron: &Id (amp tunes fee) FIGURE 2. B-H CURVE FOR TYPICAL MAGNETIC MATERIAL a radial bearing. Keith [1993] conducted an extensive study of eddy current and hysteresis effects on current/force relations in a two pole magnetic configuration similar to a magnetic thrust bearing. He found that eddy current effects in solid pole pieces, with a 0.51 mm (10 mils) gap, dominated the current/force relation as the frequency increased above approximately 2 Hz. Keith noted that this produces a significant phases n in the actuator. Knowledge of the phase lag found in the thrust bearing affects the feedback control loop design. If a magnetic thrust bearing is perfectly axisymmetric and the coil currents are held constant, there will be no eddy current Downloaded From: on 11/15/2018 Terms 2 of Use:

3 effects present. However, thrust bearings in industrial use are subject to time varying forces. The coil currents are changed to adjust the bearing load capacity in response to the applied load [Allaire, 1994c1. These time varying currents generate hysteresis and eddy current effects in thrust bearings. In turn, these induced eddy reins produce induced magnetic fields opposing the applied magnetic field These effects were studied in the magnetic thrust bearing described here. Both of these phenomena are crucial to accurate modeling of the current/force relation in force test rigs and operating industrial beatings. THRUST TEST RIG The magnetic thrust bearing geometry is shown in Fig. I. The stator is composed of an inner toroid, a base plate, Mita toroid, and a coil of wire. The rotor is simply a flat disk fixed to the shaft (also called a thrust disk or thrust runner). The magnetic thrust bearing had an outer diameter of D, 89.5 mm (3.50 in), D mm (3.09 in), D mm (2.40 in), inner diameter of D, mm (1.75 in), axial lengths of L 26.4 mm (1.04 in) and L mm (0.28 in). The thrust collar (runner) had axial length L, mm (0.56 in). It was designed for a thrust load of F N(42 lbf). The coils consisted of 300 turns of 822 wire secured in the bearing by a thin stainless steel retainer (slotted to avoid eddy currents in the retainer). The operating current (design bias current) was lo A within the operating range of 0.95 A to 2.55 A. The nominal operating air gap of the bearing WM go mm (0.030 in). The coercive force and relative permeability of the magnetic material have been measured independently via a Rowland ring test as 5.15 Ge (410 A/m) and 1376, respectively. All magnetic components were constructed of conventional solid soft iron material rather than laminated. The stator may be solid or divided into sectors to reduce eddy currents. This work considers only solid thrust bearing components. A load cell was attached to the moveable crosshead (on an Instron Universal Testing Machine) and the thrust bearing fixed to the base of the machine. Figure 3 shows a drawing of the test set up. Calibration of the testing apparatus was accomplished by hanging!mown weights from the collar holder and measuring the force. Great care, using cbims around the circumference of the bearing, was taken to ensure that the thrust collar and bearing were parallel. CURRENT CYCLE - QUASI-STATIC RESULTS Measurements of current/force relations were made for a wide range of air gaps and currents [Wakefield, At low frequencies, the predominant effect is due to hysteresis. Current cycles were run at a quasi-static rate of 0.1 A/sec and at lower current rates. All of the results within a certain range gave essentially the same results indicating that only hysteresis effects were being measured. The results presented in this paper are for two current loop tests. Fig. 4 shows force/current values for an air gap of mm (30 mils) and a major current loop from A to 235 A. For the same air gap, results for a minor loop of 0.95 A to 2.55 A (the 'design range for this bearing) are given in Figure 5. Before testing, a de-gaussing procedure was followed to bring the curve to remove any residual magnetism effects in the material. TMZUST DISK CLAMP LOZKOW IP/SIREN MACHIN( CROSSMCAD LOAD ISIS I I LOAD CELL ADAPTER THRUST DISK [1 Ii SAW PLATE waust SEARING FIGURE 3. DRAWING OF THRUST BEARING TEST SETUP The shape of each force/current plot was the same for increasing and decreasing currents. For comparison purposes, the force was evaluated at the design bias current value of 1.75 A as the perturbation current was increasing and decreasing. The difference between the two curves was as high as 12.6% for major current loops such as the one shown in Fig. 4 but reduced to 4.7% for minor loops more likely to be encountered in actual use as illustrated in Fig. 5. The repeatability of the curves was very high, indicating that the loop effect at this low cycle rate was due to hysteresis rather than eddy currents. QUASI-STATIC CURRENT/FORCE MODEL Magnetic bearings, when operated single sided as in this case, are nonlinear. The force is related to the square of the coil currents [Allaire, When the bearing is double acting, the net effect is to linearize the actuator so that the force-current relation is approximately linear. A typical equation for the flux density B in the magnetic circuit is given by B- N I (1) 2A I R I where it is assumed that all of the flux is contained in the two air gaps and there is no hysteresis. Then the force F which attracts the rotor in a single sided stator is given by = B 2 A8 - N212A Po 4/ This simple formula is inadequate to model the effects seen in the experimental data just presented. Two primary effects must be included in the quasi-static equation above: iron reluctance and iron hysteresis effects. The iron reluctance effect R I can be included in the denominator of the flux equation, summed with the air gap reluctance, and the iron hysteresis effect can be modeled as an effective current I. (2)

4 ( 4 ) where L. is the effective magnetic gap length. For this bearing, I, = mm ( in) and A. This corresponds to the current required to return the magnetic flux density B to zero. If the material bas the magnetic field intensity H decreased gradually in an oscillating fashion, the B-H curve will return to the origin of the B-H plot. However, magnetic bearings are typically operated so that the material has a coercive force present as shown by the measurements. In this case, the flux equation must be modified to include the corresponding effective current. The force equation (2) was modified to include the additional terms with the result FIGURE 4. MEASURED FORCE VS. CURRENT WITH AIR GAP MM (0.030 IN), CURRENT A TO 2.55 A F (1,g) - N2 (/ + 4 )2 Al 4 k + L. )2 ( 5 ) This is the general form employed in this paper. Normally there is an operating point for a thrust bearing about a nominal value for current l e, and gap go. Let the nominal force be that due to the air gap reluctance only with the result so - Ar2 42 A g 2 4 go (6) Camera (Amps) FIGURE 5. MEASURED FORCE VS. CURRENT WITH AIR GAP MM (0.030 IN), CURRENT 0.95 A TO 2.15 A B- + 1 ) A, (212, + 12) 2.4 For the bearing tested in this work, a 1.75 A, g o mm (30 mils) and Fo N (45.8 lb). It is appropriate to employ a dimensionless form of the force equation. Defme the dimensionless force as: (7,i) - (7 lir _ 0) Li ) 2 2 is, go ( 3 ) ( + (7) For this bearing, the air gap length is mm (0.030 in), the air gap area is 1,368 mm 2 (112 in') and the air gap reluctance is 12 1 = 4.43x102 A-tums/weber for one air gap. In the iron, the iron path length is 83.8 mm (3.3 in), the same area, and the reluctance of R= 3.5x1 A-tums/weber. As the magnetic field H decreases in the magnetic material, there will be a coercive force He remaining when zero magnetic flux density is reached. This may be represented as an effective current I. where where 7 _J 4 ' go This suggests the generic form of the quasi-static current/force relation employed in this paper to fit the measured data for the tested single sided magnetic thrust bearing: 4

5 ,te (7, y ( g b2 ) (0) where b, - IJ1 and b 2 - L,/(2)1,g0). The primary variables are the current and air gap length. Here y is a dimensionless constant of proportionality, b, represents an offset in the B-H curve for the magnetic material due to hysteresis effects, and b 2 represents the ratio of equivalent magnetic length to the nominal air PP. A least squares curve fat of the data from the thrust bearing measurements produced the following values for the current/force equation: bearing coil. The induced flux in the stator opposes the applied flux to reduce the generated magnetic bearing load capacity. The resulting frequency response effects can cause a magnetic bearing performance to deviate significantly from expected values. Eddy current effects were explored by cycling the coil current through the design range of 0.95 A to 2.55 A at various frequencies. Figure 7 shows the force/current plots for 0.1, 1.0 and 10.0 Hz with an air gap of mm (30 mils). The difference in the loop segments becomes larger as the frequency increases. This is due to higher eddy current effects as the time rate of change of the electric field increases. y = = ( 9 ) = Figure 6 shows a comparison of the curve fit with one of the measured current loops. The zero point indicates the equivalent coercive current L. The theoretical value for b, using the value of A found earlier gives b, rather than the value given above. This is an error of 98%. Similarly for the theoretically calculated term b, and the error here is 88%. The errors are due to magnetic fringing, leakage and other factors not completely obvious to the authors at this point in time. Many data nms were employed to develop the curve fit. In each case, only measurements with the design current range, 0.95 A to 2.55 A, were used, with the current changing at 0.1 Anec. Equal numbers of increasing and decreasing current data were avenged to produce the numerical values in Eq. (9). A statistical error analysis was also conducted. The distribution of error was noticeably bimodal with a mean of 0.3 percent and a standard deviation of 3.8 percent The bimodal distribution suggests the superposition of two normal distributions with differing mean values. The experimental data was taken for force/current trajectories essentially on the same hysteresis loop front 0.95 A to 2.55 A. The separation between the two halves of the hysteresis loops, one with increasing current and the other with decreasing current, is believed to have induced the bimodal distribution. UNCERTAINTY ANALYSIS An uncertainty analysis was conducted to determine the extent to which uncertainty in the calibration data produces uncertainty in the calibration parameters (y, b,, b 2) and the extent to which this model uncertainty, coupled with the measurement uncertainty during the execution of the actual experiment, will lead to uncertainty in the measured forces. This analysis resulted in an expected mean error of zero and a standard deviation of 3.96 percent. This result is consistent with the observed distribution, implying that the only major (non-random) source of error in the measurements is due to hysteresis. FREQUENCY EFFECTS Eddy currents develop due to time varying currents in the SO COMM 6.439P9) 23 FIGURE 6. LEAST SQUARES CURVE FIT AND TYPICAL MEASURED CURRENT CYCLE The ratio of force to current was evaluated for" a range of frequencies. The current value vs. frequency was generated by comparison of the measured current signal to a sinusoidal reference. A similar method was used for the force value. A ratio of these values was then taken. The magnitude is plotted in Fig. 8 and the phase angle is plotted in Fig. 9. The magnitude is relatively constant over the frequency range up to 2 Hz but drops off approximately 28% at 40 Hz. Binns et al. [1985] reports a similar 10 db/decade roll off for eddy currents in other configurations. The phase angle approximately follows a one-half power function with frequency. It drops off to approximately 16 degrees at 40 Hz. A least squares curve fit to the phase angle data gives the results ck = ca'a (10) as shown in Fig. 9. This phase lag vs. frequency trend is consistent with eddy current effects in other applications [Binns et al., A linear model was also curve fit to the data as illustrated in Fig. 9 but the fit is not very good. This decreased force/current magnitude and phase lag vs. frequency is due primarily to tangential eddy currents developed in the solid thrust bearing stator. The induced flux in the stator opposes the applied flux to reduce the generated magnetic bearing load capacity. 5

6 SO - 10 OS 1.0 IS cures( (Amps) FIGURE 7. MEASURED FORCE VS. SINUSOIDAL CURRENT AT 0.1, 1.0, 10 HZ WITH AIR GAP MM (0.030 IN) CURRENT 0.95 A TO 2.55 A 5. -as Frequency (Hz) FIGURE 8. MAGNITUDE OF FORCE/CURRENT RATIO VS. FREQUENCY FIGURE 9. PHASE ANGLE OF FORCE/CURRENT RATIO VS. FREQUENCY WITH LINEAR AND HALF FREQUENCY CURVE FITS lo The pump test rig in which these bearings will be employed runs at approximately 10 Hz with a blade pass frequency of approximately 40 Hz. Overall, the large drop off of phase angle at the running frequency and blade pass frequency makes this particular bearing not a particularly good choice for the purpose of measuring forces. An alternative bearing employing a less lossy material is currently under testing. CONCLUSIONS Numerous papers, noted in the introduction, either propose or have reported the use of magnetic bearings to determine external forces in a rotating machine or component. However, not much has been reported in the literature on verifying the theoretical equations apparently employed to extract the data. The deviations from the simple force/current relations normally quoted for magnetic thrust bearing load capacity must be taken into account when using magnetic bearings as load cells. However, testing can be carried out to quantify hysteresis and eddy current effects. Knowledge of these effects allows for the redesign of magnetic bearings to reduce uncertainties. A specific solid magnetic thrust bearing was constructed and tested. The quasi-static current vs. force relations were measured for a variety of currents and air gaps. A relatively accurate overall quasi-static force/current relation was developed which modeled the bimodal error distribution with a standard deviation of approximately 4%. It is important to discuss the significance of the bimodal nature of the error in regard to measurement of forces in rotating machines through measurement of the magnetic bearing currents. If the bearing is operated in small trajectories about a fixed, non-zero operation point on the current/force curve, the scatter in the error could be expected to be on the order of 4% but the error may not have zero mean. Further, the actual mean error will depend upon the specific current/force trajectory used to reach the operating point. A nonlinear model of the current/force relation was developed for quasi-static changes. Conventional magnetic property tests were conducted to measure the coercive force and relative permeability. Simple magnetic circuit theory was employed to determine the parameters in the nonlinear =rent/force relation but the results differed from the experimentally measured parameters by large percentages. It is apparent that magnetic fringing, leakage and other effects must be included for an accurate theoretical model. A sinusoidally varying current was also imposed upon the thrust bearing. As the frequency increases, eddy currents are introduced into the solid thrust bearing components producing significant phase lag. This bearing demonstrated poor frequency response results in the operating frequency range of its design. No model of the eddy currents has been developed yet. For more accurate measurement of thrust bearing forces, eddy current effects must be reduced as much as possible. Alternatives include selection of less lossy materials and segmentation of stator components of the thrust bearing. ACKNOWLEDGEMENT This work was partially supported by a grant from NASA Lewis Research Center with Dr. Gerald Brown as project supervisor. Downloaded From: on 11/15/2018 Terms 6 of Use:

7 REFERENCES Allake, P. E., 1989a, 'Design and Test of a Magnetic Thrust Bearing,' Journal of the Franklin Institute, Vol. 326, No. 6, December. Albin, P., lmlach, J., McDonald, J., Htmtphris, R., Lewis, D., Blair, B., Claydon, J., and Flack R., 1989, 'Design, Construction, and Test of a Magnetic Bearing in an Industrial Canned Motor Pump," Proceedings of Texas A&M Pump Symposium, Houston, TX, May. Allaire, P. E., Maslen, E. H., Humphris, R. R., Knospe, C. R., and Lewis, D. W., 1994a, "Magnetic Bearings," Handbook of Lubrication and Tribology, Vol. III, CRC Press, pp Allaire, P. E., Fittro, R. L, Maslen, E. H., and Wakefield, W. C., I994b, "Current/Force Relations in Solid Magnetic Bearings," Proceedings of REVOLVE '94, Calgary, Alberta, June 7-9. Allaire, P. E., Maslen, E. H., Lewis, D. W., and Flack, R. D., 1994c, 'Magnetic Thrust Bearing Operation and Industrial Pump Application," Presented at ASME Turbo Expo '94- Land, Sea & Air Conference, The Hague, Jtme 13-16, accepted for publication in Trans. ASME. Binns, K. J., Lawrenson, P. J., and Trowbridge, C. W., 1985, The Analytical and Numerical Solution of Electric and Magnetic Fields, Wiley, New York. Feng, T. Neumer, T., Nordman, R., Verhceven, J., and De Vis, D., 1992, "Identification of Fluid/Structure Interactions in Centrifugal Pumps,' Fifth International Conference on Vibrations in Rotating Machinery, Bath, England, 7-10 September. Flack, R. D., and Albite, P. E., 1984, 'Lateral Forces on Pump Impellers: A Literature Review," Shock and Vibration Digest, Vol. 16, No. 1, January, pp Hawkins, L. A., Murphy, B. T., Lang, K. W., 1991, "The Rocketdyne Multifimetion Tester Operation of a Radial Magnetic Bearing as an Excitation Source," Proceedings of ROMAG '91, Magnetic Bearings and Dry Gas Seals International Conference, University of Virginia, March 13-15, pp Hawkins, L. A., and Imlach, J., 1993, "Development of Experimental Method for Measurement of Magnetic Bearing Transfer Function Characteristics, Proceedings of MAO '93, Magnetic Bearings, Magnetic Drives, and Dry Gas Seals Conference & Exhibition, July, Technomics Publishing Co., pp Humphris, R. R., 1992, "A Device for Generating Diagnostic Information for Rotating Machinery,' Proceedings of MAG 92, Magnetic Bearings, Magnetic Drives, and Dry Gas Seals Conference & Exhibition, July, Technomics Publishing Co., pp Imlach, J., Blair, B. J., and Allaire, P. E, 1991, "Measured and Predicted Force and Stiffness Characteristics of Industrial Magnetic Bearings," Journal of Tribology, Trans. ASME, Vol. 113, Oct, pp Jery, B., Brennan, C. E., Caughey, T. E. and Acosta, A. J., 1985, "Forces in Centrifugal Pump Impellers; Proceedings of Second International Pump Symposium, Texas A&M University, pp Keith, F. J., 1993, implicit Flux Feedback Control for Magnetic Bearings, Ph.D. Thesis, University of Virginia, June. Lashley, C. M., Ries, D. M., Zmood, R. B., Kirk, J. A., and Anand, D. K., 1989, "Dynamics Considerations for a Magnetically Suspended Flywheel," Proceedings of 24th IECEC. Ulbrich, H, 1988, "New Test Techniques Using Magnetic Bearings,' Proceedings of First International Conference on Magnetic Bearings,' June, Springer-Verbg, pp Verhoeven, J. J., De Via, D., and Nordman, R., 1993, "Development and Operating Experience of a 5000 KW Test Boilerfeed Pump on Active Magnetic Bearings," Proceedings of Mechanical Engineers, C439/004. Wagner, N. G., and Pietruszlca, W. D., 1988, "Identification of Rotor Dynamic Parameters on a Test Stand with Active Magnetic Bearings,' Proceedings of First International Conference on Magnetic Bearings," lime, Springer-Verlag, pp Wakefield, W. C., 1994, 'Magnetic Bearings/Load Cells For a Centrifugal Pump: Design Construction and Testing," M. S. Thesis, University of Virginia. Williams, M. E., and Trumper, D. L., 1993, 'Materials for Efficient High-Flux Magnetic Bearing Actuators," NASA Conference on Magnetic Suspension, Seattle, WA, August. Zmood, R. B., Anand, D. K., Kirk, J. A., 1987, 'The Influence of Eddy Currents on Magnetic Actuator Performance," Proceedings of IEEE, Vol. 75, No. 2, February. 7