3422 IEEE TRANSACTIONS ON MAGNETICS, VOL. 42, NO. 10, OCTOBER 2006

Optimization of Stator Design in a Consequent-PoleType Bearingless Motor Considering Magnetic

Suspension CharacteristicsMasakazu Nakagawa1, Yoshikazu Asano1, Akira Mizuguchi1, Akira Chiba1, Che Xiao Xuan1, Masahide Ooshima2,

Masatsugu Takemoto3, Tadashi Fukao3, Fellow, IEEE, Osamu Ichikawa4, and David G. Dorrell5

Department of Electrical Engineering, Faculty of Science and Technology, Tokyo University of Science, Chiba 278-8510, JapanDepartment of Electronic Systems Engineering, Faculty of Systems

Engineering, Tokyo University of Science, Nagano 391-0292, JapanDepartment of Mechanical Systems Engineering, Faculty of

Engineering, Musashi Institute of Technology, Tokyo 157-8557, JapanPolytechnic University, Kanagawa 229-1196, Japan

Department of Electronics and Electrical Engineering, University of Glasgow, Glasgow G12 8LT, U.K.

In this paper, a design optimization method for a consequent-pole bearingless motor is presented. This produces stable magnetic sus-pension under motor torque generation. The suspension force reduction and direction error, which can be caused by torque generation,are limited in the proposed designs. In the optimization routine, the number of suspension and torque winding turns and air-gap lengthare carefully assessed. Three stators are constructed for experimental verification. The amplitude and direction errors for the suspensionforce are found to be within acceptable ranges and the operation of the magnetic suspension is acceptable.

Index Terms—Bearingless motor, consequent-pole, magnetic bearing, magnetic suspension.

I. INTRODUCTION

I N RECENT years, bearingless motors have been developedwhich magnetically integrate a motor drive with a magnetic

bearing. Several types of permanent-magnet bearingless motorshave been proposed [1]–[6]. In general, permanent-magnet mo-tors have attracted considerable interest because of their highefficiency. In the permanent-magnet bearingless motor, thereis a tradeoff between permanent-magnet thickness (and, hence,torque density) and suspension force generation. However, con-sequent-pole type of bearingless motors can avoid the tradeoff[7], [8] and this is illustrated in this paper.

Bearingless motors have two control systems: the torque drivesystem and the rotor suspension system. It is very advantageousto try and decouple the magnetic suspension control from thetorque drive in order to produce stable magnetic suspension of therotor. In the consequent-pole bearingless motor, the motor fluxand suspension flux are concentrated in specific teeth so that thesuspension force and torque decrease with increasing magneticsaturation in the steel. In addition, saturation will also producevariations in angular direction of the suspension force vector.These affects can be reduced by increasing the amount of steel inthe stator teeth and yoke or increasing the air-gap length so thatthe magneto motive force (MMF) drop in the teeth is reduced.Increasing the steel is difficult without increasing the core lengthor diameter, or increasing the tooth width (which will decreasethe winding slot area); so, to summarize the work in this paper,the magnetic suspension characteristics can be improved byoptimizing the air-gap length. This also requires consideration of

Digital Object Identifier 10.1109/TMAG.2006.879500

Fig. 1. Cross section of a consequent-pole bearingless motor.

the winding coil-turns since there is a finite amount of spaceavailable in the slots for the suspension and torque windingstogether. A balancing exercise is, therefore, required to ensurethat the correct torque and suspension forces can be produced.

II. MAGNETIC SUSPENSION CHARACTERISTICS

Fig. 1 shows a cross section of rotor and stator cores of a con-sequent-pole bearingless motor. The rotor has four permanentmagnets, as highlighted by the thick lines, which are magnetizedin the same radial direction to produce four North (N) air-gappoles. The flux distribution produced by these is shown. The re-turn flux paths to the rotor are via salient iron poles between thepermanent magnets. Hence, the four South (S) poles are conse-quently generated. As a result, an eight-pole rotor is constructed.The stator slots contain two single-layer three-phase winding

0018-9464/$20.00 © 2006 IEEE

NAKAGAWA et al.: OPTIMIZATION OF STATOR DESIGN IN A CONSEQUENT-POLE TYPE BEARINGLESS MOTOR 3423

Fig. 2. Comparison of magnet, suspension, and torque fluxes. (a) Stator 1.(b) Stator 2.

sets. These are the 2-pole and 8-pole windings for suspensionforce and torque generation.

Fig. 2(a) shows the flux lines and flux density distribution inStator 1 with rated current in both suspension and torque wind-ings. Three sources of flux are concentrated in Tooth (a). ispermanent magnet flux, is magnetic suspension flux, andis torque current flux. The magnetic flux density in stator Tooth(a) is 1.76 T, i.e., quite high for silicon steel. This flux densitylevel causes some saturation which leads to amplitude reduc-tion and direction error in the magnetic suspension force. Thedirection error can be a serious problem because this reduces thephase margin in the feedback suspension loops and, in the worstcase, may cause the rotor touch down. To avoid this, wideningthe tooth width was considered as a first step. Finite elementanalysis was used to analyze the machine and the optimal toothwidth was found to be large, so that the stator outer diameterhad to be increased to preserve the slot area for the windings.However, for compactness, this should be avoided.

Therefore, as an alternative, the air-gap length was increased.Cross-coupling between the suspension and torque fluxesoccurs in shared saturable steel components in the respectiveflux paths. The common steel paths (i.e., stator teeth) alsoaffect the flux-path circuit MMFs so that changing willchange the stator tooth MMFs and, hence, affect , producingcross-coupling. While increasing the air-gap length decreasesthe cross-coupling, there are also reductions in torque andsuspension force, but this can be compensated by having moreconductors in the stator slots.

In the optimization process, we need to consider the suspen-sion force reduction with torque-winding current at differentair-gap lengths. It should be noted that the suspension force,with no torque-winding current, decreases as the air-gaplength increases. However, as the air-gap length increases,the p.u. change in suspension force decreases at rated suspen-sion-winding current. Hence, there is a compromise betweenthe reduction in suspension force and increase in stator slot fillfactor since more suspension and torque winding amp-turnsare required if the air-gap length is increased. This leads us toa solution where the air-gap length is 0.88 mm, which is anincrease from 0.5 mm in the original design.

The specification of the test-machine stators is listed inTable I. Stator 1 is the original and Stators 2 and 3 are con-structed with the optimized air-gap length of 0.88 mm. Stator 3has more series turns to account for the increased air-gap

TABLE IMOTOR PARAMETERS

Fig. 3. System configuration.

length. Fig. 2(b) shows the tooth flux density distribution forStator 2. The tooth flux density is reduced by almost 0.14 T,which illustrates the reduction in flux due to the increasedair-gap length.

III. MACHINE STRUCTURE.

Fig. 3 illustrates the system control configuration. The upperblock shows the motor torque controller. The speed is controlledby a PI controller using the rotor speed feedback, which is ob-tained from an encoder. The lower block shows the magneticsuspension controller. Radial rotor displacements and aredetected by proximity sensors. The detected displacement er-rors are amplified by proportional–integral–differential (PID)controllers and the two-phase suspension current commands aretransformed into three phases. The inverter is controlled by thethree-phase current commands, and this supplies the suspensionwinding currents.

IV. EXPERIMENTAL RESULTS

The suspension current references and in the suspensionloops are measured with varying torque load. The values forand are automatically developed in the PID controllers so thatforce equilibrium is satisfied. Experiments were carried out withand without an external 2-kgf suspension force applied to theshaft along the -axis. The motor ran at 2000 r/min. In the idealcase, is constant and is zero with an external -axis force.

3424 IEEE TRANSACTIONS ON MAGNETICS, VOL. 42, NO. 10, OCTOBER 2006

Fig. 4. Suspension direction error variation with torque current.

Fig. 5. Suspension force variation with torque.

However, this was not true in the experiments. The current com-mands are automatically generated to compensate for force am-plitude and direction errors so that the force direction error isdetected by the current commands, where .

Fig. 4. shows the suspension force direction error. ForStator 1, the suspension force direction has a serious error whenthe torque current increases. At rated current, the direction erroris 11.3 , which is sufficient to affect the magnetic suspensioncharacteristics. However, for Stator 3, the direction error is only2.4 , which is acceptable for magnetic suspension.

Fig. 5 shows a comparison of the suspension forces whenthe machine is loaded. Ideally, the suspension force should beindependent of torque. The rates of decrease in the suspensionforce for Stators 2 and 3 are reduced. In addition, the suspensionforce magnitude for Stator 3 is about 1.5 times that of Stator 1.The suspension force is found to be proportional to the numberof turns in suspension conductors.

Fig. 6 shows the radial - and -positions, and rotationalspeed for Stators 1 and 3 when the speed was changed from2500 to 500 r/min. For Stator 1, the radial fluctuation of the shaftis large during deceleration. For Stator 3, the radial fluctuationof the shaft is less during deceleration. Acceleration tests werealso carried out and similar results were obtained.

V. CONCLUSION

To improve the magnetic suspension characteristics duringtorque generation, an optimized design of a stator with increasedair-gap length and increased conductors has been proposed toovercome the problem of magnetic saturation in a consequent-

Fig. 6. Radial shaft position variation during speed step change from 2500 to500 r/min. (a) Stator 1. (b) Stator 3.

rotor bearingless machine. By experiment, it was shown thatthe suspension loops operate properly even during rapid speeddeceleration, illustrating the improvement in performance.

REFERENCES

[1] K. Nenninger, W. Amrhein, S. Silber, and G. Trauner and M. Reisinger,“Magnetic circuit design of a bearingless single-phase slice motor,” inProc. 8th ISMB, 2002, pp. 265–270.

[2] H. Kanebako and Y. Okada, “New design of hybrid type self-bearingmotor for high-speed miniature spindle,” in Proc. 8th ISMB, 2002, pp.65–70.

[3] B. Steele and L. Stephens, “A test rig for measuring force and torqueproduction in a Lorenz slotless self bearing motor,” in Proc. 7th ISMB,2000, pp. 407–412.

[4] M. Neff, N. Barletta, and R. Schob, “Bearingless centrifugal pump forhighly pure chemicals,” in Proc. 8th ISMB, 2002, pp. 238–248.

[5] F. Wang and L. Xu, “Calculation and measurement of radial and axialforces for a bearingless PMDC motor,” in IEEE Ind. Appl. Conf., 2000,pp. 249–252.

[6] M. Ooshima, A. Chiba, M. A. Rahman, and T. Fukao, “An improvedcontrol method of buried-type IPM bearingless motors considering mag-netic saturation and magnetic pull variation,” IEEE Trans. Energy Con-vers., vol. 19, no. 3, pp. 569–575, Sep. 2004.

[7] T. Takenaga, Y. Kubota, A. Chiba, and T. Fukao, “A principle andwinding design of consequent-pole bearingless motors,” in JSME Int. J.Series C, vol. 46, Jun. 2003, pp. 363–369.

[8] J. Amemiya, A. Chiba, D. G. Dorrell, and T. Fukao, “Basic characteris-tics of a consequent-pole-type bearingless motor,” IEEE Trans. Magn.,vol. 41, no. 1, pp. 82–89, Jan. 2005.

Manuscript received March 13, 2006 (e-mail: chiba@ee.noda.tus.ac.jp).