A Novel Switched Reluctance Motor With C-Core Stators

IEEE TRANSACTIONS ON MAGNETICS, VOL. 41, NO. 12, DECEMBER 2005 4413

A Novel Switched Reluctance MotorWith C-Core Stators

Shang-Hsun Mao and Mi-Ching Tsai

Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan, R.O.C.

This paper presents a novel switched reluctance motor (SRM) design in which the stator is simply formed from C-cores. Unlike con-ventional SRMs, the windings of the new motor can be individually wound into the stator cores without complex winding equipment.Because of the inherent axial field distribution, this type of SRM requires a three-dimensional (3-D) finite-element analysis (FEA) modelfor detailed flux analysis. This paper proposes an approximated two-dimensional FEA model to speed up computational time. In addition,since the proper current that ensures operation in the saturated region (to maximize torque and efficiency) is often hard to determinesystemically, the paper proposes a simple method to determine the optimum operating current. Finally, the paper compares some char-acteristics of a traditional SRM with those of the proposed SRM. The comparison shows that the proposed SRM performs well in termsof torque and efficiency, and provides a higher degree of flexibility in winding design.

Index Terms—Finite-element analysis, optimum operating current, switched reluctance motor.

I. INTRODUCTION

SWITCHED reluctance motors (SRMs) have been widelyused in many industrial applications such as aerospace, au-

tomotive and domestic appliance manufacturing [1]. The majoradvantages of SRMs are high torque output, wide range of oper-ating speed, simple structure and fault tolerance. Several analyt-ical methods for SRM design have been presented [2], [3]. Be-cause of its inherent nonlinear magnetic characteristics and thedoubly salient pole structure, the finite element analysis (FEA)approach is often adopted for obtaining its accurate magneticcharacteristics [4], [5].

Two of the major design objectives when designing SRMs arehigh efficiency and low cost. Fig. 1 shows the basic structureof a conventional SRM. While the geometry and windings arenot as complex as, say, an induction motor, automated windingof this machine can still be a complex process. Also the per-formance can be limited by the area of the slots and the tight-ness of winding (i.e., the slot-fill and end-winding overhang).For example, if the winding is not tight enough, the end-turnsof winding will cause large copper loss and then the motorefficiency will be reduced. There will also be additional end-winding resistance and leakage inductance which will increasethe demand on the supply. This paper presents a novel SRM witha C-core type of stator for axial winding which is based on [6].Such a structure creates a large slot space so that the windingprocess becomes more straightforward. Also, since the C-corestators are independent of each other, they can be manufacturedand wound individually and efficiently by an automated process.Consequently the cost of winding will be reduced significantly.However, the flux distribution of this new type of SRM is inher-ently three-dimensional (3-D) and hence requires a 3-D finiteelement model for analysis. It is well known that 3-D analysisis very time consuming in simulation so in this paper, a simpli-fied two-dimensional (2-D) analysis of the original 3-D model is

Digital Object Identifier 10.1109/TMAG.2005.858372

proposed in order to speed up the simulation process. The An-soft/Maxwell finite element analysis package [7] is employedfor the required simulation and also to calculate the flux linkage,inductance and torque.

In general, the output torque of an SRM is related to thechange of co-energy so it should be designed to operate intothe saturated region for greater output torque. However, theproblem is how to determine the optimum operating current. Inthis paper, a method is developed to determine the operatingcurrent and turns-per-phase, where the flux linkage is modeledwith a single curve in the unaligned position and two curvesin the aligned position respectively [8]. By calculating themaximum increment of co-energy, the optimum excitationcurrent that produces the maximum increment of torque can bedetermined.

This paper is organized as follows. Section II presents the ge-ometry design based on the “feasible” triangle criteria [9]. Asimplified 2-D model is proposed in Section III. Determinationof number of the coil turns and the rated current is given in Sec-tion IV. The characteristics comparison with a traditional SRMis shown in Section V. Section VI concludes the paper.

II. MOTOR DESCRIPTION AND GEOMETRY DESIGN

A. Motor Description

The structure of traditional SRM has a radial winding andradial air gap. Let the electric loading be defined as [10]

(1)

where is the number of coil-turns per phase, is the phasecurrent, is the number of phases conducting simultaneously,and is the bore diameter. It can be seen that the product ofand is a constant for a given electric loading and bore diameter.However, the winding space is restrained by slot space, numberof turns, area of conductor cross section, insulation thicknessand the maximum manufacturing slot-fill. Obviously, it is dif-ficult to determine the number of turns and phase current in aconfined slot and the design flexibility will be limited by the

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4414 IEEE TRANSACTIONS ON MAGNETICS, VOL. 41, NO. 12, DECEMBER 2005

Fig. 1. Conventional four-phase 8/6 SRM.

slot space. Note that the motor performance can be restricted bythe slot space, especially in the SRM.

Consider the novel SRM shown in Fig. 2(a), where thestator is composed of eight independent C-cores which arearranged toroidally along the shaft with the windings locatedin the middle of the C-cores. Such an SRM has the followingpotential advantages.

1) Compared with the conventional SRM, the slot space ofthe novel SRM is relatively large so that there is more de-sign flexibility for the number of turns and phase magne-tomotive force (MMF).

2) The stator winding can be wound more closely and uni-formly so that the end turn of the winding is shortened.This helps to reduce the copper waste and copper loss.Also, the end-winding flux can be reduced.

3) The rotor inertia of the proposed SRM can be made small,which is suitable for high-speed applications.

4) Such a structure can easily be augmented by cascadingseveral modules on one shaft for high power operation asshown in Fig. 2(b), which illustrates two modules.

5) Thestatorsare independent, andcanbewound individuallyandautomatically.FromthesideviewasshowninFig.3(a),the material in the dashed blocks can be saved for theproposed SRM, and from the top view as shown inFig. 3(b), there is no back iron (the dashed block) in theproposed SRM compared to the traditional one. Therefore,material waste and manufacturing cost can be reducedsignificantly.

B. Geometry Design

The flux path and the geometry parameters for the new designof SRM are illustrated in Fig. 4, where the two major parameterswhich greatly influence the inductance curves are the rotor polearc, , and the stator pole arc, . The design of the pole arcsshould satisfy the basic requirements for self-starting, highertorque output, and lower torque ripple.

Fig. 2. (a) Structure of the proposed SRM. (b) Two modular expansion of theSRM.

To achieve the self-starting requirement, must be greaterthan the stroke , which is defined by

(2)

i.e.,

(3)

where is the number of phases and is the number of rotorpoles. For example, the stroke of a four-phase 8/6 SRM is 15 .To keep the aligned to unaligned inductance ratio as high as pos-sible (to maximize the current/flux linkage loop for high torque),the stator pole must be smaller than the interpolar arc of therotor, i.e.,

(4)

Furthermore, to reduce torque ripple, the positive slope of theinductance curve must overlap the negative slope of the previousphase. We thus require that the rotor pole arc should be slightlygreater than the stator pole arc so that

(5)

The above constraints are summarized and illustrated inFig. 5. The possible combinations of the rotor pole arc andstator pole arc are located in the “feasible” triangle.

The basic dimensions are: a rotor pole arc of 24 , a statorpole arc of 18 , and an air-gap length of 0.5 mm. For ease ofmanufacture, the radius of the shaft is chosen to be 4 mm,the outer radius of the rotor mm, and the length ofthe stator pole mm. To ensure the flux that can passthrough from the stator to the rotor, both the width of stator yoke

and the depth of rotor pole are set to be equal to the lengthof the stator pole. Now considering the slot spacing, the lengthof stator is then chosen to be 70 mm. To sum up the abovedesign, the geometric parameters, which are summarized as inTable I, appear to be reasonable for the constraints previouslydescribed.

III. 2-D MODIFIED MODEL

With the given geometric parameters above, a 3-D FEAmodel for the prototype SRM was developed as shown in

MAO AND TSAI: A NOVEL SWITCHED RELUCTANCE MOTOR WITH C-CORE STATORS 4415

Fig. 3. (a) Side view of the proposed SRM. (b) Top view.

Fig. 4. Flux path and the geometry parameters of the proposed SRM.

Fig. 6. The flux distributions at the aligned and unaligned po-sitions are shown in Fig. 7, where only one phase is illustratedand switched on. Obviously, the axial flux in the stator and theradial flux in the rotor appear in the 3-D flux distribution andthere is a long axial flux path in the stator. This implies a 3-Dmodel is required for magnetic field simulation in order to takeinto account all of the 3-D effects. However, it is well knownthat the use of 3-D FEA often has the following disadvantages[11].

1) The problem definitions such as model drawing, ma-terial assignment, and boundary condition can be verycomplicated.

2) The solution may not always converge because the meshof the air gap is hard to refine. The mesh of the air gapused for an SRM simulation is an important factor andcan seriously affect the accuracy of the entire solution.

3) A 3-D FEA model that uses a large number of meshes toobtain an accurate solution requires a very long computa-tion time—both in setting up the model and running theanalysis.

To improve the simulation efficiency, this paper presents asimplified 2-D FEA model as shown in Fig. 8 to achieve therequired simulation; where two stators are modeled in the sameplane. The machine is rearranged as illustrated. The aligned and


Fig. 5. “Feasible” triangle for four-phase 8/6 SRM.

TABLE IGEOMETRY PARAMETERS OF THE PROPOSED SRM

Fig. 6. 3-D FEA model.

unaligned positions can be expressed graphically as shown inFig. 8(a) and (b). It should be noticed that the width of the statoryoke in Fig. 8 is equal to the width of the stator pole in Fig. 4,making the cross-sectional area of the stator core-back constant,since the stack length of the 2-D model is equal to the length ofthe stator pole in Fig. 4. The advantages of the proposed 2-DFEA model are as follows.

1) It is simple to build using a 2-D FEA model, includingmodel geometry, material assignment, and boundaryconditions.

2) The mesh of the air gap is easy to refine for a more accu-rate solution. Note that most of magnetic energy is storedin the air gap, so that the mesh of the air gap plays a sig-nificant role in the simulation.

3) The simplified 2-D FEA model results in a great reductionof simulation time.

4) Most characteristics can be determined from the 2-Dmodel such as flux linkage curves, inductance curves,and static torque.

In this paper, a 3-D model simulation is finally employed toverify the accuracy of the 2-D simplified model. The inductancecurves obtained from the 2-D and 3-D simulations with respectto the rotor position are shown in Fig. 9 while the excitation cur-rent was 500 A. As can be seen, the inductance curve resultsfrom the 2-D simulation shows good correlation with resultsfrom the 3-D simulation. It should be noted that the 3-D sim-ulation takes several days to calculate for the inductance curve.However, the inductance curve can be obtained in few hoursusing the proposed simplified 2-D inductance simulation. Thisvalidates the method although it should be borne in mind thatthe stator-yoke leakage differences should be carefully consid-ered so that the 2-D and 3-D values approximately match.

The flux linkage curves of the aligned position and unalignedposition with respect to the current are shown in Fig. 10 andare calculated using the 2-D FEA model. This determines theoperating current and turns-per-phase as described below.

IV. OPERATING CURRENT AND NUMBER OF TURNS

PER PHASE DETERMINATION

Let the co-energy be defined by

(6)

The average torque of the SRM can be computed as [12]

(7)

where is the variation of co-energy over one stroke. Thisshows that the larger change of co-energy, the higher increasein average torque is. Nevertheless, the enhancement of outputtorque is not uniform, especially in the saturated region. Theo-retically, the maximum increment of co-energy and torque willoccur at the same current. Therefore by finding out the currentwhich produces a maximum increment of co-energy the max-imum increment of torque is also obtained since it will be pro-duced at the same current. The maximum increment of co-en-ergy is then an index for determining the current and the numberof turns-per-phase. In order to obtain the variation of co-energy,the modeling of the flux linkage curve is necessary.

For the aligned position, both linear and nonlinear curves areused to approximate the flux linkage curve as shown in Fig. 11where the linear curve 1 is modeled as a straight line and the


Fig. 7. Flux distribution when one phase is excited. (a) Aligned position (b) Unaligned position.

Fig. 8. 2-D simplified FEA model of the proposed SRM. (a) Aligned position. (b) Unaligned position.

Fig. 9. Inductance curve of 2-D and 3-D simulation with respect to rotorposition.

nonlinear curve 2 is approximated using a fourth -order poly-nomial curve starting at the saturated point S. The flux linkage

of curve 1 can be described as

(8)

Fig. 10. Flux linkage with respect to ampere turn.

where is the inductance of the coil at the aligned position.For the saturated region at the aligned position, the flux linkage

of curve 2 can be described as

(9)


Fig. 11. Flux linkage versus exciting current.

Fig. 12. Variation of co-energy with respect to the variation of exciting current.

where , and are the coefficients of thepolynomial which can be determined by means of a least-squaremethod. For the unaligned position, since the stator is not satu-rated, the flux linkage forms a straight line (curve 3):

(10)

where is the inductance of the coil.By modeling the flux linkage, the variation of co-energy can

be calculated by integrating the area bounded by the aligned andunaligned curves as shown in Fig. 12. The change in co-energyis given by

(11)

The excitation in the unsaturated region will be constant.By finding the maximum , the maximum increment ofco-energy can be determined. Theoretically, the increment ofco-energy and the increment of torque will occur for the samecurrent [from (7)]. Furthermore, the optimum excitation currentcan be determined from

(12)

where is a positive integer.

Fig. 13. Comparison between the simulated flux linkage and the fitted fluxlinkage curve.

Fig. 14. Increment of the co-energy evaluated by the proposed methoddescribed in Section IV with respect to current.

Fig. 10 shows the case when the saturated current is 700 A.Using the least-square method [13], the flux linkage can be fittedto the following three curves.

Curve 1)

Curve 2)

Curve 3)

Fig. 13 indicates that the fitted flux linkage curve is well fittedto the simulated flux linkage. Then, the increment of the co-en-ergy is illustrated in Fig. 14, where the maximum increment ofco-energy occurs when the current is 1020 A. The diameter ofthe coil wire is chosen as 0.8 mm. If the current density is takento be below 8 A/mm , then the number of turns-per-phase can


Fig. 15. Static torque increasing in 150 A per step from 150 to 2100 A.

Fig. 16. Increment of average torque simulated by Ansoft, with respect toampere turns.

be chosen as 300 so that the current is 3.4 A. From the slot area,the slot fill factor can be calculated to be nearly 0.4.

The static torque with respect to different current levels is cal-culated over one stroke as shown in Fig. 15, where the curves arefor currents from 150 to 2100 A at 150 A intervals. The incre-ment of average torque, which is evaluated by subtracting the av-erage torque of the last simulated current from that of present, isillustrated in Fig. 16. The maximum increment of average torqueoccurs at 1050 A and the maximum increment of co-energy, ascomputed above, occurs at 1020 A as shown in Fig. 14. As canbe seen, the predicted current is close to the simulated current.This helps designers to determine the required operating point.

V. COMPARISON WITH TRADITIONAL SRM

A traditional four-phase 8/6 SRM, as shown in Fig. 1, iscompared with the proposed SRM. Its basic external dimen-sions are the same as the proposed SRM; with the given slotarea and the normal slot fill factor being 0.6, the number of theturns-per-phase of the traditional SRM would be 75 turns forthe identical diameter of the coil wire. The static torque char-acteristics of the traditional SRM and the proposed SRM are

Fig. 17. Torque comparison between the traditional SRM and the proposedSRM.

Fig. 18. Copper loss comparison between the traditional SRM and theproposed SRM.

shown in Fig. 17. It is evident that the torque produced by theproposed SRM is higher than the traditional SRM at the samecurrent. The reason for this is that the number of turns-per-phaseof the proposed SRM is more than that of the traditional SRM.In other words, the current requirement of the proposed SRMis less than the traditional SRM for the same torque production.Consequently, the cost of the driver system will be reduced.

Fig. 18 shows the copper loss of the traditional SRM and theproposed SRM. It is obvious that the copper loss of the tradi-tional SRM is higher than the proposed SRM for the same torqueoutput although the turns-per-phase of the proposed SRM ismore than the traditional SRM. This is because that the copperloss is in direct proportion as the square of current and the cur-rent requirement of the proposed SRM is low so that the copperloss can be diminished. In addition, if the copper loss is stillconsidered high there is still space to rewind with thicker wirein the proposed SRM. Hence, the copper loss can be reduced bythe decrease of coil resistance. However, it is difficult to rewindfor the traditional SRM—a slot fill factor of 0.6 is quite high(since the wire insulation and slot linear are not included inthis calculation). This means that there is considerable design


flexibility in the proposed SRM when specifying the number ofturns-per-phase.

The iron loss is not discussed in this paper. The reason is thatthe iron loss of these two machines will be close to each other forthe same speed since the amount of steel and the flux levels in thetwo machines are similar; in addition, the iron loss is relativelylow so that any difference in iron loss will be relatively smallwhen compared to the overall loss.

VI. CONCLUSION

This paper has presented a novel SRM for low-cost produc-tion that possesses high slot space for ease of coil winding. Forhigh power applications, such a structure can be easily be aug-mented by stacking more modules together. To analyze the newdesign of SRM efficiently, a simplified 2-D FEA model for the3-D flux distribution simulation has been proposed to reducecomputational time. A method is also given to determine the op-erating current and to decide on the rated current for obtaininga high-efficiency motor design. Finally, a traditional SRM ofthe same size is simulated to compare with the proposed SRM.From the compared simulation results, the proposed SRM ap-pears to have better characteristics in terms of torque and ef-ficiency, and there is a degree of flexibility in the design of thephase winding since the available slot area for the coils is higher.

ACKNOWLEDGMENT

This work was supported by the National Science Council ofthe Republic of China under Grant NSC 91-2622-E-006-053-CC3. The authors are grateful to the Ansoft Corporation TaiwanBranch for providing the software. The authors would like to

thank Y. F. Fan [6] and Dr. D. Dorrell for their assistance withthis work.

REFERENCES

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[3] D. N. Essah and S. D. Sudhoff, “An improved analytical model for theswitched reluctance motor,” IEEE Trans. Energy Convers., vol. 18, no.3, pp. 349–356, Sep. 2003.

[4] Y. Tang, “Characterization, numerical analysis, and design optimizationof switched reluctance motors,” IEEE Trans. Ind. Appl., vol. 33, no. 6,pp. 1544–1552, Nov./Dec. 1997.

[5] W. Wu, J. B. Dunlop, S. J. Collocott, and B. A. Kalan, “Designoptimization of a switched reluctance motor by electromagnetic andthermal finite-element analysis,” IEEE Trans. Magn., vol. 39, no. 5, pp.3334–3336, Sep. 2003.

[6] Y. F. Fan, “Stator Used for Dynamo or Electromotor,” U.S. Patent6 188 159, Feb. 13, 2001.

[7] Ansoft Corporation, “Maxwell 2D Field Simulation,” Release Note,Pittsburgh, PA, 1995.

[8] S. H. Mao and M. C. Tsai, “An analysis of the optimum operating pointfor a switched reluctance motor,” J. Magn. Magn. Mater., vol. 282, pp.53–56, Nov. 1, 2004.

[9] T. J. E. Miller, Switched Reluctance Motors and Their Control. NewYork: Oxford Univ. Press, 1993.

[10] R. Krishnan, Switched Reluctance Motor Drives. Boca Raton, FL:CRC, 2001.

[11] R. Prieto, J. A. Cobos, O. Garcia, P. Alou, and J. Uceda, “Study of 3-Dmagnetic components by means of “Double 2-D” methodology,” IEEETrans. Ind. Electron., vol. 50, no. 1, pp. 183–192, Feb. 2003.

[12] T. J. E. Miller, Brushless Permanent-Magnet and Reluctance MotorDrives. Oxford, U.K.: Clarendon, 1993.

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Manuscript received May 3, 2005; revised September 20, 2005 (e-mail:[email protected]).

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A Novel Switched Reluctance Motor With C-Core Stators