On the Magnetic Behavior and Steady-statePerformance Estimation of a BipolarExcited Switched Reluctance Machine

Wei Jiang, Babak FahimiUniversity of Texas at Arlington

416 S. Yates StreetArlington, TX 76019

USAfahimi@uta.edu

Abstract - Switched Reluctance Machine (SRM) is gaining through electrical design presents to be a very promising andmore attention in automotive industry by the virtue of its flexible approach. Based on this perspective, this paper willrobust structure, high speed performance and fault investigate the electromagnetic behavior and steady-statetolerant nature. Bipolar excitation of SRM maintains short performance of SRM under bipolar excitation on aflux paths and achieves higher torque density and lower microscopic level. The rules behind the Short Flux Path (SFP)iron loss. This novel excitation scheme makes SRM more mode, mechanism of force generation and accurate predictionattractive to the vehicular applications which demand of machine static performance will be illustrated and validatedhigher instantaneous torque and efficiency. The present with both electromagnetic theory and FEA simulation.paper provides a detailed and thorough investigation intoa bipolar excited SRM in terms of its magnetic behavior II. FORCE CALCULATION IN BIPOLAR SRMand estimation of its steady-state performance. Using amicroscopic level of analysis in electromagnetic response of According to the electromechanical energy conversionthe SRM, this paper will give a clear and insightful theory, the electromagnetic torque generated in the SRM withexplanation on how bipolar excitation would affect the two phase that are simultaneously excited can be expressed by,magnetic field and force generation in a conventional 8/6 a WC 2 aSRM. Finite Element Analysis (FEA) is adopted as the tool T = Ao2 (0, i2 , O)di2 +to investigate and validate the findings. ()1,2(l

a1. INTRODUCTION . a0o 1iI 0)di

The electromagnetic torque of a Switched Reluctance wherethe fluxlinkage Ai canbe expressedby:Machine (SRM) is developed by the tendency of stator and AN2i.rotor poles to reach alignment. The duality between electric , Z/IO(2)circuit and magnetic circuit indicates that the magnetic flux i (2tend to distribute within the path of lowest reluctance. In In which "i" is the number of flux path. Here linearized fluxsingle-phase operation of an 8/6 switched reluctance machine, linkage expression is used to approximate the totalthe flux path flows through the stator pole, airgap, rotor pole, force/torque. This global energy method could give fairlyrotor back iron, stator yoke and back to the stator pole where accurate value for the torque, however, when fieldthe Magneto Motive Force (MMF) is applied. According to components and local force density is of special interest,the electromagnetic theory, most of the energy stored in the global energy method could not reveal any of information.airgap is converted to mechanical form in an effective way; Field based force calculation methods adopt the same ideahowever, the distribution pattern of flux renders considerable of force generation mechanism as the global energy methodlevel of iron loss in this single-phase excited machine. The and present the stress tensor with local electromagnetic fieldidea of bipolar excitation introduced in [2] utilized both the quantities. Maxwell Stress Tensor (MST) method is one of theelectromagnetic circuit characteristics and force generation simple and effective methods to calculate local force densities.mechanism to create two short magnetic flux path in SRM to In a 2D electromagnetic field, considering the continuityboost the performance of a conventional 8/6 SRM by means of theorem, the tangential and normal stress tensor on the surfaceelectrical excitation. The performance enhancement of SRM of an object is given as:

1-4244-0743-5/07/$20.OO 2007 IEEE 1338

ff = Bn H pulsation and thermal imbalance in different sections of stator-

2_H23 yoke and rotor back iron.

2puo 2Bn is the normal magnetic flux density while H, representsthe tangential magnetic field intensity. By proper finiteelement modeling [3] [4], detailed local stresses can becalculated accurately using MST method and the steady-stateperformance of the SRM under bipolar excitation can beprecisely predicted. X

be swapped such that a SFP is maintained at all times with no The continuity theorem suggests that on the unsaturatedneed for a bipolar excitation. The bipolar excitation scheme high permeability iron surface (free from any surface currenthas utilized the characteristics of magnetic circuit; it forces density), the flux lines enter perpendicular to the iron surface.SFP by introducing two adjacent MMF sources with different Although flux refraction occurs on the air-iron boundary inpolarity hence provide a high torque, thermal balanced and Fig. 6, according to Maxwell Stress Tensor, the force densityless-loss way of operation. inside the iron is still negligible comparing to its counterpart

on the iron surface due to the high permeability value of iron.IV. STEADY-STATE PERFORMANCE ESTIMATION Also, since air is not the physical carrier of stress/force, the

OF BIPOLAR SRM force can only exist on the leading sides of rotor pole.

A 2D finite element model of the 8/6 SRM machine ismodeled and simulated with commercial FEA softwareMagNet. The area where high flux density happens isdiscretized with uniform triangular mesh. The simulation iscarried out at a mechanical speed of 1600rpm and under a

..........

magneto-motive force of 1250AT/phase.In bipolar excitation, electromagnetic field components andX

force density/stress distribution on each rotor pole is the timeshifted copy of its leading counterpart. Therefore, in order tovalidate the force calculation method, one of the rotor poles inbipolar excitation is chosen to investigate the distribution of Fig. 5 Flux line plot at half entry positionfield quantities during energy conversion process.

First of all, three circular contours are placed on differentlayers at the middle of the airgap, at the rotor surface, and atstator surface; the flux density vectors are observed in thevicinity of stator and rotor poles. The half entry position,illustrated in Fig. 5, is chosen to investigate the distribution offield quantities and force components. As shown in Fig.6, theflux density magnitude on rotor surface layer presents a peakvalue at the leading pole tip position (right side of rotor pole),while on stator surface layer peak flux density value isobserved at the lagging edge (left side) of stator pole. In fact, (a) Bt on the boundary (b) Bn on the boundarythe leading rotor pole tip and lagging stator pole tip is thepoint where the flux lines enter and leave (see Fig. 5).According to the definition of magnetic flux density byMagnetic Vector Potential (MVP), the curl of MVP is fluxdensity, it is easy to appreciate that when flux lines squeezeout of the stator pole and seek the least-reluctance path to therotor pole, bending occurs in the vicinity of airgap on leadingrotor side; hence the bending tendency of flux lines produceslarge value of tangential flux density, which is reflected in the (c) ft on the boundary (d) fn on the boundaryresults of finite element analysis. Similar situation happened Fig.6 Flux density and stress components on rotor boundaryon the stator side. Therefore, the rotor surface layer is used tocalculate the local stress on the rotor. Next, sweep contour is made around the rotor geometry

surface, the tangential and normal force density components,..

r-_ i}@@-Mew2 i.e. f0 and Jr are calculated by MST method. As weg 2 3 3 kwttm 3 1@ w2.ffivG'www* i ,f2 o

IXt-1git.j__tw 0 7,, ,,:, S-tilMwW-wexpected, force density vector which is in the tangentialf1Bil m@. + 1 I ''-direction of movement exists on the leading edge of rotor pole

shown in Fig. 7. The force density value decreases as thesweep contour leaves far away from the vicinity of airgap,

r i I $1M4g JF -g ~~which confirm that of the flux plot shown in Fig. 5. Also dueM.w= AS . a XR Wi M=Its to saturation of the rotor pole tip, certain amount of stress is

gg ;:rHs,m'Lhwwwfis-X "0W' Xalso observed within very small rotor top region, as indicated(a)B~ ntreelayrs b) ~ n the ayr n Fig. 6 (c) (d). Comparing with the force density calculatedFig.4. luxdesity o threelayerson the rotor surface layer, those two ways of calculating turns

out to have very similar force density distribution (only with

1340

angular difference in space) and close peak value, as indicated another excited phase as indicated in Fig. 9 (b), which wouldin Fig. 7. shed light on an opportunity to mitigate the radial vibration in

The total motion force on one of the rotor pole is calculated multiphase excitation.with different methods and contour implementations, the final Moreover, incorporating the discussion in the previousresults shows that the MST method gives sufficient stress section, the patterns of flux path distinguish the staticdistribution information and very accurate total force performance between unipolar excited and bipolar excitedestimation. With surface contour implementation, MST machine. In unipolar excitation, when phase A and D aremethod reveals the actual motional force density distribution excited simultaneously, short flux path (SFP) is formed as inon the rotor pole as well as on the stator pole. Considering the the bipolar excitation. However when phase AB, BC, CD arecomplexity of implementation, a rotor surface arc contour excited, long flux path (LFP) exists. The effect of SFP isMST is favored. Using this contour one is able to show the reflected in distribution of the field components and the torqueradial force component distribution on rotor pole surface, and production. In Fig. 10 (a) (b), one can notice that in bipolaralso, can reflect how the motion force is exerted on the side of excitation, the MMF sources in adjacent stator poles are inthe rotor pole; a detailed justification on the validity of this different polarity while in unipolar excitation the samemethod is given in [4]. polarity; change of direction in tangential and normal flux

density in bipolar excitation is observed. Majority of flux linesclose the short magnetic flux path between adjacentrotor/stator pole pairs in bipolar case, as visually indicated inFig. 3 (d).

(a) Force density on three layers (b) force density on rotor sideFig. 7. Comparison of force density on rotor surface layer and

rotor side layer(a) Tangential force density (b) normal force density

"Atd ariietiMtD-cecacutteatdikteA art .i'mdlne etmet-yFig.9. Force density components plot

&=wbd Dom.= &wusiiti mwtdenitbdensit

Same procedur is aple to the1 6otheraexcited phaseci tanenia flx__Rtrsrac agnilfubipolar excitation, flux ~~dtensity and(force densittplotehowithsimultaneousig.occurenc mofioalforcenercuationontwo adjacentyta tai "..im 16 tkicanme frounduinmultiphasedexcitationhcomparingdtohthesingl

phase excitation because another phase is incorporated in thetorque production. From Fig.9 one can observe that as the q~daRleading rotor pole (right) is approaching the aligned position; (c) Rotor surface tangential force (d) Rotor surface normal forcethe trailing rotor pole becomes active, fringing flux on the density densitytrailing rotor pole side supplies big portion of the torque. Fig. 10. Flux density and force density distribution in unipolarTorquie generation in trailing rotor pole is the time shifted excitation and bipolar excitation

rotor back iron and stator yoke, larger flux linkage as well as rotor back iron; in unipolar excitation, flux lines only occupyforce densities are expected. Fig. 10 (c) (d) indicates higher 3/4 of stator yoke and rotor back iron in three out of fourforce density peak value in SFP than in LFP. However, the excitation stages (AB, BC and CD) and 1/4 of stator yoke andmajority of the system reluctance comes from the airgaps of rotor back iron in one excitation stage (AD); in bipolarthe machine; therefore, the increment in torque production will excitation, only 1/4 of stator yoke and rotor back iron is used.not be significant. Iron loss on rotor back iron is plotted in Fig. 12, one canThe total motional force is calculated in single phase observe that in bipolar case, iron losses only concentrate under

excitation, unipolar excitation, and bipolar excitation the phases which are excited, while in unipolar case, iron lossrespectively. It is obvious that multiphase excitation gains is spread over 3/4 of rotor back iron and the loss peak value aremore motional force than single phase excitation. And one higher than the bipolar case. Also, since SFP persists inneeds to notice that the first peak value of torque is the same bipolar case, bipolar excitation can achieve a more thermalin unipolar and bipolar excitation because phase A and D are balanced and torque enhanced performance.both excited, SFP exists in both case. When the rotor movesthree consecutive LFP is formed in unipolar excitation, lowerpeak tangential force is observed at same rotor position than in V. CONCLUSIONbipolar excitation in Figure. 11. This confirms the forcedensity plot in Fig. 10, SFP renders higher system reluctance This paper studied the magnetic behavior of bipolar excitedvalue, hence generates 400 more peak torque. Furthermore, SRM and fundamental rule of achieving a short flux pathbipolar excitation tends to present a more balanced and torque pattern. The force generation mechanism in multiphaseenhanced system than unipolar excitation. In unipolar excited SRM is investigated, explained and proved. Usingexcitation, the maximum value of torque depends on the Finite Element Analysis method and novel Maxwell Stressdirection of winding(phase A and D are excited Tensor implementation, the steady-state performance of thesimultaneously), the other three LFP produce lower peak targeted SRM is precisely estimated. The advantages of usingtorque value, shown in Fig. 11, therefore introducing bipolar excited SRM is proved and elaborated.additional torque pulsation as well as tangential vibration.

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