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SINGLE-PHASE INDUCTION MOTOR WITH ASYMMETRICALSTATORT. T. SHIMKEVICIUS a & G. R. SLEMON ba Kaunas Polytechnical Institute , Lithuanian, S.S.R.b University of Toronto , Toronto, CanadaPublished online: 27 Apr 2007.

To cite this article: T. T. SHIMKEVICIUS & G. R. SLEMON (1979) SINGLE-PHASE INDUCTION MOTOR WITH ASYMMETRICAL STATOR,Electric Machines & Power Systems, 4:2-3, 153-163

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SINGLE-PHASE INDUCTION MOTOR WITH ASYMMETRICAL STATOR

T. T. SHIMKEVICIUS

Kaunas Poly technical InstituteLithuanian S.S. R.

G. R. SLEMON

University of TorontoToronto, Canada

ABSTRACT

This paper describes a single-phase single-winding induction motor whichis self-starting without the use of a shading winding. Starting torque is pro­duced by a combination of several stator asymmetries: an airgap under the mainpole which is· tapered down in the direction of rotation, poles without windingsin the quadrature axis with solid iron flux bridges to the lagging sides of themain poles, and yoke sections which are larger on the leading than on the laggingsides of the main poles. A qualitative explanation of the action of these asym­metries is presented using equivalent circuits.

INTRODUCTION

A symmetrical single-phase induction motor has no starting torque but hasgood full speed operating characteristics. A number of means have been employedto achieve adequate starting torque, including the use of an auxiliary energizedwinding as in the split phase and capacitor motors or an auxiliary shorted wind­ing as in the shaded pole motor. While the shaded pole motor achieves a start­ing torque adequate for many loads, its efficiency is such as to restrict itssize and application range.

Several attempts have been made to produce a single-phase induction motorwith sufficient torque to start a fan or similar load without suffering theefficiency penalty of the permanently-shorted shading ring.

+Figure 1 - Stepped Airgap Motor

Electric Machines and Electromechanics: An International Quarterly. 4: 153-163Copyright © 1979 by Hemisphere Publishing Corporation 0361-6967/79/040153-11 $2.25

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154 T. T. SHIMKEVICIUS AND G. R. SLEMON

RaIl [1] introduced the reluctance-start motor in which the air gap over theloading part of the pole was approximately double that in the other part asshown in Figure 1. Baum [2] analysed this motor, attributing its starting tor­que to the asymmetry in the mutual inductances and the rotor leakage inductancesin the two sections. Poloujadoff [3] and Alternbernd [4] have presented morecomprehensive analyses of this motor. Butler and Bradley [5] have carried outan extensive experimental study of the stepped-gap motor, showing that a start­ing torque of about one-third of that of a shaded-pole motor can be achievedtogether with a significant improvement in efficiency. Hershberger and Olde~[6] have considered stepped and sinusoidally-varying air gaps with distributedwindings and have also suggested the use of asymmetrically-placed air gaps inthe stator yoke. They show that efficiency in excess of 50% and starting torqueof about 20% of maximum torque can be obtained with a stepped gap.

The objective of this paper is to examine an alternative approach to theproduction of starting torque through stator asymmetry. The motor to be discussedwas introduced by Kostrauskas, Mukulis and Shimkevicius [7,8] in 1967 and hasbeen manufactured for use in a number of applications in the U.S.S.R.

Figure 2 - Cross section of asymmetrical-stator motor

DESCRIPTION OF MOTOR

A cross section of the asymmetrical stator motor is shown in Figure 2. Therotor is of normal squirrel-cage construction. The stator is made of stampingshaving two main poles with coils and two smaller at~iliary poles.

There are several sources of asymmetry in the stator. Each main pole airgap is tapered from a maximum value at the leading edge of the main pole to aminimum value at the lagging edge in a manner similar to that employed in reluc­tance-augmented shaded pole motors [9, 10]. Solid iron shunts are insertedbetween the lagging tips of the main poles and the adjacent auxiliary poles.

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SINGLE-PHASE INDUCTION MOTOR WITH ASYMMETRICAL STATOR 155

These are somewhat similar to the magnetic wedges which have occasionally beenused between the poles of shaded pole motors to improve performance [II]. Also,the sections of yoke on the lagging sides of the main poles are thinner than onthe leading.yoke sections.

PRINCIPLES OF OPERATION

In this section, the effects of the various asymmetries in the motor statorare examined using equivalent circuit techniques. The major objective is topresent a qualitative rationale for the operation of the asymmetrical-statormotor. No attempt is made here to develop a full-scale analysis suitable foruse in motor design and optimization. However, it is expected that the equiva­lent circuits presented in this section can be readily extended to permit acomprehensive quantitative analysis using the approach presented by Poloujadoff[12] .

The motor in Figure 2 has three sources of stator asymmetry: the variableair gap under the main poles, the different cross sections of sequential yokesections, and the magnetic bridge between the main or direct axis poles and thequadrature axis poles. These asymmetries will be examined in turn to show howeach produces a component of rotating field flux at standstill, resulting instarting torque.

I

f d I Lr la

R,-l•

Rd1

Rd2E

Lr 2

~l Fr 2 Rr 2

(a) (b)

EdlE

Ed

Ed2

(c)

Figure 3 - Stepped airgap motor

a) Magnetic circuitb) Equivalent electric circuitc) Phasor diagram

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156

STEPPED AIRGAP

T. T. SHIMKEVICIUS AND G. R. SLEMON

The variable airgap feature of the motor of Figure 2 may be approximatedby the two-stage stepped airgap structure of Figure 1. The means whereby thisstructure produces a rotating field may be appreciated by developing a magneticcircuit as shown in Figure 3(a) and transforming it to an electric equivalentcircuit of the form of Figure 3(b) using the topological principle of duality[13]. In the magnetic circuit of Figure 3(a), Rdl and ~2 represent thereluctances of the leading and lagging air gap sections respectively. Fd isthe magnetomotive force of the pole winding. Fr l and Fr2 are the mmf's of therotor windings under the respective sections of air gap. The reluctances ofthe pole and yoke sections are assumed to be negligible. Because of symmetry,only half of the magnetic circuit is shown.

The equivalent electric circuit shown in Figure 3(b) is produced by insert­ing a node in each mesh of Figure 3(a) and interconnecting these nodes by ele­ments analogous to the reluctances shared by two meshes of the magnetic circuit.A reluctance R in the magnetic circuit becomes an inductance L = N2/R in theelectric circuit, where N is the number of turns on each pole. Ed representsthe induced emf due to air gap flux in each pole. The winding resistance Rwand leakage inductance LLW are added so that E represents the applied statorvoltage per pole.

Each section of rotor is represented by an appropriate inductance Lr and aresistance Re. Mutual coupling effects in the rotor have been ignored in thissimplified presentation but would have to be included in a quantitative analysis.

If the arc lengths of the leading and lagging sections of air gap in Figure1 are equal, the impedances Rr + j Lr of the two rotor branches in Figure 3(b)would also be equal. But, because of the increased gap length in the leadingsection, ~l > ~2 and Ldl < Ld2. A simple analysis of the electric equivalentcircuit therefore shows that the voltage Edl induced in the pole winding by theflux under the leading gap section leads in phase the voltage Ed2 due to theflux under the lagging gap section as shown in the phasor diagram of Figure 3(c).The corresponding displacement in time phase as well as space angle of the fluxcomponents produces a component of field rotating in the clockwise directionproducing starting torque.

It should be noted that inclusiDn of the effect Df rDtDr resistance isnecessary in Drder to demDnstrate a rDtating flux cDmpDnent. If the rDtDrbranches Df Figure 3(b) are open circuited Dr made purely inductive, Edl and Ed2will be in phase with each other.

YOKE ASYMMETRY

To iSDlate the effect Df yDke asymmetry, cDnsider the machine of Figure 2with nD airgap variatiDn under the main pDles and nD magnetic bridges as shownin Figure 4(a). A magnetic equivalent circuit is shown in Figure 4(b) in whichthe small and large yoke sectiDns have reluctances Rys and Ryi respectively.

If the yoke reluctances Rys and Ryi were equal, the machine WDuid be sym­metrical abDut its direct axis, and the direct axis flux ~d would divide equallybetween the yDke sections. This would result in zerD flux ~q in the quadraturepDles .

.The effect of simple magnetic saturatiDn in the small yDke may be demonstra­ted by assuming an appropriate saturated value fDr Rys and letting the reluctance

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SINGLE-PHASE INDUCTION MOTOR WITH ASYMMETRICAL STATOR 157

ae

(a) (b)

I

(c) (d)

(e)

Figure 4 - Motor with yoke asymmetry

a) Physical structureb) Magnetic circuitc) Equivalent electric circuitd) Simplified electric circuite) Phasor diagram.

Ry~ of the unsaturated yoke section equal zero. The corresponding electricequivalent circuit is shown in Figure 4(c). For simplicity, the stator resist­ance and leakage inductance are ignored in this and subsequent electric circuitssince they have no effect on starting torque.

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158 T. T. SHIMKEVICIUS AND G. R. SLEMON

By exploiting its symmetry, the electric circuit of Figure 4(c) may be re­placed by the simple form of Figure 4(d). Supposing the airgaps to be of equallength under the direct and quadrature axis poles, a symmetry argument wouldsuggest that the direct axis impedance of Ld in parallel with Rrd and Lrd wouldhave the same angle as the quadrature axis impedance of Lq in parallel with Rr qand Lr q• However, as shown in the phasor diagram of Figure 5(e), the effect ofthe saturable stator yoke is to cause Ed to lead Eq representing a clockwiserotation of flux from the direct to the quadrature axis.

H

e

B

Figure 5 - Fundamental magnetic field intensity H and its angle Brelated to the fundamental flux density B for ironlamination.

An additional contribution to rotating flux arises from hysteresis andeddy current losses in the yoke sections. If a magnetic core carries an oscil­lating flux density with fundamental frequency component B, the resulting fund­amental frequency component of field intensity H will lead B by angle e. Thus,

(1)

Typical graphs of Hand B as a function of B are shown in Figure 5 [14]. Themaximum value of loss angle e occurs at a relatively low flux density and maybe as large as 40-500 . At large values of flux density the relative permeability~r is low and the loss angle B is also small. If the core section has a length .t and area A, its complex reluctance is then given by

R (2)

The corresponding impedance in the electric circuit at frequency w is

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SINGLE-PHASE INDUCTION MOTOR WITH ASYMMETRICAL STATOR 159

(3)

The yoke sections may therefore be represented in the electric equivalent circuitby resistnace-inductance elements whose values are chosen for the appropriateflux densities using the information of Figure 5.

(a) I t I

(b)

Figure 6 - Motor with yoke asymmetry including the effects of yoke losses(a) Electric equivalent circuit, (b) Phasor diagram.

An equivalent electric circuit including the effects of finite reluctanceand core loss in both yokes of Figure 4(a) is shown in Figure 6(a). (In spiteof its symmetry, it is difficult to derive a simplified form of this circuit,similar to that of Figure Sed). The impedance Zy1 is larger than Zys in magni­tude and is more resistive. Analysis of the electric circuit gives the phasorrelationships of Figure 6(b). These are similar to those of Figure S(e), butthe phase displacement between Ed and Eq is somewhat greater. It is noted thatthe phase angle (90-8) between Ey1 and I y1 is less than between Eys and I ys.

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160

FLUX BRIDGE

T. T. SHIMKEVICIUS AND G. R. SLEMON

The motor of Figure 2 includes a solid iron flux bridge between each laggingmain pole tip and the adjacent quadrature pole. If the iron in the yoke and inthe quadrature pole is assumed to have high permeability, and if the flux fromthe bridge to the rotor is ignored, the bridge has no beneficial effect. Itmerely sets up a path for a leakage flux proportional to the mmf f d with accom­panying loss due to eddy currents.

Part of the effect of the flux bridge is to increase the flux ~ys in thesmall yoke sections, thus contributing to the yoke asymmetry effect. A furthereffect of the flux bridge is to act as an additional path for flux from the mainpole to the rotor. This flux is delayed in phase behind that of the main poleflux because of the eddy current losses in the flux bridge in much the same wayas occurs in a shaded pole motore

An additional effect of the flux bridge is to reduce the variation in sta­tor reluctance as seen by the rotating rotor. This causes a reduction in thedominant third space harmonic and a consequent reduction in the torque dip whichtypically occurs in a single-phase motor near one third synchronous speed. Thecontribution of this effect at standstill is, however, minimal.

Because of the interaction of the flux bridge effects with those arisingfrom other asymmetries, no separate equivalent circuits are presented here forthis effect.

EQUIVAlENT CIRCUIT OF COMPLETE MOTOR

In this section, an equivalent circuit model embodying the several asymmet­ries is presented. The magnetic equivalent circuit is shown in Figure 7(a). Themain pole airgap has been modelled for simplicity using two steps of reluctanceRdl and Rd2' However, a larger number of steps could be used if desired. Theyoke sections have been modelled as in Figure 4 with reluctances Ry! and Rys.The flux bridge has been represented as two series reluctances RbI and Rb2 fromthe main to the quadrature pole with a third reluctance Rbr from their centrepoint representing the flux path to the rotor.

The equivalent electric circuit corresponding to Figure 7(a) is shown inFigure 7(b). Each rotor section lying in the path of an airgap flux componenthas been represented by its appropriate Winding resistance and leakage induct­ance. The applied voltage to each main winding is E and the winding current isI. The resistance RW and leakage inductance of the winding LLW are included.

Figure 7(c) shows a typical phasor diagram of several of the voltage com­ponents of Figure 7(b). Since each voltage component is equal to N times thetime rate of change of its corresponding flux component in the magnetic system,the relative time phases of the voltage components are equal to the relativetime phases of the fluxes. It is noted that the time sequence of the voltagecomponents representing air gap flux is Edl' Ed2, Ebr and Eq. These occur inthe correct order to contribute to a rotating field in the clockwise directionfor the machine of Figure 2. Thus, all the asymmetry effects combine to producea starting torque.

TYPICAL OPERATING CHARACTERISTICS

Asymmetrical stator motors as described in this paper are able to producea starting torque which is about 40-50% of the rated torque of the motor.

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SINGLE-PHASE INDUCTION MOTOR WITH ASYMMETRICAL STATOR 161

(a)

(b)

(c)

Rrb r

Rrdl

----- ----:~ E

I

Figure 7 - Models for the complete motor - a) Magnetic equivalent circuitb) Electric equivalent circuitc) Phasor diagram.

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162 T. T. SHIMKEVICIUS AND G. A. SLEMDN

Efficiency at rated load is in the range 15-30% depending on size and construc­tion, while rated load power factor is about 0.6.

Table 1 shows typical experimental data from tests on four motors. Thisdata has been extracted from the 1967 paper written by the inventors of the mo­tor. Several factories in the USSR are currently producing these motors in2-pole ratings up to an output power of 60 W for application in fans, pumps andmixers.

TABLE 1

Experimental Results on Asymmetrical Stator Motors

MOT 0 R

A B C D

Line Voltage, V 220 220 220 220

Frequency, Hz 50 50 50 50

Sta r ting torq ue , mN-m 11.8 21.5 38.3 83

~aximum torque, mN-m 29.5 44.7 93.8 175.5

Rated torq ue , mN-rn 24.6 39.7 79.8 155.5

Rated apeed, r/min 2450 2330 2400 2330

Rated output power, W 6.3 9.7 20.0 38.0

Rated input current, A 0.228 0.43 0.555 1.15

Efficiency, % 21.2 17.7 27.4 24.8

Power factor, % 59.3 57.6 59.7 60.5

CONCLUSIONS

An-asymmetrical stator single-phase motor has been described, in which thestarting torque is produced by a combination of the effects of a tapered airgapunder the main pole, a solid iron flux bridge from each main pole to an adjacentquadrature pole with no winding and an asymmetry in the cross sections of theyoke sections on the leading and lagging sides of the main poles. A qualitativeappreciation of the effects of these asymmetries in causing phase displacementsin airgap flux components has been obtained by use of equivalent circuit modelsof the motor.

No attempt has been made in this paper to produce a quantitative analysisof the motor. However, it is expected that such an analysis could be achievedthrough an extension of the equivalent circuit appraoch to include rotor circuitcoupHng ,

The asymmetrical stator motor may have advantages over the familiar shadedpole motor for some applications. If its starting torque is adequate, it mayhave better utilization of materials and better rated-load efficiency than theshaded pole machine.

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SINGLE-PHASE INDUCTION MOTOR WITH ASYMMETRICAL STATOR

REFERENCES

[1] C.A. RaIl, "This Motor Meets Many Product Needs", Elec. Manufacturing,June 1937, pp. 31-35.

[2] J .L. Baum, "The Asynunetrical Stator as a Means of Starting Single-PhaseInduction Motors", AlEE Trans., Vol. 63, pp , 245-250, 1944.

163

[3] M. Poloujadoff, "Contribution a 1 etude des moteurs asynchrones monophas Ss ,Les moteurs a induction a cage d'ecureuil a entrefer non cons tant ", Rev.Gen. Elec., Vol. 68, pp. 696-701, 1959.

[4J G. Alternbernd, H. Baush, H. Jordan, "Theory of the Single-Phase Motor withStepped Airgap", Acta. Tech. CSAV, Vol. 13, pp , 403-425, 1968.

[5] O. I. Butler, K.J. Bradley, "Experimental Assessment of a Single Phase­winding Induction Motor", Electric Machines and Electromechanics Quarterly,Vol. 2, No.1, pp. 87-96, Oct-Dec. ,1977.

[6] D.D. Hershberger, J .L. Oldenkamp, "A Single-Phase Induction Motor with oneDistributed Winding", IEEE Trans., Vol. PAS-87 , pp , 1862-1866, 1968.

[7] P.I. Kostrauskas, R.D. Mukulis, T.T. Shimkevicius, "On Some Advantages ofSingle-Phase Induction Motors with Asymmetrical Stators compared withShaded-Pole Motors", Proc. Institution of Advanced Education of the Lithu­anian SSR - Electrical Engineering and Automation, Vol. 3, pp. 79-86, 1967.

[8] P.I. Kostrauskas, R.D. Mukulis, T.T. Shimkevicius, "Single-Phase MiniatureSalient Pole Asynchronous Motors", U.S. Patent No. 3,544,824, Dec. 1, 1970.

[9] H. Ooka, "Analysis of the Reluctance-Augmented Shaded Pole Motor", J. Lns t ,

Elec. Eng. (Japan), Vol. 91, pp. 145-153, 1971.

[10] S. Williamson, P. Breese, "Effect of Airgap-Profile Variations on the Per­formance of Reluctance-Augmented Shaded-Pole Motors", Proc. lEE, Vol. 124,No. 10, pp. 860-864, Oct. 1977.

[11] C.G. Veinott, "Fractional and Sub fractional Horsepower Electric Motors",McGraw Hill Book Co., New York, 1970, pp. 192-214.

[12] R. Perret, M. Po l.ouj adof f , "Characteristics Analysis of Saturated ShadedPole Induction Motors ll

, IEEE Transactions on Power Apparatus & Systems,Vol. PAS-95 , No.4, pp. 1347-1353, July/Aug. 1976.

[13J G.R. SIemon, "Magnetoelectric Devices", John Wiley and Sons, New York,1966, pp. 129-137.

[14] G.R. SIemon, T.T. Shimkevicius, "On the Complex Permeability of a Ferro­Magnetic Core", Electric Machines and Electromechanics, Vol. 3, No.2,

Jan-Mar. 1979, pp. 191-195.

Manuscript received in final form. April 13. 1919

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