MAGNETIC CIRCUIT ANALYSIS OF FLUX GUIDED RELUCTANCE MOTOR USING FINITE ELEMENT METHOD

M. Nagrial S.M.R. Sadri

Faculty of Engineering University of Western Sydney, Nepean P.O. Box 10, Kingswood, NSW 2747

AUSTRALIA

ABSTRACT This paper describes different magnetic circuits of reluctance machines having cylindrical stator and flux guided salient pole rotor and referred here as singly salient reluctance motor (SSRM). Various designs with one and multi-flux guides or barriers per pole are presented to achieve the desired Ld/Lq. These designs have been analysed using finite element method(FEM) to find the optimum design configuration. The present analysis refer to solid rotor designs due to their robustness and high speed capability.

I. INTRODUCTION The variable reluctance motor drive

technology with its competitive performance as variable speed drive has gone through steady and significant development over the last two decades [ 11. The synchronous reluctance motor is under renewed development and evaluation for variable speed drives. The recent developments have focussed on the cageless motor with current-regulated PWM inverter control. Because of the field orientation of this type of drive, and enhanced electromagnetics without the starting cage, much higher performance is possible in terms of efficiency, power factor and control capability. In order to realise these benefits the flux guided rotor construction is virtually essential, to permit sufficiently high saliency ratio to achieve competitive performance to that of induction machine.

The concept of axially laminated anisotropic rotor stems from the flux guided rotor structure by increasing the flux barrier sets to a sufficiently large number. The recent development on flux barrier rotor and axially laminated rotor has been reported [2-61. For segmental rotor and flux barriers rotor [3-41 the ratio W L q of about 6 to,7 has been reported. Axially laminated rotor has been reported by Boldea & Nasar [6] for 2 HP motor with ratio of Ld/Lq up to 16, high power factor 0.91 and efficiency of about 84%.

The purpose of this paper is to study the magnetic circuit of singly salient reluctance motor (SSRM) having flux guided rotor structure [7-131. The SSR motors can be operated as: 1) Variable reluctance drive with the phases switched sequentially. The SSRM is driven through a dc fed which relies on electronically switched supplies to its phase windings, timed to correspond with rotor position. This mode of operation is similar to that used with switched reluctance motor and brushless dc motor. 2) Synchronous reluctance motor by rotating field through an ac fxed frequency or variable frequency source. Almost in both cases; the aim is to obtain a rugged and simple construction of the motor having a high torque density, efficiency and power factor. To achieve these aims, the ratio Ldnq has to be maximised.

The advantages of such a design

IEEE Catalogue No. 9STHSO2.5 0-7803-2423-4/9S/$4.O0@199S IEEE

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are as follows: 1)

2)

3)

Easy to built from manufacturing point of view. The rotor design is more robust and can withstand high speed. Because of airgap barrier inside the rotor it has good ventilation and minimal temperature effects.

4) It can produce large saliency ratio with high synchronous inductance.

5 ) Capability of operating as VR motor and synchronous reluctance motor.

6) Because of its smooth singly saliency, noise and torque ripple reduced significantly.

7) Ease of repair. 8) Low inertia. 9) Low material cost.

The SSRM has a stator with conventional cylindrical shape and distributed winding similar to that of an induction motor. Fig 1 shows a typical 2 polar, 2 flux guided per pole SSRM. Fig 1 shows a rotor with two flux guidedpole. The outer steel sections are separated from the central section by two barrier with thicknesses T1, T2 whose positions are def ied by al, a2. The size of the cutout area which is referred as channel is adjusted as explained later (Eqn. 1).

The SSRM design could be optimised by considering the following rotor parameters [12]. 1) Channel arc y = channel arc/pole

pitch. 2) Channel depth (Dc). 3) Flux barrier thickness (T). 4) Flux barrier position CL = Flux

barrier ardpole pitch. 5) Number of flux barriers per pole.

y determines the rotor pole arc and as a result, important for increasing the saliency of the machine. The pole arc may lie within the limit as follows:

Where q = number of phases. The remaining three parameters,

pertaining to flux barrier in the rotor, also

l/q ~ ( 1 - y) 5 2/3 (1)

have major effect on the saliency and hence the performance. So the flux barrier's position and size play very important part in the saliency of the motor and saturation level in the rotor iron.

In general, the flux barriers lie substantially parallel to the d-axis flux lines and cutting across the q-axis flux lines. For an optimum design it is important to create the largest possible reluctance in the q-axis. It is preferable to limit the flux barrier thickness less than the stator tooth. The thicker flux guide( large T) will result in large saliency but at the cost of reducing Ld. The rotor of SSRM can be designed with one flux guide or multi-flux guides per pole. The central section of SSRM is integral with rotor shaft, therefore the shaft is considered as a part of rotor magnetic circuit.

The precise knowledge of variation of (LdLq) and (Ld-Lq) with rotor dimensions is important due to the fact that the output torque is a function of the inductance difference, and the power factor is dependent on inductance ratio. The minimum airgap between stator and rotor is 0.2 mm, since a small airgap improves output torque and power factor of the machine. The increased M due to an increased rotor iron result in the rotor to become less saturated. Thus the major aim to optimise the rotor design is to keep enough iron area, but not at the cost of reducing the necessary saliency. The Lq is more sensitive to the pole arc and the shape and size of flux barriers than U.

II. RESULTS The analysis of variable reluctance

(VR) motor requires a reliable model for magnetic field calculations. Because of deep saturation of the magnetic circuit and complex geometry, the finite element method (FEM) seems to be most suited. A commercially available software (MSCEMAS) has been employed for the finite element analysis of the magnetic field and inductance estimations for flux guided

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reluctance machine. The magnetic field in the machine under study is assumed two dimensional. The level of the current excitation applied, I=2.4 A, which is the rated current of the machine. The magnetic circuits of one-flux. guided, two- flux guided, three-flux guided and multi- flux guided rotors have been analysed.

Figures 2 and 3 show comparison of one flux guided rotor with variation of flux barrier position. Therefore for the sake of simplicity, the channel is removed in both designs. The right half shows the direct axis flux while the left half shows the quadrature axis flux. The design shown in fig 3 has much large saliency than the design of fig 2 (see table I) because when the barrier is positioned at a = 0.81, it can break more flux lines around its excited phase in q-axis. The experimental result and performance evaluation of one flux guided rotor design has been reported elsewhere [12].

Figures 4 and 5 show flux distributions for two flux guided rotors. In these designs the same amount of T per pole is maintained as in one flux guided design (fig 2). As shown in fig 4, the flux barriers are not located at optimum positions and Ld/Lq is not large enough. In fig 5 both flux bamers are located at optimum locations resulting in high reluctance in q-axis (see table I). It can be concluded that the design depicted in fig 5 is close to optimum for such a machine. The experimental result of a two flux guided rotor are being reported [131.

Figures 6 and 7 show two three flux guided rotor designs. Fig 6 is a three flux guided rotor without channel and its specification and inductance calculation is given in table I. Fig 7 shows a three flux guided rotor with the same configurations as in fig 6 but with channel on the surface. The results of FEM analysis in table I1 show that fig 6 is a better design due to larger Ld and approximately same Lq as in fig 7. Generally an addition of a channel increases LdLq but in this case it has

resulted in reduced Ld/Lq. The total flux barrier thickness per pole in this design is the same as in other designs. All the results are summarised in table I and II. Table I shows the comparison without channel and table I1 shows the results with channel. Fig 7 shows the channel on the surface while the other rotors with channels are not shown but they have the same size channel as in fig. 7 and the results are given in table 11.

Any design here with more than three flux guides or barriers per pole is referred as multi-flux guided design. Four flux guided and five flux guided rotors also have been investigated but not reported here as with six flux guided rotor analysis, it is possible to predict that the design will not necessarily be optimum by increasing the number of guides as shown in figures 8. The design in fig 8 has no channel on the rotor. There is a limit for increasing the number of flux guides per pole and removing iron area. Because by removing more iron area it can reduce Ld. In addition large number of barriers make it more difficult from manufacturing point of view and also increase the cost of manufacture.

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Fig 1: Flux guided RM with 2 poles

q- axis d- axis Fig 2: Flux distribution in one FG/pole machine

q- axis d- axis Fig 3: Flux distribution in one FGlpole machine

q- axis d- axis Fig 4: Flux distribution in two FG/pole machine

q- axis d- axis Fig 5: Flux distribution in two FG/pole machine

q- axis d- axis Fig 6: Flu: distribution in 3 FGlpole machine

q- axis d- axis

with channel. Fig 7: Flux distribution in 3 FGlpole machine

q- axis d- axis Fig 8: Flux distribution in 6 FC/pole machine

63 1

Table I:

(All dimensions are in mm, inductanow in mA)

Inductance calfulstlon dlux guided lotors using FEM.

Fig No

TI1 w 1 T.21 w2 l-31 w 3

a 1 a2 a 3 a4 a 5 a6

Ld 4

Ln

4

Ld/

Ld-

Fig 2

8.161 51 -

-

0.66 - -

-

-

-

207 35

5.9

172

- Fig 3

- 8.161 61 -

-

Fig No.

T I N 1 T z N 2 T3W3

CL1 a 2 a3 a 4 a 5 a 6

Ld 4

Ld/Lq

Ld-Lo

198 12

Fig3 Fig5 Fig 7 Fig 8

8.16161 4.08155 2.72150 1.36 4.08/61 2.72157 X

- - 2.72161 6

0.81 0.66 0.57 0.5 1 - 0.87 0.63 0.62 - - 0.87 0.72 - - 0.82 - - - 0.90 - - - 1

198 177 200 180 11.5 15 14 15.6

17.2 11.8 14.2 11.5

186.5 162 186 168.5

16.5

- 186

-

Fig4 Fig 5 Fig 6

4.081 4.081 2.721

4.081 4.081 2.721 58 61 57

- 2.721 61

0.50 0.74 -

0.66 0.87 -

0.57 0.63 0.87

33 14

- Fig 8

- 1.36 TI x 6

- 0.51 0.62 0.72 0.82 0.90 1

218 16

13.6

- -

- 20

-

Table II: Inductana dfulstion for the rotors with -el, using FEM. The results are similar to ones Indicaled except a channel similar to ilg. 7.

(All dimensions are in mm, inductanas in mH)

III. CONCLUSIONS The Finite Element Method has

been used to find the optimum design for flux guided reluctance motors. Some of the designs has been built and tested and reported elsewhere [12-131. The results suggest that two and three flux guided

rotors can have better performance because of their high inductance ratio and inductance difference even for a machine with power rating of 0.55kw, provided the flux guides are positioned at optimum locations. The details of such optimum configurations are also given.

1.

2.

3.

4.

5 .

6.

IV. REFERENCES Lawrenson, P.J., Stephenson, J.M., Blenkinsop, P.T., Corda, J. and Fulton, N.N. "Variable-Speed Switched Reluctance Motors" Proc. Inst. Elec. Eng. vol. 127, July 1980. pp 253-265.

Xu, L.-Y., Lipo, T.A. and Rao, S.C. "Analysis of a new variable speed singly salient reluctance motor utilising only two transistor switches'' IEEE Trans. Ind. Appl,

MarlApr. 1990. vol. 26, NO. 2, pp. 229-236,

Lawrenson, P.J. "Two speed operation of salient-pole synchronous machines" Proc.

1965. IEEE, vol. 117, pp 2311-2316,

Nagrial, M. "Design optimisation of s y n c h r o n o u s r e l u c t a n c e (SYNCREL) motor" AUPEC '93, Australia, pp 466-477, Sep 1993.

Plat, D. "Reluctance motor with strong anisotropy" Rec. IEEE-IAS Annual Meeting, pt. 1, pp 224-229, 1990.

Boldea, I., Fu, Z.X. and Nasar, S.A. "Performance evaluation of axially-laminated anisotropic rotor reluctance synchronous motor" IEEE Trans. Ind. Appl, vol. 30,

1994. NO. pp 977-983, 4, JulyIAugust

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7. Lawrenson, P.J. and Nagrial, M.H. "An improved reluctance motor" Proc Intern, IEE conference EMDA, London, July 1982.

8. Nagrial, M.H. "Segmental rotor reluctance motor design optimisation using complex method Proc ICEM, pp 262-265, Budapest, Sept 1982.

9. Nagrial, M.N. and Lawrenson, P.J. "Optimum steady-state and transient performance of reluctance motors" Proc ICEM, Vol 1 pp 321-324, Lausanne, Sep 1984.

10. Sadri, S.M.R., Nagrial, M. and Gogani, E.S. "Brushless DC motor controller for singly salient switched reluctance motor"

June 1994. SPEEDAM, pp 151-155 Italy, 8

11. Sadri, S.M.R. and Nagrial, M. "Variable reluctance motor using Motorola controller" EEC 94, Nov 1994, Sydney, Australia.

12. Nagrial, M. and Sadri, S.M.R. "VR motor with solid rotor: Design and performance" AUPEC 94, Adelaide-Australia, Proc. vol. 1, Sep 94, PP 49-55.

V. APPENDIX

Rating of the motor: (as induction motor)

0.55 KW

Stator: length bore back T.H. tooth slot area tudslot wire size coil pitch no of coil resistance/phase

5 0 " 63" 15.2" 3.8" 50.0 [sq.mm] 104 1 x 0.45 1-12,2-11 12 20 deg.c: 18 ohm

Rotor: Diameter 62.6" length 5 0 " airgap length 0.2"

W T d

a 1 a 2 a3 Y M Ls

length of flux barrier thickness of the flux guide the distance of the flux guides from the centre first flux guide pitcWpole pitch second flux guide pitch/pole pitch third flux guide pitch/pole pitch channel widtWpole pitch direct axis inductance quadrature axis inductance number of phases

13. Sadri, S.M.R. and Nagrial, M. "Design of singly salient VR motor with solid rotor" PEC'95, Singapore.

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