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Analytical design and FEM verification of a novel three-phase seven layers switched reluctance motor.

1. INTRODUCTION

Switched Reluctance Motor (SRM) is a strong motor which is taken into consideration by industries. It has high efficiency, needs low maintenances and can work in harsh environment. This type of motor is one of the challengers for low cost and simple structure in variable speed drive applications such hybrid electric vehicles, household appliances, and wind energy [1-5].

Generally speaking, there are two kinds of SRMs; Linear SRM (L-SRM) and the Rotary SRM (R-SRM). Based on this category, the general classification of SRM is shown in Figure 1.

Optimal design of different types of SRMs involve the selection of the motor's geometrical parameters to produce high output torque respects to its volume with considering the minimum ripples [6,7].

Therefore, the efficient design of SRM is a considerable way to achieve high performance and output torque [8]. The efficient design of SRM has been undertaken based on various aspects as; (I) Modification of the rotor, stator shapes [9]; for instance; Double-layer per phase isolated and multilayer SRMs are introduced in [10] by authors to improve the torque ripple and noise with considering the maximum performance. (II) The use of numerical methods to efficient design and analysis process such as finite element method [11,12]. (III) The intelligent and heuristics methods namely as Neural Network (NN) [13,14], and Genetic algorithm (GA) [15,16] play important role in the mentioned purpose of design. (IV) Optimum design of control and derive unites of motor [17-20].

Efficient and Optimal design of SRM for high performance motion control systems requires accurate knowledge of the magneto static fields that relate motor geometry and motor performance [21-23]. These contexts can be explored through extensive prototyping, which is impractical and very costly, or by accurate magnetic field simulations. Magnetic field simulation directly yields predictions of flux linkages, field energy, and torque profiles

This paper investigates the design consideration of a novel type of switched reluctance motor, which its characteristic and profile are verified with numerical verification in next sections.

2. ANALYTICAL DESIGN PROCEDURE

The designing procedure is explained step by step as follows. The first step of SRM design is to determine the required output power [P.sub.hp] and speed, which are;

[P.sub.hp] = 2 hp, n = 1500 rpm, [i.sub.p] = 12 A, [n.sub.s], [n.sub.r] = 4

where [i.sub.p], [n.sub.s] and [n.sub.r] are the peak value of current, number of stator and rotor poles. The torque of the machine is calculated as:

[T.sub.eq] = [P.sub.hp]/2[pi](N/60) = [2 x 746]/2[pi](1500/60) = 9.49 N x m (1)

From the NEMA table the frame size for a 2 hp is selected based on IEC standard as:

No. of fram size = 56 (2)

D = (3.5 inch) x 2.54 = 88.9 m (3)

The outer diameter of the stator is

[D.sub.0] = (88.9 - 3) x 2 = 171.8 mm (4)

Because of the same ratio of L respect to D, thus the stack length L is:

L = [D.sub.0] = 171.8 mm [right arrow] L [approximately equal to] 170 mm (5)

Based on mentioned standard, for selected frame size, the maximum value of shaft diameter is calculated as

[D.sub.sh] = 5/8(inch) = 16 mm (6)

Air gap length is considered as (according to the manufacturing limitations)

g = 0.5 mm (7)

Based on B-H curve for selected core material, the maximum value of magnetic field intensities is put as:

[B.sub.max] = 1.8 T (8)

And the value of magnetic field intensities in the stator pole is also:

[B.sub.s] = 1.8T (9)

The stator pole area [A.sub.s] can be written as,

[A.sub.S] = [88.9/2] x 170 x 45[degrees] x [[pi]/180] = 5931.85 x [10.sup.-6] = 5.93185 x [10.sup.-3] [m.sup.2] (10)

The flux in the stator pole [[phi].sub.s] is,

[[phi].sub.s] = 1.8 x 5931.85 x [10.sup.-6] = 10.6773 mWb (11)

The flux in the yoke py is

[[phi].sub.Y] = [pi]/2 = [10.16773/2] = 5.3386 mWb (12)

The area of the yoke [A.sub.y] can be set as,

[A.sub.Y] = [A.sub.s]/2 = 2.965925 x [10.sup.-3] [m.sup.2] (13)

The back iron thickness is obtained:

C = [A.sub.Y]/L = [2.965925 x [10.sup.-3]]/[170 x [10.sup.-3]] = 0.01744 m (14)

The stator pole height [H.sub.s] is given by,

[h.sub.s] = [[D.sub.0]/2] - C - [D/2] = [171.8/2] -17.44 x [10.sup.-3] - 44.45 = 24.01mm (15)

The rotor pole area [A.sub.r] is given by

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)

The area of the rotor core [A.sub.rc] is given by,

[A.sub.rc] = [A.sub.s]/1.6 = 3.707 x [10.sup.-3] [m.sup.2] (17)

The height of the rotor pole [h.sub.r] is

[h.sub.r] = [D/2] - g - [[D.sub.sh]/2] - [[A.sub.rc]/L] = 14.14mm (18)

The average area of [A.sub.g] is:

[A.sub.g] = 5.898 x [10.sup.-3] [m.sup.2] (19)

The flux density in the air-gap [B.sub.g] is:

[B.sub.g] = [[A.sub.s] x [B.sub.s]]/[A.sub.g] =1.81T (20)

The magnetic field intensity of the air-gap [H.sub.g] is:

[H.sub.g] = 1.81/[4[pi] x [10.sup.-7]] = 1441346.93 [AT/m] (21)

where AT is ampereturn. The flux density in the yoke [B.sub.y] is:

[B.sub.Y] = [B.sub.max]/2 = 0.9T (22)

The magnetic field intensity of the yoke [H.sub.y] is obtained from:

[H.sub.Y] = 0.05 x [10.sup.4] [AT/m] (23)

The flux density in the rotor [B.sub.r] is:

[B.sub.r] = 0.8 x [B.sub.max] = 1.44T (24)

The magnetic field intensity of the rotor [H.sub.r] is obtained from:

[H.sub.r] = 0.25 x [10.sup.4] [AT/m] (25)

The magnetic field intensity of the rotor core [H.sub.rc] is equal to [H.sub.r]:

[H.sub.rc] = [H.sub.r] = 0.25 x [10.sup.4] [AT/m] (26)

The mean path lengths of various sections are given as follows:

[L.sub.s] = [h.sub.s] + [C/2] = 24.01 + [17.44/2] = 32.73 mm (27)

[L.sub.g] = g = 0.5 mm (28)

Lr = [88.6/4] + [0.5/2] + [14.14/2] - [16/4] = 43.73mm (29)

[L.sub.rc] = [pi] (43.73) = 137.3279 mm (30)

The mean length [L.sub.y] for a circular yoke SRM;

[L.sub.Y] = n [[171.8/2] - [17.44/2]] = 242.34 mm (31)

The flux density in the air-gap [B.sub.g] is given by,

[B.sub.g] = 1.81 T (32)

The magnetic field intensity of the air-gap [H.sub.g] is calculated as,

[H.sub.g] = 1.81/[4[pi] x [10.sup.-7]] = 144.13 x [10.sup.4] [AT/m] (33)

Using the B-H characteristics for the material used for the laminations, the magnetic field intensity in Ampere-turns per meter for each portion of the machine except the air-gap is obtained. The magnetic field intensities in the stator pole, stator yoke, rotor pole and rotor core are designated as [H.sub.s], [H.sub.y], [H.sub.r] and [H.sub.rc], respectively.

[B.sub.s] = [B.sub.max] = 1.8T, [H.sub.s] = 2 x [10.sup.4] [AT/m] (34)

[B.sub.y] = [B.sub.max] = 0.9T, [H.sub.y] = 0.05 x [10.sup.4] [AT/m] (35)

[B.sub.r] = 0.8 [B.sub.max], [H.sub.r] = 0.25 x [10.sup.4] [AT/m] (36)

[B.sub.rc] = [B.sub.r], [H.sub.rc] = 0.25 x [10.sup.4] [AT/m] (37)

The magnetic circuit equation of the aligned inductance can be written as,

E = [T.sub.Ph] x i = 4 x ([H.sub.s] x [L.sub.s] + [H.sub.g] x [L.sub.g] + [H.sub.r] x [L.sub.r]) + [[[H.sub.rc] x [L.sub.rc]]/4] + [[[H.sub.Y] x [L.sub.Y]]/4] = 1600.79 AT (38)

Now, the total ampere-turns E required for the machine operation at full load can be calculated.

It is also known that E = [T.sub.Ph] x i. Since the peak current [i.sub.p] is assumed initially, the turns per phase can be calculated by;

[T.sub.Ph] = [1600.39/12] = 133.39 turns (39)

[T.sub.ph] can be calculated. The aligned inductance at maximum current is calculated as,

[L.sub.aligned] = [1600.39 x 1.8 x 5.931 x [10.sup.-3]]/[12.sup.2] = 118.67 mm (40)

Based on the obtained geometrical and magnetic parameters the SLSRM is modeled and analyzed utilizing 3D-FEM in next parts.

3. THE STRUCTURE OF NOVEL THREE-PHASE SEVEN LAYERS SWITCHED RELUCTANCE MOTOR

The new SLSRM structure is shown in Figure 2. It consists of seven magnetically independent stator and rotor sets. In this structure, each stator set includes four salient poles having 45[degrees] arc length with coils wrapped around them. The each set of seven rotor layers comprises of four salient poles with same arc lengths and without windings coils. The motor volume and dimensions are just like the designed single layer 6/4 SRM but it is divided into 7 slices. Each layer of rotor is 12.7[degrees] shifted than another rotor poles which is obtained from:

[DELTA][theta] = [[360/Startor Poles]/Number of Layers] = [[360/4]/7] = 12.7[degrees] (41)

where [DELTA][theta] is deviation of rotor angle in each layer. As the coils in each layer are turned on together, coils wrapping is safer and also less maintenances is needed because of less isolation problems exiting in usual SRMs construction. Since each stator in the SLSRM has independent phase and all the coils in each layer install to an independent control signal, there is no custom isolation problems which exist in conventional SRMs. This make the SLSRM structure applicable in compare with other types of SRMs. In fact, in this machine can wrap bigger coil which produces higher output torque per volume. The motor assembly of SLSRM is shown in Figures 2(a) and (b). Also, the 3D-FEM model of single layer 6/4 SRM is shown in Figure 3 for comparison study.

4. THE COILS ENERGIZING SCHEMATIC

For running the SLSRM, the coils of three stator layers are energized at the same time. Then, this procedure is repeated for other layers, step by step. Always, one of the layers exists that is shared for next strokes. This schematic is continuing for seven steps until 360[degrees] rotor rotation. This type of energizing leads to the rotor produces more torque and also decreases the torque ripple.

To study the operation of the novel SLSRM, finding out the region of the rotor firing angle of the layers is significant. On the other hand, the rotor should be in the position which can produce positive torque. If the firing angle of the rotor doesn't choose proper, the negative torque may produce which acts like brake for the motor. As it's explained before, in this seven layers structure, three layers of motor can be energized in order to produce positive torque. These layers should be shifted in compare with the whole layers to produce continuous positive torque. The principle of the operation of this motor is described in Table 1.

5. FINITE ELEMENT RESULTS AND ANALYSIS

A precise model is needed for the physical motor simulation to incorporate the essential dynamics of the motor [24-29]. The Finite Element Method can be one of the best choices for providing realistic and precise model [30-33]. In this paper, to obtain the field distribution for SLSRM the three-dimensional finite element method (3D-FEM) is used which can be conveniently calculating the motor parameters. The variation energy minimization technique is used to solve for the electric vector potential. This method uses electric vector potential known as T-[OMEGA] formulation which is described in details by authors in the previous papers. The modeling and analysis of the 4/4 SLSRM and the conventional 6/4 SRM are performed by the MagNet CAD package [34]. It should be noted that the machine operates in saturation region for both motor and generator modes, based on its nature.

The magnetic flux density (B) of the proposed SLSRM is obtained and shown in Figure 4 for the beginning of alignment, half aligned and fully aligned positions. For comparative study, the conventional single layer SRM with the same volume and area is also simulated and analyzed by 3D-FEM. The flux density of this 6/4 SRM is illustrated in Figure 5 for unaligned, half aligned and fully aligned positions.

As illustrated in Figure 4, the maximum value of the flux density (in phase A) is about 2.1 Tesla when three layers are energized, in SLSRM for half-aligned position. In this figure the first shown layer is in the fully aligned position. The second layer is not full aligned yet (half aligned) and the third one is at the first region of alignment (beginning of the alignment). The second and the third layers are turned on in the next step in which another layer is turned on to make the motor have three turned on layers at a moment, again. This process makes a high continues positive torque.

In the conventional single layer SRM the magnitude of the flux density is about 2.38 Tesla for half-aligned position as it's depicted in Figure 5. It means that the SLSRM is able to produce more flux density in comparison with the single layer SRM with same volume in identical conditions.

The motor reluctance variation which is the effect of the rotor position variation is a significant parameter and causes the flux variation in rotor and stator poles. The inductance as well as flux linkage profiles are two fundamental characteristic for SRM control. In Figure 6 and Figure 7 the flux linkage of the motor with respect to the rotor position are shown for SLSRM and SRM, respectively.

As depicted in Figure 6, the maximum flux of the novel SLSRM is about 442 mWb at fully aligned, also the minimum flux is about 36 mWb at the beginning of alignment. The flux value is about 42 mWb for half aligned position. However, Figure 7 shows that the maximum flux is about 37 mWb at fully aligned, the minimum flux is about 10 mWb at the beginning of alignment and for half aligned position the flux value is about 27 mWb. From obtained fluxes, it can be resulted that the flux linkage of SLSRM in different rotor positions is higher than conventional SRM. As a summery; the total flux linkage of each phase of SLSRM has 260%, 55% and 19% increase in beginning of alignment, half-aligned, and fully aligned positions, respectively.

For performance evaluation of the two motors, the produced torque could be evaluated in same conditions. In this regard, the produced static torque is obtained (Figure 8) and its shape with respect to the rotor position is shown for the phase current of 3 A and 150 turns coil, from beginning of alignment to fully aligned position. Also, the same curve is obtained for the conventional 6/4 one layer SRM for comparative study and is illustrated in Figure 9.

As depicted in Figure 8, the maximum torque of the novel SLSRM is about 1.3 N-m at half aligned, also the minimum torque is about 0.95 N-m at the beginning of alignment. The torque value is about 0.9 N- m for fully aligned position. However, Figure 9 shows that the maximum torque is about 0.65 N- m at half aligned, the minimum torque is about 0.11 N- m at the beginning of alignment and for fully aligned position the torque value is about 0.01 N- m. Form these results, it can be concluded that the produced torque of SLSRM in different positions is higher than conventional SRM. In fact the output torque of SLSRM has 2, 8.6 and 1.5 times higher value than SRM in half-aligned, beginning of alignment and fully aligned positions, respectively. As stated before, the total volume of both motor is equal; therefore, the torque/volume characteristic of the SLSRM is higher than conventional SRM with noticeable value.

6. CONCLUSION

In this paper, a novel 4 by 4 SRM namely as SLSRM, with seven magnetically independent layers was proposed, analytically designed and modeled utilizing 3D-FEM in various conditions. The comparative study with a single layer conventional 6/4 SRM were shown that the magnitude of flux density has been faced with an increase in SLSRM. Furthermore, the flux linkage value had 260%, 55% and 19% increase in beginning of alignment, half-aligned, and fully aligned positions, respectively, which shows the increased potential ability of the motor. Moreover, the output torque of SLSRM has 1.5-8.6 times higher value than SRM to prove its high efficiency in same condition The comparative study shows that more than one the layer energizing in SLSRM causes the torque ripple decreases. In addition it was concluded that the torque/volume characteristic of the SLSRM is higher than conventional SRM with noticeable value about twice. This configuration allows more space for coil windings which means users can wrap bigger coil and the motor produces more torque. Moreover, the isolation problem in the coils of layers is also solved and motor cooling is easier.

ACKNOWLEDGMENT

This work was supported by grant from Iran National Science Foundation.

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Ebrahim Afjei (1), *, Alireza Siadatan (1), and Hossein Torkaman (2)

(1) Faculty of Electrical Engineering, Shahid Beheshti University, G.C., Tehran, Iran

(2) Faculty of Electrical and Computer Engineering, Power and Water University of Technology (Shahid Abbaspour University of Technology), Tehran, Iran

Received 7 April 2013, Accepted 3 May 2013, Scheduled 29 May 2013

* Corresponding author: Ebrahim Afjei (e-afjei@sbu.ac.ir).

Table 1. The energizing principle of the SLSRM.

         Layer   Layer   Layer   Layer   Layer   Layer   Layer
           1       2       3       4       5       6       7

Step 1    ON      ON      ON      --      --      --      --
Step 2    --      ON      ON      ON      --      --      --
Step 3    --      --      ON      ON      ON      --      --
Step 4    --      --      --      ON      ON      ON      --
Step 5    --      --      --      --      ON      ON      ON
Step 6    ON      --      --      --      --      ON      ON
Step 7    ON      ON      --      --      --      --      ON
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Author:Afjei, Ebrahim; Siadatan, Alireza; Torkaman, Hossein
Publication:Progress In Electromagnetics Research
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Geographic Code:7IRAN
Date:Aug 1, 2013
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