Optimum Rotor Shaping for Torque Improvement of Double Stator Switched Reluctance Motor

Abstract

Although the power density in Double Stator Switched Reluctance Motor (DSSRM) has been improved, the torque ripple is still very high. So, it is important to reduce the torque ripple for specific applications such as Electric Vehicles (EVs). In This paper, an effective rotor shaping optimization technique for torque ripple reduction of DSSRM is presented. This method leads to the lower torque pulsation without significant reduction in the average torque. The method is based on shape optimization of the rotor using Finite Element Method and Taguchi's optimization method for rotor reshaping for redistribution of the flux so that the phase inductance profile has smoother variation as the rotor poles move into alignment with excited stator poles. To check on new design robustness, mechanical analysis was used to evaluate structural conformity against local electromagnetic forces which cause vibration and deformation. The results show that this shape optimization technique has profound effect on the torque ripple reduction.

1. Introduction

Switched Reluctance Motors (SRM) has unique capabilities of operation in super high speeds and harsh environment. So, they are good candidates for industrial and automotive applications. Because of absence of the excitation winding on the rotor, they are not susceptible to rotor winding faults and demagnetization or flying off the magnets. Also, owing to its stiff structure and the absence of the magnetic source on the rotor, an SRM is inherently robust and cheap.

In spite of its advantages, SRM has a nonlinear and complex behavior due to local saturation of some rotor and stator iron parts and doubly salient structure. This affects the overall performance of the motor. Two of the SRM disadvantages are high torque ripple and low power density as compared to PMS motors. Switched-reluctance motors produce acoustic noise and vibration caused by torque ripple and normal forces acting on the rotor and stator surfaces. Application of these motors where silent operation is desirable, such as in home appliances, has, thus, been limited. Therefore, a large improvement in power density and torque ripple is necessary for SRM before it can be chosen as suitable candidate for such applications. The improvement in power density was made possible by new design of double stator switched reluctance motor which was introduced in [1]. However, the problem of high torque ripple is remained unsolved in this motor too.

Over the last two decades different advanced control and design strategies have been developed for torque ripple reduction, but due to high torque pulsation especially at low speeds those controls and design strategies has not been effective to reach the acceptable torque characteristics. In [2] a new technique of generating optimal current commands for SRM drives is presented. Authors have used a small set of Fourier coefficients rather than a large set of discrete points. Reference [3] presents a torque ripple minimization controller realized by indirect position and speed sensing for switched reluctance motors (SRMs). A method of torque ripple reduction for low speed SRM drives has been presented in [4]. The method includes a new PWM current control strategy where the current follows a contour for constant torque production.

A new current shape required for a low torque ripple switched reluctance motor for high speed applications is introduced in [5]. An early attempt to minimize torque ripple using Torque Sharing Functions (TSFs) is presented by Illic-Spong et al. in [6]. This method uses exponentially rising and decreasing TSFs. A method which minimizes the peak current requirements of the phase while requires linear change in the rotor angular variation during phase commutation is investigated in [7]. An advanced control system that uses the linear motor and load model and decouples the control requirements of the SRM phases originated from the work of Taylor et al. [8, 9]. Author in [10] presents a review on previous methods used to mitigate torque ripple in SRM drives. Authors in [11] presented a genetic algorithm for switched reluctance motor design optimization. They used a novel multi-objective optimization method based on a Genetic-Fuzzy Algorithm (GFA) for torque ripple mitigation. In [12], to reduce the torque pulsation, a novel SRM appropriate for use in hybrid electric vehicles with more rotor poles than stator poles is represented. This paper claims that a 6/10 SRM produces a higher average torque and lower torque pulsation compared with a 6/4 SRM. Reference [13] introduces a new and efficient commutation algorithm for torque ripple reduction. The commutation algorithm is speed dependent and uses a real time approach instead of pre-calculated stored data. In [14], a new rotor shape design is presented to mitigate the torque ripple of switched reluctance motor. Authors in [15] describe a proposal for a new stator pole face having a non-uniform air-gap and a pole shoe attached to the lateral face of the rotor pole. These additions minimize the undesired torque ripple. The effects of each design parameter are investigated using a time-stepping finite-element method. Authors in [16] use additional teeth per rotor and stator pole to mitigate the torque ripple. Reference [17] briefly describes an approach to determine the optimum magnetic circuit parameters to minimize low speed torque ripple for switched reluctance (SR) motors. In [18] an electromagnetic analysis of the switched-reluctance (SR) machine with saw-shaped (shark) pole surfaces was presented. This design aspect facilitates an increase of the ‘maximum/minimum’ inductance ratio, relative to the flat-pole structure. Authors in [19] investigated the effect of the rotor profile on the produced torque of SRM. Authors in [20] present a numerical multiobjective optimization procedure by using finite element simulation, the Kringing model and Pareto archived evolution strategy. Reference [21] introduces a new and efficient commutation algorithm for torque ripple reduction. The commutation algorithm is speed dependent and uses a real time approach instead of pre-calculated stored data. Authors in [22] present the design and operation of a twophase four-two pole SRM for a high-speed air blower. In [23] a novel method of eliminating the torque ripple in the instantaneous torque profile of SRM is presented, and a method to generate the precise reference phase current waveforms for even open loop operational design through global optimization is investigated.

Before invention of double stator switched reluctance motor (DSSRM) [1], as shown in Fig. 1, power density of the switched reluctance motor was not comparable with that of PM motors. So, PM motors are more popular than switched reluctance motors in many applications. In conventional SRM, force components are used inappropriately, therefore, the developed torque was lower than motor real capability. To overcome that deficiency, larger normal force components in DSSRM are used to produce a higher average torque. In the switched reluctance motor, the normal force density is much larger than the tangential force density, whereas the normal force is troublesome and the tangential force is used for torque production. It was necessary to design a new structure which uses the larger part of the produced force to move the rotor. In DSSRM, the motion direction is aligned to flux path (as shown in Fig. 2) and the larger force component is moving the rotor. The most important advantage of DSSRM is its high power density, and its adverse characteristic is the high torque pulsation in domestic and automotive applications where the high torque pulsation is not acceptable.

Fig. 1.Cross section of 4- phase DSSRM

Fig. 2.DSSRM flux lines whit phase ‘a’ excited to move the rotor clockwise

In this paper, we try to reduce the torque ripple of DSSRM by modification in force components which depends on the profile of stator phase inductance. Our preliminary analysis resulted in an initial rotor shape. However, due to mechanical and manufacturing constraints, initial shape is substituted by 4 holes in the rotor poles. Next, we optimized the holes radii and positions by using the Taguchi’s optimization Method. The outline of the rest of this paper is as follows; section II presents a brief description of the DSSRM construction and model. Section III explains the optimization process. Section IV presents the results of torque ripple for new design, and Section V investigates the mechanical conformity of the new rotor shape against vibration and deformation.

 

2. DSSRM Description

Energy Conversion Efficiency in SRM is defined in [1] as follows:

Where, Fmotional , is the net force generated in the direction of motion, and Fnon–motional is the total force perpendicular to the motion direction. In this machine, two stators are used. These stators are made of laminated ferromagnetic material (M-19) and are equipped with concentrated windings. The two stators are located on the interior and exterior of a cylindrical rotor. The rotor is formed by segments of laminated M-19, which is hold together using a non-ferromagnetic cage. In the proposed DSSRM, the number of stator and rotor poles (segments) is 8 and 6, respectively. DSSRM is a reluctance motor with higher ECE compared to ordinary Switched Reluctance Motor. Reluctance variation is the main cause of the developed torque in SR motors; therefore, it is important to improve phase inductance profile to improve its performance. Looking at flux path in DSSRM as shown in Fig. 2, it can be realized that two sides of the inner and outer stator phase windings such as and (a1', a2) can be assumed as the separate windings, which simplify the analysis (Fig. 3). The electrical model of DSSRM includes one resistance which models the equivalent coil resistance and one variable inductance modeling the equivalent coil inductance. Because one side of the equivalent coil involves the outer stator phase and the other side involves the inner stator phase, the equivalent coil inductance is almost identical with each stator phase winding and its resistance is the average of outer and inner stator phase windings (Fig. 4). In this model, determination of the accurate inductance of equivalent coil is important.

Fig. 3.Flux lines of one equivalent coil

Fig. 4.Schematic of equivalent circuit of DSSRM

Nonlinear relationship between the flux linkages and the currents has made it much more difficult to analytically represent the phase inductance or the flux linkages as a function of current and position for the entire ranges of operation. Therefore, the calculation of related machine variables are typically performed using a numerical analysis method, such as Finite Element (FE) method. In this paper, to compare the conventional SRM with the proposed DSSRM, a FE analysis considering magnetic saturation has been carried out. FEM is a powerful tool to calculate the inductance of the equivalent coil at different positions and different currents. This will result in a look up table for equivalent coil inductance. Since the rotor is a part of the magnetic flux path, the motion and saturation of the rotor in some positions changes the flux path reluctance and causes the change in the equivalent coil inductance. So, inductance is a function of the rotor position and the stators currents.

According to Fig. 4, the circuit equations of DSSRM canbe written as:

Summarizing (2), (3) and (4)

The torque equations in linear region of inductance are

Where V is the input voltage, R is the equivalent coil resistance, i(t) is the equivalent coil current, is the flux linkage, 𝜔 is the mechanical angular velocity and Wc is the magnetic energy. As it can be seen from equation (6), the smooth torque profile depends on the slope of L(θ) and constant results in the constant torque. Since is a result of the rotor position, rotor pole shaping is the best option to smooth the inductance slope and suppress the torque pulsation.

 

3. Rotor Shaping and Optimization Process

To smooth the torque profile, it is necessary to change the inductance profile gradually as the rotor pole moves into alignment with the excited stator poles. The proposed shape must be analyzed in accordance with the present motor structure because the stator windings are already designed and the rotor must be examined in the existing structure. Fig. 2 shows clearly that the flux paths of the two stators windings are independent; so, any change in the rotor structure must be performed for each of two flux paths. To reduce the rate of the inductance change, it is necessary to increase the flux path reluctance as the rotor moves. One way to increase the reluctance of the flux path is to increase the saturation at the tip of the rotor poles. The maximum rate of inductance change happens when the alignment between the rotor and stator poles begins. So, in this position the rotor reluctance should be increased to cause the smoother inductance change. To do so, the rotor may be cut as shown in Fig. 5. The proposed rotor shape in Fig. 5 causes the saturation in the rotor pole tips close to the edges as shown in Fig. 6. Fig. 7 shows the smoothness obtained in phase inductance caused by this new shape.

Fig. 5.Suggested preliminary rotor pole shape for DSSRM

Fig. 6.Magnetic flux density in the rotor structure after rotor shaping

Fig. 7.Equivalent coil inductance before (--) and after (-) rotor shaping

Manufacturing the rotor shape of the Fig. 5 is difficult and operation of rotor will this rotor shape will make noise and vibration problems; so, we propose to use four circular holes to shape the rotor poles close to the shape in the Fig. 5 which is shown in Fig. 9.

Fig. 8.Static torque before (--) and after (-) rotor pole shaping

Fig. 9.Use of the circular holes for practical rotor shaping

In Fig. 9, ri is the radius of ith circle and θi is the angle between center of circle i and the horizontal dashed line.

Torque ripple is defined as:

The average Torque of DSSRM before changing the rotor structure is 21.26 Nm, the maximum and minimum torques are 33.8 Nm and 12.2 Nm respectively. According to equation (7), torque ripple before changing the rotor structure is 101.6％. In the next step, we use Taguchi’s method to optimize the holes attributes for minimum torque ripple.

Orthogonal Arrays (OAs) which have a profound background in statistics [24, 25], play an essential role in Taguchi’s method. Orthogonal arrays were introduced in the 1940s and have been widely used in designing of the experiments since then. They provide an efficient and systematic way to determine control parameters so that the optimal result can be found with only a few experimental runs. Taguchi’s method uses orthogonal arrays to design experiments according to number of optimization parameters and parameters levels. Taguchi’s experiments designs are presented under the name ‘Taguchi’s Tables’. Therefore, using Taguchi’s method is extremely easy and efficient. Taguchi’s Method has several stages as follows:

3.1 Problem initialization

The optimization procedure starts with the problem initialization, which includes the selection of a proper OA’s and suitable objective function. The selection of an OA mainly depends on the number of input parameters and their levels. Initial parameters levels are selected based on the user experience or the maximum and minimum of the optimization range as follows:

Where, LD is called the level difference.

3.2 Conduct experiments

After determining the input parameters and objective function, each experiment can be calculated and the obtained results are used for analysis based on the user requirements.

3.3 Identify optimal level values

Using definition for an objective function it is possible to determine the best design parameters according to the experimental results.

In Fig. 10 all steps in Taguchi’s method are presented briefly.

Fig. 10.A simple flowchart of Taguchi's Method

 

4. Results and Discussion

Selected parameters and levels are given in Table 1. They were selected such that the rotor structure is closely similar to the rotor structure in Fig. 5. Defining an objective function, it is possible to determine the best design parameters. Our objective function is:

Table 1.Eight variables and their different levels

In our optimization process, the maximum permissible average torque decrease is chosen as 3％ that is why the 20.62Nm is selected as the critical value for changing the penalty factor (p).

The best design provides the maximum value of the function F. For F values given in Table 2, the best design parameters are obtained at row 14 and the parameters levels in experiment 14 are shown in Table 3. The produced torque of DSSRM before and after rotor pole shaping and the equivalent coil inductance are shown in Figs. 11 and 12 respectively. As shown in Fig. 11, the new proposed rotor shape has a noticeable effect in smoothing the static torque.

Fig. 11.Static torque before (--) and after (-) optimization

Fig. 12.Equivalent coil inductance before (--) and after (-) optimization

Taguchi’s experiments results are shown in Table 2.

Fig. 13 shows that the rotor shape after optimization improves the inductance profile more than the saw shaping.

Fig. 13.Equivalent coil inductance after saw shaping of the rotor (-) and after optimization (--)

As it can be seen in row 14 of Table 2, the minimum torque ripple is 30.7％ at average torque of 20.76 Nm.

Table 2.The results of Taguchi’s method

The optimum rotor shape and optimum parameters valuesare shown in Fig. 14 and Table 3 respectively. In Table 4 torque characteristics before and after optimization are compared.

Fig. 14.Optimal rotor shape design

Table 3.Optimal parameters

Table 4 shows clearly the effectiveness of the proposed rotor structure.

Table 4.Torque characteristics of DSSRM before and after optimization

 

5. Mechanical Analysis

In this section, the proposed rotor shape including 4 holes in the rotor structure is analyzed mechanically to check for the rotor conformity. One of the most critical parts of the rotor is the wall between two larger holes. To evaluate the conformity of the rotor structure a 3D Finite Element analysis was used. In the first step the electromagnetic equations were solved using 3D FEM to obtain the local forces affecting the rotor structure. Then, mechanical equations involving the local electromagnetic forces from step 1 were solved using 3D FEM in speed of 1500 rpm. The maximum stress in the rotor structure and the rotor deformation for one position are shown in Figs. 15 and 16 respectively. As it can be seen, the maximum stress of the rotor structure is much less than the critical deforming stresses (the mechanical stress in which deformation starts is 49 GPa) for the optimized rotor shapes. So, the proposed rotor structure can be used for suppression of torque pulsation.

Fig. 15.Maximum rotor mechanical stress

Fig. 16.Rotor deformation (Scaled by 30000)

 

6. Conclusion

Based on inductance profile variation of DSSRM, an optimum rotor shape is developed for double stator switched reluctance motor, resulting in lower torque pulsation without noticeable decrease in average torque. The proposed rotor shape is practical and easy to manufacture. Taguchi’s optimization method is used for optimization Process. The optimal shape reduces the torque ripple by 69.3 ％ as compared with original DSSRM. The proposed rotor structure was investigated from mechanical point of view. Mechanical analysis showed that the new rotor structure is stiff against vibration and deformation. The new design makes DSSRM more suitable for Electric Hybrid Vehicles (EHVs) and other low torque ripple applications.