Microsoft Word - ETASR_V11_N3_pp7187-7190 Engineering, Technology & Applied Science Research Vol. 11, No. 3, 2021, 7187-7190 7187 www.etasr.com Minh et al.: Electromagnetic Torque Analysis of SRM 12/8 by Rotor/Stator Pole Angle Electromagnetic Torque Analysis of SRM 12/8 by Rotor/Stator Pole Angle Dinh Bui Minh School of Electrical Engineering Hanoi University of Science and Technology Hanoi, Vietnam Linh Dinh Hai School of Electrical Engineering Hanoi University of Science and Technology and College of Electromechanical and Civil Engineering Vietnam National University of Forestry Hanoi, Vietnam Tuan Le Anh Hanoi University of Industry Hanoi, Vietnam Vuong Dang Quoc School of Electrical Engineering Hanoi University of Science and Technology Hanoi, Vietnam . Abstract—This paper presents the harmonic torque reduction by the different rotor pole angles of a three-phase 12/8 switched reluctance motor via an analytical model and simulation method. Improving torque performance by stator and rotor angles was applied for three-phase switched reluctance motor at stator pole/rotor pole ratios of 6/4, 8/12, 18/12, and 24/18. The average torque and the torque ripple effect by stator and rotor pole embrace have been recently studied in many projects. Due to the fact that leakage flux, flux density, and inductance are affected by the stator and rotor pole angles non-linear and linear leakage flux curves occur. Many stator and rotor pole angle combinations for the three-phase switched reluctance motor have already been done via a finite element method. In this paper, turn-on and turn- off angles will be figured based on stator and rotor pole embraces. Keywords-Switched Reluctance Motor (SRM); pole arcs; torque; Finite Element Method (FEM) I. INTRODUCTION Nowadays, the Switched Reluctance Motor (SRM) is considered as the most appropriate candidate to drive small scale electric vehicles due to advantages such as its simple construction, wide constant power regions, and effective torque speed characteristics. The SRMs have been applied in various fields [1-5]. A convenient design of the SRM has a significant importance for an efficient performance of the motor. Some design parameters must be considered such as the number of phases, stator pole arc, air gap thickness, and other SRM geometry elements. The effect of the SRM geometry on the motor performance has been examined thoroughly. In [6], the influence of pole embrace has been investigated on the performance of the SRM by the Finite Element Method (FEM) with stator and rotor pole embraces changing from 0.2 to 0.5. According to the highest average torque and lowest torque ripple, the proper pole embraces have been selected for the optimum design of the SRM [7-9]. II. ELECTROMAGNETIC TORQUE ANALYSIS The rotor and stator pole arc angles are a critical part in the design of the SRMs. The rotor pole arc (βr) must be equal or greater than the stator pole arc (βs), because the number of rotor poles is less than the number of stator poles (βs ≤ βr). When the βs is smaller than the step angle, then none of the phases can have rising inductance slope. The rotor pole angle should be greater than the sum of stator and rotor pole arcs [10]: �� � ��; �� � �� � �� � ; min���, ��� � �� �. � (1) Fig. 1. Cross-section of a three-phase SRM 12/8 βr equal to (a) 15 0 , (b) 18 0 , (c) 20 0 , (d) 22 0 for βs=15 0 , 15 0 , 15 0 , and 12 0 respectively. Corresponding author: Dinh Bui Minh (dinh.buiminh@hust.edu.vn) Engineering, Technology & Applied Science Research Vol. 11, No. 3, 2021, 7187-7190 7188 www.etasr.com Minh et al.: Electromagnetic Torque Analysis of SRM 12/8 by Rotor/Stator Pole Angle The initial size L is estimated from the output power and torque with speed of 1500rpm. With an initial assumption for the L and with respect to the average torque proportionality with LD 2 , the values of L and D have been calculated via the analytical method. The three phase SRMs 12/8 with rotor angle (15 0 ÷ 22 0 ) are listed in Table I. TABLE I. TECHNICAL PARAMETERS OF SRM 12/8 Technical Parameters Value Units Stator poles 12 Stator pole angle 15 degrees Stator lam dia 140 mm Stator bore 90 mm Stator pole depth 15 mm Stator duct layers 2 Rotor pole angle 15, 18, 20, 22 degrees Rotor slot depth 11 mm Airgap 0.3 mm Number strands in hand 9 Phases 3 Turns per phase 12 Power 1200 W Speed 1500 rpm Torque 12 N.m Rotor pole τr (360/Nr=360/8) 45 degrees Stator pole τr (360/Ns=360/12) 30 degrees The static torque curves (�� � have been implemented with FEM with current ranging from 0 to 50A depending on the rotor angle, i.e.: �� � �� �� ����, ��� (2) The rotor embrace ratio as and stator embrace ratio ar are determined by: !� � "#$# , !� � "� $� (3) In order to maximize the static electromagnetic torque, the stator embrace angle values of 0.45, 0.5, 0.55, 0.6, or 13.5 0 , 15 0 , 16.5 0 , 18 0 have been applied to the finite element simulation to get the static torque, and the rotor angle is verified from 0 to 45 0 as shown in Figure 2. Fig. 2. The static torque curves and rotor position stator pole embrace for rotor embrace of 0.4. The static torque curves have been also evaluated with rotor embrace ratio of 0.5 and stator pole embrace values of 0.45, 0.5, 0.55, 0.6 or 13.5 0 , 15 0 , 16.5 0 , 18 0 . The stator pole embrace is changed from 0.45 to 0.6 with 0.05 steps for constant rotor pole embrace of 0.5 as shown in Figure 3. It is obtained that the combination of 0.40 rotor pole and 0.5 stator pole embraces produces the highest peak output torque which is 31.046Nm. Besides, the combination of stator and rotor pole embraces at 0.40 value has the minimum output torque which is 30.920Nm. Fig. 3. The static torque curves and rotor position stator pole embrace for rotor embrace of 0.5. The stator pole embrace is changed from 0.45 to 0.6 with steps of 0.05 for a constant of 0.40 rotor pole embrace depicted in Figure 3. It is seen that the combination of 0.5 rotor pole and 0.50 stator pole embraces produces the highest peak output torque which is 31.191Nm. In the same way, the combination of stator pole embrace and 0.50 rotor pole embrace has the minimum output torque which is 31.094Nm. As can be seen from the results, while the highest output torque is obtained by the combination of 0.40 rotor pole and 0.5 stator pole embraces, the lowest output torque is obtained by the combination of 0.6 rotor pole and 0.6 stator pole embraces. According to these combinations, the optimum values of pole arcs stator/rotor can be selected for better motor design. The average torque is calculated and the best combination of stator and rotor pole embrace can be selected for optimum analysis. The results on the effect of pole embrace are given in Figure 4 for different combinations of the stator and rotor pole embraces. Fig. 4. Average Torque vs rotor embrace. Engineering, Technology & Applied Science Research Vol. 11, No. 3, 2021, 7187-7190 7189 www.etasr.com Minh et al.: Electromagnetic Torque Analysis of SRM 12/8 by Rotor/Stator Pole Angle Figure 5 shows the average torque and torque ripple, and the embarce stator for various values of the embrace rotor. The average torque is maximum or on top of the curve (as=0.5) at rotor pole arc ar=0.3. With the 4 rotor poles and 6 SRM stator poles, the rotor/stator pitches are 45/30 degrees. Thus, the rotor embrace ar=0.3 is 30 mechanical degrees and the stator embrace is ar=0.5. This means that the rotor pole angle and stator angle have the same value of 15 degrees. The electromagnetic torques with different rotor and stator embraces are presented in Table II. From those results, the best combination of as=0.3 and ar=0.5 is selected to verify the dynamic torque performance. Fig. 5. Torque ripple/average torque rate vs rotor embrace. TABLE II. AVERAGE TORQUE (Nm). ar as=0.2 as=0.3 as=0.4 as=0.5 as=0.6 0.2 12.09608 18.2667 20.69018 19.97587 17.31098 0.3 10.9917 17.04873 21.39854 22.89821 21.54776 0.4 8.411142 12.35922 16.03515 19.25603 21.00559 0.5 4.228949 7.167675 10.4344 13.63371 16.0756 0.6 1.233799 3.079451 5.558719 8.299413 10.63121 0.7 0.150363 0.761016 2.154871 4.085025 5.991545 III. DYNAMIC SIMULATION AND EXPERIMENTAL RESULTS The finite element model has been presented to validate the dynamic torque of 1500rpm and phase current I=50A. The turn on and turn off angles are determined in (4). The torque curve plot is depicted in Figure 6. The torque ripple ranges from 5 to 9N.m. % �&' � (&' � )���*����&++ � (&++ � )���*��� � , � (4) The dynamic torque and efficiency with different rotor and stator angles are compared in Table III. The SRM 12/8 with βs=15 0 , βr=18 0 is the maximum average torque and minimum torque ripple. The harmonic torque of SRM 12/8 is classified with multiples of 3 oders such as 3 th , 6 th , 9 th , 12 th and 15 th because the SRM 12/8 has 3 phases in stator and 4 coils/phase (Figure 7). The total torque of SRM 12/8 can be calculated by 3 th , 6 th , 9 th , 12 th and 15 th . The 3 th harmonic component is still significant on the torque ripple. Therefore, this study will investigate different stator and rotor embrace angles on the harmonic torque and total torque. Fig. 6. Dynamic torque curve at 1500rpm. TABLE III. SRM 12/8 ELECTROMAGNETIC PERFORMANCE COMPARISON Parameters Unit 15 0 /15 0 15 0 /16.5 0 15 0 /18 0 15 0 /20 0 Maximum possible torque Nm 8.466 8.6722 8.6466 8.5649 Average torque Nm 7.642 8.0111 8.1424 7.9893 Average torque Nm 7.496 7.9467 8.159 8.1269 Torque ripple Nm 4.223 1.9376 1.9682 2.4121 Torque ripple [%] % 57.93 23.812 23.958 29.622 Electromagnetic power W 916.1 1022.5 1032.4 1023.3 Input power W 1092 1198.8 1207.6 1195.1 Output power W 872.7 976.22 985.65 976.53 Total losses (on load) W 219.4 222.55 221.99 218.59 System efficiency % 79.91 81.435 81.618 81.71 Shaft torque Nm 6.945 7.7685 7.8435 7.771 Fig. 7. Harmonic torque. The dynamic torque test bench installation for SRM 12/8 and permanent magnet generator in the torque transduce is shown in Figure 8. The torque sensor TM300 is connected to PC to get the data during testing. Fig. 8. Dynamic torque test bench. The speed and torque values with different time steps are presented in Figure 9. In the time interval from 1s to 5s, the Engineering, Technology & Applied Science Research Vol. 11, No. 3, 2021, 7187-7190 7190 www.etasr.com Minh et al.: Electromagnetic Torque Analysis of SRM 12/8 by Rotor/Stator Pole Angle speed and torque are very stablized and vary trivially. However, torque ripple appears in the begining time (0.02s). These values are also recorded in starting stage and constant speed. The dynamic torque with different rotor positions is shown in Figure 10. The values on the torque at stator 15 and rotor 22 reach approximately 10Nm. Fig. 9. Dynamic speed (top) and torque (bottom). Fig. 10. Dynamic torque with differnt rotor positions. IV. CONCLUSION The current paper has developed stator and rotor embrace/pitch influenced on the average torque and torque ripples via FEM [10, 11]. For high speed of the SRM, the control method is single voltage or current pulse because the magnetic circuit is saturated. 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