DC Excited Flux-Switching Motor: Rotor Structural Optimization

2014 17th International Conference on Electrical Machines and Systems (ICEMS),Oct. 22-25, 2014, Hangzhou, China DC Excited Flux-Switching Motor: Rotor Structural Optimization S. D. Chishko*, Y. Tang, J. J. H. Paulides, and E. A. Lomonova Electromechanics and Power Electronics Group, Eindhoven University of Technology, The Netherlands E-mail: [email protected] Abstract — This paper investigates the effect of various rotor structures on the torque production capability of DC excited flux-switching motors. In these machines two set of windings, excited with DC and three-phase AC currents, are placed within the stator and the rotor structure should ensure that the applicable magnetic circuit is present to achieve both a high and smooth torque. As such, the rotor structure is an important factor that affects the performance of DC excited flux-switching motors. Results show that it is possible to increase the mean torque by varying the rotor tooth width or decreasing the torque ripple value by shaping the rotor tooth tip. I. In this benchmark design, the angle of the rotor tooth tip equals that of the stator tooth tip as well as the opening of each stator slot. The stator and rotor yoke heights equal the corresponding tooth widths, i.e. Hsy = Wst, Hry = Wrt. INTRODUCTION The unpredictable fluctuation in the price of rare-earth materials creates a requirement in minimizing the usage of permanent magnets in industry. Hence, efficient and low-cost electrical motors as alternatives of permanent magnet (PM) motors become increasingly interesting for various industrial applications [1] such as electric vehicles [2]. One of the most promising candidates is the DC excited flux-switching motor (DCEFSM) [3]-[5]. This motor has a double-salient structure, similar to a switched reluctance motor (SRM) [6]. However, in the stator of a DCEFSM there are two sets of windings, excited with DC and three-phase AC currents, respectively. The advantages of this motor are: • the absence of permanent magnets, • a rigid solely laminated rotor and • an extended speed range with high efficiency [7]. Although that the torque density of this motor in the constant torque region is generally lower in comparison to PM motors. Further, there are noticeable torque ripples during the operation of this motor. Both torque production and ripple of DCEFSMs can be improved by optimizing the rotor structure [8]. This paper investigates the physical relationship between rotor structure and torque production of DCEFSM using finite element analysis (FEA). Based on this investigation, methods to optimize the rotor structure, to reduce torque ripple and increase torque density, are proposed. II. BENCHMARK MOTOR STRUCTURE The DCEFSM structure under consideration in this paper is shown on the Fig. 1. It has 5 rotor teeth and 6 stator segments. Fig. 1. Cross-section of the benchmark topology of the DC excited fluxswitching motor. III. ROTOR STRUCTURE OPTIMIZATION In this section, the influence of varying the rotor structure on the torque production of considered DCEFSM is investigated. To highlight this influence, stator dimensions, currents, and minimum air gap length, which is 1 mm, are kept the same for all motor structures investigated in this paper. Current densities in AC and DC windings are assumed to be equal. The torque production of the motors with various rotor structures is investigated using 2D finite element model (FEM), in which magnetic saturation is considered. For the ease of comparing, all the torque values are presented in a normalized scale in this paper, where the mean torque achieved by the benchmark motor is chosen as the nominal value. To evaluate different levels of torque ripples, a torque ripple value is defined as ܶ୮୩ଶ୮୩ (1) ȉ ͳͲͲΨǡ ܶ୰ ൌ ܶ୫ୣୟ୬ where Tpk2pk is a peak-to-peak value of the torque, Tmean is the mean torque during one electric period. 2867 978-1-4799-5162-8/14/$31.00 ©2014 IEEE 1.4 Normalized torque 1.3 1.2 7-tooth-rotor torque Benchmark 5-tooth-rotor torque 1.1 1 0.9 0 60 120 180 240 Rotor position, [Elec. Deg.] 300 360 Fig. 2. Torque comparison of 5-tooth and 7-tooth rotors. The first method to increase the mean torque is to increase the number of rotor teeth. For a fair comparison rotor tooth tip angle and rotor yoke height remain the same. The results of simulations are shown on Fig. 2. Due to the saturation effect the gain in mean torque is 1.26 times, which is slightly lower than 7/5 times expected from [7]. However, the torque ripple value of this 7-tooth DCEFSM is 11.53%, higher than that of the benchmark structure. Also the rotor mass increases. The torque density determined as a mean torque divided by the motor volume is not representative here because the motor volume is the same every time. Thus, the torque density value is directly proportional to the mean torque value. Hence, specific torque, which is the torque density per rotor active mass Mrot is used for comparison in the paper ܶ୫ୣୟ୬ (2) ܶୱ୮ୣୡ ൌ Ǥ ‫ܯ‬୰୭୲ In the benchmark motor Tspec is 20.2 (Nm/kg), while in the 7-tooth DCEFSM it is 21.7 (Nm/kg). Thus, the specific torque gain is 7%. Changing the number of rotor teeth from 5 to 7 provides a visible gain in the mean torque, however, to maintain the same speed 7-tooth rotor requires 7/5 times higher AC supply frequency, which can be a drawback in certain applications. Phase back-EMF curves, within this paper normalized to the magnitude of the main harmonic of no-load back-EMF of the benchmark motor, are shown in Fig. 3. 1.5 B. Tooth Width The second method to increase the mean torque of the DCEFSM is to increase the rotor tooth width. This phenomenon can be explained through the analogy of the DCEFSM with the switched reluctance motor (SRM). Similar to SRM, the torque production of the DCEFSM is influenced by the difference between the aligned and unaligned inductances. However, in contrast with SRMs, in DCEFSMs the mutual inductance between DC and AC windings instead of the self-inductance of each phase is crucial [9]. Thus, the idea behind the rotor tooth width variation is to increase the aligned mutual inductance between DC and AC windings. This can be achieved by widening the rotor tooth tips, as shown in Fig. 4. These results of rotor teeth width variation are listed in Table 1. This summarizes that the maximum mean torque is achieved when the rotor tooth angle is increased to 23° mechanical. With this angle, the mean torque can be increased by 14% with keeping the torque ripples at the same value. However, the mean torque starts decreasing when the tooth tip angle is larger than 27° mechanical resulting from increased flux leakage. TORQUE PRODUCTION Tooth tip width, mech. deg. 15 17 19 21 23 25 27 29 31 5-rotor-tooth no-load back-EMF 7-rotor-tooth no-load back-EMF Normalized back-EMF 1 0.5 1.5 1 0.5 0 -0.5 Benchmark motor self-inductance Benchmark motor DC-AC mutual inductance Motor with wider tooth self-inductance Motor with wider tooth DC-AC mutual inductance -1 0 -1.5 0 -0.5 0.2 0.4 0.6 0.8 1 1.2 Time, [ms] 1.4 1.6 1.8 60 120 180 240 Rotor position, [Elec. Deg.] 300 360 Fig. 4. Comparison of the inductances of the benchmark motor and the motor with wider rotor teeth. The mean value of the benchmark motor’s AC phase self-inductance is taken as the nominal value. -1 -1.5 0 TABLE I DCEFSM WITH VARIOUS ROTOR TEETH WIDTHS Normalized mean Torque ripples, % torque 1.00 6.75 1.06 5.03 1.10 8.18 1.13 7.22 1.14 6.99 1.14 8.47 1.14 7.29 1.12 6.95 1.10 7.89 OF THE In the following investigation, the rotor tooth tip angle of 23Û mechanical, as shown in Fig. 5a, is used as one of the optimization results. Specific torque (2) in this motor is 18.8 (Nm/kg), 7% lower than in the benchmark motor. Normalized inductance A. Tooth Number The torque of the benchmark motor is presented in Fig. 2. Torque ripple value in the benchmark DCEFSM is 6.75%. 2 Fig. 3. Comparison of the no-load back-EMF for 5-tooth and 7-tooth rotors. 2868 and maximum air gap length. As Table 2 shows, the usage of an eccentric tooth tip can help to decrease the torque ripples by approximately 2%. However, in the meantime the mean torque, hence torque density, decreases. As such, for every specific design the tooth tip width and offset R for the eccentric tooth tip is a tradeoff between torque ripple and mean torque. 1.4 1.3 Normalized torque C. Tooth shape In Fig. 2, in both torque waveforms of the 5- and 7-tooth rotor, a 6th harmonic torque ripple is present. This can be analyzed from the viewpoint of the harmonics in the phase flux linkage and back-EMF. As such, a presence of the 5th and 7th harmonic is observed in the waveforms of the phase backEMF and flux linkage. In this respect, the 5th flux harmonic moves opposite to the direction of the rotor’s rotation, while the 7th moves in the same direction, hence both of them contribute to the 6th harmonic disturbances of the torque. To reduce the harmonics of the phase flux linkage waveform, thus reducing the torque ripples, various rotor shapes are investigated, as shown in Figs. 5b-g. The FEA results of torque production in the DCEFSM with these rotor shapes are shown in Fig. 6. It can be seen that a rotor with eccentric tooth tip, as shown in Fig. 5b, gives the minimum torque ripple value among all the investigated rotor shapes. On the contrary, a teeth-pairing rotor, shown in Fig. 5g, which is advantageous in flux-reversal machines [10], has the worst performance in this case. 1.2 1.1 1 0.9 0.8 0 60 120 180 240 Rotor position, [Elec. Deg.] 300 360 Fig. 6. Torque produced by different rotor shapes. a) b) c) A comparison of phase back-EMF (normalized to the benchmark motor no-load fundamental back-EMF) related to the wider teeth rotor, with eccentricity coefficient 0 and eccentricity coefficient 0.63, are shown on Fig. 8. d) e) f) g) h) i) Fig. 5. Cross-sections of investigated rotor structures: a) rotor with increased-tooth-width; b) rotor with eccentric-tooth-tip; c) rotor with left-rounding; d) rotor with right-rounding; e) rotor with leftchamfering; f) rotor with right-chamfering; g) rotor with pair-teeth; h) rotor with rounded-slots; i) rotor with fan-characteristics. Fig. 7. Eccentric tooth tip determination. 2 No-load back-EMF Back-EMF under load No-load back-EMF with eccentricity Back-EMF under load with eccentricity Investigation is thus further performed on the rotor with eccentric tooth tip, as shown in Fig. 5b. The effect of eccentric tooth tip is similar to the eccentric pole shoes in salient-pole synchronous generators [11]. With the most optimal tooth tip radius, it is possible to decrease the higher harmonics and make the phase back-EMF curve more sinusoidal. However, this also increases the average air gap length, thus decreasing the aligned mutual inductance of the motor and so reduces the mean torque. The dependency, used for the optimization, is presented in Fig. 7, where Dro is the rotor outer diameter and R is the circle center offset that determines the ratio between the minimum 2869 Normalized back-EMF 1.5 1 0.5 0 -0.5 -1 -1.5 -2 0 60 120 180 240 Rotor position, [Elec. Deg.] 300 360 Fig. 8. Comparison of the phase back-EMF for the rotor with tooth tip eccentricity coefficient 0 and eccentricity coefficient 0.63. TABLE II VARIATION OF TOOTH TIP ECCENTRICITY Normalized mean Eccentricity Torque ripples, % torque coefficient, 2R/Dro 0.00 1.14 6.99 0.05 1.14 6.62 0.10 1.13 6.22 0.15 1.13 5.78 0.20 1.12 5.34 0.24 1.12 4.81 0.29 1.11 4.28 0.34 1.10 3.67 0.39 1.09 3.44 0.44 1.08 3.12 0.49 1.07 2.79 0.54 1.05 2.46 0.59 1.03 2.2 0.63 1.01 1.98 0.68 0.98 2.02 forces due to torque production. The results are presented in Fig. 11 and 12. Normalized torque 1.2 1.1 1 Rotor after tooth variation Rotor with improved mechanical properties Rotor with improved cooling properties 0.9 0 60 120 180 240 Rotor position, [Elec. Deg.] 300 360 Fig. 10. Torque comparison of unconventional rotor structures. It needs noting that the notch in the shape of back-EMF occurs due to the DC winding slot separating the stator segment into two parts and decreasing the permeability of a magnetic circuit at that position. The harmonic spectrum of the phase back-EMF, of Fig. 8, for the first 15 harmonics is demonstrated in Fig. 9. 1.8 No-load back-EMF Back-EMF under load No-load back-EMF with eccentricity Back-EMF under load with eccentricity Normalized back-EMF 1.6 1.4 1.2 1 0.8 0.6 0.4 Fig. 11. Stresses in the conventional rotor. 0.2 0 0 1 2 3 4 5 6 7 8 9 10 Number of harmonic 11 12 13 14 15 Fig. 9. Harmonic spectrum of phase back-EMF. D. Mechanical considerations Besides the considerations on the torque production, certain rotor shapes can also have advantages in other aspects. For example, Fig. 5h shows the structure of the rotor that can withstand high mechanical loadings for high-speed applications. Figure 5i proposes a rotor that creates additional air pressure to improve cooling. The FEA results of torque production of the DCEFSM with these two rotor structures are shown in Fig. 10, in comparison with a widened rotor tooth tip. Rotors in Fig. 5a and 5h have similar torques but the rotor in Fig. 5i has lower torque due to the lower aligned inductances. To access the improvement on the mechanical stress achieved by the structure in Fig. 5h, 3D FEA is performed on both models with the rotor structures shown in Fig. 5a and 5h, respectively. The simple static mechanical models are created where a solid body represents the rotor that experiences centrifugal forces due to rotation and tangential and radial Fig. 12. Stresses in the rotor with rounded-slots. As Fig. 11 shows, the highest mechanical stresses appear at the line of the connection between the yoke and the tooth. This line is the mechanical stress concentrator. Figure 12 shows the stress distribution on the rotor in Fig. 5h with the same torque production. The stress is more 2870 distributed, hence reducing the maximum stress. Therefore, the rotor can withstand higher mechanical loadings at the price of relatively larger rotor mass. IV. OPTIMIZATION RESULTS The most suitable rotor structure, within the constraints as set forth within this paper, is presented in Fig. 13. In this rotor, the rotor tip angle is increased from 15° mechanical as in the benchmark structure to 23° mechanical. The shape of the rotor is also adapted to obtain an eccentric tooth tip with coefficient 0.63. The FEA result of torque production of the DCEFSM with this most suitable rotor structure is present in Fig. 14, in comparison with that of the benchmark motor. It can be seen that, with the optimized rotor the torque ripple of this DCEFSM is reduced while the mean torque is maintained. In this paper the effect of various rotor structures on the torque production capability of DC excited flux-switching motors has been investigated. It is shown that the change from 5-tooth rotor to 7-tooth can give a gain in the mean torque up to 25% at the cost of a 1.4 times higher in AC supply frequency as well as a higher back-EMF. The torque in DC excited flux-switching motors can be influenced by implementing different rotor structures. This is due to the variation in aligned and unaligned AC-DC winding mutual inductance. This allows the mean torque to be increased up to 14% by widening the rotor tooth tip. In addition, by using the rotor tooth tip eccentricity, it is possible to decrease the motor torque ripple value from 6.75% to 2%. Furthermore, the investigation shows that adaption on the rotor structure can also provide advantages, such as better cooling and more distributed mechanical stress. ACKNOWLEDGMENT Authors wish to express their gratitude for the opportunity of this research to the ARMEVA project, co-funded by the European Union under FP7 Programme. REFERENCES [1] Fig. 13. Cross-section of the optimized motor. V. CONCLUSION DC excited flux-switching motors are advantageous for their simple structure, rigid rotors, and extendable speed range. However, there is room for improvement on the design of this type of motors to increase the torque density and to reduce the torque ripple. Normalized torque 1.05 1 Benchmark motor torque Optimized motor torque 0.95 0 60 120 180 240 Rotor position, [Elec. Deg.] 300 360 Fig. 14. 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