The Effects of Magnetic Circuit Geometry on Torque Generation of 8/14 Switched Reluctance Machine

Transcription

1 213 XXIV International Conference on Information, Communication and Automation Technologies (ICAT) October 3 November 1, 213, Sarajevo, Bosnia and Herzegovina The Effects of Magnetic Circuit Geometry on Torque Generation of 8/14 Switched Reluctance Machine Senad Smaka, Mirsad Cosovic, Semsudin Masic University of Sarajevo Faculty of Electrical Engineering Sarajevo, Bosnia and Herzegovina ssmaka@etf.unsa.ba; mcosovic@etf.unsa.ba; smasic@etf.unsa.ba Abstract The effects of magnetic circuit geometry on torque generation of switched reluctance motor with higher number of rotor poles are investigated in this paper. Specifically, the torque generation of novel switched reluctance machine with 8 stator and 14 rotor poles (SRM 8/14) is explored. A few suggested values of design ratios are derived for this novel SRM. The machine characteristics are computed using two-dimensional finite element method (2-D FEM). Keywords-switched reluctance machine; design parameters; finite element method. I. INTRODUCTION In the last decades, switched reluctance machine (SRM) has become an important alternative in various applications, in particular for vehicle propulsion and wind power conversion. Some of the most important advantages of SRMs are simple construction with no permanent magnets or windings on the rotor, low manufacturing cost, robustness, suitability for high speed operation, high reliability, simple cooling, and low maintenance. High torque ripple, acoustic noise, vibrations, EMI noise generation, numerous wires between machine and converter, and special converter topology are major disadvantages of SRMs. Also, SRMs have highly nonlinear and complex behavior due to local and bulk saturation in various parts of the stator and rotor cores. This affects the overall efficiency of the switched reluctance motor drives and makes them slightly less favored candidates over the commonly used permanent magnet synchronous machine and induction machine [1]. Therefore, advancements in SRMs design and control are necessary to boost the level of acceptance of these machines. Several novel configurations of SRMs that are presented recently open the possibility to improve characteristics of switched reluctance machines. These novel configurations have higher number of rotor poles than stator poles. They are based on new pole design formula presented in [1] and [2]. References [3] and [4] investigates the performance of two novel configurations of SRMs for traction applications. It is shown that the novel configurations of SRMs can have better performance in comparison to conventional switched reluctance machines. In this paper, a novel four-phase SRM with 8 stator and 14 rotor poles (SRM 8/14) is investigated. The machine configuration is described in Section II. The effect of the rotor outer diameter, the stator and rotor pole taper angles, the stator yoke width, the stator and rotor pole arc angles, and the rotor pole height on torque generation is explored. The machine characteristics are computed using software Ansoft Maxwell. The results of 2-D FEM parametric analysis are presented in Section III. Finally, the conclusions are given in Section IV. II. SRM CONFIGURATION SRMs are typically designed as regular machines in which the rotor and stator poles are symmetrical about their centerlines and equally spaced around the rotor and stator circumference [5]. Regular machines can have three to seven phases and various combinations of stator and rotor poles [1]. Usually, conventional SRMs have the number of rotor poles N r computed as N r Ns 2 = ± (1) where N s is number of stator poles. Pole design formula presented in [1] and [2] proposed a new relationship between number of stator poles N s and maximum number of rotor poles N r = 2N 2 (2) s where N s is even number greater than 4. The SRM 8/14, considered in this paper, is regular fourphase configuration with number of rotor poles calculated by (2). This machine has maximum torque zone of mech and stroke angle of mech. Number of strokes per revolution is 56. Fig. 1 shows part of the SRM 8/14 cross-section with main geometrical parameters emphasized. Rotor is shown at the unaligned position with respect to the phase A. The coils on two opposite stator poles are connected in series, thus forming phase winding with number of turns N ph /13/$ IEEE

2 R sy β r R ry Phase A δ γ s D r /2 R sh N ph 2 D s /2 decreased for given excitation current and the produced torque can be quite low if the rotor outer diameter is large. In this case, the stator and rotor poles are not heavily saturated. For example, the SRM 8/14 design with D r = 215 mm has the maximum magnetic flux density on the stator and rotor poles of 1.85 T and 1.72 T, respectively. On the other hand, when the rotor diameter is small, the slot area can be large, and N ph can be increased. In this case, magnetomotive force is high, and the stator poles experience heavy magnetic saturation. Due to small rotor outer diameter and severe magnetic saturation, the output torque is decreased. The SRM 8/14 design with D r = 185 mm has the maximum magnetic flux density on the stator and rotor poles of 2.12 T and 1.94 T, respectively. Figure 1. Part of the SRM 8/14 cross-section. 1 III. SRM 8/14 DESIGN AND PARAMETRIC ANALYSIS In this paper, Ansoft Maxwell software based on twodimensional finite element method is used to create the SRM 8/14 model and to perform parametric analysis. Parametric analysis of the SRM 8/14 is conducted prior to optimization in order to derive the initial design of the machine. The machine under design has following rated data: 4 kw, 65 V, 18 rpm, A. The SRM 8/14 is designed for hybrid electric vehicle propulsion. Due to limited installation space it has fixed envelope dimensions, i.e. stator outer diameter D s, stack length l stk, and air gap length δ are kept constant for all designs of the SRM 8/14. Variable parameters are: the rotor outer diameter D r, the stator pole taper angle γ s, the stator yoke width h sy (h sy = D s /2 R sy ), the rotor pole taper angle, the rotor pole arc angle β r, the rotor pole height h rp (h rp = D r /2 R ry ), and the stator pole arc angle. The number of series turns per phase winding N ph is computed to maintain given maximum slot fill factor of 58 % for machine designs that have variable either D r, γ s, h sy, or. Also, the excitation current is constant, and the turn-on and turn-off angles are selected to maximize the output torque for all design variations. A. Rotor diameter Fig. 2 shows average steady-state torque and number of series turns per phase winding as a function of the rotor outer diameter. The cross-sectional views in Fig. 2 show the selected machine structures at the rotor outer diameter varying from 185 mm to 215 mm. Since the machine envelope is fixed, the stator pole height h sp is changed with the rotor outer diameter. According to standard output equation, the average torque is proportional to the square of the rotor outer diameter [1]. Therefore, to increase the output torque, the machine can be designed with larger rotor outer diameter; however, the slot area is small, and then, N ph is decreased in order to maintain maximum slot fill factor. The magnetomotive force is Rotor diameter (mm) Figure 2. Average torque and turns per phase versus rotor outer diameter. From Fig. 2, it is clear that there is the best value of the rotor outer diameter for torque production. In this case, the highest average steady-state torque is obtained at D r = 22.5 mm, which give the ratio between the rotor and stator outer diameters D r /D s of.75. This ratio varies between.4 and.7 for standard SRMs that have more stator poles than rotor poles (SRM 8/6, SRM 6/4, etc.), with most designs around.5 [1]. The SRM 8/14 has narrower stator poles than standard SRMs due to higher number of rotor poles. It is clear that the additional space between adjacent stator poles of the SRM 8/14 can be used to increase the rotor outer diameter without compromising the produced magnetomotive force. Maximum average steady-state torque that is obtained is 252 Nm. B. Stator pole taper angle Fig. 3 shows average steady-state torque and number of series turns per phase winding as a function of the stator pole taper angle. The stator pole taper angle is changed from (for the initial geometry analyzed in section A) to 1. The rotor outer diameter is fixed to D r = 22.5 mm, which is the ''optimum'' value for torque production. If the stator pole taper angle is increased, then the number of turns per phase winding is decreased, magnetic saturation is

3 eased and torque production is improved. However, if γ s is too large, then N ph is decreased further and torque is decreased due to low magnetomotive force. Thus, there is a best value of γ s for torque production. In this case, the average steady-state torque is maximized for γ s = 8, with maximum value of Nm. This value is by 2.8 % higher than the maximum value of average torque shown in Fig. 2, which is obtained for γ s =. The SRM 8/14 design with γ s = 8 has the maximum magnetic flux density on the stator pole by 4.8 % lower than design without tapered poles improvement is achieved with the stator yoke width reduced by 1.3 % in comparison to that design, leading to the lower weight and higher torque density of the machine. Fig. 5 shows the distributions of the magnetic flux density of machine designs A, B and C corresponding to the ones in Fig. 4. The stator and rotor poles are partially overlapped, so the magnetic flux density has very high values, especially on the stator pole. Design A, with narrow stator yoke, has the maximum magnetic flux density on the stator yoke of 1.83 T. This value is higher than saturated flux density of used lamination material M19_29G, which is approximately 1.7 T. In this case, magnetic saturation has negative influence on torque generation. In the case when h sy is 13 mm (design B), the produced average torque has maximum value. Maximum flux density on the stator yoke is 1.55 T; thus, the stator yoke can carry the peak stator flux without saturating. Also, there is a margin to the ''knee'' point of B H curve in order to prevent saturation when two different phases overlap. Design C has wide stator yoke and relatively small slot area. The stator yoke iron in not saturated, but the number of turns per phase winding is reduced and the output torque is rather low Stator pole taper angle (Degree) Figure 3. Average torque and turns per phase versus stator pole taper angle T 1.55 T 1.23 T C. Stator yoke width Fig. 4 shows average steady-state torque and the number of series turns per phase winding as a function of the stator yoke width. The rotor outer diameter is 22.5 mm and stator pole taper angle is A Stator yoke width (mm) Figure 4. Average torque and turns per phase versus stator yoke width. It is shown that h sy has the best value to maximize torque production. In this case, the best value of h sy is 13 mm, which give the ratio between the stator pole width and the stator yoke width of.7. Maximum torque is by 1.5 % higher than it was obtained for the best design shown previously in Fig. 2. This B C A: h sy = 1.2 mm B: h sy = 13 mm C: h sy = 15.8 mm Figure 5. Flux density variation and stator yoke width. The conversion loops ψ I of the three selected designs A, B, and C, previously shown in Fig. 4, are shown in Fig. 6. Flux linkage (Wb) mm 13 mm 15.8 mm A: h sy = 1.2 mm, N ph = 82 C: h sy = 15.8 mm, N ph = 58 B: h sy = 13 mm, N ph = Current (A) Figure 6. Conversion loops for different stator yoke widths. The area of conversion loop, which is proportional to the torque, is smallest for design C. The flux linkage of design A is highest due to high number of turns per phase winding. However, the area of conversion loop of design A is smaller

4 than that of design B, particularly because of the magnetic saturation that exists even when the rotor is at the unaligned position. D. Rotor pole taper angle Fig. 7 shows the static (locked rotor) torque as a function of rotor position when the rotor taper angle is changed from to 2 and for constant excitation current. All other geometrical parameters of the machine were constant. Angle mech represents the unaligned rotor position and angle mech depict the aligned position between axes of the stator poles of excited phase and the rotor poles. Increasing the width of the rotor pole base has a relatively small effect on peak static torque. Its value is changed between Nm at = and 21.1 Nm at = 2 (higher by 2.3 %). The peak static torque is achieved soon after overlapping of the stator and rotor poles start, i.e. at the angle of approximately 4. Then, the static torque decreases due to saturation. In this area, it can be seen the most pronounced effect of tapering the rotor poles on the static torque. The average torque increases with increasing rotor pole taper angle. Its value at = 2 is by 4.5 % higher than that obtained at =. However, increasing the width of the rotor pole base leads to an increase in the rotor mass, so the ratio between the average steady-state torque and mass of the active parts of the SRM 8/14 is not improved. E. Rotor pole arc angle In this section, the effect of the rotor pole width on static and average steady-state torque of SRM 8/14 is explored. The rotor pole arc angle is changed from 6.5 to 14, which led to changes in the rotor pole width from 11.5 mm to 24.6 mm. Other geometrical and winding parameters are not changed. The static torque profile at constant operating current obtained for different rotor pole arc angles, i.e. β r < (7.5 ), β r = (1.5 ), β r > (12.5 ), is shown in Fig β r =7,5 β =1,5 r β =12,5 r 15 = = 1 = Rotor position (Mechanical degree) Figure 9. Static torque profile at different rotor pole arc angles Rotor position (Mechanical degree) Figure 7. Static torque profile at different rotor pole taper angles. Fig. 8 shows the average steady-state torque as a function of the rotor pole taper angle Rotor pole taper angle (Degree) Figure 8. Average torque versus rotor pole taper angle. The SRM 8/14 design with narrow rotor poles (β r = 7.5 ) has wide interpolar gap, which means that magnetic flux lines travels longer in air gap at the unaligned position. Therefore, this machine has high reluctance and low unaligned inductance. Also, this design has low aligned inductance due to reduced axial cross-section area of the rotor pole. The inductance rate of change as a function of rotor position of this configuration is slow, the rotor poles are saturated, and generated static torque is rather low. The reason for a lower peak static torque in SRM 8/14 with wide rotor poles (β r = 12.5 ) can be explained by negative torque generation. In this case, the rotor poles are very close to each other. Therefore, when a phase is energized, some of the flux lines could penetrate the rotor pole with decreasing inductance profile, resulting in a negative torque. It is clear that static torque profile of SRM 8/14 configuration with β r = 1.5 is better than that of other designs. Fig. 1 shows the average torque as a function of the rotor pole arc angle. The highest values of the average torque are achieved at the rotor pole arc angles that are approximately equal to the stator pole arc angles (β r ). Excessive

5 narrowing or widening rotor pole is not justified. The maximum value of the average torque is obtained when the ratio between rotor pole arc angle and rotor pole pitch is.4. highest in SRM 8/14 configuration with h rp = 11 mm, because it has very wide rotor yoke and, hence, a reduced reluctance of rotor core at the aligned position. In line with this is the fact that this configuration has the highest average steady-state torque (Fig. 12) Rotor iron mass (kg) Rotor pole arc angle (Degree) Figure 1. Average torque versus rotor pole arc angle Rotor pole height (mm) 25 F. Rotor pole height In this section, the effect of the rotor pole height on generated torque is explored. The rotor pole height h rp is varied from mm to 61.6 mm, with step of approximately 5 mm. Since the rotor diameter is constant, changing the rotor pole height directly affects only the rotor yoke width. Fig. 11 shows the peak static torque as a function of the rotor pole height. Maximum torque (Nm) Rotor pole height (mm) Figure 11. Peak static torque versus rotor pole height. When the rotor pole height is changed from h rp = to h rp = 11 mm, peak static torque increases from to about Nm; then, the increase in h rp practically has no effect on peak static torque. It can be seen that the highest peak static torque is generated if the rotor pole height is between 2 mm and 5 mm. It was found that, if the rotor pole height is within this range, peak static torque is produced practically always at the same rotor position. The aligned inductance to unaligned inductance ratio is Figure 12. Average torque and rotor iron mass versus rotor pole height. However, the mass of the rotor core in this case is large, i.e. the ratio of average steady-state torque to rotor mass is rather low. Acceptable values of the average steady-state torque to rotor core mass ratio, exceeding 13.3 Nm/kg, are achieved if the rotor yoke width is between 1 mm and 2 mm and the rotor pole height is between 51 mm and 61 mm. G. Stator pole arc angle The effect of the stator pole arc angle on the number of turns per phase winding and torque of SRM 8/14 is investigated in this section. The stator pole arc angle is varied from 6.5 to 14.5, while other geometrical parameters are not changed. Since the bore diameter is constant, described variation of the stator pole arc angle led to changes in the stator pole width from 11.5 mm to 25.6 mm. The static torque profile at constant operating current and different stator pole arc angles, i.e. < β r (7 ), = β r (1 ), > β r (12 ), is shown in Fig. 13. The effect of the stator pole width on torque profile is similar as described earlier in section E, in which the effect of the rotor pole width is discussed. The configurations with wider stator poles have higher torque generated near the unaligned position. Also, the rotor position in which peak static torque is generated is moving towards the unaligned position if the stator pole width is increasing. The number of turns per phase winding is higher for configuration with narrow stator poles ( = 7 ). In this case, heavy saturation of pole corners significantly affects generated torque especially when the stator and rotor poles are partially overlapped. If the stator poles are very wide or very narrow in comparison to the rotor poles, there is an increase of full overlap region in which the stator and rotor poles are

6 completely overlapped. In this region, there is almost no change in the inductance and produced torque is low. This is especially noticeable for SRM 8/14 design with = 7, which has the full overlap region width of 1.5, while the design with = 1 practically has no full overlap region =7 =1 = Rotor position (Mechanical degree) Figure 13. Static torque profile at different stator pole arc angles. Fig. 14 shows the average steady-state torque as a function of stator pole arc angle. The maximum value of the average steady-state torque is obtained when the stator pole arc angle to stator pole pitch ratio is set to Stator pole arc angle (Degree) Figure 14. Average torque and turns per phase versus stator pole arc angle IV. CONCLUSIONS This paper analyzes the effect of design parameters on the torque generation of the SRM 8/14. Design parameters were changed individually. To analyze the simultaneous effect of design parameters on the different characteristics of the machine, it is necessary to conduct the optimization. The method and results of design optimization of the SRM 8/14, which is currently performing, will be presented elsewhere. It turned out that the rotor diameter and the stator and rotor poles width have the biggest effect on the developed torque. Due to higher number of rotor poles, novel configuration SRM 8/14 can have narrower stator and rotor poles than conventional SRM (e.g. SRM 8/6). In turn, the stator slot area can be increased. Therefore, the rotor can be wider than in conventional SRM, i.e. the rotor outer diameter to stator outer diameter ratio can be greater than.7. It is shown that the SRM 8/14 with the same width of the stator and rotor poles or with the stator pole slightly wider than the rotor pole can generate the highest average steady-state torque. The SRM 8/14 might require a better power switching devices than standard four-phase SRM due to its higher number of strokes per revolution leading to higher switching frequency. Also, controller design and rotor position estimation could be challenging. Implementation of the SRM 8/14 in traction drives requires further analysis especially regarding constant-power operating range since its relatively low conduction time of the phase current could be disadvantage at high speed operation. REFERENCES [1] P. C. Desai, M. Krishnamurthy, N. Schofield, A. Emadi, Novel Switched Reluctance Machine Configuration with Higher Number of Rotor Poles than Stator Poles, IEEE Transactions on Industrial Electronics, vol. 57, no. 2, pp , February 21. [2] P. C. Desai, The Novel Concept of Switched Reluctance Machines with Higher Number of Rotor Poles, Ph.D. dissertation, Illinois Institute of Technology, Department of Electrical and Computer Engineering, Chicago, Illinois, USA, 9. [3] S. Smaka, S. Masic, M. Cosovic, I. Salihbegovic, Switched Reluctance Machines for Hybrid Electric Vehicles, in Proceedings of XIX International Conference on Electrical Machines (ICEM), paper RF- 6521, Rome, Italy, September 21. [4] B. Bilgin, A. Emadi, M. Krishnamurthy, Comparative Evaluation of 6/8 and 6/1 Switched Reluctance Machines for Traction Application in Plug-In Hybrid Electric Vehicles, in Proceedings of 211 IEEE International Electric Machines & Drives Conference (IEMDC'11), pp , Niagara Falls, Canada, May 211. [5] T. J. E. Miller, Switched reluctance motors and their control, Magna Physics Publishing and Clarendon Press, Oxford, Great Britain, 1993, pp ,