IEEJ Journal of Industry Applications Vol.6 No.6 pp.362 369 DOI: 10.1541/ieejjia.6.362 Paper Characteristics Analysis of Claw-Pole Alternator for Automobiles by Nonlinear Magnetic Field Decomposition for Armature Reaction Katsumi Yamazaki a) Senior Member, Ren Suzuki Student Member Motoharu Nuka Non-member, Makoto Masegi Non-member (Manuscript received Dec. 26, 2016, revised March 13, 2017) In this study, we investigate the characteristics of claw-pole alternators for automobiles from the results of both calculation and experiments. Nonlinear 3-D finite element analysis is employed to take the claw-pole shape into account. The calculated characteristics are compared with the experimental results in order to confirm the validity of the analysis. Then, the magnetic field is decomposed according to the field sources in order to understand the effect of armature reaction. It is clarified that the large armature reaction in the claw-pole alternator causes saturation of the electricaloutput and anincreasein the harmonic losses inthe machine. The possibility of improving the characteristics by reducing the armature reaction is also clarified. Keywords: claw-pole alternator, armature reaction, output, finite element method 1. Introduction Claw-pole alternators are widely used for generators of automobiles (1). According to an increase in electric parts in automobiles, required electricity considerably increases in recent years. Therefore, the output maximization of the clawpole alternators becomes one of the most important issues in automobile technologies. The claw-pole alternators can be categorized into synchronous generators. However, the operation conditions for the automobiles are quite different from the other applications. The stator and rotor cores are highly saturated due to the limitation of machine size. The armature current is very large because of low battery voltage connected to the alternator. As a consequence, the design methodologies for the other synchronous generators cannot be adopted. In particular, there are few papers that dealt with the effects of the armature reaction caused by the large armature currents in the claw-pole alternators because the armature-reaction flux cannot be accurately separated by the equivalent circuits, whose parameters are determined under the assumptions of linear superposition (2). However, it is considered to be very important for the machine designs to estimate correct impact of the armature reaction on the machine characteristics. From these viewpoints, we investigate the characteristics of claw-pole alternators for automobiles from both results of nonlinear 3-D finite element analysis (FEA) and experiments. The calculated characteristics are compared with the experimental results in order to confirm the validity of the analysis. Then, the magnetic field is decomposed according to the field sources by considering the magnetic saturation in order to understand the effect of armature reaction by the large armature current. Finally, the possibility of characteristics improvement by reducing the armature reaction is discussed. 2. Analyzed Machine and Calculation Method Table 1 lists the specification of the analyzed machine. Laminated electrical steel sheets are used for the stator core, whereas the rotor core is made from solid carbon steel. Figure 1 shows the circuit connection. The AC output voltage of the alternator is converted to the DC voltage by a full wave rectifier circuit. A battery and a load resistance are connected to the output of the converter. The resistance is controlled to maintain the DC voltage V DC to be 13.5 V. The field current is set to be 5.2 A. Figure 2 shows the finite element meshes. In the case of the claw-pole alternator, the 3-D analysis is indispensable to take into account the rotor shape. The nonlinear time-stepping FEA coupled with armature voltage equation is applied, as follows: ( ) A(x, t) μ(x, t) Table 1. = n f N f I f S f + n a N a i a (t) S a (1) Machine specification a) Correspondence to: Katsumi Yamazaki. E-mail: yamazaki. katsumi@it-chiba.ac.jp Department of Electrical, Electronics, and Computer Engineering, Chiba Institute of Technology 2-17-1, Tsudanuma, Narashino, Chiba 275-0016, Japan SIGMA & HEARTS CO., LTD. 99 Moo 4, Bangna-Trad Kim. 23, Bangsaothong, Samutprakarn, 10540, Thailand c 2017 The Institute of Electrical Engineers of Japan. 362
Fig. 1. Circuit connection Fig. 3. sources Potential decomposition according to field Figure 3 shows the block diagram of the procedure to obtain A f (x, t) anda a (x, t). The result of μ(x, t) obtained by (1) is memorized and given to (4) and (5). The waveform of i a (t) is also given to (5). As far as we know, this procedure is firstly applied to full 3-D FEA for synchronous machines with field windings, whereas 2-D FEA is applied in reference (2) (5). Then, the total armature flux linkage Φ p is also decomposed into Φ f and Φ a, which are produced by I f and i a (t), as follows: Fig. 2. 3D finite element mesh (3,407,976 tetrahedrons) dφp R a i a (t) = R p i a (t) (2) dt where x and t are position and time, respectively; A(x, t) is the magnetic vector potential, μ(x, t) is the permeability; N f and N a are the number of field and armature winding turns, respectively; I f is the field current; i a (t) is the instantaneous armature current; n f and n a are the unit vectors along these currents, respectively; S f and S a are the cross-sectional areas of these currents, respectively. Φ p is the armature-flux linkage per phase, R a is the armature winding resistance; R p is the equivalent load resistance per phase, which is determined by considering the equivalence of AC and DC electrical outputs, as follows (See Appendix): R p = π2 18 R DC (3) where R DC is the DC resistance including the internal resistance of the battery. The eddy currents in the stator and rotor cores are neglected. The number of time-steps per period is set to be 256. In order to investigate the effects of armature reaction, the total potential A(x, t) is decomposed into A f (x, t) anda a (x, t), which are produced by I f and i a (t), respectively (2) (5). In this case, A f (x, t)anda a (x, t), satisfy following equations: ( ) Af (x, t) μ(x, t) ( ) Aa (x, t) μ(x, t) = n f N f I f S f (4) = n a N a i a (t) S a (5) Therefore, A f (x, t) anda a (x, t) can be obtained by the linear FEA due to (4) and (5) with μ(x, t) that is determined by (1). Φ p =Φ f Φ a (6) where Φ f = N a A f n a dv/s a (7) Va Φ a = N a A a n a dv/s a (8) Va where V a is the volume of the armature winding per phase. 3. Results and Discussion 3.1 Magnetic Saturation in the Machine Figure 4 shows the calculated relative permeability distribution at the rotor core. The core is highly saturated, in particular, the center axial part surrounded by the field winding and the roots of the claws. Although this saturation decreases at high speeds, the relative permeability at most core region is less than 1000 even at the maximum speed estimated in this paper. As mentioned in the introduction, this considerable saturation is caused by the compact design for automobile Fig. 4. Calculated relative permeability distribution at rotor core 363 IEEJ Journal IA, Vol.6, No.6, 2017
application. As a consequence, the procedure shown in Fig. 3 is indispensable to estimate the correct impact of the armature reaction. We have already reported the similar situation in high-torque-density synchronous machines for traction motors of automobiles in reference (2). However, the magnetic saturation in this claw-pole alternator is more considerable. 3.2 Comparison of Experimental and Calculated Results Figure 5 shows the experimental and calculated no-load voltages. It is observed that the voltage is slightly overestimated by the calculation. It must have been caused by the permeability deterioration of the stator and rotor cores by manufacturing process because this error is not observed at the linear region with small field current. Figure 6 shows the experimental and calculated electrical outputs. Both the experimental and calculated results indicate that the output of the machine is saturated at the rated rotor speed. 3.3 Magnetic Field Distributions To understand the Fig. 5. Experimental and calculated no-load voltages (1500 r/min) Fig. 6. Experimental and calculated electrical outputs (I f = 5.2 A) Fig. 7. Calculated flux-density components (2000 r/min, I f = 5.2 A). 364 IEEJ Journal IA, Vol.6, No.6, 2017
Fig. 9. Calculated voltage vector diagram other hand, in the case of the load condition, the flux is concentrated at one side of the rotor surface. This must have been caused by the armature-reaction flux Φ a, which direction is nearly opposite to that of the field flux Φ f. To understand the flux distribution under the load condition in Fig. 7, let us observe the total and decomposed fluxes calculated by (4) (8). Figure 8 shows the results. The Φ f is nearly uniform in the claws, whereas Φ a mainly flows through the rotational head side of the claws to reduce the variation in the flux density according to Faraday s law. As a consequence, the total flux Φ p, which is the sum of these fluxes, is concentrated at the opposite side of the claws. 3.4 Output Characteristics Due to Vector Diagram Figure 9 shows the calculated voltage vector diagram due to (2), which can be rewritten, as follows: Fig. 8. Total and decomposed (B r, B θ ) (2000 r/min) V p = jωφ p R ai a = jωφ f jωφ a R a I a (9) reason of the output saturation in Fig. 6, the magnetic field in the alternator is investigated. Figure 7 shows the calculated distributions of flux-density components at center cross section and rotor surface. In the case of the no-load condition, the radial component of the flux density B r is nearly uniform at the rotor surface. On the where V p, Φ p, Φ f, Φ a and I a are the fundamental phasors of phase voltage, total flux, field flux, armature reaction flux, and armature current, respectively. The first and second terms in the right hand member in (9) can be written as follows: jωφ f = jωm f I f (10) jωφ a = jωl a Ia (11) 365 IEEJ Journal IA, Vol.6, No.6, 2017
Fig. 10. Calculated harmonic flux densities (I f = 5.2 A) where M f is the mutual inductance between field and armature windings, L a is the armature reaction inductance. In Fig. 9, the phase angles of V p and I a are set to be zero to adjust the real-part axis in order to understand the amplitude of armature-reaction voltage easily. Figure 9 indicates that the voltage component by the 366 IEEJ Journal IA, Vol.6, No.6, 2017
armature reaction becomes almost in opposite direction to that by the field current at high speeds. In addition, the amplitudes of these voltage components become considerably larger than that of the output phase voltage V p, which is fixed in the automobile application. In this case, following approximation can be made at high speeds: jωφ f jωφ a 0 (12) Substituting (10) and (11) into (12) yields: Ia M f I f (13) L a This expression means the maximum armature current at high speeds when Vp and I f are constant. It is clarified that the output saturation shown in Fig. 6 is caused by the large armature reaction due to large armature current and low voltage. Note that the result of Fig. 9 and the insight of (13) cannot be confirmed without the calculation procedure shown in Fig. 3. 3.5 Increase in Harmonics The vectors in Fig. 9 correspond to the fundamental voltages. On the other hand, the harmonic fluxes must remain because the fundamental components of the field and armature reaction flux are nearly cancelled each other at high speeds. Figure 10 shows the calculated harmonic fluxes decomposed by Fourier transformation (6). The fundamental and 3 rd harmonic fluxes are expressed by the vectors because the radial and circumferential components of the flux density are dominant, whereas the 2 nd harmonic flux is expressed by the circles because the axial component is dominant. The figure indicates that the fundamental flux under the load condition decreases as compared to the no-load condition according to the armature reaction flux. On the other hand, the harmonic fluxes considerably increase. In detail, the 2 nd harmonic flux increases at the top of every tooth, whereas the 3 rd harmonic flux increases at the whole part of the teeth between the different phase windings. This must have been caused by the decrease in the effect of magnetic saturation according to the decrease in the fundamental flux. We have already reported the similar phenomenon in permanent magnet synchronous motors in reference (7). However, the generation of the axial 2 nd harmonic flux shown in Fig. 10 is a peculiar phenomenon of the claw-pole machines. Figure 11 shows the radial and axial components of the flux density on the plane A and B shown in Fig. 10. The axial flux is maximized at plane B and minimized at plane A. This is caused by the unbalance of rotor surface area on r-θ plane by the claw pole. A part of the flux flow along the axial path to the other pole. Figure 12 shows the calculated harmonic stator iron losses. The figure indicates that the fundamental stator iron loss under the load condition is smaller than that under the no-load condition because of the decrease in the fundamental flux, as shown in Fig. 10. On the other hand, the harmonic losses are considerably larger than that under the no-load condition. As a consequence, the total stator iron loss increases with load. Note that the actual total iron loss is larger than the sum of the harmonic losses in Fig. 12 because the rotor eddy currents and stator in-plane eddy currents are neglected in the analysis. On the other hand, the reaction fields caused by these Fig. 11. Radial and axial components of flux density (No-load) Fig. 12. Harmonic stator iron losses (5000 r/min, I f = 5.2 A) eddy currents are considerably smaller than that by armature current. 3.6 Attempts for Reduction of Armature Reaction Finally, let us discuss the characteristics improvement of the claw-pole alternator by reducing the armature reaction. From (13), it is revealed that the maximum output current under constant armature voltage and field current is approximately proportional to M f /L a. Therefore, the output must increase by reducing the armature reaction inductance L a while controlling decrease in M f as small as possible. 367 IEEJ Journal IA, Vol.6, No.6, 2017
Fig. 13. Attempt to improve characteristics by reducing armature reaction Table 2. Calculated characteristics variation by proposed shape (V DC = 13.5 V, I f = 5.2 A) the large armature currents. As a consequence, it causes the saturation of the electrical output and considerable harmonic iron losses at high speeds. The simple expression of the maximum armature current is also derived from the results of the 3-D nonlinear magnetic field decomposition. The possibility of the characteristics improvement of the claw pole alternator by reducing the armature reaction is also clarified by the calculation. The efficiency increase by the proposed alternator as compared with the conventional one is estimated to be 5 points at the rated speed. Further work is required to establish the forging manufacturing process for the proposed claw-pole shape. Further work is also required to estimate accurate iron loss by considering the in-plane eddy currents in stator cores and slot harmonic eddy currents in rotor cores. References To realize this situation, we have designed a new clawpole shape, as shown in Fig. 13. By considering the results in Fig. 8, the air gap at the left side of the claw is enlarged in the proposed shape to prevent the path of armature reaction flux Φ a andtoreducel a. In this case, M f may also decreases according to the increase in the total magnetic resistance. However, this decrease should be smaller than that in L a because Φ f flows through all the surface of the claws, whereas Φ a mainly flows through the rotational head side of the claws, as shown in Fig. 8. Table 2 lists the variation in the machine parameters and characteristics calculated by the FEA. As it is expected, the variation in M f by the design change is significantly smaller than that in L a at any speeds. The slight increase in M f at high speeds must have been caused by the variation in the permeability distribution in the stator core according to the decrease in Φ a.theeffect of decreasing L a by the proposed design at high speeds is smaller than that at low speeds. However, the effect of the output increase at high speeds is larger than that at low speeds because the armature reaction becomes larger at high speeds, as shown in Fig. 9. As a consequence, the output increases by 5.4% at 5000 r/min, whereas it increases by 3.6% at 2000r/min. The effect of loss reduction is also larger at high speeds. On the other hand, the total electrical loss of the proposed machine rather increases at low speeds because of the increase in the armature copper loss. According to these variations, the efficiency increase is estimated to be 5.0 points at 5000 r/min, whereas it is estimated to be 0.6 points at 2000 r/min. From these results, the importance of estimating armatureaction effects described in the previous sections is clarified. 4. Conclusions The effects of the armature reaction in claw-pole alternators for automobile application are investigated from both results of experiments and 3-D nonlinear time-stepping FEA. The experimental and calculated results are found to be in agreement. It is clarified that the armature reaction in the claw-pole alternator is very large due to the low voltage and ( 1 ) S. Hayashi, Y. Fujita, H. Kometani, and S. Sakabe: Three dimensional magnetic field analysis of a Lundell alternator, T. IEE Japan, Vol.114-D, No.12, pp.1284 1293 (1994) ( 2 ) K. Yamazaki and M. Kumagai: Torque analysis of interior permanentmagnet synchronous motors by considering cross-magnetization: Variation in torque components with permanent-magnet configurations, IEEE Trans. on Industrial Electronics, Vol.61, No.7, pp.3192 3201 (2014) ( 3 ) G.-H. Kang, J.-P. Hong, G.-T. Kim, and J.-W. Park: Improved parameter modeling of interior permanent magnet synchronous motor based on finite element analysis, IEEE Trans. on Magnetics, Vol.36, No.4, pp.1867 1870 (2000) ( 4 ) J.A. Walker, D.G. Dorrell, and C. Cossar: Flux-linkage calculation in permanent-magnet motors using the frozen permeabilities method, IEEE Trans. on Magnetics, Vol.41, No.10, pp.3946 3948 (2005) ( 5 ) K. Yamazaki, K. Nishioka, K. Shima, T. Fukami, and K. Shirai: Estimation of assist effects by additional permanent magnet in salient pole synchronous generators, IEEE Trans. on Industrial Electronics, Vol.59, No.6, pp.2515 2523 (2012) ( 6 ) K. Yamazaki and A. Abe: Loss investigation of interior permanent magnet motors considering carrier harmonics and magnet eddy currents, IEEE Trans. on Ind. Appl., Vol.45, No.2, pp.659 665 (2009) ( 7 ) K. Yamazaki and Y. Seto: Iron loss analysis of interior permanent magnet synchronous motors -Variation of main loss factors due to driving condition, IEEE Trans. on Ind. Appl., Vol.42, No.4, pp.1045 1052 (2006) Appendix Let us derive the equivalent AC resistance per phase R p expressed by the DC resistance R DC as (3). Following equation can be assumed by considering the equivalence of AC and DC electrical outputs: 3 V p 2 R p = V 2 DC (A1) R DC Where V p and V DC are the phase and DC voltages, respectively. On the other hand, following expression can be assumed in the case of the full wave rectifier circuit: V DC = 3 6 π V p (A2) Substituting (A2) into (A1), we have (3). 368 IEEJ Journal IA, Vol.6, No.6, 2017
Katsumi Yamazaki (Senior Member) received the B.Eng., M.Eng., and Dr.Eng. degrees from Waseda University, Tokyo, in 1987, 1989, and 1996, respectively. In 1989, he joined the Toshiba Corporation, Tokyo. Since 2007, he has been a professor with Chiba Institute of Technology, Narashino, Japan. His research interests include the analysis and the design optimization of motors. Dr. Yamazaki was the recipient of the Best Poster Paper Awards in IEEE CEFC 2004, ICEM 2006, and IEMDC 2011, respectively. He was a recipient of the 3 rd Prize Paper Award of the Electric Machines Committee of the IEEE IAS in 2011 and the Best Paper Award in the IEEE Transactions on Energy Conversion in 2015, respectively. Ren Suzuki (Student Member) received the B.Eng. degree from Chiba Institute of Technology, Narashino, Japan, where he is currently working toward the M.Eng. degree. His main research interests include the analysis of claw pole alternators. Motoharu Nuka (Non-member) received B.Eng. degree from Chiba Institute of Technology, Narashino, Japan. Now, he is the chairman of SIGMA & HEARTS CO. LTD. Makoto Masegi (Non-member) received B.Eng. degree from Niigata University, Niigata, Japan. He is a chief engineer in SIGMA & HEARTS CO. LTD. He engages in the design of claw-pole alternators. 369 IEEJ Journal IA, Vol.6, No.6, 2017