2016 International Conference on Advanced anufacture Technology and Industrial Application (ATIA 2016) ISBN: 978-1-60595-387-8 Design and Analysis of the Dimension of the Ps for the DS using EC Jian-guo BU, Xu-dong LAN, Kai-xiong LV and ing ZHOU School of Aerospace, Tsinghua University, BeiJing, China *Corresponding author Keywords: Dual-memory, Equivalent magnetic circuit method, Flux-mnemonic synchronous motor, Flux-control characteristic, Parallelogram hysteresis model. Abstract. The Dual-magnet memory synchronous motor (DS) utilize two kinds of permanent magnets (Ps), namely the aluminum-nickel-cobalt (-Ni-Co) and neodymium-iron-boron (Nd- Fe-B) materials, to provide effective flux-mnemonic feature. The radially placed Nd-Fe-B P provides main flux, and the tangentially placed -Ni-Co P provides controllable flux. The tangentially placed -Ni-Co P can be forward or backward magnetized by the d-axis current. The flux-control characteristic of the DS affected by the size of the two kinds of Ps has been studied in-depth using the equivalent magnetic circuit method (EC) combined with the parallelogram hysteresis model (PH). And finally, the finite element method (FE) simulation is carried out to verify the validity of the proposed EC. Introduction ore-electric is a way to Lightweight and improve performance for the piston aviation Heavy fuel engine (PAHFE). The fly-wheel motor is the main way to meet the needs for more power. The fly-wheel motor is installed on the crankshaft. It is not only used as a fly-wheel, but also used as starter or generator, thus flux-controllable property is its research focus. Compared with the traditional P motor, the flux of the memory motor can be controlled on-line by current pulse, and it omits the long time excitation current compared with the hybrid excited motor, as a result, the efficiency is improved. So the memory motor is one of the best choice for the fly-wheel motor. The -Ni-Co P is usually used for the memory motor because of its lower coercivity, higher remanence and nonlinear hysteresis loop. It was first proposed by V. Ostovic, the Germany scholars, in the IEEE industry applications conference[1]. Presently, Jung Ho Lee, the researcher of Hanbat National University has studied the magnetization and demagnetization characteristics of the AC-pulsed type memory motor[2]; Professor K. T. Chau of the Hong Kong University has further studied the characteristic of the DC-pulsed type memory motor[3, 4]; The concept of doubly salient memory (DS) motors has been proposed by the doctor GongYu, a field circuit time stepping finite element method coupled with the parallelogram hysteresis model (PH) is also employed[5]. However, the magnetic energy product of -Ne-Co P is too small, thus the energy index of such motor is low. In order to solve this problem, the DS has been proposed by Professor Chen of Tianjin University [6]; The DS has first been used in washing machine by Toshiba Company Japan[7]; Professor K. T. Chau of the Hong Kong University has studied the DC-pulsed type Dual-agnet memory motor (D)[8, 9], the magnet proportion for the D has been studied using the EC, and also the design method of the D has been proposed. However, because of the complicated magnetic circuit of the D, the optimization of the size of the P is not studied in-depth. The EC combined with the PH has been proposed in this paper. The flux-control characteristic of the motor affected by the size of the P has been studied, the optimization design is given, and the experimental verification has been done by the FE.
Analysis of the agnetization Process of the -Ni-Co P Based on the PH In order to simplify the model and consider the hysteresis effect, the PH proposed by [5] is used in this paper, as Fig 1 shows. The hysteresis loop is composed of two groups of parallel lines that have different slopes. Different hysteresis loops have different calculation remanence but the same coercivity. The vertex and 1 are the points of saturated forward and backward magnetization respectively, and the absolute value of magnetic field intensity at this point is H. The vertex K and K1 are the knee points of the saturated forward and backward magnetization respectively, the absolute value of magnetic field intensity is H K. l the parallel lines can be expressed as (1), (2) and (3). B 0 rh Brk, k 1, 2,3. (1) 0 rh Br B ( H HC ) H H C (2) 0 rh Br B ( H HC ) H H C where, the intermediate parallel lines is defined as reversion line that is expressed as (1). The left line segment is defined as backward magnetization line that is expressed as (2), the right one is defined as forward magnetization line that is expressed as (3), µ 0 is the permeability of vacuum, µ r is the differential permeability. Different hysteresis loops express different states of the P. It is determined by three parameters those are H Pk, H Qk and B rk. (k=1, 2, 3). H Pk is the magnetic field intensity of the point Pk that the reversion line cuts the forward magnetization line; H Qk is the magnetic field intensity of the point Qk that the reversion line cuts the backward magnetization line, and B rk is the calculated remanence. Changing B rk will change the state of the P, and it is easy to get H Qk and H Pk by (1), (2) and (3). As Fig.1 shows, let the P perform at point a that means the state (H Q1, H P1, B r1 ). (3) K Demagnetization line Air gap line 2 Q 2 H Q3 H Q1 H C H H H Q2 K 1 Q 3 Q1 Air gap line 1 a b d BT ( ) B r O B r 2 B r3 B r1 B r Reversion line H H P3 P1 H K H C H P2 H P1 agnetization line K1 P 2 P 3 H ( ka / m) Reversion line Air gap line 3 Figure 1. PH. In the case of forward magnetizing, d-axis positive current is provided, then the state of the P moves to point P2 along the reversion line Q1P1 and the forward magnetization line P1P2. B r2 can be calculated as (4). Br Hi H H B B ( H H ) H H H H Br1 Hi H P2 0 r r r 2 i C 0 R P2 i H HC (4)
When getting rid of the d-axis positive current, the work point of the P moves along the reversion line Q2P2, and finally the P stays at point b that means the state (H Q2, H P2, B r2 ). In the case of backward magnetization, d-axis negative current is provided, then the state of the P moved to point Q3 along the reversion line P2Q2 and backward magnetization line Q2Q3, B r3 can be calculated by (5). Br Hi H H B B ( H H ) H H H H Br 2 Hi HQ2 0 r r r3 i C 0 R Q2 i H HC When getting rid of the d-axis negative current, the work point of the P moves along the reversion line Q3P3, and stays at point d, that means the state (H Q3, H P3, B r3 ). The forward and backward magnetization flow chart is as Fig 2. Start (5) Get the state of P ( H H ) B rk Qk Pk agnetization or demagnetization Demagnetization agnetization B rk Update H H as (1),(2),(3),(4) Qk Pk B rk Update H H as (1),(2),(3),(4) Qk Pk Adjust the work point END Figure 2. Forward and backward magnetization flow chart. Analysis of Equivalent agnetic Circuit for the DS Simplified Equivalent agnetic Circuit odeling for the DS As Figure 3-a shows, the DS is 8/48 internal rotor structure. The radially placed Nd-Fe-B P provides main flux, and the tangentially placed -Ni-Co P provides controllable flux. The tangentially placed -Ni-Co P can be forward or backward magnetized by controlling the d-axis current. Figure 3-b is the simplified magnet circuit modeling, two halves of the Nd-Fe-B P in series and then parallel with the -Ni-Co P provide flux for the outer magnetic-circuit.
Stator AirGap Armature Winding NiCo NiCo NdFeB Rotor NdFeB NdFeB (a) Figure 3. Simplified odel: (a) 1/8 motor model. (b) Simplified magnet circuit modeling. Ignoring the rotor resistance and iron core saturation, Figure 4-a shows the equivalent magneticcircuit, where F is the magnetic force provided by Ai-Ni-Co P, R is the reluctance of Ai-Ni-Co P, R Nd is the reluctance of Nd-Fe-B P, F d is the d axis magnetic force, R δ is the main reluctance, R σ is the leakage reluctance, R t is the stator teeth reluctance, R y1 is the stator yoke reluctance, R y2 is the rotor yoke reluctance, Φ σ is the flux leakage, Φ δ is the air gap flux, Φ Nd is the flux provided by Nd-Fe-B P, Φ is the flux provided by Ai-Ni-Co P, F m is the magnetic force provided by the two kinds of Ps. For analyzing more easily, the rotor yoke reluctance can be taken as the internal resistance of the two Nd-Fe-B Ps, the simplified magnet circuit shows as Figure 4-b, and the following equation must be satisfied: R R R (6) Nd y2 4 N d (b) 1 1 1 R R R R R n t y1 (7) F FR d d (8) Rn R Rn F q Rt R Fq R y 1 F m 2F F m 2R 2F 2R Nd Nd 2F Nd 4R Nd R y2 2F Nd R Nd (a) Original Equivalent agnetic-circuit Based on PH (b) Simplified Figure 4. Equivalent magnetic-circuit. For the DS, the coercivity of Nd-Fe-B P is very high, the magnetization line coincides with its reversion line, and generally the Nd-Fe-B P works in the first or second quartile of the hysteresis loop. The coercivity of the Ai-Ni-Co P is very low, it goes through the four quartiles, and finally works in the second or third quartile. Figure 5 shows the forward and backward magnetization process, the line above is the magnetization line of Nd-Fe-B P, and the parallelogram is the hysteresis loop of Ai-Ni-Co P.
B/ T D I H B b i A a E C G c B G B C B E A B a B c d m F F h F b F i F a F e F F c g Fd F F / A h g B g m e B e Figure 5. Forward and backward magnetization process of the dual-magnetic It can be seen from the equivalent magnetic-circuit that the two kinds of Ps provide flux for the outer magnetic-circuit in parallel. Ignoring the magnetomotive force drop of the rotor pole shoe, the magnetomotive force for the outer magnetic-circuit provided by them is the same. Then the unit value of the magnet density of the two P s working point can be derived, as (9) shows. Where, b mnk is the unit value of the magnetic induction of the Nd-Fe-B P s working point, b m is the unit value of the magnetic induction of the Nd-Fe-B P s no-load working point, H Cn is the calculated coercivity of the Nd-Fe-B P, h Nd is the magnetization direction thickness of the Nd-Fe- B P, H ca is the calculated coercivity of the Ai-Ni-Co P, and h is magnetization direction thickness of the Ai-Ni-Co P. (1- b ) H h b m = 1- H h mnk cn Nd ca Then the internal magnetic field intensity of the Ai-Ni-Co P can be showed as (10) (9) (1- b ) H h H m = h mnk cn Nd The unit value of the magnetic inductance of the Nd-Fe-B P s load working point can be calculated by (11) when the q axis magnetization magnetomotive force is provided. f+ F sum b mnk = 1- (11) 2H cn h Nd where, F sum is the drop of the magnetomotive force of all the outer magnet-circuit, f is the magnetization magnetomotive force. When no-load, set it as zero. (1) Forward magnetization When the motor works in the low-speed constant-torque condition, the higher magnetic field intensity is needed. The positive d-axis current-pulse would be generated by the windings to magnetize the -Ni-Co P. The Nd-Fe-B P with the -Ni-Co P goes into the D and d points of the first quartile along their hysteresis loop respectively. And after getting rid of the d-axis current-pulse, the two Ps return to the C and c points in the second quartile along their reversion line respectively. The magnetomotive force F c is provided by the two Ps collectively, and the internal magnetic inductance of the Nd-Fe-B P is B NdC, the internal magnetic inductance of the -Ni-Co P is B c. At this time, the flux provided by the two Ps for outer magnetic-circuit is showed as (12). m NdC Nd c B A B A (12) where, A Nd is the flux sectional area per pole provided by the Nd-Fe-B P, and A is the flux sectional area per pole provided by -Ni-Co P. (10)
(2) Backward demagnetization When the speed is over rated, weakening the flux to extend its speed is necessary. So the negative d-axis current-pulse would be generated to backward magnetize the -Ni-Co P. The Nd-Fe-B P and -Ni-Co P move to point H in the second quartile and point h in the third quartile along their backward magnetization line respectively. After getting rid of the d-axis current-pulse, The Nd-Fe-B P and -Ni-Co P move to point G in the second quartile and point g of the third quartile along with their reversion line respectively. The magnetomotive force F g is provided by the two Ps in common, and the internal magnetic inductance of the Nd-Fe-B P is B NdG, the internal magnetic inductance of the -Ni-Co P is B g. Here, B g is negative, the flux provided by the two kinds of Ps for outer magnetic-circuit is showed as (13). B A B A (13) m NdG Nd g (3) Solving the No-load magnetic-circuit Because of the using of Dual-Ps with different properties, the two kind of Ps affect each other, the magnetic-circuit becomes complicated. Thus, it is important to study the characteristics of the no-load static field. As figure 1 shows, when the -Ni-Co P is forward or backward magnetized, the working point moves along the magnetization line. Where the working point would stay depends upon the intersection point of the motor s air gap line and the magnetization line. The air gap line is mainly determined by the motor s magnetic-circuit and the dimension of the P. So it s important to optimize the magnetic-circuit and the dimension of the two kinds of Ps. In order to make sure that the motor works steadily, the working point should stay above the knee-point k such as working on air gap line 1. When the motor works on the air gap line 2, it means that the -Ni-Co P is backward magnetized to B r2. When the motor work on the air gap line 3, it means that the -Ni-Co P has already been negatively magnetized. The -Ni-Co P shorted the magnetic-circuit of the Nd-Fe-B P. Therefore, as the influence of the Nd-Fe-B P, the -Ni-Co P can t keep its magnetizing level after magnetized. It should be adjusted as (14). Brk w( Hi HQk ) Hi HQk H B B ( H H ) H H H H Br Hi H 0 r r rk i C 0 r i Qk H HC The iterative method is used to solve the No-load magnetic circuit because of the saturation of the magnetic-circuit. The solving process is showed as Figure 6. (14) B/ T D I H B b i A a E C G c B G B C B E A B a B c d m F F h F b F i F a F e F F c g Fd F F / A h g B g m e B e Figure 6. agnetization/demagnetization process of the dual-magnetic.
Analysis of the Dimension of the PS Based on the Flux Control Characteristic This paper has studied the relationship between the flux control characteristics and the dimension of the P based on the EC mentioned ahead. The Effect of the Dimension of Two Kinds of Ps on the aximum forward agnetization Level (FL) of the -Ni-Co P The maximum FL of the -Ni-Co P is the calculated remanence that can be reached when it is saturatedly magnetized without load. The width of the Nd-Fe-B P is set as 30mm or 35mm, the width of the -Ni-Co P is set as 8mm or 12mm. This paper has studied the relationship between the thickness and the maximum FL at different width. (a) b =8mm, b Nd =30mm (b) b =12mm, b Nd =30mm (c) b =8mm, b Nd =35mm (d) b =12mm, b Nd =35mm Figure 7. The relationship between the size of Ps and the maximum DL of the -Ni-Co P. Figure 7 shows that the maximum FL is in inverse proportion to thickness and width of the Nd- Fe-B P and width of the -Ni-Co P, and is in direct proportion to thickness of the -Ni-Co P. It drops sharply with the increased thickness of the Nd-Fe-B P and -Ni-Co P when the thickness of the Nd-Fe-B P is small, and slowly when it is large. The maximum FL of the -Ni-Co P is determined when the dimension of the magnetics is determined. In order to make sure that the motor works steadily, (15) is suggested to be satisfied. B rkac 0.8T Brkf 1.0T 0.8Brk Brkf 1.0T Where, B rkac is the actual maximum FL. The Effect of the Dimension of the two Kinds of Ps on Direct-axis agnetization agnetomotive Force (F) The F is one of the key parameters for the memory motor, the larger the F is, the lager the magnetization current of the winding is, and the heat capacity of the inverter would also be larger. Fig 8 shows the F for different magnetization levels of the -Ni-Co P. Where, Fig 8(a), (c), (e) show the curve of the forward-f varied with thickness of the Nd-Fe- B P and -Ni-Co P when B rk =0.8 T at different width of the Nd-Fe-B P, it can be seen that the forward-f increases when thickness of the -Ni-Co P increases. Because of the negative magnetomotive force of the Nd-Fe-B P, the forward-f also increases when thickness of the Nd-Fe-B P increases, and the effect is obvious when the width increases. Figure 8 (b), (d), (f) show the curve of the backward-f varied with thickness of the Nd-Fe-B P and the -Ni-Co P when B rk =-1.0 T at different width of the Nd-Fe-B P. It can be seen that the backward-f increases when the thickness of the -Ni-Co P increases. Because of the enhancement of the Nd-Fe-B P, the backward-f decreases when the thickness of the Nd- Fe-B P increases, and the effect is obvious when the width of that increases. (15)
(a) b =12mm,b Nd =35mm B rkf =0.8 T (b) b =12mm,b Nd =35mm B rkr =-1.0 T (c) b =12mm,b Nd =30mm B rkf =0.8 T (d) b =12mm,b Nd =30mm B rkr =-1.0 T (e) b =12mm,b Nd =25mm B rkf =0.8 T (f) b =12mm,b Nd =25mm B rkr =-1.0 T Figure 8. The relationship between the size of Ps and D/DF. The Effect of the Dimension of the P on the ultiple of Flux-weakening (FW) The controllable-flux of the DS can be expressed by the FW. The FW is defined as the ratio of the air gap flux density when the -Ni-Co P is maximum forward-magnetization and that when the -Ni-Co P was maximum backward-magnetization, it is obvious that the FW is related to the width of the P. The thickness of the Nd-Fe-B P is set as 6mm, and the thickness of the -Ni-Co P is set as 12mm, the paper has studied the relationship between the FW and the width of the P. Fig. 9 is the variation curve of the FW along with width of the P at different forward/backward magnetization level (F/BL). It can be seen that the FW decreases sharply along with the increase of the width of the Nd-Fe-B P, and slow-down when the width of the Nd- Fe-B P becomes larger. The FW also increases along with the increase of the width of the - Ni-Co P. When the FL is 0.8 T and the BL is -1.0 T, it can be seen from the Figure 10 that the maximum air gap flux density and the minimum air gap flux density is linearly increased with the width of the Nd-Fe-B P and the -Ni-Co P separately. (a) B rkf =0.6 T, B rkr =-1.0 T (b) B rkf =0.8 T, B rkr =-1.0 T Figure 9. The relationship between the wide of Ps and /DL. (a) aximum air gap flux (b) inimum air gap flux Figure 10. The relationship between the wide of Ps and air gap flux. Fig. 11 shows the variation curve of the FW along with the FL and BL separately when the width of the Nd-Fe-B P and the -Ni-Co P is 35 mm and 12 mm separately.
It can be seen that the FW is linearly increased with the FL, but is nonlinearly increased with the BL. The larger the BL, the more quickly the FW increased. It means that the ability of flux-enhance is limited, and the flux-controllable is mainly implement by backward magnetization. So the BL is generally set as 1.0 T to ensure that FW is large enough. Verify by FE Figure 11. The relationship between the /DL and FW. Based on the results above, the FW is set above 5, the maximum air gap flux is set above 0.9 T and the maximum forward-f is set below 2000 A, the dimensions of the two kinds of Ps are determined by the minimum volume of the two kinds of Ps. That is 15 mm 7 mm 50 mm (width thickness length ) for the -Ni-Co P and 33 mm 4 mm 50 mm (width thickness length) for the Nd-Fe-B P. The winding is set to be 2 turns. The FE model is built, and the comparison between the results of the FE and EC is done. Fig.12 presents the working point of the -Ni-Co P. It can be seen that the error between the EC and FE is about 10%, and the maximum is below 20%. Fig13 shows the air gap flux with different magnetization level, the error between the EC and FE is larger when the -Ni-Co P was demagnetized, but it is below 15%. Fig14 presents the amplitude of the no-load voltage with different magnetization level, the error is also below 15%. The FW with different magnetization level is show in Fig.15, it can be seen from Fig.15 (c) that the error between the EC and FE is larger when the demagnetization level increases, and it is below 10%. Figure 12. Work point with different /D.L Figure 13. Air gap flux density with different /DL. Figure 14. The amplitude of the no-load voltage with different magnetization level with different /DL. (a) EC (b) FE (c) Error. Figure 15. FW with different /DL. Finally, the F to different magnetization level is showed in Fig16. Fig16(a) shows the error between the EC and the FE under forward-magnetization, it is below 20% when the FL is
below 0.8 T, it will increase sharply when the FL is increased above 1.0T. Fig16. (b) Shows the error between the EC and the FE under backward-magnetization, the error would increase as the BL increases, it will exceed 20% when the BL increases above 1.2T. The increased error is due to the saturation of the magnetic circuit when the L increases. However, it won t affect the validity of the EC when the maximum FL and BL is usually set below 0.8T and 1.0T separately. (a) forward-magnetization (b) backward-magnetization Figure 16. The F to different /D. Conclusion This paper has studied the flux control characteristic of the DS affected by the dimensions of the two kinds of Ps, the EC combined with the PH is proposed. Several results based on this research that can be used for the DS design are obtain: Firstly, the maximum-fl of the -Ni-Co P is in inverse proportion to thickness and width of the Nd-Fe-B P and width of the -Ni-Co P, and is in direct proportion to thickness of the -Ni-Co P. Secondly, the -Ni-Co P s ability of flux-enhance is limited, and the controllable flux is mainly implemented by backward magnetization. Thirdly, the forward magnetization is harder than the backward magnetization. And finally, the FE results verified the validity of the EC proposed by this paper. References [1] Ostovic, V., emory otors - "A new class of controllable flux P machines for a true wide speed operation", in Proc. Conf. Rec. IEEE-IAS annual meeting. 2001. pp. 2577-2584. [2] Jung, H.L. and P.H. Jung, "Permanent magnet demagnetization characteristic analysis of a variable flux memory motor using coupled Preisach modeling and FE", IEEE Transactions on agnetics, vol. 44, no. 6, 2008, pp. 1550-3. [3] Yu, C. and K.T. Chau, Design, "Analysis, and Control of DC-Excited emory otors", IEEE Transactions on Energy Conversion, vol. 26, no. 2, June 2011. pp. 479-489. [4] Liu, C., J. Zhong and K.T. Chau, "A Novel Flux-Controllable Vernier Permanent-agnet achine", IEEE Transactions on agnetics, vol. 47, no. 10, Oct 2011, pp. 4238-4241. [5] Yu, G., et al., "Analysis of doubly salient memory motors using Preisach theory", IEEE Transactions on agnetics, vol. 45, no. 10, Oct 2009, pp. 4676-9. [6] Chen Yiguang, Wang Ying, Shen Yonghuan., et al., "agnetic circuit design and finite element analysis of wide-speed controllable-flux PS", Proceedings of the CSEE, vol. 25, no. 20, Oct 2005, pp. 157-161. [7] aekawa, S., et al., "Study of the agnetization ethod Suitable for Fractional-Slot Concentrated-Winding Variable agnetomotive-force emory otor", IEEE Transactions on Power Electronics, vol. 29, no. 9, Sep 2014., pp. 4877-4887.
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