JOURNAL OF APPLIED PHYSICS 111, 07A719 (2012) Field weakening capability investigation of an axial flux permanent-magnet synchronous machine with radially sliding permanent magnets used for electric vehicles Jing Zhao,1 Dansong Cheng,2 Ping Zheng,2,a) Xiangdong Liu,1 Chengde Tong,2 Zhiyi Song,2 and Lu Zhang2 1School of Automation, Beijing Institute of Technology, Beijing 100081, China 2School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150080, China (Presented 31 October 2011; received 23 September 2011; accepted 9 November 2011; published online 21 February 2012) Due to the advantage of high power density compared with the conventional radial flux machines, the axial flux permanent-magnet synchronous machines (PMSMs) are very suitable candidates for the power train of electric vehicles (EVs). In this paper, a new axial flux PMSM adopting radially sliding permanent magnets (PMs) to fulfill field-weakening control and to improve the operating speed range is investigated. The field-weakening structure and principle of the axial flux PMSM with radially sliding PMs are proposed and analyzed. The influence of radially sliding PMs on electromagnetic performances and parameters is analyzed based on FEM. The field-weakening method with radially sliding PMs, which is a mechanical method, is compared and combined with traditional electrical method. Due to the optimized combination of the two methods, the field-weakening capability of the machine is much improved and the maximum speed can reach up to six times of the base speed with constant power, which is very satisfying for EV drive application. VC 2012 American Institute of Physics. [doi:10.1063/1.3676230]

I. INTRODUCTION

Permanent-magnet synchronous machines (PMSMs)

have gained popularity due to higher power density and effi-

ciency recent years. However, because of the fixed magnetic

flux provided by the PMs, it is hard to operate above base

speed where the back electromotive force (EMF) equals the

supplied limit voltage. Thus, various field weakening meth-

ods to increase the speed of PMSM are proposed and researched.15 Based on the voltage equation as shown in

(1), traditional electrical method, i.e., increasing the d-axis

demagnetizing current and decreasing the q-axis current, is

usually adopted.

ulim ј xrАffiffiffiLffiffiqffiffiiffiffiqffiffiБffiffi2ffiffiffiюffiffiffiffiffiffiffiLffiffiffidffiffiiffidffiffiffiюffiffiffiffiffiwffiffiffifffiffiffiffiffi2ffi;

(1)

where ulim is the supplied limit voltage, x is the electrical speed, Ld and Lq are the d- and q-axis inductances, id and iq are the d- and q-axis current, wf is the flux linkage produced by the permanent magnet (PM). An axial flux PMSM used for traction of electric vehicles (EV) is researched in this paper due to its advantage of high power density compared with the conventional radial flux PMSMs.5,6 However, most axial flux PMSMs adopt surface PMs and have large air gaps, which results in small d- and q-axis inductances and, thus, makes the field weakening more difficult to execute for wide range operation by using traditional electrical methods. To satisfy the speed requirement for the drive motor of the EV, this paper investi-

gates a novel axial flux PMSM with new mechanical method of adopting radially sliding PMs to fulfill field-weakening control and to improve the operating speed range. II. STRUCTURE AND PRINCIPLE An axial flux PMSM with power rating of 10 kW and base speed of 3000 rpm is researched in this paper. It is comprised of two parts: a conventional stator with three-phase windings and a novel rotor with radially sliding PMs. schematic diagram of the field weakening mechanism of radially sliding magnets is shown in Fig. 1. Different from the conventional disk machine, the PMs are supported in a PM carrier on the rotor and the PMs can slide radially under the action of centrifugal force opposed by springs. When the PMs are at the initial position, the diameter of the stator iron is the same as that of the PMs, i.e., the PMs face stator iron directly; but the diameter of the rotor iron is bigger than that of the PMs to provide the space for the PMs sliding outward. When the speed increases to base speed, the PMs are designed to start sliding

a)Author to whom correspondence is addressed. electronic mail: [email protected]

FIG. 1. (Color online) Schematic diagram of the field weakening mechanism of radially sliding PMs.

0021-8979/2012/111(7)/07A719/3/$30.00

111, 07A719-1

VC 2012 American Institute of Physics

07A719-2 Zhao et al.

J. Appl. Phys. 111, 07A719 (2012)

FIG. 2. Diagram of radial section of the axial flux PMSM when PMs slide outwards. outward under the centrifugal force. Thus, the flux linkage wf produced by the PM will be reduced because the area of PMs facing stator iron decreases. With the fixed limit voltage, the speed x will increase consequentially with flux linkage decreasing, which is the field weakening principle of the mechanical method. III. INFLUENCE ON THE ELETROMAGNETIC PERFORMANCES A. Magnetic flux density distribution When the PMs are at the initial position, the inner radius and outer radius of the stator iron and the PMs are 75 mm and 123 mm, respectively. The magnetic flux distributes evenly in the air-gap and stator iron. When the speed is up to the base speed, the PMs move outwards radially under the action of centrifugal force opposed by springs, as illustrated in Fig. 2. Area I includes stator iron and rotor iron but no PMs. The flux density in air-gap and stator iron will be much reduced without PM in this area; area II includes stator iron, rotor iron and PMs, which is the same as normal axial flux PMSM, so the flux density in air-gap and stator iron change little; In area III, part of every PM moves out and the equivalent reluctance in this area

FIG. 4. The d- and q-axis inductances vs the distance of PMs sliding outwards. becomes much bigger without the stator iron. Thus, the flux produced by the PMs in area III is much reduced. When the PMs slide outwards to different distances, the no-load flux density distributions in the air-gap and stator yoke along the radius direction are shown in Fig. 3. It can be seen that the simulation results are in good agreement with analysis and the average flux density decreases with the PMs sliding outwards. B. Inductances According to equation (1), it is necessary to evaluate the changing law of d- and q-axis inductances when the PMs slide outward. As is known, the inductance is proportional to the permeance in the Magnetic Circuit of the machine and the permeance varies with magnetic saturation degree changing. Based on the analysis results in Sec. III A, it can be deduced that the magnetic saturation degree in stator iron is much reduced when the PMs slide outward. Then the permeance and the inductance will increase with the PMs sliding outwards. For the same current amplitude, the 3 D FEM calculated d- and q-axis inductances7 versus the distance of PMs sliding outwards are shown in Fig. 4. It can be seen that the Calculated results are in agreement with the analysis. As the PMs slide outwards, the d- and q-axis inductances increase rapidly at first and then slowly or change little. C. Flux linkage Section II mentioned that the flux linkage wf produced by PMs will decrease as the PMs slide outwards. However, it is necessary to quantitatively research the flux linkage at no load and load. The flux linkage wno-load at no-load, which is produced by PMs independently, is calculated by 3 D FEM. When only the mechanical method is adopted to weaken the magnetic field, the armature current in the stator is kept constant and only has a q-axis component. The flux linkage wload

FIG. 3. (Color online) Flux density distribution along the radial direction: (a) in air-gap and (b) in stator yoke.

FIG. 5. The flux linkage and torque versus the distance of PMs sliding outwards.

07A719-3 Zhao et al.

J. Appl. Phys. 111, 07A719 (2012)

FIG. 6. Field weakening capabilities: (a) torque vs speed curves and (b) power vs speed curves.

at load is produced expressed as wload

by ј

qboАffitffihffiLffiffiqfficffiiffiuffiqffiffiБrffirffi2ffieffiffiюnffiffitffiffiwffiiffiqffiffifffia2ffiffi.ndTPhMe sc,awlchuilcahtecdanflubxe

linkage at no load and load are shown in Fig. 5. It can be seen

that the decreased ratio of flux linkage at no-load is higher

than that at load. When the PMs slide outwards to 35 mm and

50 mm, the flux linkage at no load are decreased by 54.54%

and 86.35%, and the flux linkage at load are decreased by

34.96% and 46.02%, respectively. The field weakening effect

at no load is satisfying. However, the machine has poorer

field weakening effect at load because of the q-axis induct-

ance Lq increasing during the PMs sliding process. It indicates that using only this mechanical method is not enough to

obtain good field weakening capability.

D. Torque

The torque characteristic of this novel axial flux machine is also investigated based on 3 D FEM. With constant armature current only assigned on the q axis, the average torque versus the distance of the PMs sliding outwards is shown in Fig. 5. It can be seen that the changing law of the torque with the PMs sliding is very similar to that of the flux linkage at no load, which is caused by the inductance characteristic of the machine. The d- and q-axis inductance of this machine are very close as seen in Fig. 4, then the torque Tem can be simplified as

Tem ј pwf iq:

(2)

Thus, when iq is constant, Tem is proportional to flux linkage at no load.

IV. FIELD WEAKENING CAPABILITY The integrated field weakening capability of the machine, i.e., torque and power versus the speed, are investi-

gated. The field weakening capabilities by using mechanical

method of PMs sliding and electrical method of adjusting the

d- and q-axis current are compared, which are shown in Fig.

6. It can be seen that field weakening capabilities of the two

methods are similar: the speed is increased by no more than

two times of the base speed by either of the two methods,

and the power cannot keep constant above the base speed. It

is necessary to combine the mechanical and electrical meth-

ods together. The matching principle of the current and the

distance of the PM sliding outwards is to ensure the speed x

and torque Tem as high as possible and keep the power Pem as constant as possible above the base speed. Considering the

variety of the inductances, the PMs sliding distance and the

distribution of d- and q-axis current are carefully chosen

based on equations (1)-(3),

Pem ј wf iqulim=qАffiffiffiLffiffiqffiffiiffiffiqffiffiБffiffi2ffiffiffiюffiffiffiffiрffiffiLffiffiffidffiffiiffidffiffiffiюffiffiffiffiffiwffiffiffifffiffiЮffiffi2ffi:

(3)

The optimized match of the mechanical method and electrical method shows very satisfying field weakening capability. The torque and power versus the speed are shown in Fig. 6. It can be seen that the maximum speed can reach up to six times of the base speed with constant power, which is impossible by adopting either mechanical method or electrical method independently.

V. CONCLUSIONS A novel axial flux PMSM with radially sliding PMs is investigated in this paper. The structure of the machine is described. The field weakening principle is analyzed. The influence of PMs sliding outwards on the electromagnetic performances and parameters are analyzed and calculated by 3 D FEM. The field weakening capabilities by using mechanical method of PMs sliding and the electrical method of adjusting the d- and q-axis current are compared. The results show that neither of the methods can provide satisfying field weakening capability. With the optimized matching of the two methods, satisfying field weakening capability of the machine is obtained.

ACKNOWLEDGMENTS This work was supported in part by National natural science Foundation of China under Project 50877013 and 51077026, and in part by the 863 Plan of China under Project 2011AA11A261. 1S. C. Oh and A. Emadi, IEEE Trans. Veh. Technol. 53, 912 (2004). 2L. D. Ferraro, F. Caricchi, and F. G. Capponi, IEEE Trans. Power Electron. 21, 720 (2006). 3M. Aydin, S. Huang, and T. A. Lipo, IEEE Ind. Appl. Conf. 2, 1250 (2002). 4L. D. Ferraro, F. G. Capponi, R. Terrigi, F. Caricchi, and O. Honorati, IEEE Ind. Appl. Conf. 41, 1 (2006). 5J. A. Tapia, D. Gonzalez, R. R. Wallace, and M. A. Valenzuela, IEEE Ind. Appl. Conf. 3, 1427 (2004). 6K. Sitapati and R. Krishnan, IEEE Trans. Ind. Appl. 37, 1291 (2001). 7Y. S. Chen, Z. Q. Zhu, and D. Howe, IEEE Trans. Magn. 41, 3940 (2005).

J Zhao, D Cheng, P Zheng, X Liu, C Tong

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