2026 IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 4, JULY 2004

Design of a Compact Winding for an Axial-FluxPermanent-Magnet Brushless DC Motor Used

in an Electric Two-WheelerP. R. Upadhyay, K. R. Rajagopal, Senior Member, IEEE, and B. P. Singh, Senior Member, IEEE

Abstract—This paper describes the design of a compact windingfor an axial-flux permanent-magnet brushless dc motor used in anelectric two-wheeler. Once the motor design is carried out usingthe conventional method and the dimensions of the motor, magnet,etc. are determined, the electric loading and the magnetomotiveforce (MMF) required to obtain the peak torque can be calculated.From the knowledge of the MMF requirement, a compact and effi-cient winding configuration has been achieved using a parametricstudy. The factors considered for the winding design are: 1) oper-ating voltage; 2) number of poles; 3) cross-sectional area availablefor the winding; 4) conductor size; 5) number of parallel paths; 6)length of mean turn; 7) and the peak torque for a given value ofAT/pole/phase. The motor voltage is decided based on the speedof the motor and aspects of the battery and the controller. Theselected winding configuration for an 80-Nm peak torque, 48-V,three-phase motor is having 48 coils with each coil of 18 turnsmade out of 15 standard wire gauge copper wire. The resistanceper phase is calculated as 0.0203 .

Index Terms—Axial-flux motor, dc motor, electric motor, elec-tric two-wheeler, motor, permanent-magnet (PM) motor, winding.

I. INTRODUCTION

THE ELECTRIC two-wheeler is a viable solution for urbanmobility due to its efficient and pollution-free operation.

The permanent-magnet (PM) motor is best suited as the drivemotor of the electric vehicle (EV) due to its high efficiency,high torque output, high power density , and maintenance-freeoperation. Especially for electric two-wheelers, the axial-fieldPM brushless (BLDC) motor is a good choice. The axial fieldmotor has a high torque-to-weight ratio, and its aspect ratio fitsmore comfortably in the wheel, as the motor can be used as adirect drive motor.

In this paper, a slotless axial-field PM BLDC motor havingthe stator coil sandwiched between PM rotor discs has beendesigned for driving a two-wheeler having a laden weight of250 kg and maximum speed of 60 km/h. The vehicle has to beaccelerated from 0 to 45 km/h in 9 s. The performance require-ments for the motor have been calculated as follows:

Maximum speed: 800 r/min;Maximum torque: 80 Nm;

Manuscript received October 15, 2003.P. R. Upadhyay is with the Department of Electrical Engineering,

Nirma Institute of Technology, Ahmedabad 382481, India (e-mail:pru_nirma@yahoo.com).

K. R. Rajagopal and B. P. Singh are with the Electrical Engineering Depart-ment, Indian Institute of Technology Delhi, New Delhi 110016, India (e-mail:kr_rajagopal@ieee.org; bpsingh@ee.iitd.ernet.in).

Digital Object Identifier 10.1109/TMAG.2004.829820

Fig. 1. One-sixteenth magnetic circuit of axial-field PM BLDC motor. (1) and(5) Rotor cores. (2) and (4) Permanent magnets. (3) Stator core.

Rated torque (RMS over a range): 48 Nm;Maximum power: 6 hp;Continuous power: 3 hp.

The motor has 16 poles, and hence 1/16th part need only beanalyzed to calculate the performance of the motor. A 1/16thpart of geometry involving half sections each of one N-pole andone S-pole is shown in Fig. 1, which is used for analyzing themagnetic circuit.

Here, is the airgap flux per pole. By following the methodgiven by Upadhyay et al. [1] and solving the above magneticcircuit, the motor torque expression can be worked out as

T (1)

whereaverage flux density in the airgap;current density;conductor packing factor;width of the coil;height of the coil window;number of magnet poles;number of slots per pole per phase;number of turns per slot;outer radius of the coil;inner radius of the coil.

Extensive parametric analyses have been carried out with var-ious combinations of magnet length and the axial depth of thecoil with a fixed axial length between the stator core and therotor core. It is observed that the torque is a function of bothmagnet length and the coil depth. The torque initially increaseswith the increase in the magnet length because of increase influx density but beyond certain value torque decreases due toreduction in electric loading. This enables to select optimummagnet length and coil depth for the desired torque. The ana-lytical results are verified using the finite-element (FE) method

0018-9464/04$20.00 © 2004 IEEE

UPADHYAY et al.: DESIGN OF A COMPACT WINDING 2027

and it is observed that the magnet length of 13 mm and axialcoil depth of 12 mm is optimum for developing the torque of48.32 Nm and the airgap flux density is 0.282 T [1]. The totalAT per coil is determined as 540 and 937 for the rated torque andthe peak torque, respectively, which is scalar product of Turnsper slot and the peak current in the coil.

II. VOLTAGE RATING

The selection of voltage rating depends mainly on three basicaspects; motor aspect, controller aspect, and the battery aspect.

A. Motor Aspect

For a given torque, the required value of the ampere-turn (AT)can be determined. For a given value of AT, with increase inbattery voltage the current decreases while, the number of turnincreases to maintain AT requirement. Hence, the length of theconductor increases. The cross-sectional area of the conductoralso decreases with current reduction. This implies that the totalarmature copper loss I R is not affected by battery voltage.The induced electromotive force (EMF) is directly proportionalto the operating speed [2]–[5]; hence, the battery voltage alsoshould increase with the operating speed.

B. Motor Controller Aspect

For the same power rating of the controller, the controller losswill be smaller for increased battery voltage. The switching de-vices are available in voltage ranges, and for a particular cur-rent rating of the device the cost is not affected much withinthe voltage range. These ranges are generally referred as, up to100 V, up to 600 V, etc. Considering the 50% derating of thedevice, 48 V for the drive circuit and hence, for the battery issuitable for economical operation of the vehicle.

C. Battery Aspect

The battery voltage is also one of the factors affecting theefficiency of the battery. The efficiency of the battery pack ishigher for higher voltages. For example, a 48-V battery is 27%more efficient, requiring fewer amperes to move the EV thana 36-V battery. Thus increasing the distance travel for the sameexpenditure of the energy and resulting in lower cost to recharge.

Considering above three aspects, it is decided to take motorrated voltage to be 48 V for 800 r/min motor.

III. WINDING DESIGN

As 48 V is applied to an axial-field PM BLDC motor, anytwo phases are conducting simultaneously. So as to limit theback-emf to affordable limit, it is decided to have four parallelpaths per phase. There are four coils per parallel path and 16coils per phase in three phase star connected configuration ofthe stator winding. The induced EMF per slot can be written as

E (2)

where is the angular speed of the motor.From the geometrical data given in Fig. 2, the resistance of the

coil and the induced EMF per coil are determined as follows:

Fig. 2. Sectional and side view of coil.

Fig. 3. Induced EMF variation with number of turns.

Fig. 4. Resistance variation with number of turns.

Mean length of turn mmLength of conductor per coil NsArea of conductor window Kc mm .

Considering to be 0.75 and resistivity of copper to bem, the resistance per coil is given as

(3)

and the resistance per parallel path R RThe desired peak current can be determined from the AT per

slot corresponding to the rated peak torque, which is 937 at therated peak torque

(desired) (4)

It can be seen that the resistance, back EMF, and desired peakcurrent are functions of number of turns. From these relation-ships, the number of turns per slot can be determine to satisfy allthe three parameters. A program is prepared to plot the changein all three parameters with the change in number of turns. Thegraphical results are shown in Figs. 3–5.

2028 IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 4, JULY 2004

Fig. 5. Current variation with number of turns.

Fig. 6. Actual and desired current changes.

For more turns, resistance increases, and the current de-creases. Therefore, to get the desired value of torque, morebattery voltage is required. On the other hand, for fewer turns,operation will not be satisfactory at the rated voltage. Theactual current I is calculated based on the induced EMF andresistance

IV E

R(5)

To arrive at an optimum number of turns, the desired currentand the actual current are plotted for different values of numberof turns as given in Fig. 6. The number of turns is selected tobe 18 based on Fig. 6. The cross-sectional area available for 18conductors of the coil is 54 mm , and therefore, the area calcu-lated for each conductor will be 3 mm . The nearest availablesize of the conductor is 15 standard wire gauge. After allowingfor the insulation thickness of 0.035 mm. The effective diam-eter worked out to 1.9 mm. The proposed connection diagramof stator coil and the conductor arrangement are shown in Fig. 7.

In the above arrangement, the resistance calculated per par-allel path is 0.0812 , and the resistance per phase will be

Fig. 7. Coil connections and conductor arrangements.

0.0203 . The volume per coil is 8142 mm , and for 48 coils, thetotal copper volume and weight are worked out to be 391 cmand 3.47 kg, respectively. The copper losses in this compactwinding for continuous rated power of 3 hp is 100 W, whichgives efficiency in order of 95%.

IV. CONCLUSION

For the given total axial length of motor, there is an optimummagnet length at which the torque is the maximum. Resistanceof the coil, induced EMF per coil, and the current are functionsof number of turns for the fixed value of AT. The desired peakcurrent and the actual coil current are plotted , and the intersec-tion of both of these results the best solution for the number ofturns and the peak current of the motor. The optimum value ofnumber of turns for given AT results in significant reduction inthe copper required; hence, this work is helpful to the designerfor the design of compact winding of an axial-field PM BLDCmotor.

REFERENCES

[1] P. R. Upadhyay, K. R. Rajagopal, and B. P. Singh, “Computer aideddesign of an axial-field PM brushless DC motor for an electric vehicle,”J. Appl. Phys., vol. 93, no. 10, pp. 8689–8691, May 2003.

[2] D. C. Hanselman, Brushless Permanent Magnet Design. New York:McGraw-Hill, 1994, ch. 6, pp. 137–153.

[3] D. Patterson and R. Spee, “The design and development of axial flux per-manent magnet brushless DC motor for wheel drive in a solar poweredvehicle,” IEEE Trans. Ind. Applicat., vol. 31, pp. 1054–1061, Sept/Oct.1995.

[4] W. S. Leung and J. Chan, “A new design approach for axial fieldelectrical machine,” IEEE Trans. Power App. Syst., vol. PAS-99, pp.1679–1685, July–Aug. 1980.

[5] F. Caricchi, F. Crescimbini, O. Honorati, A. Di Napoli, and E. San-tini, “Compact wheel direct drive for EV’s,” IEEE Ind. Appl. Mag., pp.25–32, Nov./Dec. 1996.