IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 4, APRIL 2010 1015

Design and Analysis of 42-V Coreless Axial-Flux Permanent-MagnetGenerators for Automotive Applications

Saeid Javadi��� and Mojtaba Mirsalim�����

Electrical Engineering Department, Amirkabir University of Technology, Tehran 15916, IranCenter of Excellence in Power Engineering, Amirkabir University of Technology, Tehran 15916, Iran

Electrical Engineering Department, St. Mary’s University, San Antonio, TX 78228 USA

This paper presents the design and analysis of a novel structure of an axial-flux permanent-magnet machine with ironless stator togenerate sinusoidal electromotive force with very low harmonics. The structure is of a special design that is suitable for flux weakeningin variable speeds. Flux weakening is done by a mechanical actuator to change the position of windings relative to each other. To confirmthe machine performance and the design, analytical and three-dimensional finite-element numerical methods are implemented. Thesimulations results of the proposed generator coincide very well with the experimental results on a prototype 42-V system realized in thelaboratory.

Index Terms—Automotive, axial flux, coreless, flux weakening, 42-V system, permanent-magnet (PM) generator.

I. INTRODUCTION

T HE main trend in automotive design is to replace me-chanical equipment with electric devices to increase the

efficiency, feasibility, and controllability of the system. Thecontinuous progress in the new high magnetic field rare-earthpermanent magnets (PMs) such as neodymium–iron–boron(Nd–Fe–B), the most powerful PMs available today, has showngreat opportunities for novel topologies of electric machinesto be used in automobile industry [1], [2]. With the implemen-tation of rare-earth Nd–Fe–B magnets that today are widelyproduced with low cost, it is possible to get high power densityin a small volume that helps designers to produce high-perfor-mance machines with minimum loss and materials [1].

One of the main parts of an automobile is the electric gener-ator to produce electricity for different parts of the system. Inmodern vehicles, the demand for on-board electric energy gen-eration is rapidly growing in order to satisfy new requirementsfor passengers’ comfort and safety. This growth, which is pre-dicted to reach higher power in the very next years, is forcingmanufactures to explore new solutions concerning the wholeelectrical system inside the vehicle. First of all, the present 12-Vsystem will be substituted by a 42-V system, which guaranteesbetter handling of the higher power level, without increase incable weight and power losses due to high currents [3].

The automotive electric system in use for the last four decadesis based on the Lundell generator. The power demand with newloads being added to the automotive power system in a vehicleis close to 3 kW. Examples of such loads are electric air con-ditioners, electric steering systems, electric brakes, or high-en-ergy discharge lamps. At this level of demand, the system based

Manuscript received May 14, 2009; revised August 31, 2009; acceptedOctober 21, 2009. First published November 20, 2009; current ver-sion published March 19, 2010. Corresponding author: S. Javadi (e-mail:s_javadi_arani@yahoo.com; saeid.javadi@aut.ac.ir).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TMAG.2009.2036256

on the Lundell machine and the 12-V dc bus voltage becomesinefficient. The losses in the alternator are significant and the in-creased currents require thicker wiring harnesses. Consideringthe concern for improved fuel economy and reduced emissions,the need for an electric system with improved efficiency is ap-parent whereas the increase in cost can now be justified withenergy savings [3].

Axial-flux machines are among the most suitable candidatesfor several automotive applications due to their compactnessand lightness, together with their high efficiency [4], [5]. Acoreless configuration eliminates any ferromagnetic material,and thus eliminating the associated eddy current and hysteresislosses. Also, these machines can be stacked axially allowing fora simple mechanical construction [1]. Because of the absenceof core losses, a coreless stator axial-flux permanent-magnet(AFPM) machine can operate at higher efficiency than conven-tional machines [4], [6], [7]–[10]. Adoption of ironless wind-ings results in a significant reduction in the stator weight, so thata small size actuator can be employed for shifting of winding.Moreover, by implementing an ironless stator core, no coggingtorque would be produced.

For a large pole-number, the diameters of the magnets andcoils are fixed and limit the radial length of the active area. Thiscan result in a generator that has quite a large radius but smallactive length. For small, low-power turbines that tend to runrelatively quickly this is not a problem, but as power increasesand a reduction in speed is desired, the number of poles shouldincrease, and now the radial length of the active area can besmall compared to the radius. Such a problem can be reducedby using trapezoidal or rectangular magnets whereby pole pitchand active length can be decoupled from each other [11].

The development of a coreless generator considered in thispaper is focused on the design and space harmonic analysis of amodified structure of an AFPM generator with rectangular mag-nets. It will be shown that due to the simple structure, control-lable output voltage, low amount of harmonics, and higher effi-ciency, this generator can be a suitable choice for automobilesand an alternative to the conventional Lundell generator. Themachine type selection is based on several key advantages, in-

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1016 IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 4, APRIL 2010

Fig. 1. Proposed machine structure.

Fig. 2. Flux paths.

cluding high power density, being brushless, easy maintenanceand low manufacturing cost relative to the conventional Lun-dell generators and other proposed PM machines [3]. The dcload voltage of the designed generator under loadings at dif-ferent speeds is assumed to be 42 V.

II. MODELING AND DESIGN

The schematic structure of the proposed AFPM generatorshown in Fig. 1 consists of two stators and one rotor. This gener-ator has a simple structure to manufacture, and also no iron coreswhich reduces the weight. The two ironless stator windings areplaced in the air gap with 1-mm mechanical clearance from therotor disc on each side. The rotor disc consists of rectangularflat-shaped high-energy Nd–Fe–B magnets glued into the emp-tied spaces of similar size of magnets on an aluminum rotor-sup-porting part. Because of this low magnet permeability structure,the machine is less sensitive to air gap variations. Therefore,manufacturing tolerances could be loosened to reduce the cost.Also, solid mild steel back plates are placed on the outer of thetwo stators. Using a nonmagnet material for the armature sup-port structure ensures minimal axial magnetic forces betweenthe rotor and stator, thereby making the assembly easier, whileensuring the generator has no cogging torque. Fig. 2 shows theschematic rotor poles with an opposite arrangement (N-S type)and the associated flux paths for the proposed generator.

Concentrated armature coils of each stator are easily gluedonto nonmagnetic nonconducting material such as bony fiber

that has lower weight and cost relative to magnetic materials,and is resistive against temperature and pressure. In this struc-ture, one stator is stationary whereas the other can be turned.By connecting the two stator windings in series, the resultantvoltage can be obtained as follows [7]:

(1)

where , , , and are the mechanical phase shift be-tween the windings of the two stators, the number of pole pairs,root-mean-square (rms) voltage per phase per stator, and rmsvoltage per phase, respectively. If the phase shift is equal tozero, then maximum voltage is induced which is suitable forlow-speed ranges. At higher speeds, the phase shift between thetwo stator windings is increased to obtain the desired voltage atthe output terminals of the generator. In other words, an approx-imately fixed output voltage can be generated for a wide speedrange. Using this configuration a mechanical field weakening isimplemented that is cost effective without power electronic de-vices. To do so, it was necessary to form “gear teeth” on one ofthe bony fiber plates (the second part of Fig. 11) to make it turnby a pivot.

The three-phase output voltage of the generator is then rec-tified by diodes to obtain the required 42-V dc output voltage.The open circuit dc voltage of the generator is obtained asfollows:

(2)

where , , and are output frequency, the number of coilturns in series per phase, and the magnetic flux per pole, re-spectively. Of course, the voltage drop of the diodes and totalresistances should also be taken into account.

The output volt-ampere ratings (VA) of the machine can beobtained by [12]

(3)

where , , , and f/p are the output power co-efficient, the mean diameter of stator, the axial length, and thesynchronous speed of the generator, respectively. The output co-efficient is related to magnetic and electric loading of the ma-chine. The electric loading is similar to the Lundell generator[13], [14].

Equation (4) can be used to obtain the required number ofconcentrated coils [11]

(4)

In (2)–(4), and the volume limitation the designer is faced with,the authors chose eight poles and six concentrated coils for theproposed three-phase generator.

Looking radially inwards onto the machine shown in Fig. 1and ignoring curvature allows the machine to be represented asshown in Fig. 3 where the x- and z-coordinates represent thecircumferential and axial directions, respectively. The modelassumes the radial direction to be infinite. Although strictly a

JAVADI AND MIRSALIM: DESIGN AND ANALYSIS OF 42-V CORELESS AFPM GENERATORS 1017

Fig. 3. Schematic for the analytic model.

Fig. 4. Model for Laplace solution.

three-dimensional (3-D) problem, a satisfactory analytical so-lution for the flux density distribution produced from magnetscan be found by solving Laplace’s equation for the two-dimen-sional Cartesian problem defined in Fig. 3.

The problem is symmetrical on either side of the center line,allowing it to be considered in the form of Fig. 4. A solutionis now possible using the analysis described in [15] where themagnet is presented by an equivalent described current.

The analytic formula for normal component of magnetic fluxdensity in the middle of air gap in Fig. 4 is as follows:

(5)

where , , , , and are pole pitch at differentradii, the width of PM in circumferential direction, the PMthickness, the residual flux density, and the relative permeabilityof PM, respectively.

To calculate flux and the induced voltage, it is assumed thatthe coil geometry of the stator is in the form of Fig. 5 and hence,only two arms in the radial direction are effective to producevoltage as follows:

(6)

(7)

where , , and are the number of turns of one coil,the coil width in radial direction, and the width of differentialelement of the main arm of coil, respectively. Also, , ,

, and are sectional areas of and poles swept by the

Fig. 5. Coil geometry.

Fig. 6. Different positions of the right arm of a coil passing by a pole.

Fig. 7. Equivalent magnetic circuit.

first and second arms, respectively. It is clear that only one armis in front of a pole at a time and thus, only one of the sectionalareas , , , and is considered in the calculation offlux at that moment, which is dependent on the arm position. Asan illustration, different positions for the differential element ofthe first arm with width in front of a North Pole are depictedin Fig. 6. For the positions shown in the figure, , , and

are all equal to zero and is the covered area underneaththe North Pole.

To calculate the resistance and inductance of a coil, one mayassume that the turns of a coil shown with dotted linesin Fig. 5 are located in the middle of coil with outer and inner

1018 IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 4, APRIL 2010

Fig. 8. Machine structure.

Fig. 9. DC load and the equivalent circuits.

Fig. 10. Prototype generator (in EMTR laboratory).

average radii and , respectively. Now, the resistances percoil and per phase can approximately be obtained as follows:

(8)

(9)

where , , and , are the cross-sectional areaof wire, the number of coils in parallel per phase, and the numberof coils in series per phase, respectively.

To simplify the calculation of armature inductance, it is as-sumed that the resultant magnetic flux density produced by acoil in the air gap is in axial direction [11]. The equivalent mag-netic circuit for one phase of the proposed generator is shown

Fig. 11. Detailed structure of the machine. (a) PMs, (b) stator winding, and (c)prototype machine.

in Fig. 7. By observing Fig. 8, the reluctances can be obtainedas in the following:

(10)

where and , , , , and are theaxial distances of the middle of the first stage coil from the back

JAVADI AND MIRSALIM: DESIGN AND ANALYSIS OF 42-V CORELESS AFPM GENERATORS 1019

TABLE IDESIGN DATA OF THE PROPOSED MACHINE

iron core, the middle of the first stage coil from the second stagecoil, the middle of the second stage coil from other back ironcore, the average area of one coil, and the core area. By usingFig. 7, it is clear that and

(11)

Therefore

(12)

where and are the inductance values of one coil, andper-phase, respectively.

Fig. 9 shows the circuit and its equivalent model for auto-motive applications. The equivalent circuit parameters and the

Fig. 12. Meshed model of half of the generator.

Fig. 13. Models of windings in zero and nonzero mechanical phase shift.

generator efficiency are obtained as in the following [11]:

(13)

where , , , , and are equivalent dc resis-tance, equivalent resistance due to diode commutating induc-tance, open circuit dc voltage, output dc voltage, and efficiency,respectively. The resistances of the connections from the gener-ator to the diode rectifier and to the load have not been consid-ered in (13). If required, these can be taken into account by in-creasing the generator resistance as appropriate. The termhas been added to (13) to account for the voltage drop in thediodes.

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Fig. 14. Phase shift angle versus speed for the proposed generator.

Fig. 15. Magnetic flux density distribution in back iron and PMs.

III. PROTOTYPE GENERATOR AND SIMULATION

A prototype generator was constructed for verification. It wastested for various loads at different speeds to evaluate its perfor-mance. The generator and detailed structure of the machine isshown in Figs. 10 and 11. Two parallel coils per phase on eachside are connected in series with each other according to (1). Itshould be noted that one of the stators can be turned by a smallactuator to get the desired voltage and performance. The designdata are summarized in Table I.

The meshed model of the generator is shown in Fig. 12. It issufficient to analyze half of the machine structure due to sym-metry. For 3-D finite-element method (FEM) calculation withmotion, the model is divided in two moving and stationary parts.

Fig. 16. Comparison of the experimental, 3-D FEM, and analytical no-loadvoltages at 800 rpm. (a) Experimental, (b) 3-D FEM, and (c) analytical method.

Fig. 17. Harmonic spectrum of the voltage at 800 rpm.

In this model, the rotor is placed in the meshed volume andturned whereas the stator is kept stationary.

JAVADI AND MIRSALIM: DESIGN AND ANALYSIS OF 42-V CORELESS AFPM GENERATORS 1021

Fig. 18. Magnetic flux density variations versus circumferential distance in dif-ferent radii using analytical method.

Fig. 13 shows the relative position of the two windings withrespect to each other. One stator is stationary and another ismovable to get the desired dc output voltage. The required phaseshift in electrical degrees for the proposed generator to get 42 Vat no load from zero to 12 000 rpm is depicted in Fig. 14.

It is clear that to get 42 V in loading condition, the curve isshifted to the right side because of the voltage drop on generatorand rectifier circuit elements.

Fig. 15 shows magnetic flux density values in back iron andthe PMs. The variations are not smoothly distributed in someparts of the figures due to the coarse mesh density and numer-ical errors. It is observed that the flux density in back iron isbelow 1.8 T which is lower than the field saturation value of themagnetic iron.

The comparison between the experimental and theoreticalno-load output voltage at 800 rpm for a zero phase-shift betweenthe windings is shown in Fig. 16. The results are approximatelythe same. The harmonic analysis for the experimental no-loadoutput voltage of Fig. 16 is shown in Fig. 17. The total harmonicvoltage (THD%) is under 6.9%, which is suitable.

The magnetic flux density versus circumferential distance bythe 3-D FEM and analytical methods are shown in Figs. 18 and19, respectively. It is deduced from the figures that the resultscompare very well. The maximum value of flux density is 0.595

Fig. 19. Magnetic flux density variations versus circumferential distance in dif-ferent radii using 3-D FEM.

Fig. 20. Comparison between theoretical and experimental efficiencies versusdc load current at 800 rpm.

T for a 10-mm air gap between PMs and back iron, suitable forair core electric machines.

The efficiency and the dc output voltage at 800 rpm are, re-spectively, shown in Figs. 20 and 21. The maximum discrepancyis less than 4%. The main source of losses in the machine is fromstator copper losses. As it was expected, the graphs are linear,because armature reaction is insignificant in ironless stators.

Assuming an average speed of 2000 rpm for automotive gen-erators, a dc voltage of 42 V at rated load is desired. Usually, thestarting speed of the automotive generator is 2000 (rpm) and the

1022 IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 4, APRIL 2010

Fig. 21. Comparison between theoretical and experimental dc output voltageversus dc load current at 800 rpm.

Fig. 22. Experimental no-load output voltage at 2000 rpm.

Fig. 23. Comparison between theoretical and experimental dc output voltageversus load current at 2000 rpm.

desired dc voltage under loading is 42 V. The winding is of airwinding type, which means we can have higher current valuesfor the same condition as in a conventional Lundell generator.Fig. 22 shows the test no-load voltage at 2000 rpm which is ap-proximately sinusoidal. The efficiency and the dc output voltageat 2000 rpm are, respectively, shown in Figs. 23 and 24.

One can deduce from the plots that the output voltage ishigher than the desired 42 V and the efficiency is higherthan 91% for a load current of 15 A (normal current). Thephase-shifting between the two stators is required to maintainthe output voltage at a 42-V value. As an example, from Fig. 14,we need a phase shift of close to 66.4 for a speed of 2000 rpm.

Fig. 24. Comparison between theoretical and experimental efficiencies versusload current at 2000 rpm.

IV. CONCLUSION

The main objective of this paper was to introduce, analyze,and verify a modified structure of axial flux generators for auto-motive applications. Simple and robust structure of the proposedmachine and lower manufacturing cost with better performanceare the main advantages achieved. The generator is a brushlessPM machine which is an advantage especially at high speeds.Because of its simple structure, controllable output voltage, andvery low harmonic components, the proposed generator can bea suitable choice and an alternative to the conventional Lundellgenerator in 42-V systems. Due to coreless stator, the armaturereaction is very small, which is advantageous in voltage regula-tion. It also has lower losses and higher efficiency.

REFERENCES

[1] J. F. Gieras, R. J. Wang, and M. J. Kamper, Axial Flux PermanentMagnet Brushless Machines. Norwell, MA: Kluwer, 2004.

[2] W. Mo, L. Zhang, A. Shan, L. Cao, J. Wu, and M. Komuro, “Improve-ment of magnetic properties and corrosion resistance of NdFeB mag-nets by inter-granular addition of MgO,” Trans. Alloys Compounds,vol. 461, no. 1, pp. 351–354, Aug. 2007.

[3] M. Comenscu, A. Keyhani, and M. Dai, “Design and analysis of42-V permanent-magnet generator for automotive applications,” IEEETrans. Energy Convers., vol. 18, no. 1, pp. 107–112, Mar. 2003.

[4] S. Javadi and M. Mirsalim, “A coreless axial-flux permanent-magnetgenerator for automotive applications,” IEEE Trans. Magn., vol. 44, no.12, pp. 4591–4598, Dec. 2008.

[5] M. Mirzaei, M. Mirsalim, and S. E. Abdollahi, “Analytical modelingof axial air gap solid rotor induction machines using a quasi-three-di-mensional method,” IEEE Trans. Magn., vol. 43, no. 7, pp. 3237–3242,Jul. 2007.

[6] S. M. Hosseini, M. Mirsalim, and M. Mirzaei, “Design, prototyping,and analysis of a low cost axial-flux coreless permanent-magnet gen-erator,” IEEE Trans. Magn., vol. 44, no. 1, pp. 75–80, Jan. 2008.

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[9] F. Crescimbini, A. D. Napoli, L. Solero, and F. Caricchi, “Compact per-manent-magnet generator for hybrid vehicle applications,” IEEE Trans.Ind. Applicat., vol. 41, no. 5, pp. 1168–1177, Sep./Oct. 2005.

[10] L. Del Ferraro, F. Caricchi, F. Giulii Capponi, and G. De Donato,“Axial-flux PM starter/alternator machine with a novel mechanical de-vice for extended flux weakening capabilities,” in Proc. IEEE 39th IASAnnu. Conf., Oct. 3–7, 2004, vol. 3, pp. 1413–419.

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[11] J. R. Bumby and R. Martin, “Axial-flux permanent-magnet air-coredgenerator for small-scale wind turbines,” Proc. Inst. Elect. Eng., vol.152, pp. 1065–1075, Sep. 2005.

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Saeid Javadi was born in Aran and Bidgol, Iran, on March 21, 1969. He re-ceived the B.S. degree in communication engineering and the M.S. degree inelectrical power engineering from Amirkabir University of Technology, Tehran,Iran, in 1992 and 1999, respectively. He is pursuing the Ph.D. degree in the De-partment of Electrical Engineering, Amirkabir University of Technology.

His research interests are numerical and analytical analysis of electromag-netic fields, and electrical machines.

Mojtaba Mirsalim (SM’04) was born in Tehran, Iran, on February 14, 1956. Hereceived the B.S. degree in EECS/NE and the M.S. degree in nuclear engineeringfrom the University of California, Berkley, in 1978 and 1980, respectively, andthe Ph.D. degree in electrical engineering from Oregon State University, Cor-vallis, in 1986.

Since 1987, he has been at Amirkabir University of Technology, Tehran,where he has served five years as the Vice Chairman and more than seven yearsas the General Director in Charge of Academic Assessments, and is currentlya Full Professor in the Department of Electrical Engineering where he teachescourses and conducts research in energy conversion, electrical machine design,and hybrid vehicles, among others. His special fields of interest include the de-sign, analysis, and optimization of electric machines, FEM, renewable energy,and hybrid vehicles. He is the author of more than 110 international journal andconference papers and three books on electric machinery and FEM. He is thefounder and at present, the director of the Electrical Machines and TransformersResearch Laboratory. His web page is available at http://ele.aut.ac.ir/~emtrl.