Design and Loss Assessment of Air Cored AxialFlux Permanent Magnet Machines

Oliver Winter, Student Member, IEEE, Christian Kral, Senior Member, IEEE and Erich Schmidt, Member, IEEE

Abstract—This paper focuses on different calculation methodsof Joule losses in a winding and Halbach magnet arrays for aircored axial flux motors. The classical approach (I) for windinglosses results in eddy current losses without proximity effect butwith induced currents for the passing magnetic field. The secondmethod (II) derives the frequency dependent resistance includingskin and proximity effects to calculate the winding losses due tohigher current harmonics generated by pulse width modulation(PWM) excitation. The calculation of eddy currents (III) inducedby higher harmonics in the magnet array is used to evaluate twodifferent assembly strategies concerning the joule losses withinthe magnets. Based on the results from these three methods,final design decisions were made. A full-scale prototype in-wheelhub motor was manufactured and measured to assess the chosendesign.

Index Terms—Halbach-array-based permanent-magnet motors,air cored, direct drive, electrical machines, finite element meth-ods, permanent magnets

I. INTRODUCTION

Highly efficient in-wheel hub motors may drive urban lightweight vehicles in the near future. In order to optimize theirperformance, all loss sources need to be determined andminimized [1]. The AC resistances and losses in transformerwindings are subject of ongoing investigations [2]-[4] dueto the general need for both higher efficiency and minimumcost. If a Litz wire is used for the motor winding, the samefindings for winding losses can be applied. The aim of thecurrent work is to separate the influences of combined skinand proximity effects and the proximity effect due to externalfields applied to an axial flux stator winding. The classicalanalytical approach is used to calculated the joule losses due toexternal fields (method (I)). 2D FEA calculations visualize thecombined skin and internal proximity effect and the derivedspecific frequency dependent resistance is used to comparedifferent Litz wire arrangements (method (II)). Segmentationof magnets reduces the eddy current loss drastically [5],[6].Rare-earth Halbach arrays are usually segmented and in thispaper the effect of isolating and non-isolating contacts betweenthe individual magnets is studied (method (III)).

The authors gratefully acknowledge the support of the AustrianResearch Promotion Agency (Oesterreichische Forschungsfoerderungsge-sellschaft mbH, Klima- und Energiefonds, Neue Energien 2020) for theresearch project 829727 HeAL - High efficient ironless drive for lightweightvehicles.

Oliver Winter and Christian Kral are with the AIT Austrian Instituteof Technology GmbH, Mobility Department, Electric Drive Technologies,Giefinggasse 2, 1210 Vienna, Austria. Telephone: +43(5)0550 6559; e-mail:oliver.winter@ait.ac.at; web: http://www.ait.ac.at.

Erich Schmidt is with the Vienna University of Technology, Institute ofEnergy Systems and Electrical Drives, Gusshausstrasse 25-29, 1040 Vienna,Austria.

In order to achieve highest motor efficiency, these threemethods were analyzed and applied to realize a full-scaleprototype. The results from method (II) lead to the selection ofan appropriate Litz wire and method (III) is used to show thatadditional electric insulation reduces the eddy current losses inthe magnet array considerably. No load measurements showgood agreement to method (I) and the measured efficiencymap can be used for subsequent vehicle simulations.

II. METHOD (I) - CLASSICAL ANALYTICAL APPROACH

Since the 1960s, the formulation

P ′e−classic =πσcuω

2d4cuB2

64(1)

is used to calculate the length specific power dissipation ina wire exposed to a uniform magnetic field with peak fluxdensity B. In this equation σcu represents the electric conduc-tivity and dcu is the diameter of the conductor. A sinusoidalwaveform of the magnetic flux density with the electric angularfrequency ω is assumed. Moreover the diameter is assumedto be small compared to the skin depth. The orientation ofthe magnetic flux density is perpendicular to the axis ofthe conductor. Based on (1), different wire configurationswere investigated and summarized in Tab. I. It is obvious,that the utilization of Litz wire for a stator winding withcomparatively high fundamental frequency (231 Hz in thiscase) is recommend.

III. METHOD (II) - 2D FEA WINDING ANALYSIS

The second approach using 2D Finite Element Analysis(FEA) in the frequency domain models the individual strandsof the wires and to applies harmonic AC current excitationswith a series of frequencies. Both skin and proximity effectsare taken into consideration but without the exposure toexternal field. It is important to note in this context that theinvestigated motor has no iron core, so there are no ironteeth. Instead, the winding is embedded and fixed in a resinconstruction which magnetically behaves like empty space.The analyzed interaction between the individual strands isvisualized in Figs. 1 and 2. Two different wire configurationsare compared under the same excitation of 1 A at 16 kHz.Fig. 1 shows an example for a stranded rectangular wire with30 strands of 0.5 mm diameter and Fig. 2 shows the resultfor a rectangular wire of the same size but with 280 strandsof 0.15 mm diameter. Both skin and internal proximity effectscan be observed. The major difference between the two exam-ples is the current density which varies between 2.19 A/mm2

and 2.61 A/mm2 in Fig. 1 and just between 2.85 A/mm2 and

TABLE I: Calculation of Classical eddy current losses, stator current fundamental frequency 231 Hz, peak flux density 0.85 T.

Wire Acu / mm2 Rdc20 / Ω/m P ′e−classic / W/mSlot fill factor

Aslot =(2.5×3.6 mm2)

Single 1×dcu = 2.5 mm 4.91 3.6e-03 83.18 0.55Litz 30×dcu = 0.5 mm 5.98 3.0e-03 3.99 0.65Litz 280×dcu = 0.15 mm 4.98 3.5e-03 0.30 0.55

Fig. 1: 2D FEA result, combined skin and internal proximityeffect, current density distribution with sinusoidal excitationIrms = 1 A@16 kHz, 30×dcu= 0.5 mm stranded rectangularwire.

Fig. 2: 2D FEA result, combined skin and internal proximityeffect, current density distribution with sinusoidal excitationIrms = 1 A@16 kHz, 280×dcu = 0.15 mm stranded rectangu-lar wire.

2.86 A/mm2 in Fig. 2.. The absolute values of the currentdensities is not in the same range due to different fill fac-tors. This comparison illustrates the current gradients withinindividual strands, which cause increased local heating. Thecurrent density field solution is used to calculate the ohmiclosses by

P ′e(ω) =1

2σ

∫A

J∗ · J dA (2)

and with an applied excitation current of Irms = 1 A. The fre-quency dependent resistance can then be calculated accordingto

R′(ω) =P ′e(ω)

I2rms

. (3)

Fig. 3: Motor section considered in electromagnetic 3D FEA(magnet array and winding encapsulation are semi-transparent.

By substituting the PWM current ripple amplitude of 2.75 Aand 5.5 A for 20 kHz and 10 kHz, respectively, the eddy currentlosses due to skin and proximity effects without external fieldeffects are calculated, as shown in Tab. II. The comparison ofthe influence of higher harmonic current components showsagain the superior properties of stranded wires especially forhigher switching frequencies.

IV. METHOD (III) - 3D FEA OF EDDY CURRENT LOSSESIN THE MAGNET ARRAY

The current ripples generated by PWM excitation causeeddy currents and consequently ohmic losses in the magnetsof an axial flux machine. A 3D FEA tool is used to model(cf. Fig. 3) an ironless axial flux permanent magnet machine(AFPM) and to calculate the performance and the alreadymentioned magnet losses. The excitation was realized by asinusoidal current signal superimposed with a triangular signalto simulate the PWM current ripple as shown in Fig. 5. Aresult of a FEA example of the transient calculation (modelsize 450.000 tetrahedral elements) is shown in Fig. 5. In thiscase, the model was defined with isolation boundaries betweenthe touching magnet faces representing an adhesive layer. Thesecond example for the magnet assembly was investigatedwithout an isolation boundary in between and the resultsshowed that the ohmic losses increased from 2.5 W to 4.1 W.Even though the absolute power loss compared to the overall

TABLE II: Frequency dependent resistance of different wire configurations obtained by FEA with current ripples of2.75 A@20 kHz and 5.5 A@10 kHz.

Wire definitionR′acR′dc|10 kHz

R′acR′dc|20 kHz

P ′e−sp|10 kHz

mW/mP ′e−sp|20 kHz

mW/m

Single 1×dcu = 2.5 mm 1.220 1.600 133.8 43.9Litz 30×dcu = 0.5 mm 1.055 1.217 96.4 27.8Litz 280×dcu = 0.15 mm 1.003 1.013 109.1 27.6

0 0.5 1 1.5 2 2.5

−30

−20

0

20

30

Time /ms

FEA

inputcurrent/A

Fig. 4: Characteristic FEA current source input includingPWM ripples.

Fig. 5: 3D FEA result, current density plot, view on the surfacefacing the winding, isolation boundary between the magnets.

losses is marginal, an adhesive layer between the magnets wasapplied in the full-scale prototype which is described in thenext section.

V. REALIZATION

The findings of the presented investigations were incorpo-rated for designing and realizing an in-wheel hub motor, see

TABLE III: Motor design specification [7].

Description Symbol Nominal valueContinuous output power Pnom 3500 WPeak power (10 s) Ppeak 5Pnom

Speed at 80 km/h nn 660 rpmContinuous torque Tnom 55 NmPeak torque (10 s) Tpeak 5TnomNominal torque/active weight 4.8 Nm/kgPeak torque/active weight 24 Nm/kgNominal rms current Inom 18.6 A

(i)

(iii) (iii)

(iv)

(v)

(ii) (ii)

(vi)

Fig. 6: Cross section of motor: (i) light-weight metal hub, (ii)bearings, (iii) two equal CFRP half rims, (iv) air cored windingwith GRP connection to the hub, (v) two magnet rings madeof Halbach arrays, (vi) brake disk, [7].

[7]. The main motor specification is given in Tab. III and Fig. 6shows the schematic cross section of the motor. The designaims were minimum weight and high efficiency. Therefore,light weight materials like CFRP & GRP (carbon & fibre

CFRP half rim

Winding

GRPconnection

Fig. 7: Demonstration model of ironless in-wheel AFPM.

Fig. 8: Winding before encapsulation.

reinforced plastics) parts, a light metal hub and an air coredwinding were used. To omit the rotor back iron, two Halbachmagnet arrangements were placed on the CFRP half rimyielding an ironless in-wheel AFPM. A demonstrator is shownin Fig. 7. The distributed Litz wire (280×dcu = 0.15 mm)winding before encapsulation with PU (polyurethane) resinthrough vacuum casting is shown in Fig. 8.

The CFRP half rim assembled with the segmented Halbachring is shown in Fig. 9. As described in the previous section,the individual magnets are insulated an adhesive layer.

VI. MEASUREMENTS

To validate the structural, electromagnetic, and thermaldesign, a functional prototype was operated on a test benchand all relevant data was recorded. The measurement setupis shown in Fig. 10. The AFPM was equipped with a forcedair cooling system including flow rate control to simulatedifferent vehicle velocities. The torque Ttt and the speed nttwere measured by a Kistler 4503 torque transducer at theconnecting shaft to the load machine. For the performance

Fig. 9: Manufactured Halbach array attached to the CFRP halfrim.

AFPMwith forcedair cooling

Torquetranducer

Loadmachine

Supply andinverter

PowermeterWT3000

PowermeterPZ4000

Inverter

DC supply

Parallel

connector

Enco

der

sign

al

ia,b,c(t)

iDC(t)

va,b,c(t)

vDC(t)

Lab

contr

oland

data

aquis

tiati

onsy

stem

Inverter controland monitoring

va,b,c(t), ia,b,c(t)

v(t), i(t), vDC(t), iDC(t)

Ttt(t), ntt(t)Control of coolingairflow rate ,PT100 temperatures

Fig. 10: Measurement setup.

tests and heat runs, the load machine was speed controlledand the AFPM was torque controlled driven by a two levelinverter with external inductances to limit the current ripple.The DC supply voltage vDC and the supply current iDC to theinverter were recorded to calculate the drive efficiency and twopowermeters measured the line currents ia,b,c and the voltagesva,b,c. A Yokogawa WT3000 was used to get mean electricalvalues with 500 ms averaging windows. For detailed currentand voltage analyses, a Yokogawa PZ4000 was used.

A. No load losses

A section of the demonstrator, shown in Fig.7, was cutout to visualize the internal structure. Despite the absence ofa real winding (just encapsulation resin) and magnet arrays(replaced by PU mold construction material), the demonstratorwas suitable to derive windage and frictional bearing losses.

100 200 300 400 500 600 7000

10

20

30

40

50

60

70

Speed ntt /rpm

Pow

erlosses

/W

Measured prototype losses

Measured dummy losses

Prototype - method (I), calculated

Fig. 11: No load measurements, comparison between dummyand prototype.

100 150 200 250 300 350 400 450 500 550 600 650

10

20

30

40

50

60

0.60.60.60.60.60.60.6

0.6

0.6

0.6

0.6

0.80.80.80.80.80.80.8

0.8

0.8

0.8

0.8

0.880.880.880.880.880.880.88

0.88

0.88

0.88

0.88

0.90.90.90.90.90.90.9

0.9

0.9

0.9

0.9

0.920.92

0.920.92

0.920.92

0.92

0.92

0.92

0.92

0.940.94

0.940.94

0.940.94

0.94

0.94

0.94

0.94

0.950.95

0.950.95

0.95

0.95

0.95

0.95

0.95

0.960.96

0.96

0.96

Speed / rpm

Torque/Nm

Fig. 12: Calculated efficiency map.

Since the bearing losses can be estimated analytically (cal-culation of the friction torque according to specification datafrom the bearing manufacturer (SKF R©)), the result of thismeasurement are the windage losses. No load measurementswere also carried out on the prototype motor with an openwinding connection. The results are shown in Fig. 11. Themeasured power losses and losses minus classical eddy currentlosses according method (I) show good agreement. Based onthese measurements, the calculated efficiency map consideringno load and ohmic losses in the winding for this AFPM isshown in Fig. 12. To compare the loss models with reality,the efficiency map for motor operation (180 measurementpoints) was measured and is shown in Fig. 13. The ohmiclosses in the magnents are not considered in the calculatedexample, which may lead to the difference between Fig. 12 andFig. 13. For the application of the efficiency map in subsequentvehicle simulations, the windage losses have to be determinedaccording to the surrounding flow regime that depends on thewheel housing and the vehicle speed.

100 150 200 250 300 350 400 450 500 550 600 650

10

20

30

40

50

60

77787980

8182

82

83

83 84

85

85

85

86

86

86

87

87

87

8888

88

88

8989

89

89

9090

90

90

9191

91

91

9292

92

92

92

9393

93

93

93

9494

94

94

94

94

95

95

95

95

95

96

96

9696

96

96

96

Speed /rpm

Torque/N

m

Fig. 13: Measured efficiency map.

VII. CONCLUSION

Two different methods for calculation of losses in strandedwires are presented in this paper. Analytical and 2D FEAcalculations allow investigations on the influence of the num-ber of strands versus copper fill factor and losses. To coverall electromagnetic loss sources in an ironless axial fluxpermanent magnet machine, a 3D FEA model is used tocalculate the eddy current distribution in the magnets due tocurrent ripples caused by PWM supply. An adhesive layeror a small air-gap between the magnets has the potential toreduce the losses considerably. The final result, a full-scaleprototype, is briefly described and measurement results areused to validate the calculated losses and the correspondingefficiency maps.

REFERENCES

[1] T. Nguyen, K. Tseng, C. Zhang, and S. Zhang, “Loss study of a novelaxial flux permanent magnet machine,” in Proceedings of the 2011 IEEEInternational Electric Machines Drives Conference, (IEMDC’11), pp.1143–1148, May 2011.

[2] C. Sullivan, “Optimal choice for number of strands in a litz-wire trans-former winding,” IEEE Transactions on Power Electronics, vol. 14, no. 2,pp. 283–291, Mar. 1999.

[3] Y. Suzuki, I. Hasegawa, S. Sakabe, and T. Yamada, “Effective electro-magnetic field analysis using finite element method for high frequencytransformers with litz-wire,” in Proceedings of the International Confer-ence on Electrical Machines and Systems, (ICEMS’08), pp. 4388–4393,Oct. 2008.

[4] H. Rossmanith, M. Doebroenti, M. Albach, and D. Exner, “Measurementand characterization of high frequency losses in nonideal litz wires,” IEEETransactions on Power Electronics, vol. 26, no. 11, pp. 3386–3394, Nov.2011.

[5] J. Ede, K. Atallah, G. Jewell, J. Wang, and D. Howe, “Effect of axialsegmentation of permanent magnets on rotor loss in modular permanent-magnet brushless machines,” IEEE Transactions on Industry Applications,vol. 43, no. 5, pp. 1207–1213, Sept.-Oct. 2007.

[6] P. Sergeant and A. Van den Bossche, “Segmentation of magnets to reducelosses in permanent-magnet synchronous machines,” IEEE Transactionson Magnetics, vol. 44, no. 11, pp. 4409–4412, Nov. 2008.

[7] O. Winter, S. Ucsnik, M. Rudolph, C. Kral, and E. Schmidt, “Ironless in-wheel hub motor design by using multi-domain finite element analyses,”in Proceedings of the International Symposium on Power Electronics,Electrical Drives, Automation and Motion, (SPEEDAM’12), pp. 1474 –1478, Jun. 2012.