4092 IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 7, JULY 2013

A Flux Focusing Axial Magnetic GearVedanadam M. Acharya, Jonathan Z. Bird, and Matthew Calvin

Laboratory for Electromechanical Energy Conversion and Control, University of North Carolina at Charlotte, Charlotte, NC28223 USA

This paper investigates a novel axial magnetic gear using ferrite magnets. In order to increase the air-gap flux density the ferritemagnets are arranged in flux focusing configuration. The simulation results presented in this paper indicate that a relatively high torquedensity can be achieved when using only ferrite magnets.

Index Terms—Axial flux, finite element analysis, magnetic gear, permanent magnet.

I. INTRODUCTION

A magnetic gear (MG) enables a contactless mechanism forspeed amplification to be achieved. MGs do not require

gear lubrication, they have inherent overload protection andthey have the potential for quiet operation and high conversionefficiency [1]–[3]. A MG, as shown in Fig. 1, consists ofpole-pair permanent magnets (PMs) on an inner rotor rotatingat , a middle rotor with ferromagnetic steel poles thatcan rotate at , and pole-pair PM outer rotor rotating at. The inner and outer rotors that contain PMs interact with

the middle steel poles to create space harmonics [3]. If therelationship between the poles is chosen to bethen the rotors will interact via a common space harmoniccomponent [3], and the angular rotational velocities for eachrotor are related by

(1)

Unlike their radial counterpart axial MGs have not been studiedto a great extent. Mezani presented an axial MG using surfacemounted (NdFeB) magnets with a gear ratio of 5.75:1 and 200mm diameter; the torque density was calculated to be 70 Nm/L[4]. While Hirata presented a surface mounted axial MG with a10:1 gear ratio and a 120 mm diameter with a torque density of19 Nm/L [5]. A novel 6.5:1 MG with radially positioned rotormagnets and axial flux flow through ferromagnetic steel poleswas presented by Li [6]. In this design the calculated torquedensity was 11 Nm/L. It is well known that axial flux motorshave the potential for higher torque densities when compared totheir radial counterparts [7], [8]. Therefore, if sized correctly anaxial MG topology should also be able to achieve higher torquedensities than the radial equivalent. However, currently this hasnot been demonstrated in the literature.Current MG designs use large quantities of rare-earth magnet

material and unfortunately the high cost of rare-earth materialmakes the MG uncompetitive with alternative technology [9],[10]. This paper investigates the torque capabilities of a novelaxial flux focusing magnetic gear (AFFMG) that uses ferritemagnets.

Manuscript received November 05, 2012; revised December 18, 2012, Jan-uary 25, 2013, and February 08, 2013; accepted February 12, 2013. Date of cur-rent version July 15, 2013. Corresponding author: J. Z. Bird (e-mail: jonathan.bird@ieee.org).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TMAG.2013.2248703

Fig. 1. Magnetic gear using surface mounted permanent magnets.pole-pairs, steel poles and pole-pairs on outer rotor.

II. AN AXIAL FLUX FOCUSING MAGNETIC GEAR

The AFFMG topology is shown in Fig. 2. In this embodimentthe magnets are magnetized along the azimuthal direction andthe flux is forced to pass through the steel poles in the axialdirection. The flux density can be increased if the area of themagnet is chosen to be greater than the area of the steel polefacing the air-gap. The same governing speed relationship asgiven by (1) applies. The pole combination ,and was chosen because Gouda indicated that a lowergear ratio has a higher torque density [11]. In this analysis rotor3 is assumed to be stationary . The gear ratio is then

(2)

where . The geometric parameters used to study thisAFFMG are defined in Fig. 3 and values are given in Tables Iand II. The inner and outer radii are kept constant and themagnetand steel pole spans are kept equal, and .The flux focusing ratio for rotor 1 is defined as the ratio betweenthe magnet area, , facing the steel pole

(3)

and steel pole area, , facing the air gap

(4)

Assuming that there is no external leakage flux and since thereare two magnets facing each steel pole the flux focusing ratio,for rotor 1, can be defined as

(5)

0018-9464/$31.00 © 2013 IEEE

ACHARYA et al.: A FLUX FOCUSING AXIAL MAGNETIC GEAR 4093

Fig. 2. An axial flux focusing magnetic gear with , andpole pairs.

Fig. 3. Geometric parameters used by the axial magnetic gear.

TABLE IFIXED GEOMETRIC PARAMETERS AND MATERIAL PROPERTIES

Substituting (3) and (4) into (5) gives

(6)

Similarly, for the stationary rotor 3 the flux focusing ratio is

(7)

Using the parameters given in the tables the initial concentrationratios for rotor 1 and stationary rotor 3 is 4.6 and 2.9, respec-tively. Solid 416 steel is being used because it is assumed thatthe input speed has a maximum value of 20 RPM and thereforethe induced eddy currents are low when using solid steel at thisspeed [12]. The use of solid steel also helps to make the me-chanical construction more robust.

TABLE IIINITIAL AND FINAL GEOMETRIC SWEEP PARAMETERS

Fig. 4. (a) The axial flux density in the air gap adjacent to the high-speed rotor(at ) and (b) the corresponding spatial harmonics.

Fig. 5. (a) The axial flux density in the air gap adjacent to low-speed rotor (at) and (b) the corresponding spatial harmonics.

III. HARMONIC ANALYSIS

The mechanism for torque production can be explained byexamining the field harmonic analysis shown in Fig. 4to Fig. 6.In Fig. 4 and Fig. 5 the axial flux density, , in the air-gaps isshown along with the corresponding spatial harmonic compo-nents. Due to the magnetic poles it is seen that the 7th harmonicand 15th harmonic are dominant. Fig. 6 shows the flux densityin the air-gap adjacent to the low speed rotor when the low speedmagnets are not present. In this case the 15th harmonic is stillpresent and this is due to the high speedmagnet harmonics being

4094 IEEE TRANSACTIONS ON MAGNETICS, VOL. 49, NO. 7, JULY 2013

Fig. 6. (a) The axial flux density in the air-gap adjacent to the low-speed rotorwhen low speed magnets are not present, (b) Corresponding spatial harmonics.

Fig. 7. Torque with respect to changes in axial length .

Fig. 8. Volume and mass torque density as a function of axial length, .

modulated by the 22 steel pole pieces. Thus, without the centralsteel poles there would not be a connection between rotors.

IV. TORQUE DENSITY

In order to maximize the torque density the axial length, ,for the stationary rotor was varied while keeping the other pa-rameters constant. The torque and torque density plots shown inFig. 7 and 8 were obtained. It can be noted that the maximumvolume and mass torque density occurs when .Keeping at the optimal value and then varying the torqueand torque density plots as shown in Fig. 9 and 10 were ob-tained. It can be noted that a maximum volume and mass torquedensity of 60 and 14 Nm/kg, respectively, occurs when

. The resulting geometric form shows that the AFFMGhas the highest torque density when it takes a pancake topology.

Fig. 9. Torque with respect to changes in axial length .

Fig. 10. Volume and mass torque density as a function of axial length .

Fig. 11. Torque density with respect to changes in arc span .

Fig. 12. Torque with respect to axial length .

Fig. 12 and Fig. 13 show the torque and torque density char-acteristics when the axial length, , for rotor 2 is varied. A peakvolume and mass torque density of 65 and 15.5 Nm/kg, respec-tively, occurs when the axial thickness is . Thecalculated torque as a function of angular position, when usingthe final parameters in Table II, is shown in Fig. 14. Unlike theradial counter-part [12] the predicted torque ripple is observedto be relatively high.The average axial force on the high and low speed rotors was

calculated to be 8 and 8.2 kN, respectively. Although this valueis high it is within the rated operating condition of many com-mercially available angle contact bearings. In order to reducecost the experimental design will use rectangular magnets asshown in Fig. 15. The magnets can be retained in place usingthe steel poles and end-plates.As a comparison a sizing analysis using a surface mounted

axial MG with ferrite magnets, as shown in Fig. 16, wasalso conducted. The same volumetric dimensions as used by

ACHARYA et al.: A FLUX FOCUSING AXIAL MAGNETIC GEAR 4095

Fig. 13. Volume andmass torque density with respect to changes in axial length.

Fig. 14. Predicted torque on both the high and low speed magnetic gear rotorswhen using flux focusing ferrite magnets.

Fig. 15. Mechanical assembly for flux focusing magnetic rotors.

Fig. 16. Surface mounted axial magnetic gear using ferrite magnets.

AFFMG were used. After varying the magnets’ axial thicknessand it was determined that a peak torque density of 41

Nm/L could be obtained. This is a significantly lower valuewhen compared with the AFFMG design. The torque as afunction of angular position for the surface mounted axial MGis shown in Fig. 17. It can be observed that this surface mounteddesign also unfortunately has a relatively high torque ripple.

Fig. 17. Predicted torque on both the high and low speed magnetic gear rotorswhen using surface mounted ferrite magnets.

V. CONCLUSION

A new type of axial flux focusing magnetic gear topologyhas been proposed. A torque performance analysis for this newtopology was conducted when utilizing ferrite magnetic mate-rial. The use of ferrite magnets makes the magnetic gear ma-terial cost relatively low. While the mechanical construction ofan axial magnetic gear will be challenging it has been shownthat a relatively high torque density can be achieved. In orderto achieve a high torque density the axial length of the MG wasreduced relative to the radial length this reduced the low-speedrotor concentration ratio. This indicates that higher torque den-sities could be achieved if more poles were utilized.

ACKNOWLEDGMENT

The authors would like to thank the JMAG Corporation forthe use of their FEA software. This material is based upon worksupported by a Grant provided by the University of North Car-olina Coastal Studies Institute.

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