This research was sponsored by the North Carolina Coastal Studies Institute

A Magnetic Gearbox with an Active Region Torque Density of 239Nm/L

K. K. Uppalapati, J. Z. Bird, J. Wright, J. Pitchard

Department of Electrical and Computer Engineering University of North Carolina at Charlotte, NC, USA

j.bird@uncc.edu, kuppalap@uncc.edu

M. Calvin, W. Williams Department of Engineering Technology

University of North Carolina at Charlotte, NC, USA wbwillia@uncc.edu

Abstract—In this paper a 1:4.25 ratio ferrite magnet and NdFeB magnet flux-focusing magnetic gearbox with a high pole count is analyzed. A simple parameter sweep analysis is used to show that higher than previously published torque density values are achievable. Experimental results are then presented for the NdFeB design that confirm the calculations and also demonstrate that the proposed magnetic gearbox can operate with a low torque ripple.

I. INTRODUCTION A magnetic gear (MG) enables a contactless mechanism

for speed amplification to be achieved. MGs have an inherent torque limiting capability and they have the potential for quiet operation and high conversion efficiency [1-3]. Unlike in direct-drive generators [4] there is no current loading (thermal) constraint and therefore the torque is limited only by the magnetic loading, this enables the MG to operate at a high sustained magnetic sheer stress level without the need for liquid cooling. An example of coaxial MG using surface mounted magnets is shown in Fig. 1. If the inner rotor contains p1 pole-pairs and rotates at ω1 and the outer rotor contains p3 pole-pairs and rotates at ω3 then if a middle rotor containing, n2, steel segments is placed between the inner and outer rotors and the number of steel segments is chosen to be =2 1 3n p p+ (1) it can be shown that the angular speed relationship between each rotor is given by [1, 3]

ω ω ω2 31 2 3

1 1

n p

p p= − (2)

Neglecting losses the power relation between rotors is 1 1 2 2 3 3 0T T Tω ω ω+ + = (3) and the torque within the MG satisfies 1 2 3 0T T T+ + = (4)

The volumetric torque density of a rotary machine can be compared by using the torque density, Td, metric

2do

TT

r dπ= (5)

where T = peak torque, ro=outer radius and d = stack length. To-date it has been experimentally shown that an active

region torque density of up to 151 Nm/L is achievable when

using a coaxial MG topology [5] and when the coaxial MG is integrated into a motor an active region torque density of up to 100 Nm/L has been experimentally demonstrated [6]. In order to increase the torque density further various MG topologies have been investigated such as a harmonic MG [7], a planetary MG [8] an axial MG [9], cycloid MG [10] and a transverse flux MG [11]. However, the authors know of no MG that has experimentally demonstrated torque densities in excess of 200Nm/L. The objective of this paper is to experimentally demonstrate that a scaled-up coaxial MG is capable of operating at a significantly higher torque density than previously published values [2-3, 5-19].

Fig. 1. A coaxial magnetic gear using surface mounted permanent magnets with p1=4 pole-pairs on the inner high-speed rotor, n2=17 steel poles on the

low-speed rotor and p3=13 pole-pairs on the outer rotor.

II. A FLUX FOCUSING MAGNETIC GEAR The flux-focusing magnetic gear (FFMG) under

investigation in this paper is shown in Fig. 2(a) and the corresponding initial parameters are given in Table I and defined in Fig. 2(b). The scaled-up model is designed by doubling the number of poles used by a sub-scale FFMG that was presented in [5]. In order to more directly compare scaling the gear ratio was kept at 1:4.25 as in [5]. The main objective was to experimentally verify the volumetric torque density capability rather than find the most optimal solution. Therefore, due to time constraints a judicious parameter sweep analysis was conducted using finite element analysis (FEA) that enabled a good solution to be obtained, but the authors acknowledge it is likely not the optimal solution.

978-1-4799-5776-7/14/$31.00 ©2014 IEEE 1422

In this paper it is assumed that the magnet and steel pole-spans are equal on the high-speed and stationary rotor such that θ1s=θ1m=360o/(4p1) and θ3s=θ3m=360o/(4p3). In addition, the outer radius of the stationary rotor and inner radius of the high-speed rotor are held fixed at ro3=110 mm and ri1=25 mm. As the objective of the parameter sweep is to maximize volumetric torque density the inner rotor radius was kept small. As in [20] the cage rotor bar span was initially held fixed at θs2 = 360o/p3 ≈ 7o and the torque was calculated when varying the outer radius of the high-speed rotor, ro1, and the length of the cage rotor bars, l2. The cage bar length is defined as l2 = ro2 - ri2. The resulting torque density plot is shown in Fig. 3 for the case when ferrite magnets are used. It can be noted that the torque density is always maximum when the cage bar length is l2 = 5 mm. At l2 = 5 mm and r1o = 90 mm the peak torque density when using ferrite magnets is calculated to be 92.2 Nm/L. Fig. 4 verifies that θs2=7o gives the highest torque density and is not affected by changes in high-speed outer rotor radius values.

TABLE I. FIXED GEOMETRIC PARAMETERS AND MATERIAL PROPERTIES

Description Value Unit

Inner rotor (high speed)

Pole pairs, p1 8 - Inner radius, ri1 25 Mm Steel pole span, θs1 π/16 radians Airgap, g 0.5 mm

Cage rotor Steel poles, n2 34 -

Outer rotor (stationary)

Pole pairs, p3 26 - Outer radius, ro3 114 mm Steel pole span, θs3 π/52 radians Airgap, g 0.5 mm

Material Ferrite magnet, Hitachi NMF12F 0.46 T NdFeB magnet, N40H, Br 1.25T T

416 steel resistivity (cage rotor) 57.0 µΩ-cm 1018 steel resistivity (inner/outer rotor) 15.9 µΩ-cm

Active region stack length, d 75 mm

TABLE II. FINAL GEOMETRIC SWEEP PARAMETERS

Description Value Unit Inner rotor Outer radius, ro1 90 mm

Cage rotor Cage bar length, l2 5 mm Pole span, θs2 7 degrees

Outer rotor (stationary) Inner radius, ri3 96 mm

The same parameter sweep analysis was conducted when using NdFeB magnets. Fig. 5 and 6 show the torque density values when the parameters ro1, l2, and θs2 are varied. Surprisingly the peak torque density using NdFeB magnets occurred at the same geometric values as when using ferrite magnets, namely l2=5 mm, r1o = 90 mm, θs2=7o. The peak toque density was calculated to be 266.9 Nm/L. Using the final geometric parameters given in Table I and II the FFMG takes the form shown in Fig. 7. In Fig. 7 the magnets have been made rectangular in order to reduce manufacturing cost and additional steel rotor pole lips have been added in order to

retain the magnets in place, the addition of the lips increases the outer radius to ro3 = 114 mm. This results in a final calculated torque density of 92.3 Nm/L and 244.5 Nm/L for the ferrite and NdFeB magnet designs respectively. The calculated torque as a function of mechanical angle when only one rotor is rotating (pole slipping) for both ferrite and NdFeB designs is shown in Fig. 8. It can be seen that (4) is satisfied and the torque is maximum on the low speed cage rotor.

(a)

(b) Fig. 2. (a) Scaled-up flux focusing magnetic gear using initial geometric values with p1=8 pole-pairs on the inner high speed rotor, n2=34 steel poles on the low-speed rotor and p3=26 pole-pairs on the outer stationary rotor. (b) The geometric

parameters.

The FEA calculated efficiency at various input speeds

from 10 to 100 RPM with ferrite and NdFeB magnets is shown in Fig. 9. An efficiency of 98.0% with ferrite magnets and 97.5% with NdFeB magnets is predicted at the 20 RPM input design speed. The calculated efficiency reduces

ri1

ro1

ri3

ro3

ri2

ro2θm1 θs1

θs3 θm3

θs2l2

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significantly as speed increases due to the increased eddy current loss in the solid steel bars. The loss is greatest in the cage rotor bars [20].

Fig. 3. Volumetric torque density for changes in the cage rotor bar length, l2and high-speed outer rotor radius, ro1, when using ferrite magnets (θs2=7o)

Fig. 4. Volumetric torque density for cage rotor bar span, θs2, and high-speed outer rotor radius, ro1, when using ferrite magnets (l2=5mm)

Fig. 5. Volumetric torque density for changes in the cage rotor bar length, l2

and high-speed outer rotor radius, ro1, when using NdFeB magnets (θs2=7o)

Fig. 6. Volumetric torque density for cage rotor bar spans, θs2, and high-speed outer rotor radius, ro1, when using NdFeB magnets (l2=5mm)

Fig. 7. Final design of scaled-up FFMG

Torq

ue [N

m]

Mechanical angle [degrees] (a)

Torq

ue [N

m]

Mechanical angle [degrees] (b)

Fig. 8.Torque on the three rotors when slipping when using (a) ferrite and (b) NdFeB magnets, the active region stack length is 75mm

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8286

903 5 7 9 11 13 15

60

70

80

90

100

4 5 6 7 8 9

707580859095405060708090

100

7478

8286

90

3 5 7 9 11 13 15

170

190

210

230

250

270

4 5 6 7 8 9 10

707580859095

170190210230250270

0 4 8 12 16 20 24 28-300-250-200-150-100

-500

50100150200250300

0 4 8 12 16 20 24 28-800-600-400-200

0200400600800

High speed rotor outer radius, ro1 [mm] Cage rotor bar

length, l2 [mm]

Torq

ue d

ensi

ty [N

m/L

] To

rque

den

sity

[Nm

/L]

Cage rotor bar span, θs2 [Degrees]

High speed rotor outer radius, ro1 [mm]

High speed rotor outer radius, ro1 [mm]

Cage rotor bar length, l2 [mm]

Torq

ue d

ensi

ty [N

m/L

]

Torq

ue d

ensi

ty [N

m/L

]

Cage rotor bar span, θs2 [Degrees]

High speed rotor outer radius, ro1 [mm]

Cage rotor

Outer rotor

Inner rotor

Cage rotor

Outer rotor

Inner rotor

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Effic

ienc

y [%

]

Speed [RPM] Fig. 9. Calculated efficiency of the scaled-up FFMG with ferrite and

NdFeB magnets

III. DEFLECTION ANALYSIS The large magnetic forces created by the inner and outer

rotor magnets result in the deflection of the thin central cage rotor bars. The deflection will result in a reduction of the air-gap between the rotors and will affect the torque transmitted. In the worst case the deflection of the cage bars could close the air-gap. In order to determine the deflection of the cage bars caused by the inner and outer rotor magnets, the iterative magnetomechanical deflection analysis technique presented in [21] was utilized. Based on the axial length analysis conducted in [22] it was shown that for the scaled-up FFMG a 75 mm axial length created a deflection of only 0.045 mm when using NdFeB magnets. As the designed air-gap is 0.5 mm this amount of deflection was deemed acceptable.

IV. EXPERIMENTAL VALIDATION The mechanical assembly for the FFMG is shown in Fig.

10. The assembled inner rotor, cage rotor and fully assembled FFMG on the dynamometer test-stand is shown in Fig. 11. The experimentally constructed FFMG used NdFeB magnets. A comparison of the radial flux density, Br, created by the inner rotor when surrounded by air is shown in Fig. 12 while Fig. 13 shows the extracted dominant 8th harmonic comparison for the inner rotor field. The experimental value was observed to be 95% of the value obtained by using FEA.

Fig. 14 and Fig. 15 show the measured no-load torque and torque ripple on the cage rotor. The average torque is 110.5 Nm with a torque ripple of 1.5 Nm (1.4% of the measured torque).

Fig. 16 shows the measured torque under different load conditions at the 20 RPM design speed. A maximum torque of 731 Nm was measured beyond which the rotor slipped poles. This measured torque is 2.5 % (19 Nm) lower than the FEA calculated value of 750 Nm. This gives an active region volumetric torque density of 238.7 Nm/L. The corresponding torque ripple on the low-speed cage and high-speed inner rotor is shown in Fig. 17. A torque ripple of 2 Nm on the inner rotor and 1.6 Nm on cage rotor was measured at the peak torque condition.

Fig. 10. Exploded view of the mechanical assembly

(a) (b)

(c)

Fig. 11. (a) Inner rotor assembly, (b) cage rotor assembly with inner rotor and (c) complete test bench setup

Rad

ial f

lux

dens

ity [T

]

Mechanical angle [degrees] Fig. 12. Experimental and FEA comparison of radial flux density at

r=90.25mm created by the inner rotor when surrounded by air.

10 20 30 40 50 60 70 80 90 1009293949596979899

100

Inner rotor

Cage rotor

Stationary outer rotor

0 45 90 135 180 225 270 315 360-0.6

-0.4

-0.2

0

0.2

0.4

0.6FEA Experimental

Ferrite magnets

NdFeB magnets

1425

Rad

ial f

lux

dens

ity [T

]

Mechanical angle [degrees] Fig. 13. Comparison of 8th harmonic of the radial flux density , Br, of inner

rotor field

Torq

ue o

n ca

ge ro

tor [

Nm

]

Time [sec] Fig. 14. Experimental torque on cage rotor under no load condition

Torq

ue ri

pple

on

cage

roto

r [N

m]

Time [sec] Fig. 15. Experimental torque ripple on the cage rotor under no load condition

Fig. 18 shows the measured FFMG efficiency at different load and speed conditions. It can be observed that the efficiency comes down as the load and speed increase. An efficiency of 96.5% was measured at the 20 RPM full load design speed.

Fig. 19 shows a comparison between the FEA calculated and measured efficiency at the maximum load condition a relatively good match was achieved. The main discrepancy in the results is believed to be due to the FEA model not accounting for the bearing and the friction losses.

Torq

ue [N

m]

Time [sec] Fig. 16. Experimental measured torque on the low speed and high speed

rotors under various load conditions

Torq

ue ri

pple

[Nm

]

Time [sec] Fig. 17. Experimental measured torque ripple on the low speed and high

speed rotors

Effic

ienc

y [%

]

Speed on low speed rotor [RPM] Fig. 18. Measured efficiency for different input speeds at different

load conditions

0 60 120 180 240 300 360-0.45

-0.3

-0.15

0

0.15

0.3

0.45

0 5 10 15 20 25102

104

106

108

110

112

0 3 6 9 12 15-0.8-0.6-0.4-0.2

00.20.40.60.8

0 3 6 9 12 15 18 210

75

150

225

300

375

450

525

600

675750

0 1 2 3 4 5-1.5

-1

-0.5

0

0.5

1

1.5

10 20 30 40 50 60 70 80 90 100919293949596979899

FEA Experimental

25 % load

25 % load

50 % load

50 % load

75 % load

75 % load

100 % load

100 % load

Low speed rotor

High speed rotor

Low speed rotor High speed rotor

100% load 75% load

50% load 25% load

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Effic

ienc

y [%

]

Speed on low speed rotor [RPM] Fig. 19. Comparison of measured and predicted efficiency for

different input speeds at maximum load

Table III and IV summarizes the active region and full assembly volumetric and mass torque density values. It can be noted that the full assembly and active region volumetric torque density values are relatively close however the active region and measured mass torque density values are significantly different. This is mainly due to the fact that the measured mass included the shafts and additional assembly fixtures some of which do not change the volumetric size. These parts were not significantly optimized.

Fig. 20 indicates that for this design there is a trade-off between the active region mass torque density and volumetric torque density. For instance, when only the inner radius of the inner rotor is increased the mass torque density increases but at the cost of a reduced volumetric torque density. If the mechanical assembly structure can be designed to be low mass the mass torque density capability of this type of FFMG could therefore be substantial.

TABLE III. ACTIVE REGION TORQUE AND TORQUE DENSITY VALUES

FEA Experimental

Magnet type Ferrite NdFeB NdFeB Units

Torque 282.6 750.0 731.0 Nm Volumetric torque density 92.3 244.5 235.8 Nm/L Mass torque density 16.6 36.2 35.2 Nm/kgTorque-per-kilogram of magnet 51.2 90.1 87.8 Nm/kg

TABLE IV. FULL ASSEMBLY TORQUE DENSITY VALUES

FEA Experimental

Magnet type Ferrite NdFeB NdFeB Units

Volumetric torque density 82 214.9 209.4 Nm/L Mass torque density - - 15.77 Nm/kg

Vol

umet

ric t

orqu

e de

nsity

[Nm

/L]

Mas

s tor

que

dens

ity [N

m/k

g]

Inner radius of inner rotor, ri1 [mm] Fig. 20. Active region torque density variation when the inner rotor

of the inner rotor is varied

Rad

ial f

lux

dens

ity [T

]

Fig. 21. Comparison between the dominant harmonics for the radial flux density, Br, for the sub-scale [5] and scaled-up FFMG

Azi

mut

hal f

lux

dens

ity [T

]

Fig. 22. Comparison between the dominant harmonics for the azimuthal flux density, Bθ, for the sub-scale [5] and scaled-up FFMG

V. HARMONIC ANALYSIS The dominant harmonics within the rotor air-gap play

the primary torque transferring role between rotors. In the scaled-up design the inner and outer rotor’s dominant harmonics are the 8th and 26th while in the sub-scale design the 4th and 13th harmonics are dominant [5]. Fig. 21 and Fig. 22 compare the magnitudes of the radial, Br, and azimuthal, Bθ, flux density dominant harmonics for the

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20 30 40 50 60 70 80 90170

180

190

200

210

220

230

240

250

20 30 40 50 60 70 80 9030

35

40

45

50

55

60

65

70

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

Sub-scale designScaled-up design

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.80.8

Sub-scale designScaled-up design

Mass torque density

Volumetric torque density

Experimental

FEA

Inner air-gap Outer air-gap

Inner air-gap Outer air-gap

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scaled-up and sub-scale designs within the inner and outer air-gaps respectively. It can be observed that for the scaled-up design the Br harmonic in the inner and outer air-gap is increased by 32% and 24% respectively. While the dominant Bθ harmonic in the inner and outer air-gap is increased by 36% and 37% respectively. A comparison of the shear stress values calculated in the outer and inner air-gaps for the scaled-up and sub-scale FFMG [5] designs is shown in Table V. The shear stress, σs, is calculated from [4]

2d

s

Tσ = (6)

where Td is the torque density calculated at the air-gap. Due to the gearing the torque created in the outer air-gap is significantly higher and this results in the shear stress being larger in the outer air-gap. This level of shear stress is not typically achievable using direct drive generators [4].

TABLE V. AIR-GAP MAGNETIC SHEAR STRESS AND TORQUE DENSITY

Design Air-gap Radius [mm]

Torque [Nm]

Torque Density [Nm/L]

Shear Stress

[kN/m2]

Scaled-up Outer 95.75 559 258.8 129.4

Inner 90.25 172 89.6 44.8

Sub-scale Outer 39.75 86.8 229.5 114.7

Inner 33.25 26.7 100.9 50.4

CONCLUSIONS This paper has demonstrated that it is possible to create a

MG with a torque density above 200Nm/L with a low torque ripple. The high torque density was achieved by scaling-up an existing coaxial magnetic gear design and utilizing a relatively small air-gap. The authors believe that using careful design analysis techniques even higher torque densities are achievable.

ACKNOWLEDGMENT The authors would gratefully like to thank JMAG Corporation for the use of their FEA software.

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[14] N. Niguchi and K. Hirata, "Cogging torque analysis of magnetic gear," IEEE Trans. Ind. Elec., vol. 59, pp. 2189-2197, May 2012.

[15] L. Bronn, R.-J. Wang, and M. J. Kamper, "Development of a shutter type magnetic gear " in Proc. 19th Southern African Univ. Power Eng. Conf., Johannesburg, 2010.

[16] N. W. Frank and H. A. Toliyat, "Analysis of the concentric planetary magnetic gear with strengthened stator and interior permanent magnet inner rotor," IEEE Trans. Ind. Appl., vol. 47, pp. 1652-1660, July 2011.

[17] L. Shah, A. Cruden, and B. W. Williams, "A variable speed magnetic gear box using contra-rotating input shafts," IEEE Trans. Mag., vol. 47, pp. 431-438, 2011.

[18] L. Jian, K. T. Chau, et al., "Comparison of coaxial magnetic gears with different topologies," IEEE Trans. Magn., vol. 45, pp. 4526-4529, 2009.

[19] X. Liu, K. T. Chau, et al., "Design and analysis of interior-magnet outer-rotor concentric magnetic gears," Jour. Appl. Physics, vol. 105, pp. 07F101-07F103, 2009.

[20] K. K. Uppalapati, J. Z. Bird, et al., "Performance of a magnetic gear using ferrite magnets for low speed ocean power generation," in 4th IEEE Energy Conv. Cong. Expo., Raleigh, NC, Sept. 15-20th, 2012.

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