A high-performance linear magnetic gearK. Atallah, J. Wang, and D. Howe Citation: Journal of Applied Physics 97, 10N516 (2005); doi: 10.1063/1.1853900 View online: http://dx.doi.org/10.1063/1.1853900 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/97/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Performance improvement of magnetic gear and efficiency comparison with conventional mechanical gear J. Appl. Phys. 115, 17A314 (2014); 10.1063/1.4863809 Design and transient behavior of magnetic gears J. Appl. Phys. 115, 17E706 (2014); 10.1063/1.4859075 Design and analysis of interior-magnet outer-rotor concentric magnetic gears J. Appl. Phys. 105, 07F101 (2009); 10.1063/1.3058619 Effect of skewing the rotor teeth on the performance of doubly salient permanent magnet motors J. Appl. Phys. 99, 08R320 (2006); 10.1063/1.2172199 A high-performance axial-field magnetic gear J. Appl. Phys. 99, 08R303 (2006); 10.1063/1.2158966

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A high-performance linear magnetic gearK. Atallah, J. Wang, and D. HoweDepartment of Electronic & Electrical Engineering, The University of Sheffield, Mappin Street, Sheffield S13JD, United Kingdom

sPresented on 11 November 2004; published online 17 May 2005d

Currently, the demand for high force density linear actuators is being met almost exclusively byemploying a leadscrew and nut to transform rotary to linear motion. The paper describes analternative technology, viz., a linear magnetic gear, which employs rare-earth magnets, and whichsimulation studies have shown to have a highly competitive force density. ©2005 AmericanInstitute of Physics. fDOI: 10.1063/1.1853900g

I. INTRODUCTION

The increasing demand for high force density actuatorsis currently being met almost exclusively by employing aleadscrew and nut to transform rotary to linear motion. How-ever, the efficiency of such helical transformation systemscan be relatively poor, particularly for low helix angles. Inaddition, wear and reliability can be significant issues, andlubrication may be required. An alternative approach is toemploy a linear magnetic gear to increase the force capabil-ity of a linear brushless motor. To date, such an approach hasreceived little, if any, attention.

The paper describes the design and performance of alinear magnetic gear having the tubular topology shown inFig. 1, whose principle of operation is similar to that of therotary magnetic gear, which was described in Refs. 1 and 2.It is shown that, when rare-earth magnets are employed, sucha linear magnetic gear can have a transmitted force density inexcess of 1.7 MN/m3. Thus, when combined with a linearpermanent magnet brushless motor, such a magnetic gearcould offer significant advantages in many applications.

II. PRINCIPLE OF OPERATION

Fundamental to the operation of the magnetic gear is themodulation of the magnetic field produced by each of the

concentric tubular permanent magnet armatures by the ferro-magnetic ringsspole piecesd, which are disposed betweenthem, such that the appropriate space harmonic having thesame number of poles as the other permanent magnet arma-ture results. It can be shown2 that the number of pole pairs inthe space harmonic flux density distribution produced by ei-ther permanent magnet armature is given by

pm,k = ump+ knsu,

m= 1,3,5, . . . ,̀ ,

k = 0, ± 1, ± 2, ± 3, . . . , ±̀ , s1d

and the linear velocity of the flux density space harmonics isgiven by

vm,k =mp

mp+ knsvr +

kns

mp+ knsvs, s2d

wherep is the number of pole pairs on the armature,ns is thenumber of ferromagnetic pole pieces, andvr and vs are thelinear velocity of the armature under consideration and thelinear velocity of the pole pieces, respectively.

From Eq.s2d, it can be seen that the velocity of the spaceharmonics, which result due to the introduction of the ferro-magnetic rings, viz.,kÞ0, is different to the velocity of thearmature whose magnetic field they modulate. Therefore, inorder to transmit thrust force at a different velocity, the num-ber of pole pairs of the other permanent magnet armaturemust be equal to the number of pole pairs of a space har-monic for whichkÞ0. Since the combinationm=1, k=−1

TABLE I. Parameters of linear magnetic gear.

Parameter

Number of pole pairs on high speed armature ph=4Number of active pole pairs on stationary armature pl =9Number of active ferromagnetic rings ns=13Airgap length 1 mmOutside diameter 90 mmActive length of high-speed armature 100 mmTotal length of stationary armature 144.4 mmTotal length of low-speed armature 157.7 mm

FIG. 1. Schematic of 3.25:1 linear magnetic gear.

JOURNAL OF APPLIED PHYSICS97, 10N516s2005d

0021-8979/2005/97~10!/10N516/3/$22.50 © 2005 American Institute of Physics97, 10N516-1

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results in the highest asynchronous space harmonic, the num-ber of pole pairs of the other armature must be equal tosns

−pd. The gear ratio is then given by

Gr =ns − p

ps3d

when the modulating ferromagnetic rings are held stationary,i.e., vs=0. On the other hand, if the other permanent magnetarmature is held stationary, the thrust force is transmitted tothe ferromagnetic rings and the gear ratio becomes

Gr =ns

p. s4d

This may be the preferred operating arrangement since itsimplifies the overall mechanical design of the gear and en-ables a higher force to be transmitted, the increase beingdependant on the gear ratio, which changes from that whichresults with stationary ferromagnetic rings, i.e., Eq.s3d com-pared with Eq.s4d.

III. SIMULATION STUDIES

Table I gives the parameters which have been assumedfor the linear magnetic gear shown in Fig. 1, which isequipped with sintered NdFeB permanent magnets having aremanence of 1.25 T. Two-dimensional axis-symmetric mag-netostatic finite element analysis has been employed to pre-dict the flux density wave forms and the torque transmissioncapability of the gear.

Figure 2 shows the variation of the radial component offlux density due to the high-speed, low pole number perma-nent magnet armature in the airgap adjacent to the stationaryhigh pole number armature, while Fig. 3 shows the corre-sponding space harmonic spectrum. It can be seen that thepresence of the ferromagnetic rings results in a number ofasynchronous, viz.,kÞ1, space harmonics, the largest ofwhich is the nine pole-pair space harmonicsm=1,k=−1d,which interacts with the nine pole-pair permanent magnetson the stationary armature to transmit a thrust force.

Similarly, Fig. 4 shows the variation of the radial com-ponent of flux density due to the permanent magnetsmounted on the stationary armature in the airgap adjacent to

FIG. 2. Variation of radial flux density due to high-speed permanent magnetarmature in airgap adjacent to the stationary armature.

FIG. 3. Space harmonic spectrum of radial flux density due to high-speedarmature in airgap adjacent to stationary armature.

FIG. 4. Variation of radial flux density due to the stationary permanentmagnet armature in airgap adjacent to high-speed armature.

FIG. 5. Space harmonic spectrum of radial flux density due to stationarypermanent magnet armature in airgap adjacent to high-speed armature.

10N516-2 Atallah, Wang, and Howe J. Appl. Phys. 97, 10N516 ~2005!

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the high-speed armature, while Fig. 5 shows the correspond-ing space harmonic spectrum. It can be seen that the pres-ence of the ferromagnetic rings results in a dominant fourpole-pair asynchronous space harmonicsm=1,k=−1d, whichinteracts with the four pole-pair permanent magnets on thehigh-speed armature to transmit thrust force.

Figure 6 shows the variation of the maximum thrustforce, which is exerted on the low-speed and high-speed ar-matures as they move linearly. As can be seen, a force of,1600 N can be transmitted, and given the active dimen-sions of the gear, a force density of,1.7 MN/m3 can beachieved. Figure 7 shows how the system force density of acombined linear magnetic gear and a linear permanent mag-net brushless machine varies with the gear ratio and the forcedensity of the linear machine, 0.3 and 0.6 MN/m3 beingtypical for naturally cooled and liquid-cooled permanentmagnet linear brushless motors, respectively. As can be seen,

the system force density for a gear ratio as low as 3.25:1 canbe 100% greater than that of a naturally cooled linear motorand 50% greater than that of a liquid-cooled linear motor.Therefore, combining a linear magnetic gear with a perma-nent magnet linear motor results in a system having a sig-nificantly higher torque density than the latter.

IV. CONCLUSIONS

A high-performance linear magnetic gear has been pre-sented. It has been shown that, by employing rare-earth mag-nets, a thrust force density of,1.7 MN/m3 can be achievedfor the proposed magnetic gear. It has also been shown that ahigh systemsi.e., combined linear magnetic gear and linearelectrical machined force density can be achieved, even witha relatively low gear ratio.

1K. Atallah and D. Howe, IEEE Trans. Magn.37, 2844s2001d.2K. Atallah, S. D. Calverley, and D. Howe, IEE Proc.-Elect. Power Appl.151, 135 s2004d.

FIG. 6. Variation of maximum force on low-speed and high-speedarmatures.

FIG. 7. Variation of system force density with gear ratio for a linear mag-netic gear force density of 1.7 MN/m3.

10N516-3 Atallah, Wang, and Howe J. Appl. Phys. 97, 10N516 ~2005!

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