A Design Approach to Reduce Rotor Losses
in High-Speed Permanent Magnet
Machine for Turbo-Compressor
Han-Wook Cho1,Seok-Myeong Jang1,and Sang-Kyu Choi2
Department of Electrical Engineering,Chungnam National University,Daejeon305-764,Korea
Korea Institute of Machinery and Materials,Yuseong-gu,Daejeon305-343,Korea
In this paper,a design approach to reduce rotor losses in high-speed permanent magnet machines for turbo-compressor is discussed.In particular,the influence of materials chosen for the retaining sleeve is highlighted.The two topologies of high-speed permanent magnet machines with Inconel718and Carbon-Fiber/Epoxy sleeves are employed for comparison of computed rotor losses by two-dimensional finite-element method and analyticalfield anaysis.It is shown that the Carbon-Fiber/Epoxy is superior to Inconel718in terms of reducing rotor losses.
Index Terms—High-speed permanent magnet machines,retaining sleeve,rotor losses.
I.I NTRODUCTION
D U
E TO THEIR high efficiency,small size,and light weight,
high-speed electrical machines are likely to be key tech-nology for many future applications of motion control and drive systems.Permanent magnet machines were thought to be the ob-vious choice,since they have high efficiency,high power density, and low acoustic noise.They are being employed in applications such as compressors,centrifuges,and vacuum pumps,and a variety of different issues have been investigated[1],[2].
A major challenge in permanent magnet machines is how to retain the magnet at high-speed operating range.In order to maintain the mechanical integrity of a high-speed perma-nent magnet machine rotor intended for high-speed operation, the rotor assembly is often retained within a stainless steel or Carbon-Fiber/Epoxy sleeve.The sleeve is exposed tofields pro-duced by the stator from either the slotting or the magneto-mo-tive force(mmf)harmonics that are not synchronous with the rotor.These nonsynchronousfields cause the significant rotor losses.An optimum design of permanent magnet machines re-quires the accurate prediction for these rotor losses[3],[4].
In this paper,two high-speed permanent magnet machines with identical rated power and rated speed have been designed and analyzed.On the basis of two-dimensional(2-D)finite-el-ement method(FEM)and analyticalfield analysis,this paper deals with the rotor losses in high-speed permanent magnet machines.In particular,the difference of the rotor losses between the Inconel718and Carbon-Fiber/Epoxy sleeves is quantitatively made clear in this work.Finally,the prototype machine with Carbon-Fiber/Epoxy sleeve is fabricated to reduce rotor losses.
II.T WO T OPOLOGIES OF H IGH-S PEED
P ERMANENT M AGNET M ACHINE
The two topologies of high-speed permanent magnet ma-chines considered in this paper are drawn in Fig.1.Two
Digital Object Identifier
10.1109/TMAG.2006.879086
Fig.  1.The two topologies of high-speed permanent magnet machines.
(a)Model I:rotor with Inconel718sleeve.(b)Model II:rotor with Carbon-Fiber/
Epoxy sleeve.
TABLE I
M ATERIAL P
ROPERTIES
machines have identical rated power(50kW)and rated speed
(70krpm),but different rotor topologies.They consist of
a permanent magnet rotor with Inconel718(Model I)and
Carbon-Fiber/Epoxy sleeve(Model II),respectively.The ma-
chines have identical24-slots stators with a distributed winding,
and two-pole diametrically magnetized permanent magnet ro-
tors,which produce an essentially sinusoidal airgapflux density
distribution.Table I describes the relative permeability and
resistivity of the Inconel718and Carbon-Fiber/Epoxy sleeves,
respectively.
0018-9464/$20.00©2006IEEE
Fig.2.Mesh plot of the flux density distribution —Model
I.
Fig.3.Mesh plot of the flux density distribution —Model II.
III.R OTOR L OSSES
The proposed calculation method of rotor losses contains two main steps.In the first step,using a one-slot-pitch magneto-static finite-element analysis (FEA),the flux density distribu-tion in the machine is calculated.The harmonics data caused by the slot geometry and the mmf is generated by the 2-D fast Fourier transform (FFT)analysis of the flux density distribu-tion.In the second step,rotor losses are computed with the pro-posed rectilinear model considering the multiple harmonics and the Poynting vector.These analysis strategies are described in more detail in [5]and [6].
To obtain flux harmonics on the rotor surface,the total of 30FE magnetostatic models of the machine for different rotor posi-tions —one-slot pitch (15mech.deg.)—are solved.The normal flux density is evaluated over the surface of the sleeve from each solution and data from all solutions are arranged in a 2-D ma-trix.Then,using the 2-D FFT analysis,the amplitudes of the flux harmonics are analyzed.
Figs.2and 3show the mesh plot of the flux density dis-tribution of the analysis model with Inconel718and Carbon-Fiber/Epoxy sleeves,respectively.Tables II and III show the most signi ficant time and space flux harmonics of each analysis model.The space even-order harmonics are absent,
because of the presence of odd symmetry in the space distribution of the flux density.The number of slots per pole of the analysis model is 12.Therefore,the rotor signi ficant harmonics are time order of a multiple of 24th with space order of 23rd,25th,47th,and 49th,etc.
The analytical model for the prediction of field quantities is represented in Fig.4.The amplitude of the current sheet is chosen to produce the same normal flux density on the sur-
TABLE II
F LUX H ARMONICS —M ODEL I (I NCONEL718S LEEVE
)
TABLE III
F LUX H ARMONICS —M ODEL II (C ARBON -F IBER /E POXY S LEEVE
)
Fig.4.Analytical model for the prediction of field quantities.
face of the rotor pole-face as does the corresponding harmonic.The governing field equation,in terms of the Coulomb
gauge,
,is given
by
(1)
where
is the magnetic vector potential
and
and de-note the permeability and conductivity of each layer,respec-tively.The angular
velocity is equal
to
,
where
and are the time order and supply frequency,respectively.It is assumed that the permanent magnet and shaft region have uni-form permeability,and the stator has zero conductivity,due to its lamination.Neglecting end effect,the tangential and normal flux density in a particular layer can be obtained as
follows:
(2)(3)
where
is de fined
as
(4)
where ,
and is the pole pitch.Therefore,flux
density ,magnetic field
intensity ,and electric field
intensity can be computed readily and analytically.
CHO et al.:A DESIGN APPROACH TO REDUCE ROTOR LOSSES IN HIGH-SPEED PERMANENT MAGNET MACHINE FOR TURBO-COMPRESSOR 3523
TABLE IV
R OTOR L OSS D ENSITY —M ODEL
I
TABLE Vsleeve
R OTOR L OSS D ENSITY —M ODEL
II
The Poynting vector is a powerful means of obtaining the total power entering or leaving a region [6].The Poynting
vector is de fined in terms of the vector product of the electric field intensity and the magnetic field intensity over the surface of a region.For a sinusoidal electromagnetic field at steady state,the avera
ge power transmitted through a surface is calculated using the Poynting vector in the following
form:
(5)
where is the amplitude of the electric field intensity in the
axial direction
and
is the amplitude of the conjugate of the tangential magnetic field intensity.The rotor losses in the analysis models are reported in Tables IV and V .The rotor signi ficant losses have time order of 24th,
48th with space order of 23rd,25th,47th,and 49th,as expected.Due to the relatively high conductivity of the retaining sleeve,most of the losses are produced in the retaining sleeve,also as expected.As shown in Tables IV and V ,when the sleeve conductivity is low (model II),the rotor losses are prevailing in the sleeve and permanent magnet,and when the sleeve conductivity is relatively high (model I),the permanent magnet losses decrease and the sleeve losses increase in spite of the large airgap length.Fig.5shows the comparison of rotor losses between model I and model II for the time and space harmonics.It can be seen that the model II is reduced nearly 5.9times,which means the Carbon-Fiber Epoxy sleeve is appropriate for the rotor loss reduction.Fig.6(a)shows the developed permanent magnet rotor with the proposed Carbon-Fiber/Epoxy sleeve (model II)and Fig.6(b)shows the assembled stator core and water cooling
housing.
Fig.5.Comparison of rotor
losses.
Fig.6.Developed high-speed permanent magnet machine.(a)Permanent magnet rotor with Carbon-Fiber/Epoxy sleeve and (b)assembled stator with water cooling housing.
IV .C ONCLUSION
The 2-D finite-element method and analytical field anal-ysis have been used to investigate the rotor losses of high-speed permanent magnet machines having Inconel718or Carbon-Fiber/Epoxy sleeves under identical rated power and rated speed.A comparative study has shown that the permanent magnet machine with Carbon-Fiber/Epoxy sleeve has 5.9times lower rotor losses than the one with Inconel718sleeve in spite of large flux harmonics amplitude.The permanent magnet machine with Carbon-Fiber/Epoxy sleeve is adopted to appli-cations of the high-speed machine to reduce the rotor losses.
A CKNOWLEDGMENT
This work was supported by MOCIE through IERC and KEMCO program,Korea.
R EFERENCES
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[2]J.D.Ede,Z.Q.Zhu,and D.Howe,“Rotor resonances of high-speed
permanent magnet brushless machines,”IEEE Trans.Ind.Appl.,vol.38,no.6,pp.1542–1548,Nov./Dec.2002.
[3]N.Bianchi,S.Bolognani,and F.Luise,“Potentials and limits of
high-speed PM motors,”IEEE Trans.Ind.Appl.,vol.40,no.6,pp.1570–1578,Nov./Dec.2004.
[4]W.L.Soong,G.B.Kliman,R.N.Johnson,R.A.White,and J.E.Miller,
“Novel high-speed induction motor for a commercial centrifugal com-pressor,”IEEE Trans.Ind.Appl.,vol.36,pp.706–713,May/June 2000.[5]S.M.Abu Sharkh,M.R.Harris,and N.Taghizadeh Irenji,“Effect of
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98.Manuscript received March 13,2006;revised April 26,2006(e-mail:hwcho@cnu.ac.kr).

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