Eddy-Current Loss Analysis of Copper-Bar
Windings of Ultra High-Speed PM Motor
Toshihiko Noguchi

Takehiro Komori

IEEE Senior Member
Shizuoka University
3-5-1 Johoku, Naka-Ku, Hamamatsu, Shizuoka, Japan
E-Mail: ttnogut@ipc.shizuoka.ac.jp

IEEE Student Member
Shizuoka University
3-5-1 Johoku, Naka-Ku, Hamamatsu, Shizuoka, Japan
E-Mail: f0330112@ipc.shizuoka.ac.jp

Abstract— This paper describes a loss analysis of an eddy
current generated in the copper-bar windings of a 1.5-kW,
150,000-r/min PM motor fed by a 12-V power supply, which
is applicable to an automotive supercharger. The proximity
effect in the winding conductors is a result of the eddy-current
caused by the magnetic fields generated by the neighboring
conductors. The analysis results show that the proximity losses
can be significantly reduced by an appropriate magnetic
shielding and segmentation of the conductors.

the inlet air compression, and smaller mechanical dimensions
than those of the conventional displacement compressor based
system. Furthermore, such a mechanical-linkage-free systemgives freedom of the mechanical design around the engine,and makes it possible to reduce overall mechanical losses aswell as to eliminate the complicated linkage mechanism.
This paper discusses an optimum design of the ultra highspeed PM motor of which specific application is theelectrically operated supercharger of the automotive engine.
The motor is fed by a three-phase inverter with a 12-V battery
as a DC power supply; thus the motor design must meet ahigh-current and high-frequency operation requirement
without sacrificing the motor efficiency and the power density.
The investigated motor has a rated output power of 1.5 kW
and the maximum rotation speed of 150,000 r/min,
respectively. In order to achieve this goal, various technicalissues must be solved, e.g., drastic reduction of thesynchronous impedance, minimization of the iron and thecopper losses, further improvement of the motor efficiency andKeywords—«high speed drive», «permanent magnet motor»,«adjustable speed drive», «automotive
supercharger»,«automotive component».
I. INTRODUCTION
A supercharger is an auxiliary machine to enhance the output
power of a combustion engine and to reduce the engine
displacement simultaneously. Employing the supercharger isalso effective to improve the combustion efficiency, theexhaust gas quality and the engine torque response. The
conventional supercharger has a mechanical linkage with theengine, and it compresses inlet air into the engine cylinders bymeans of the mechanical power provided by the crank shaft.
Figure 1 (a) illustrates a mechanical configuration of theconventional supercharger. As shown in the figure, many of
the superchargers employ a displacement compressor because
its operation speed is limited by a low revolution speed of theengine. However, the displacement compressor has drawbacks
such as lower efficiency and lower boost pressure, comparedwith a centrifugal compressor, which prevents further
performance improvement of the supercharging system. In
order to solve these problems, electrification of thesupercharger is significantly important and is very promising
approach as a next-generation auxiliary machine system.
Figure 1 (b) shows an outline of the electrically operated
supercharger where an ultra high-speed permanent magnet(PM) motor is used to drive the centrifugal compressor insteadof the displacement compressor. Since the electricallyoperated supercharger allows use of the centrifugal
compressor and achieves a mechanical-linkage-free system,
many advantages are obtained, e.g., more efficient operation,higher rotation speed, higher boost pressure, faster response of

Displacement
compressor

EngineBelt & Pulley(a) Conventional system.
Inverter

1212-V
V PS
Battery

UltraUHS
high-speed
motor
motor

EngineCentrifugal
compressor(b) Electrically operated system.
Fig. 1. System configurations of conventional and electricallyoperated supercharging systems.

Table 1. Design target of ultra high-speed PM motor.
Assumed engine

1.5 L class

Rated output power

1.5 kW

Rated speed

150,000 r/min

Rated torque0.0955 Nm

Overload and duration

3kW (200 % over load) for 1 s

the power density, mechanical stabilization in high-speed
operation range, and so forth. In addition, these electricaldesign requirements must be satisfied all together with acompact and robust mechanical design. On the way of
optimization process in the machine design, a finite element
method (FEM) based electromagnetic field analysis isconducted to make fine-tuning of the detailed motor shape andto maximize the efficiency and the power density at the sametime. In this paper, the eddy current in the copper-bar
windings and the proximity effect caused by the eddy current
are focused on.

Permanent magnet
Stator core

Winding bars
Shaft

Winding
Stator teeth

30 mm

Fig. 2. Analysis model with two-turn windings.

II. REQUIRED SPECIFICATIONS OF ULTRA HIGH-SPEED PM
MOTORAssuming a 1,500-cc class automotive engine, the ultra highspeed PM motor is required to have the rated power of 1.5 kW
at the maximum rotation speed of 150,000 r/min to achieve theelectrically operated supercharging system. When boosting theinlet air pressure extremely fast response is required because
the compressor must be accelerated from several ten thousandr/min to the maximum rotation speed in approximately 0.5 s,
which surpasses a response time of the conventional
supercharger. In order to meet this requirement, the motor
must have a short-duration overload capacity, which is adouble of the rated output power for 1 s. Table I shows target
specifications of the motor determined by the above
requirement.
III. BASIC DESIGN CONCEPT OF ULTRA HIGH-SPEED PM
MOTOR
In order to achieve the highest efficiency and the highest
power density among varieties of the electric motors, a twopole three-phase surface permanent-magnet synchronous
motor (SPMSM) is focused on as the best choice for the ultra
high-speed motor drive because of the simple rotor structureand no magnetizing current, which implies higher efficiency
than other motors. The stator has a six-tooth six-slot structure
and the concentrated windings, which is remarkably effective
to reduce the copper loss and the leakage inductancethoroughly as well as the synchronous inductance. Each phasehas a pair of the double-turned windings in parallel, and thewindings are not ordinary wires but copper bars whose shapeis like an alphabetical letter “b.” It is necessary to reduce asmuch stator iron loss as possible even at 150,000 r/min
operation, so high-performance 6.5-% silicon electromagnetic
steel plates whose thickness is only 0.1 mm are employed tocompose a laminated stator iron core.

Fig. 3. Stator iron core with two-turn windings.
Table 2. Design parameters of ultra high-speed PM motor.
Motor typeSurface Permanent Magnet
Synchronous Motor (SPMSM)

Number of phases

Three-phase

Number of poles

2 poles

Stator configuration

Concentrated winding structure

Winding configuration

2 turns, 2 parallels per phase

Electromagnetic steel plates

Permanent magnet
Bearings

10JNEX900(0.1-mm thick, 6.5-% silicone,
μs=23000, Bmax=1.8 T)
N-39SH Nd-Fe-B(Br=1.28 T, BHc=955 kA/m,
BHmax=310 kJ/m3)
Angular ceramic-ball bearings withgrease lubrication

On the other hand, the rotor consists of a Nd-Fe-B permanent
magnet and a molybdenum alloy shaft. Use of the Nd-Fe-B
permanent magnet allows not only motor efficiency
improvement but also drastic reduction of the rotor size andthe inertia. In addition, such a strong Nd-Fe-B permanent
magnet that has BHmax = 310-kJ/m3 makes it possible towiden the air gap, which is essential to reduce the synchronous
inductance and to obtain a sinusoidal electromotive force(e.m.f.) regardless of the concentrated stator winding structure.
Table II is a summary of the basic conceptual design
parameters of the ultra high-speed PM motor to beinvestigated in this paper.

Magnetic flux
Eddy current

Conductor(a) Strand eddy current in single conductor.

Fig. 5. Mesh division (1/2 model) of analysis model.

Circulating current
Conductor(b) Circulating current
Fig. 4. Eddy current loss mechanism in conductor.
IV. EDDY CURRENT LOSS GENERATED IN CONDUCTORS BY
INTERLINKAGE OF FLUXThe strong permanent magnet is very effective to widen
the air gap, which is indispensable to reduce the synchronous
inductance. On the other hand, when the rotation speed isincreased, a leak magnetic flux cannot be ignored due to thewidened air gap. Possible loss factors in addition to the ironloss and the copper loss are the eddy-currents in the
conductors of the motor windings as follows;(1) strand eddy currents (circulating currents within
individual wire strands), and(2) bundle proximity currents (circulating currents
between different strands of the same wire bundle).
In general, the leakage magnetic flux is classified in thefollowing three classes; a) main flux by the permanent magnet.
b) leakage magnetic flux generated in the vicinity of the airgap, and c) slot leakage magnetic flux generated between afront end opening and a bottom portion of the slot. The
external field in the slot arises from the slot leakage flux
crossing between the slot walls combined with the fringing
flux emanating from the slot opening. A stator magnetic flux
substantially flows in a diameter direction in the tooth.
Therefore, the leakage magnetic flux generated in the slots israther small. However, in the case of the motor with a large
air gap, the leaked magnetic flux generates an eddy current in
the conductors. Figure 4 shows a conceptual illustration of
the eddy current loss mechanism in the conductors. Figure 4(a) shows the eddy current in a single conductor. An external
AC field induces the eddy current inside each strand as a resultof Faraday’s law. This eddy current flows so that they tend to
generate a flux, that disturbs changes of the magnetic field.

Fig. 6. Mesh division of conductor.
Figure 4(b) shows a circulating current between the different
strands. Assuming that the shorted strands in the slot are notconnected to any external circuit, the total slot current in thepresence of an external ac field must be zero but the individual
strands can experience non-zero currents because of thecirculating current. On the other hand, if the slot strands areconnected to an external circuit, the total current in the
conductors can be attributed to a superposition of theexternally-applied armature current and the effects of an
external magnetic field. Bundle proximity current is dependentof the magnetic flux interlinked with the different strands andthe impedance of the circuit network by the strands. By usingtransposed strands in a slot, it is possible to roughly equalize
the strength of the magnetic field received by the strands in theslot. Thus, the voltage induced in the different strands iscancelled and becomes zero. For these reasons, the circulating
current is not caused as a principle.
V. SPECIFICATIONS OF ANALYSIS MODEL
The purpose of this paper is to investigate the effects of themagnetic shielding and the segment conductors on the strand
proximity losses in the stator windings of the ultra high-speed
motor by using a three-dimensional finite element method (3D FEM) analysis. Figures 5 and 6 illustrate a half portion of
the generated mesh (993033 elements and 309961 nodes in thewhole mesh) and a mesh of the conductors, respectively.
Besides, it is analyzed at 2-degree angle intervals. In addition,
the mesh of the conductors are suitable for loss evaluation
because it is possible to calculate the deviation of the magnetic
flux distribution due to the skin effect. Modeling of the coilend allows to visualize current path of the strand eddy current
and to evaluate the eddy current loss that arises within thespecified strand.

Magnetic flux
density :T

Eddy current
2
density :A/m

Seeingdirection

Fig. 7. Magnetic flux density distribution (birds-eye view)
Magnetic flux
density :T

Fig. 10. Eddy current density in conductor.

Eddy current
2
density :A/m
Magnetic flux
density :T(a) Magnetic flux density. (b) Eddy currents density.
Fig. 8. Magnetic flux density and eddy current density in2
Eddy current density (A/mm )conductor.
120
100
80
60
40
20
0
-20
-40
-60
-80
-100
-120

Slot top
Slot middle
Slot bottom

0

60

120
180
240
Electrical angle (deg)

300

360

Fig. 9. Eddy current density in conductor. (Z-axis directions)
In order to emphasize the effects of the eddy current in thecopper-bar windings, the permanent-magnet thickness ischanged from 3.75mm to 5mm, compared with the machine
shown in Fig. 3 to investigate the effects of the magnetic
shielding and the segment conductors more accurately.
VI. ANALYSIS RESULTS
A. Analysis of benchmark model
Figure 7 represents an example of the resultant magneticflux density distribution at 150,000 r/min. The rotor position is
60 deg. As shown in the result, the maximum value of themagnetic flux density in the back yoke is approximately 1.4 T;
thus, the significant magnetic saturation is hardly observed in
the iron core. Figure 8 shows the magnetic flux density
distribution and the eddy current density distribution at
150,000 r/min under the condition of 0 A of the conductor
current in the slot. From the analysis, it is confirmed that theJoule loss
3
density :W/m(a) Magnetic flux density.
(b) Loss density.
Fig. 11. Magnetic flux density and loss density in conductor.
eddy current is generated in the conductor by interlinkage ofthe leakage magnetic flux. Figure 9 shows the eddy current
density in a z-axis direction at different winding positions at
150,000 r/min. The measured positions of the eddy current
density are set in area closest to the tooth of the iron core. It
can be seen that the eddy current loss are concentrated at theedge of the top conductor which may create the hot spots.
Figure 10 shows the eddy current density distributions when
the coil ends have been eliminated. It can be found that theeddy current concentrates at the edge of the top conductor
closest to the tooth. It is possible to confirm the eddy current
caused by a circumferential-direction component of themagnetic flux as well as the eddy current caused by adiameter-direction component. Thus, the direction of eddy
current flowing in the conductor depends on the time variationof the magnetic leakage flux. Figure 11 shows the magnetic
flux density distribution and the eddy current density
distribution in the conductor. Figure 11(a) shows that the slot
leakage field level is the highest in the slot opening region andthe lowest in the slot bottom region. Figure 11(b) also showsthat the loss density is the highest in the conductor located in
the slot opening region, while it is the lowest in the conductor
located in the slot bottom region. These results show that theeddy current loss is approximately proportional to the squareof the slot leakage magnetic field.
B. Effect of magnetic shielding
Figure12 shows five analysis models for evaluation of themagnetic shielding. Each tooth shape is as follows, (a)straight-shape tooth tip, (b) chamfering-shape tooth tip, (c)square-shape tooth tip, (d) trapezoidal-shape tooth tip, and (e)bridge-shape tooth tip. Figure 13 shows the eddy current loss

0.08

θ=2 deg
θ=164 deg
θ=352 deg
Bottom of slot(c) Square-shape
tooth tip.

(d) Trapezoidal-shape
tooth tip.

(e) Bridge-shape
tooth tip.

Eddy current loss in conductor (W)Fig. 12. Teeth shapes for comparative study.
80
60
92.4W

40
20

43.8W
14.4W

0

13.7W

11.8W

Straight Chamfering Square Trapezoidal Bridge-shape-shape-shape-shape-shapeFig. 13. Eddy current losses in conductor with respect
to teeth shapes.
Slot depth (mm)
1

2

3

4

5

6

7

8

Radial direction

Circumferential direction
Fig. 14. Positional relation between segment conductors inslot and slot depth.
comparison result in the conductor with respect to the teeth
shapes. In the case of the straight-shape tooth tip, the leakage
magnetic flux interlinked with the conductor increases because
the flange portion is not formed at the end of the tooth. In thecase of the chamfering-shape tooth tip, as the leakage
magnetic flux interlinked with the conductor is detrimentally
increased in comparison with those in the straight-shape toothtip, the eddy current loss remarkably increases. In addition, it
is found that the flange can reduce the leakage of the magnetic
flux from the rotor magnet to the conductors, and the eddy
current loss can be effectively reduced by employing the tooth
tips for the magnetic shielding.
C. Magnetic flux density in conductor with respect to slot
depth
Figure 14 shows the relationship between the segment
conductor in a slot and the slot depth. Figure 15 shows the

0.04
0.02
0.00
-0.02

0

2

4

6

8

10

12

14

-0.04
-0.06
-0.08
Slot depth (mm)Fig. 15. Magnetic flux density in conductor with respect toslot depth.
Eddy current loss in conductor (W)(a) Straight-shape tooth tip. (b) Chamfering-shape tooth tip.

Magnetic flux density (T)

0.06

22
20
18
16
14
12
10
8
6
4
2
0

1

2

3

4

5

6

7

8

Coil number

Fig. 16. Eddy current loss in segment conductor.
magnetic flux density in the conductor with respect to the slot
depth, which corresponds to the change of the rotation angle.
The magnetic flux density in the conductor gradually
decreases from 2 deg according to the rotation angle, andbecomes the minimum value at 164 deg and the maximum
value at 352 deg. Thus, the eddy current loss is increased
because the first coil part at the tip is arranged in the vicinityof a portion where the magnetic flux density variation appears
to be the greatest in the magnetic circuit. In the conductor at
the bottom of the slot, the magnetic leakage flux hardly varies,
which means almost no eddy current flows through theconductor. Figure 16 shows the eddy current loss of the layers
in the segment conductor. From this result, it is confirmed thatthe first coil part at the tip occupies a dominant part of theeddy current loss. Thereby, the eddy current loss in the coilcan be largely reduced when the conductor is placed at thebottom of the slot.
D. Effect of segmentation of conductor
The Segment conductor is formed in one strand with aprescribed cross-section by combining a plurality of divided
element wires. The cross-sectional area of the conductor is
split into multiple radial widths corresponding to the radial
position. Figure 17 shows the eddy current density distribution
and loss density distribution in the conductor divided in fourcross sectional. It is confirmed that the eddy current density is
reduced because of by dividing the conductors having small
cross sectional area. Figure 18 shows corresponding
relationship between the eddy current loss and the number of150

Eddy current
2
density :A/m

Joule loss
3
density :W/m

Front side (150,000 r/min, 150 Apeak)Far side (150,000 r/min, 150 Apeak)
Front side (1 r/min, 150 Apeak)Far side (1 r/min, 150 Apeak)Phase current (A)

100
50
0
-50

-100
-150

(a) Eddy current density.
(b) Loss density.
Fig. 17. Eddy current density and loss density in segment

60

40

300

360

DC copper loss
Loss due to nonuniform current density
Eddy current loss

50
Loss (W)

Eddy current loss in conductor (W)

120
180
240
Electrical angle (deg)

70

50

30
43.8W

40.9W

40
30
20

26.2W

10
0

60

Fig. 19. Phase current.

conductor.

20

0

24.5W

10
0

Normal4
2
Number of segments

6Fig. 18. Number of segments and eddy current loss in segment
conductor.

25000

50000 75000 100000 125000 150000
Rotational speed (r/min)Fig. 20. Total loss in conductor.

References

the divided the segments. In the case of dividing to two
conductors, it is small in the rate of decrease of the eddy
current loss compared to segment-less conductor. This isbecause of locally concentrating the eddy current generated at
top of the segment conductor. Thus, the windings of slot top
is divided into the segment conductor by division widths
corresponding to the magnetic flux density change ratio atdifferent the segments conductor position, and the eddy
current loss generated in each the segment conductor issuppressed. Figure 19 shows 150 A peak phase current at
150,000 r/min and 1 r/min. In the case of dividing to two
conductors, it is possible to confirm an uneven distribution of
the current density between the first coil and the second coil.
Figure 20 shows the total loss in the conductor with respect tothe rotational speed. It is confirmed that the loss due tononuniform current density is increased in proportion to therotational speed.
VII. CONCLUSION
This paper described the mechanism of inducement of thestrand eddy current and the circulating current generated incopper-bar windings by interlinkage of the magnetic flux. In
addition, it is found through 3D-FEM analysis that the eddy
current loss of the conductor is reduced by the magnetic
shielding and the segment conductors. The prototype shownin Fig. 3 will be experimentally examined in detail in the
future works.

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