DESIGN OF COMPACT PERMANENT-MAGNET
SYNCHRONOUS MOTORS WITH CONCENTRATED
WINDINGS
CSABA DEAK , ANDREAS BINDER
Key words: Synchronous motor, Permanent magnet, Concentrated winding.
The design and comparison of three permanent magnet motors for a constant power of
45 kW at 1 000 rot/min rated speed, and 3 000 rot/min maximum speed, with
concentrated windings and different kinds of water jacket cooled stator and PM rotor is
presented. Motor A and motor B have surface mounted magnets and equal tooth widths
with coils wound on each tooth, but different number of stator slots, while motor C has
buried magnets and unequal tooth widths and coils wound on each second tooth. The
simulation results show that motor A has the smallest current rating and the highest
power factor but has the biggest cogging torque and torque ripple at load. Motor B
produces the smoothest torque and smallest cogging torque but also the highest total
losses. Motor C yields the lowest total losses and has the better thermal behavior but
has the lowest power factor and the highest current rating.
1. INTRODUCTION
Modern variable speed drives demand compact electrical motors with high
power- and torque density, which produce at the same time small losses. As an
alternative for the squirrel cage asynchronous motor, which is used nowadays in
the middle power range, three inverter-fed permanent magnet motors were
designed with help of finite element program FEMAG for a constant power of 45
kW and 230 V phase voltage at 1 000 rot/min rated speed and 3 000 rot/min
maximum speed. In order to increase the torque density and to reduce the losses,
the so called modular synchronous machine with concentrated tooth coil windings
is applied due to the short winding overhangs, which lead to reduced copper losses
and reduced axial length [1–3].
The three models were designed with identical number of poles (2p = 24),
stator inner- and outer diameter and active length (Table 2). Differences are in the
stator and rotor geometries. Motor A and B have surface mounted magnets and
equal tooth widths with coils wound on each tooth, while motor C has buried
Darmstadt University of Technology / Department of Electrical Energy Conversion, Darmstadt,
Germany, E-mail: "Csaba Deak" <cdeak@ew.tu-darmstadt.de>
Rev. Roum. Sci. Techn. – Électrotechn. et Énerg., 52, 2, p. 183–197, Bucarest, 2007
184
Csaba Deak, Andreas Binder
2
magnets and unequal tooth widths with coils wound on alternate teeth. The basic
design for the motors is described and the calculated steady state electromagnetic
performance as well as the thermal behavior is evaluated, showing that motor A
has the smallest current rating and the highest power factor but has the biggest
torque ripple. Motor B produces the smoothest torque but also the highest total
losses, while motor C has the best thermal utilization and the lowest total losses,
but has the lowest power factor due to the higher current rating.
2. BASIC DESIGN
2.1. MOTOR GEOMETRY
Three different stator and two different rotor designs were considered and
optimised in order to determine the better solution for the power & torque demand
(45kW/430 Nm at 1000 rot/min 45kW/143 Nm at 3 000 rot/min) and the thermal
demands of Thermal Class F (limit of average winding temperature 145 °C). The
geometries and the winding configurations are presented in Fig. 1, where U, V and
W are the three phases, while + and – are the wounding directions of the coils.
The identical stator outer diameter, active iron length and the shaft diameter
allow the application of an identical water jacket cooling system as well as
identical end shields, bearings, shafts, position sensors and motor mounting,
simplifying thus a lot the manufacturing process of the prototypes. The identical
stator inner diameter and the identical pole number give the advantage, that the two
rotors can be eventually interchanged in order to test the behaviour of the different
stator-rotor combinations.
c
a
b
Fig. 1 – Geometry and winding configurations: a) motor A; b) motor B; c) motor C.
3
Permanent magnet synchronous motors with concentrated windings
185
2.2. STATOR DESIGN
Motor A has 24 semi-closed slots with constant tooth width and coils wound
on each tooth (Fig. 1a) resulting in eight coils per each phase, all connected in
parallel [1]. Round copper wire is used for the windings. The number of slots per
pole and phase is q = 0.5 which means a ratio of 2/3 between the coil width and
the pole pitch and thus a rather low pitching factor kp of 0.866 for the fundamental.
The distribution factor kd is unity due to the tooth-wound coils and multiplied
with the pitching factor it gives the winding factor kw [2]. The deep and narrow
slots produce a big slot stray flux, leading to a rather low power factor, but are
necessary in order to compensate the low winding factor with a high current
loading A, thus an increased number of turns per phase (Table 1).
Motor B has 18 semi-closed slots with constant tooth width and coils wound
on each tooth (Fig. 1b) resulting in six coils per phase. The number of slot per pole
and phase is q = 3/8 which means a ratio of 8/9 between the coil width and the pole
pitch and thus a big winding factor kw of 0.945 for the fundamental. This
configuration produces two sub-harmonics of the air gap field at load, which
results in a higher harmonic leakage causing a lower power factor. Due to the
winding arrangement, three coils have to be connected in serial and then connected
in parallel with the other three coils. In this case each phase conductor consists of 5
internal wires (strand in hands). The big disadvantage is the occurrence of
additional copper losses due to the 1st order current displacement. This effect is
totally eliminated in motor A due to the fact that all coils are connected in parallel
and thus the phase conductors consist of only one wire per turn.
Motor C (Fig. 1c) has 24 open slots and unequal tooth widths [1]. The
alternate teeth have parallel sides to carry prefabricated coils. The appropriate
width of the intermediate teeth allows increasing the coil pitch so that a ratio close
to unity between coil width and pole pitch and thus a high winding factor can be
obtained [1, 2]. This is 0.98 for the fundamental (Table 1). Each slot holds one coil
side of one phase, which means that the number of slot per pole and phase is
q = 0.25. The resulting four coils per phase are connected in parallel, so no 1st order
current displacement occurs. Profiled copper wire is used for the windings, thus an
increased slot fill factor of 59% is achieved. The deep and narrow slots together
with the big sub harmonic air gap field at load, which will occur at a q = 0.25
configuration, cause a low power factor, but give a good field weakening
capability [2].
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Csaba Deak, Andreas Binder
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Table 1
Winding parameters
Motor
Number of turns per coil
Number of parallel connections
Number of strand in hands
Number of turns per phase
Connection of phases
Wire diameter/dimensions (mm)
Slot fill factor
Winding factor (of fundamental)
Resistance per phase (at 145°C) (mΩ)
A
96
8
1
96
Y
1.6
0.41
0.866
70
B
27
2
5
81
Y
1.5
0.39
0.945
57
C
60
4
1
60
Y
1.6 ×2.5
0.59
0.98
47
2.3. ROTOR DESIGN
High energy NdFeB permanent magnets are used with a remanence of
BR = 1.1 T (150°C) and a coercive field strength of HcB = 712 kA/m. The rotors of
motor A and motor B are identical with magnets mounted on the rotor surface and
fixed with a bandage (Fig. 1a, b). In order to reduce the cogging torque and the
torque ripple at load, the pole coverage of the magnets was reduced to 77% of the
pole pitch [1]. In order to reduce the losses in the magnets due to air gap field space
harmonics, segmented magnet poles are considered (Table 2).
Motor C is designed with buried magnets, so no bandage is necessary
(Fig. 1c). The iron contour above the magnets allows an optimisation of the air gap
geometry by an appropriate modelling of the rotor surface and thus a nearly
sinusoidal rotor field is obtained [1], if slot opening influence is neglected. The
variable air gap has a minimum of δ0 = 0.5 mm in the pole axis (Table 2).
3. ELECTROMAGNETIC PERFORMANCE
3.1. NO-LOAD OPERATION
The open circuit air gap flux density and the cogging torque are determined
by 2D numerical calculation at no-load. From the no-load field distribution (Fig. 2)
it can be seen, that the intermediate teeth of motor C have a flux concentration at
the stator bore due to their small width at the wedges. This means that this small
area is saturated already at no-load. The flux density distribution in the air gap
(Fig. 3) for four pole pitches shows that motor A and motor B have a mainly
trapezoidal air gap flux density. The influence of the small inter-pole gaps as well
as of the semi-closed slot openings is clearly visible, as well as the influence of
segmentation of the surface magnets. The slot openings produce the biggest
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Permanent magnet synchronous motors with concentrated windings
187
distortion of the radial air gap flux density distribution, considered in the middle of
the air gap.
Due to the open slots, thus bigger slot openings and the unequally distributed
slots, this effect is much bigger for motor C causing a high harmonic content of the
air gap field even if the rotor surface optimisation yields a nearly sinusoidal rotor
field [1].
Table 2
Motor dimensions
Motor
Stator outer diameter (mm)
Stator bore diameter (mm)
Active length (mm)
Stator yoke height (mm)
Number of stator slots
Stator tooth width (mm)
Stator slot opening (mm)
Air gap (mm)
Bandage (mm)
Number of poles
Magnets / pole
Magnet height (mm)
Magnet width (mm)
Pole coverage ratio αm (%)
Rotor yoke height (mm)
Shaft diameter (mm)
A
314
181
180
11
24
13
6
0.7
0.7
16
7
4.7
3.6
77
12.4
100
B
314
181
180
11
18
17.3
8
0.7
0.7
16
7
4.7
3.6
77
12.4
100
C
314
181
180
19
24
22*
9
0.5 (=δ0)
–
16
7
4.8
3.6
77
9.6
100
* teeth with coils
The gaps between the magnet segments of one pole do not have an influence
on the air gap field as it was the case with motor A and motor B, because of the
smooth rotor iron surface.
The cogging torque of a motor depends on the ratio between the number of
slots and poles, the stator/rotor geometry and also on the pole coverage of the
magnets. Here un-skewed stator and rotor are considered.
The influence of the pole coverage on the cogging torque and on the torque
ripple at load at rated current and field oriented control (Isd = 0) was examined in
[1] for motor A for a pole coverage varying between 55% and 100%, resulting in a
minimum ripple at 77 % pole coverage.
The cogging torque of motor A is reduced by 40% compared to 100% pole
coverage ratio and is 5.3% of the rated torque. With the same pole coverage, Motor
B has a much smaller cogging torque of 0.7% of rated torque while motor C
produces a cogging torque of 1.9% of the rated torque (Fig. 4).
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Csaba Deak, Andreas Binder
a
b
c
Fig. 2 – Calculated no-load field distribution: a) motor A; b) motor B; c) motor C.
6
7
Permanent magnet synchronous motors with concentrated windings
a
b
c
Fig. 3 – Calculated radial component of air gap flux density distribution at no-load:
a) motor A; b) motor B; c) motor C.
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Csaba Deak, Andreas Binder
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Cogging torque [N·m]
190
Rotor position
Fig. 4 – Cogging torque at αm = 77%.
3.2. LOAD OPERATION
The three motors are designed for power converter operation with a
fundamental r.m.s. phase voltage of 230 V. They have to generate a steady-state
torque of 430 Nm at 1 000 rot/min rated speed and 143 Nm at maximum speed of
3 000 rot/min. This requires a high current loading A, which leads to a rather big
synchronous reactance and a low power factor at field oriented control, where only
q-component current Isq is applied. In order to determine the necessary currents at
rated and maximum speed for given torque, the current Is and angle γ (angle
between q-axis and Is) are varied until the demanded torque and the maximum
phase voltage is reached. The power factor can be improved if also a negative dcomponent current Isd is supplied to the windings (Fig. 5). This will shift the
current phasor Is towards the voltage phasor Us. At constant phase current Is, Isq is
reduced due to Isq=Is–Isd and thus Us is shifted towards the q-axis, reducing the
angle ϕ between phase current and voltage. By increasing γ, Us will be reduced due
to the increased Isd while the power factor cosϕ will increase [1].
Varying γ between 0 and 35°el, the torque will increase at the beginning, and
then it decreases again. The reason for this behaviour is the reluctance torque,
which is prominent, when also d-component current is applied. The voltage
decreases with increasing γ and reaches the value 230 V at 16°el for motor A, 20°el
for motor B and 18°el for motor C, respectively. At these angles the torque still has
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Permanent magnet synchronous motors with concentrated windings
191
the requested value and the power factor is increased by 0.1 compared to operation
with γ = 0 °el.
The results of the simulated steady state electromagnetic performance are
presented in Table 3 for rated speed and Table 4 for maximum speed respectively.
a
b
c
Fig. 5 – Phasor diagrams at rated speed: a) motor A; b) motor B; c) motor C.
Table 3
Electromagnetic performance at rated speed
Motor
A
B
C
1 000
1 000
1 000
Phase voltage (V)
230
230
230
Frequency (Hz)
133.3
133.3
133.3
95
103
114
Speed (rot/min)
Phase current (A)
Angle γ (°el)
16
20
18
Power factor
0.72
0.66
0.6
Torque (Nm)
430
430
430
Torque ripple (of rated torque)
Current loading (A/cm)
Current density (A/mm2)
2
7
1.04
6.4
962
880
721
5.9
5.8
7.1
Thermal load A · J (A/cm · A/mm )
5 683
5 131
5 142
Ohmic losses (at 145 °C) (W)*
1 902
1 807
1 834
992
899
865
Iron losses in stator (W)*
*Calculated for sinusoidal voltage and current supply.
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Csaba Deak, Andreas Binder
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Table 4
Electromagnetic performance at maximum speed
Motor
Speed (rot/min)
Phase voltage (V)
Frequency (Hz)
Phase current (A)
Angle γ (°el)
Power factor
Torque (Nm)
Torque ripple (% of rated torque)
Current loading (A/cm)
Current density (A/mm2)
Thermal load A · J (A/cm · A/mm2)
Ohmic losses (at 145 °C) (W)*
Iron losses in stator (W)*
A
3 000
230
400
67
64
1
143
7.3
678
4.1
2 827
946
944
B
3 000
230
400
67
61.8
0.98
143
0.7
572
3.77
2 156
765
1 068
C
3 000
230
400
68.5
61.7
0.97
143
2.7
433
4.2
1 834
643
1 237
*Calculated for sinusoidal voltage and current supply.
Analysing the torque ripple at rated speed (Fig. 6) results, that motor B has
the smoothest torque with the smallest ripple, while motor A and motor C produce
similar torque ripple amplitudes.
Additional losses, which occur in the windings due to 1st and 2nd order current
displacement and in the magnets due to flux pulsation are calculated at sinusoidal
and voltage source inverter supply. A PWM operation with 3 kHz inverter pulse
frequency was simulated (Table 5).
Fig. 6 – Torque ripple at rated speed.
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Permanent magnet synchronous motors with concentrated windings
193
Table 5
Additional losses in windings and in magnets [W]
Speed (rot/min)
Supply
Winding
Magnets
Supply
Winding
Magnets
Motor A
1 000 3 000
182
42.7
812
153.6
87
4.3
87
4.3
Motor B
1 000 3 000
Sinus
560
2122
49.4
180
Inverter
156
156
3.6
3.6
Motor C
1 000 3 000
242
31.9
761
76.5
66
–
66
–
3.3. COMPARISON OF THE ELECTROMAGNETIC PERFORMANCES
Comparing the designed motors A, B and C, based on no-load and load
calculations, we can see that motor A has the smallest current rating and the
highest power factor at rated speed but has the biggest thermal load due to I 2R
losses as well as the biggest cogging torque and torque ripple at load.
Motor B produces the smoothest torque at all investigated operating points but has
also the highest total losses due to increased additional eddy current losses especially at
high frequencies. This is a major setback for the thermal behaviour. Regarding the
current rating and the power factor, motor B stands between motor A and C.
Compared to motor A, motor C produces smaller cogging torque and torque
ripple but needs a 20% higher current at rated speed. Nevertheless due to the 30%
smaller phase resistance it generates smaller ohmic losses and has a lower thermal
load at both points of operation.
The bigger slot openings cause a bigger harmonic distortion of the air gap
field, even if the rotor field is almost sinusoidal due to the rotor outer contour
optimisation, so that the power factor of motor C is the lowest at rated speed.
The currents at maximum speed of motor B and motor C for 143 Nm are
almost the same as the current of motor A due to the higher synchronous reactance,
which allows a better field weakening ability.
The fractional slot configuration leads to increased losses in the magnets especially
at higher speed which could cause an overheating of the magnets. In the considered cases
the lowest magnet losses occur for motor C at both rated and maximum speed while in
motor B the surface mounted magnets and the bigger slot openings due to lower slot
number than motor A shows the highest losses in the magnets.
4. THERMAL ANALYSIS
An identical water-jacket cooling system at 45°C is designed for all three
motors with a circumferential spiral cooling duct with 14 turns and with a heat
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Csaba Deak, Andreas Binder
12
transfer coefficient of αK = 9 468 W/m2K, which corresponds to 9 l/s water flow
rate and 1.66 m/s water velocity [1].
A 2D thermal calculation was performed with help of finite element program
ANSYS to verify the thermal behaviour of the motors, first without any resin
impregnation in the slots. Due to the symmetrical heat distribution, only two
magnet poles are simulated for motor A and motor C and four magnet poles for
motor B with the corresponding stator segments.
Due to the smaller slot fill factor (lower heat transfer) and bigger copper
losses, motor A would excessively heat up without resin impregnation with a
maximum temperature of above 200°C in the windings while motor C would reach
a maximum temperature of above 300°C which is more than the temperature limit
of the isolation. To avoid this, the coils are embedded in resin. For simulation, a
heat conduction average value of resin and air of 0.165 W/mK has been used. In
this way the maximum temperature is reduced to 144°C (Fig. 7a) and 203°C
respectively (Fig. 7b).
The heat transfer of motor C is the best due to the high slot fill factor and so the
temperature does not exceed 110 °C (Fig. 7c) at rated and maximum speed (Table 6).
a
c
b
Fig. 7 – Temperature distribution at rated speed: a) motor A; b) motor B; c) motor C.
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Permanent magnet synchronous motors with concentrated windings
195
Table 6
Calculated winding temperatures
Motor A
Speed (rot/min)
Motor B
Motor C
1 000
ϑHotspot (°C) (max. 155°C)
144
203
110
ϑaverage (°C) (max. 145°C)
119
155
100
Speed (1/min)
3 000
ϑHotspot (°C) (max. 155°C)
133
239
98
ϑaverage (°C) (max. 145°C)
112
181
89
Motor B on the other hand exceeds the temperature limit at both rated and
maximum speed due to the additional 1st order losses caused by current
displacement.
5. CONCLUSIONS
Three permanent magnet motors were designed with concentrated tooth coil
windings for a constant power of 45 kW and 230 V phase voltage at 1 000 rot/min
rated speed and 3 000 rot/min maximum speed. Due to the high electromagnetic
utilisation and the fractional slot winding design, the power factor of these models
ranges only between 0.5…0.6, but it is improved by 0.1 with help of negative dcurrent supplied to the windings.
The models are designed with identical number of poles, stator inner- and
outer diameter and active length. Motor A and motor B have surface mounted rotor
magnets and equal tooth widths with coils wound on each tooth, while motor C has
buried magnets and unequal tooth widths with coils wound on alternate teeth.
The calculated electromagnetic performance at no-load and load operation
shows, that motor C has a better thermal utilisation, smaller cogging torque and
torque ripple at load, yields lower total losses at rated speed due to the smaller
phase resistance but has a smaller power factor and 20% higher current rating than
motor A. Motor B produces the smallest torque ripples but also the highest total
losses due to increased additional eddy current losses which lead to high
temperatures in the windings at high speed, exceeding the thermal limits of the
insulation.
Motor A and motor C are currently built as prototypes (Figs. 8, 9).
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Csaba Deak, Andreas Binder
a
14
b
Fig. 8 – Built prototype stators (under construction): a) motor A; b) motor C.
a
b
Fig. 9 – Built prototype rotors (under construction): a) motor A; b) motor C.
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Permanent magnet synchronous motors with concentrated windings
197
The two motors will be tested in order to verify and evaluate the calculation
results. Then the two rotors will be interchanged and the new stator-rotor
combinations will be tested also.
Received on 16 July 2006
REFERENCES
1. C. Deak, A. Binder, Highly utilised permanent magnet synchronous machines with tooth-wound
coils for industrial applications, Proc. Electromotion‘05, Lausanne, Switzerland, Sept. 2005,
CD-ROM.
2. T. Koch, A. Binder, Permanent magnet machines with fractional slot winding for electric traction,
Proc. ICEM’02, Brugge, Belgium, Aug. 2002, CD-ROM.
3. D. Ishak, Z. Q. Zhu, D. Howe, Permanent-magnet brushless machine with unequal tooth widths
and similar slot and pole numbers, IEEE Transactions on Industry Applications, 41, 2,
March/April 2005, pp. 584–590.