XIX International Conference on Electrical Machines - ICEM 2010, Rome
Impact of slot geometry and rotor position on
AC armature losses of Interior PM Synchronous
Machines
S. Hahlbeck, D. Gerling
Φ
Abstract -- This paper examines the influence of slot
geometry in means of the impact of pole shoes at the stator
teeth on ac armature losses in concentrated windings of
Interior Permanent Magnet (IPM) synchronous machines. It is
shown that the rotor position as well as the stator teeth
geometry affects the ac armature losses in the concentrated
windings. Here a configuration without a pole shoe tends to
have higher losses due to the stronger effect of the rotor stray
flux onto the stator windings.
Index Terms—AC losses, AC machines, Armature losses
concentrated winding, Permanent Magnet machines, slot
leakage flux, stator pole shoe, Proximity losses
I.
INTRODUCTION
I
n applications with high requirements for torque and
power density often IPM synchronous machines with
concentrated windings are used. For automotive
traction drive applications (e.g. hybrid-electrical vehicles)
there is also the requirement to have an electric motor based
on a production-geared design with low costs. For this it is
of high advantage during machine assembly to have no pole
shoes at the stator teeth. It enables a process where the
preassembled single-tooth windings are mounted directly
onto the stator teeth. The assembly process of the stator is
much simpler and less cost intensive since two completely
independent and fully automatable processes are possible for
stator assembly.
Major disadvantage of this production-geared stator
design can be found in the electromagnetic design of the
motor. As is known from [5] the electromagnetic torque of
an IPM synchronous machine is dependent on the air gap
length. The air gap length is a function of the nominal air
gap length, the width of the slot opening and the slot pitch.
The slot opening width and the slot pitch are usually
expressed by the Carter-Factor. When omitting the pole
shoes the Carter Factor will increase and the torque constant
of the motor will decrease at the same time. Furthermore
cogging torque and torque ripple will increase due to the
salient pole design in the stator. Usually skewing is
necessary to decrease cogging torque and torque ripple
again. By skewing the rotor or stator the torque constant
drops even further.
These are effects which decrease the torque and power
density of the machine. This is in contrast to the goal of
designing a motor with very high torque and power density.
Therefore a compromise out of raw material costs and
production driven costs is to be found.
In this paper a second impact caused by a stator pole
design without pole shoes is investigated – the higher ac
Steffen Hahlbeck is with the Dept. of Advanced Engineering, Daimler
AG, 70546 Stuttgart Germany (e-mail: steffen.hahlbeck@daimler.com).
Dieter Gerling is head of the institute of electrical drives at the Univ. of
Federal Defense Munich, 85577 Neubiberg Germany (e-mail:
Dieter.Gerling@unibw.de).
978-1-4244-4175-4/10/$25.00 ©2010 IEEE
armature losses in the stator windings. In [1] the proximity
losses of Switched Reluctance Machines (SRM) were
analysed. Inherent to the functional principle of SRM the
rotor stray flux has a very strong impact onto the proximity
losses in the windings when the rotor position changes from
unaligned to aligned position. In [3] and [4] an analytical
model is presented for calculations of proximity losses for
Surface Permanent Magnet (SPM) synchronous machines
and results are compared with finite element (FE)
calculations. The impact of rotor stray flux is omitted in both
the analytical and FE model. Since the analysis in this paper
is done for IPM synchronous machines, which represent a
hybrid of the SRM and the SPM, the rotor stray flux is to be
considered when calculating the ac armature losses.
DEFINITION OF PROXIMITY, AND SLOT LEAKAGE LOSSES
Proximity losses are caused by the effect of not uniformly
distributed current density in the wire cross section when
another nearby wire is energized with a high frequency
current. This effect comes from the impact of the magnetic
field of the second wire onto the regarded wire, when both
wires are placed in free air. This not uniformly distributed
current density (the current density is higher at parts of the
surface of the wire than inside the wire) leads to increased
losses in the AC case versus the DC case.
The slot leakage effect is the effect of not uniformly
distributed current density in the wire cross section coming
from the magnetic leakage field crossing the slot cross
section of an electrical machine because of the finite
magnetic conductivity of the iron material and the (usually
quite small) slot opening. The slot leakage effect can be
amplified by the rotor flux of a permanent magnet rotor
when the rotor flux crosses the slot opening and
superimposes the slot leakage flux. Both, proximity losses
and slot leakage losses, can occur in the windings of IPM
machines of the type regarded here. The skin effect is
neglected since frequencies and wire diameters are too small
in the considered applications.
II.
III. STUDY ASSUMPTIONS
For the analysis an IPM synchronous machine design with
20 poles and 24 stator slots is chosen. This slot / pole
combination has a very high winding factor and low cogging
torques as well as torque ripples [2]. The major measures
and definitions of the motor are provided in Table I. The
motor design is analysed by using 2D Finite Element
Method (FEM) and transient analysis. The ac armature
losses in the windings are calculated by using a quarter
model of the motor (see Fig. 1). The model is solved in 45
loadsteps. For every loadstep the rotor is rotated one
mechanical degree in counter clockwise direction.
TABLE I
Rotor poles
20
Active length [mm]
70
Stator slots
24
Air gap length [mm]
0.8
Slot-per-phase-per pole
0.4
Winding factor
0.933
Stator OD [mm]
290
Slot fill factor [%]
50.6
Air gap diameter [mm]
229.2
Slot opening width
[mm]
5.5
In that way the model takes into account the movement of
the rotor as well as saturation effects in the teeth and rotor
bridges. The single wires of one coil of phase A are
connected to an electrical circuit which simulates each wire
with its active length and connects the whole coil to a
sinusoidal current source. All other coils are treated the same
way as it is done for static simulations. The load in these
coils is applied as a current density on each wire. By
calculating armature losses just in one coil of the machine,
complexity in pre-processing and simulation time are
decreased dramatically. An investigation in [1] showed an
error in overestimating the ac losses of about 20 % by this
simplification.
this a very fine mesh is needed for the wires and within the
slot. As a useful comparison unity the results are displayed
as ohmic losses for one coil or coil side. The losses in the
end windings are neglected here since the current
distribution from the 2D FEM is not valid within the end
windings. In Fig. 2 the ac versus dc losses for one coil of the
two models as a function of rotor position are presented. In
the model with pole shoes the losses are increased due to ac
effects by a factor of 1.64 to 13.1 W. For the model without
pole shoes it is even a factor of 2.01 which results in total
losses for the coil of 16.1 W.
35
AC+DC losses with pole-shoe
AC+DC losses without pole-shoe
DC losses
30
25
Pv [W]
MAJOR MEASURES AND DEFINITIONS OF THE ANALYSED MOTOR
20
15
10
5
0
5
10
15
20
25
30
35
40
delta [°mech]
Fig. 2 Comparison of ac + dc to dc losses for different rotor positions
Fig. 1 Quarter model of the machine with pole shoes at the stator teeth
As working point for the analysis a speed of 5000 rpm at
a load of 20 Nm is chosen. At this speed the electrical
frequency is 833 Hz. The phase current is 86 Arms. The
machine has a concentrated double-layer winding with four
parallel paths per phase and two coils in series per path. So
the current in the analysed coil becomes 21.5 Arms. Each coil
consists of 24 windings and is wound with 3 strands in hand,
where each strand wire has a diameter of 1.18 mm (pure
copper). Neglecting the resistance of the end-windings,
which are not modelled in 2D analysis, one coil has a
resistance of 0.017 Ω. This results in DC losses of 8 W for
one coil in average. After analysing the original design with
pole shoes the model geometry is changed. The pole shoe at
each stator tooth is cut away and the analysis is repeated
using identical boundary conditions.
IV. ANALYSIS RESULTS
The results from the FEM simulations are among others
the current density distributions in each wire of the coil. For
Both models show high losses during rotor positions with
low phase currents. This means the circulating eddy currents
due to slot leakage flux and proximity effect never become
zero even though the total phase current in the coil is zero.
For these rotor positions with very low currents the ac loss
characteristic of the two models is almost identical. This is
due to the fact that the slot leakage flux is the same for both
cases. The rotor positions in between 15°mech and 24°mech
show higher slot leakage flux for the model without stator
pole shoes. These are rotor positions with high values of
dΦ/dt in the air gap. This occurs when the next rotor pole
moves along the coil or in other words when the first coil
side is opposite to the rotor q-axis. Here in case of the tooth
with pole shoes the rotor flux is transferred within the pole
shoe and does not affect the winding layers as strong as it is
the case for the stator without pole shoes.
In Fig. 3 the loss distribution separated for each coil side
is shown. Since the rotor moves counter clockwise the rotor
poles move from the lower to the upper coil side in the
model. The lower coil side has higher losses – in numbers
35 %. As known from the investigations in [1], the coil side
at the stator pole which is first penetrated by the rotor stray
flux has the higher losses. These losses are located almost
only in the two winding layers closest to the air gap as can
be seen from Fig. 4. In the first winding layer eddy currents
show high values for both current directions even though the
phase current has its amplitude in positive direction (out of
the plane). All lower layers just influence each other as
examined in [3].
20
upper coilside
lower coilside
18
16
14
Pv [W]
12
10
8
6
4
2
0
5
10
15
20
25
delta [°mech]
30
35
40
Fig. 3 Comparison of losses in upper and lower coil side for the model
without pole shoes.
low phase currents the efficiency drop is not as high as
expected from the increase of ac to dc losses, which is 100%.
Nevertheless due to the higher losses in the windings the
continuous power of the machine will be significantly lower.
When deciding for a manufacturing method of the
concentrated windings the drop of 2 % in machine
efficiency, as represented by this working point, is to be
compared with the cost-benefits in manufacturing costs and
the effects in the overall system efficiency of the powertrain.
For sure the motor active length needs to become longer if
the same maximum torque shall be reached. The investigated
motor without pole shoes has an 11 % lower maximum
torque. This would be exactly the increase in active length
needed.
VI. CONCLUSIONS
By transient FE analysis the impact of the rotor stray flux
on the ac armature losses in the windings of an IPM
synchronous machine was shown. Two different stator
configurations, one with stator pole shoes and one without
the pole shoes were analysed. The results show 22 % higher
ac losses in the configuration without pole shoes. The
possible cost-benefits of the production-geared design (stator
design without pole shoes) are paid with a lower motor
efficiency due to higher ac winding losses and with lower
maximum torque due to the increase in the effective air gap
length.
Fig. 4 Current densities in coils at 18°mech for the model without stator
pole shoes.
V. DISCUSSION OF RESULTS
The results of the FE simulations show the strong impact
of rotor stray flux of IPM synchronous machines onto ac
armature losses in the windings when simplifying the stator
pole design. As mentioned earlier the wide slot opening of
the machine without pole shoes increases the Carter Factor
which results in a lower torque constant. This is a main
disadvantage for low speeds till base speed. In the
field-weakening area, when the electrical frequency becomes
the main reason for losses in the means of iron losses, the
efficiency decreases further due to higher ac losses in the
windings.
In measurements for the machine with pole shoes at this
working point, a machine efficiency of 80 % was reached.
This quite low efficiency for an IPM machine is caused by
the low dc-link voltage which is available in the use-case of
a hybrid-electrical vehicle. For that the machine is in high
field-weakening area at a speed of 5000 rpm which results in
a low efficiency at low loads due to high iron and copper
losses. Iron losses could be reduced here by a lower number
of poles. But due to the available cross-section for the
machine design, which is a thin ring in between a diameter
of 199 mm (inner rotor diameter) and 290 mm (outer stator
diameter), the yokes in rotor and stator become very thin and
a higher pole number is to be chosen.
The simulation results yield even to an increase of 22 %
in copper losses when omitting the pole shoes compared to
the model with pole shoes. From this the machine efficiency
for the investigated working point becomes 78 %. Due to the
VII.
[1]
[2]
[3]
[4]
[5]
REFERENCES
C. Carstensen, “Eddy Currents in Windings of Switched Reluctance
Machines” Ph.D. dissertation, Dept. of Electrical Eng., RWTH
Aachen, 2007
F. Magnussen, H. Lendenmann, “Parasitic Effects in PM Machines
with Concentrated Windings”, IEEE Trans. on Industry Applications
Vol. 43 No. 5, Sep./Oct. 2007
P. B. Reddy, Z. Q. Zhu, S.-H. Han and T. M. Jahns, “Strand-Level
Proximity Losses in PM Machines Designed for High-Speed
Operation”, ICEM 2008, 2008
P. B. Reddy, T. M. Jahns, A. M. El-Refaie, „Impact of Winding Layer
Number and Slot/Pole Combination on AC Armature Losses of
Synchronous Surface PM Machines Designed for Wide ConstantPower Speed Range Operation“, Industry Appl. Society Annual
Meeting, 2008
Vogt, Karl, et al.: “Berechnung elektrischer Maschinen”, 6th ed.,
Wiley-VCH Verlag, Weinheim, 2008
VIII.
BIOGRAPHIES
Steffen Hahlbeck, born in 1981. He studied Electrical Engineering at the
University of Applied Sciences, Mittweida, Germany, where he got his
degrees as B.Eng. and M.Sc. in 2004 and 2006, respectively. His
employment experience includes the series development and advanced
engineering for electrical drives at Daimler AG, Sindelfingen and Stuttgart,
Germany.
Dieter Gerling, born in 1961, got his diploma and Ph.D. degrees in
Electrical Engineering from the Technical University of Aachen, Germany
in 1986 and 1992, respectively. From 1986 to 1999 he was with Philips
Research Laboratories in Aachen, Germany as Research Scientist and later
as Senior Scientist. In 1999 Dr. Gerling joined Robert Bosch GmbH in
Bühl, Germany as Director. Since 2001 he is Full Professor and Head of the
Institute of Electrical Drives at the University of Federal Defense Munich,
Germany.