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Comparison of Permanent Magnet Rotor Designs for Different Vehicle Classes and Driving Scenarios: A Simulation Study

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The most important magnet layouts in rotors of hybrid permanent-magnet synchronous machines (PMSM) for electric vehicles are compared in a variety of characteristics. The effect of different rotor designs on the vehicle performance and energy consumption is evaluated for a small battery electric vehicle (BEV) for different drive cycles. With electromagnetic and mechanical Finite Element Method (FEM) calculations as well as a longitudinal vehicle simulation platform, the • Torque, power, ripple, and noise characteristics • The energy consumption in a small passenger vehicle • The suitability for high-speed applications of the electric machine (EM) are simulated and compared. Five rotor types are included in the study, which represent the most seen designs in popular electric vehicles: V-Shape, Straight type, multilayer U-Shape, Spoke type, and Spoke+Straight type. As the methodical approach, the electric motor from the Toyota Prius 2004 is taken as base design and only the magnet arrangement in the rotor is varied. The rotors are equal in length, diameter, material selection, and magnet mass, only the arrangement of the magnets is varied. Hence a change in the performance of the EM can only be due to the magnet arrangement. It can be shown that noticeable differences between the designs exist and that the choice of the rotor plays an important role. The differences mainly result from the characteristic magnet flux shape in the air gap together with the different reluctances of each individual design. An evaluation of the results reveals that all types have their advantages and disadvantages without one design standing out very much in all disciplines. In the overall rating, the V-Shape slightly leads the ranking. It has the broadest area of high efficiency and, thus, the best energy consumption in a mixed driving scenario of a small BEV. Its energy consumption is 3.5% better than with the worst design, which is the Spoke type in this context. The Spoke type in turn has the highest peak power and torque, being 11%/13.5% better than the worst design in these disciplines. A disadvantage of the Spoke type is its low mechanical resilience against centrifugal forces, making this design not well suited for high-speed EM applications. The multilayer U-Shape design has the least torque production herein, while it has very low iron losses and noise (63% less cogging torque and 73% lower torque ripple than with the worst design) due to its particularly low air gap flux harmonics. This makes this design better suitable for high-speed EM where iron losses get more dominant over copper losses. The Straight type is the most versatile rotor design, having no very bad discipline and a good overall rating.
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ARTICLE INFO
Article ID: 14-10-02-0016
© 2021 The Authors
doi:10.4271/14-10-02-0016
History
Received: 13 Aug 2020
Revised: 12 Feb 2021
Accepted: 20 May 2021
e-Available: 02 Jun 2021
Keywords
Permanent-magnet
synchronous machines,
Electric vehicle, Rotor
design, Magnet
arrangement, Permanent
magnet, Electric machine,
Reluctance torque, Energy
consumption, Optimization,
Simulation
Citation
Hemsen, J., Negri, T.,
Trost,C., and Eckstein, L.,
“Comparison of Permanent
Magnet Rotor Designs for
Dierent Vehicle Classes
and Driving Scenarios: A
Simulation Study,SAE Int.
J. Elect. Veh. 10(2):2021,
doi:10.4271/14-10-02-0016.
ISSN: 2691-3747
e-ISSN: 2691-3755
Comparison of Permanent Magnet
Rotor Designs for Dierent Vehicle
Classes and Driving Scenarios:
A Simulation Study
Jonas Hemsen,1 Tommaso Negri,1 Christian Trost,1 and Lutz Eckstein1
1Institute for Automotive Engineering-RWTH Aachen University, Germany
Abstract
The most important magnet layouts in rotors of hybrid permanent-magnet synchronous machines (PMSM) for
electric vehicles are compared in a variety of characteristics. The eect of dierent rotor designs on the vehicle
performance and energy consumption is evaluated for a small battery electric vehicle (BEV) for dierent drive
cycles. With electromagnetic and mechanical Finite Element Method (FEM) calculations as well as a longitudinal
vehicle simulation platform, the
Torque, power, ripple, and noise characteristics
The energy consumption in a small passenger vehicle
The suitability for high-speed applications
of the electric machine (EM) are simulated and compared.
Five rotor types are included in the study, which represent the most seen designs in popular electric
vehicles: V-Shape, Straight type, multilayer U-Shape, Spoke type, and Spoke+Straight type.
As the methodical approach, the electric motor from the Toyota Prius 2004 is taken as base design and
only the magnet arrangement in the rotor is varied. The rotors are equal in length, diameter, material selection,
and magnet mass, only the arrangement of the magnets is varied. Hence a change in the performance of the
EM can only bedue to the magnet arrangement.
It can be shown that noticeable dierences between the designs exist and that the choice of the rotor
plays an important role. The dierences mainly result from the characteristic magnet flux shape in the air gap
together with the dierent reluctances of each individual design. An evaluation of the results reveals that all
types have their advantages and disadvantages without one design standing out very much in all disciplines.
In the overall rating, the V-Shape slightly leads the ranking. It has the broadest area of high eciency and, thus,
the best energy consumption in a mixed driving scenario of a small BEV. Its energy consumption is 3.5% better
than with the worst design, which is the Spoke type in this context. The Spoke type in turn has the highest peak
power and torque, being 11%/13.5% better than the worst design in these disciplines. A disadvantage of the
Spoke type is its low mechanical resilience against centrifugal forces, making this design not well suited for
high-speed EM applications. The multilayer U-Shape design has the least torque production herein, while it has
very low iron losses and noise (63% less cogging torque and 73% lower torque ripple than with the worst design)
due to its particularly low air gap flux harmonics. This makes this design better suitable for high-speed EM
where iron losses get more dominant over copper losses. The Straight type is the most versatile rotor design,
having no very bad discipline and a good overall rating.
© 2021 The A uthors. Pub lished by SAE Inte rnational. Th is Open Access a rticle is publ ished under th e terms of the Creat ive Commons
Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits distribution, and reproduction in any medium,
provided that the original author(s) and the source are credited.
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2 Hemsen et al. / SAE Int. J. Elect. Veh. / Volume 10, Issue 2, 2021
  IntroductionandScope
Due to the ever-increasing global warming, environmental
issues, and air quality problems in highly populated urban
areas, governments a ll over the world strongly strive to reduce
the impact of combustion-driven vehicles on the climate,
which today accounts for 15% of the worldwide emitted green-
house gases [1]. To reduce this amount, zero-emission vehicles
for passenger and freight transpor tation are directly promoted,
and high subsidies are granted for research in the
respective elds.
Independent from the used electric storage technology
in the vehicle (e.g., battery or hydrogen), electric machines
(EMs) are required for transforming electrical into
mechanical energy, propelling the vehicle with high effi-
ciency and without local emissions. Among many different
EM topologies, the Permanent-Magnet Synchronous Motor
(PMSM) represents the state-of-the-art EM in hybrid
electric vehicles (HEV) and battery electric vehicles (BEV)
due to its advantages in terms of power density and effi-
ciency compared to Asynchronous Machines and Switched-
Reluctance Machines [2]. It is employed by the most
popular electrified vehicle models in today’s market such
as the Toyota Prius, Nissan Leaf, BMW i3, Tesla Model 3,
Jaguar I-Pace, and many others. However, even for PMSM,
the variety of geometrical shapes is high. The design of the
rotor and the inserted magnets can bedifferent and directly
influences losses, torque-speed characteristic, noise and
more. Interior permanent magnet (IPM) designs with
inserted magnets have proven to besuperior to surface-
mounted permanent magnet designs for traction applica-
tions. This is due to their rotor saliency, leading to higher
power stability in the field-weakening area, lower magnet
mass, less vulnerability to demagnetization, and higher
efficiency [3, 4, 5, 6], or at least to easier manufacturability
at a similar performance [7].
Various interior PMSM rotor geometries have been
designed and compared in previous studies. In the following
the most important studies are briey analyzed. Yang etal.
conducted a very comprehensive comparison including
mechanical considerations and conclude that the V-Shape
rotor design achieves the best overall performance. However,
the investigated rotor designs are very similar and do not
represent all available options [5]. Liu etal. investigated more
different designs including Spoke-Type design and also
identify the V-Shape as the best candidate. Here, no mechan-
ical stress calculations and no cycle loss evaluations are
included [8]. Huynh and Hsieh included cycle and thermal
simulations in t heir comparison. ey conclude that IPMs are
well suited for urban driving and that a higher share of reluc-
tance torque is benecial for eciency at highway driving [9].
Hwang etal. compared ve dierent IPM designs and found
out that, for a similar performance, the V-Shape uses the least
magnet material. Cycle simulations, mechanical ca lculations,
and eciency evaluations are not included in this study [10].
None of the reviewed and presented studies provides a
comprehensive study including electromagnetic performance,
constraint consideration such as demagnetization and
mechanical stress limits, and cycle loss evaluation. is gap
is lled with the herein presented work. Additionally, the
process to generate the results is presented and can easily
beadopted to obtain similar results, e.g., for other than the
included vehicle classes.
From the analysis of the many technical solutions inves-
tigated in the named studies and adopted by car manufac-
turers in the spatial arrangement of the permanent magnets,
it appears evident that each design brings both advantages
and disadvantages. Hence the aim of the presented research
paper is to provide a comparison of dierently designed hybrid
PMSMs1 with regard to the shape and position of the perma-
nent magnets inside the rotor iron lamination. e methodical
study of these motors can help in the choice of the most
suitable one in the different driving environments and
vehicle applications.
For the considered rotor designs, the following param-
eters are calculated and evaluated:
Torque (power) over speed
Losses and maximum eciency
Energy consumption in urban and highway
driving scenarios
Risk of demagnetization of the permanent magnets
Noise behaviour: Cogging torque and torque ripple
Von Mises stress in and deformation of the rotor iron
By comparing these parameters, those rotor designs,
which provide the lowest noise, best eciency, or highest
torque, can beidentied. Additionally, the best rotor designs
for specic driving scenarios are found.
  Methodologyofthe
Study
e analysis of the EMs is carried out on two levels:
1. Electromagnetic performance calculation with a
Finite Element Method (FEM) soware for
electromagnetic eld calculations called FEMAG. e
results comprise the torque, power, eciency, torque
ripples, cogging torque, and demagnetization.
2. Mechanical stress calculation in the iron of the rotor
and determination of the maximum achievable rotor
speed with a 3D FEM Model and the MATLAB
Partial Dierential Equation (PDE) Toolbox.
In order to beable to compare the dierent rotor designs,
one specic EM is depicted and modelled with dierent
1 By means of a spec ial rotor design, so -called hybr id synchronous mac hines
(a subset of the PMSM) exploit the torque production mechanism of both
reluctance eect a nd Lorentz force.
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Hemsen et al. / SAE Int. J. Elect. Veh. / Volume 10, Issue 2, 2021 3
magnet arrangements. e dierences in the EM design for
the single calculations are for the sake of comparability
restricted to a minimum. Only the shape and spatial layout
of the permanent magnets inside the rotor of the PMSM is
varied, while the other parameters of the motor including
magnet mass, radii, materials, slots, windings, etc. are inher-
ited from the 2004 Toyota Prius EM [11] and le unchanged.
Prior to the calculation and comparison, each implemented
rotor type is subject to an optimization process in order to
nd those geometrical parameters, which provide good power
and torque output without the high risk of demagnetization.
This is done to ensure comparability, which can only
beclaimed if, for each geometry, a good set of parameters is
found. In order to optimize the geometry, an extensive param-
eter variation is conducted and the best candidate that does
not exceed a constraint limit (e.g., permanent-magnet demag-
netization) is chosen. e steps of the applied methodology
are described in the following:
1. Modelling and calculation of the Toyota Prius 2004
machine and verication of results by comparison
with recorded benchmarking data in [11].
2. For each rotor design: Replacement of the rotor
model, optimization of the geometry, and calculation
of machine characteristics with FEM and post-
processing.
3. For each rotor design: Energy consumption
evaluation by means of a longitudinal simulation. e
simulation is parametrized with data from a small
passenger vehicle and the eciency and torque
characteristic obtained in the previous step. Two
dierent driving cycles are simulated for each rotor
design in order to separately investigate the urban
(Urban Dynamometer Driving Schedule, UDDS,
cycle) and the extra-urban (Highway Fuel Economy
Test, HWFET, cycle) driving conditions.
4. Calculation of critical stress in the iron of each
rotor design.
5. Results analysis.
e EM FEM calculations are veried by publicly available
data from [11] (Step 1) and have been used in previous projects
[12, 13]. e longitudinal si mulations are c arried out with a simu-
lation library, which is used for many years at the Institute of
Automotive Engineering of RWTH A achen University and wh ich
was veried in numerous projects. However, when simulation
tools are used , it is always possible that deviat ions from real-world
results exist. Herein, the comparability of the concepts is the
focus, and thus deviations between simulations and real world
do not impact the resulting statements of this study.
  EmployedEMModel
e used machine that serves as the basis for al l further calcu-
lations is taken from the 2004 Toyota Prius [11]. It provides
50kW of peak power and has 8 rotor poles, 48 stator slots,
and 3 phases, the latter resulting in two “slots per pole per
phase.” is ratio is also seen, e.g., in the BMW i3, the Lexus
LS 600h, or the Toyota Camry. e motor thus represents a
standard drive EM for very small BEV or parallel HEV. e
slot geometry and the one-layer winding layout are visualized
in Figure 1. e slot parameters are listed together with all
other motor parameters in the Appendix in Table A.1.
RA
H
H1H2
SW
RI
½
TW
R2
R1
 FIGURE 1  Slot geometry of the modelled motor (left) and winding layout (right).
© The Auth ors
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4 Hemsen et al. / SAE Int. J. Elect. Veh. / Volume 10, Issue 2, 2021
  ChosenRotorDesigns
Considering the literature and the previous studies in [5, 8, 9,
14, 15, 16, 17, 18, 19], the selection process of the most prom-
ising candidates for the study resulted in the geometries
presented in Figure 2. In the following, the reasons for the
selection of each rotor design are stated and justied.
e V-Shape, employed in all hybrid and electric drives
of Toyota (Prius 2004, Prius 2010, Lexus LS 600h, or
Toyota Camry), represents the basis of the comparison
and has been regarded in [5] and [8] as the best
combination between constant torque output and
eld-weakening capability.
e Straight type, employed by Honda in the 2005
Accord, is remarkable for its layout simplicity against its
good magnetic ux density capability [15].
e multilayer U-Shape is the most complex
conguration, made of multiple permanent magnet
layers with a wide variety of geometrical parameters to
beset. It is expected to provide a high share of reluctance
torque, which makes the machine more ecient and less
critical in error cases such as winding short circuits.
Such design is used in the BMW i3.
e Spoke type has the interesting magnetic ux
concentration capability, which locally allows very high
air gap magnetic ux densities [6], possibly leading to
high torques. Furthermore, the Spoke type is expected to
provide easy and cheap rotor manufacturing through
rotor segmentation and easy inserting of the magnets
from the center.
e Spoke+Straight type rotor consists of a newly
designed combination of Spoke and Straight type, with
the aim of mixing both of their advantages. is type is
included to see if a combination of both types can
provide advantages over the other types, as seen in [18].
With these selected rotor types, a wide range in multiple
domains exists: Dierent levels of saliency are represented
(leading to dierent shares of reluctance and electromagnetic
torque) as well as rotor designs with dierent manufacturing
complexities. Furthermore, the most common layouts from
on-the-road applications are depicted. SPMs are not
considered herein as they do not nd application in modern
vehicle drives due to their disadvantages of low reluctance
torque, easy demagnetization, dicult magnet xation, and
poor power stability.
  Results
5.1.  Torque
5.1.1. Reluctance Torque In terms of machine design
for automotive applications, a high share of reluctance
torque is favorable, which has several reasons:
For a given torque target, it allows to decrease the
magnet size or strength in the rotor, lowering costs.
With less magnet ux linkage, the back electromotive
force is lower and eld weakening can start at
higher speeds.
In the eld-weakening area, the torque does not drop
rapidly because high reluctance torque keeps the overall
torque high. is leads typically to a longer constant
power area, which is specically important in
automotive applications.
In an error case such as a phase short circuit, it is
benecial to not have a high magnet ux linkage. Short-
circuit currents are lower and brake torque of the EM is
lower and, thus, leads to a less-critical driving situation.
e following equation shows the torque output T as the
sum of reluctance torque Trelucand electromagnetic torque
Telec(inNm) for the given root-mean-square (rms) currents Iq
and Id (in A) and inductances Lq and Ld (in H) in the quadra-
ture (q) and direct (d) axes, poles p, and permanent magnet
ux linkage Ψpm (i n Vs).
TT
TpIpII
LL
elec relucpmq qd
dq
=+ =***+****-
()
33
Y
Eq. (1)
The equation could be simplified, but in this longer
version, it reveals the two fundamental components of the
 FIGURE 2  Considered rotor designs from left to right: V-Shape, Straight, U-Shape, Spoke, and Spoke+Straight
permanent magnets.
© The Auth ors
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Hemsen et al. / SAE Int. J. Elect. Veh. / Volume 10, Issue 2, 2021 5
resulting torque: e le side of the summation equals the
Lorentz or electromagnetic torque produced by the magnetic
ux linkage, while the right side equals the reluctance torque.
It can also beseen by this equation that only machines with
a saliency (LdLq) have the physical ability to produce a
reluctance torque. For machines with symmetric rotor poles
(Ld=Lq), the complete reluctance torque term becomes zero.
Small values of Ld and large values of Lq favor reluctance
torque production. In order to consistently describe the dier-
ence between the d-axis and the q-axis inductances, the
saliency ratio, dened as Ld/Lq, is introduced in the following.
e smaller the saliency ratio gets the higher will, conse-
quently, the reluctance torque of the PMSM be.
For each rotor design, the nonlinear and saturation-
dependent inductances and the permanent-magnet ux have
been identied by means of the electromagnetic FEM calcula-
tions. e used soware exploits a mi xed analytical-numerical
method, presented in [20]. Exemplarily the results are shown
in Figure 3 for the V-Shape type. e current angle β on the
x-axis describes the distribution of current in the q-direction
and d-direction according to Equations 2 and 3, where I
describes the phase rms current in amperes (A).
II
q=
()
*
cos
b
Eq. (2)
II
d=
()
*sin
b
E q. (3)
e gure shows that the inductances are dependent
on the current and current angle, respectively, on the satu-
ration of the iron. From these results, the saliency ratio is
determined at maximum current and optimal β (the angle
leading to the maximum overall torque output) and at a
xed β = 45° (Table 1).
e given saliency ratios (Ld/Lq) at 45° indicate that the
Spoke+Straight type rotor provides the highest share of reluc-
tance torque, closely followed by the V-Shape type and the
L
dLq
PsiPM
I
I
Current angle (β) [
˚
]Current angle (β) [
˚
]
Current angle (β) [˚]Current angle (β) [˚]Current angle (β) [˚]Current angle (β) [˚]
I
I
Lq
Ld
 FIGURE 3  Results of inductance calculation for the V-Shape rotor.
© The Auth ors
TABLE 1 Saliency ratios of the dierent rotor designs.
Rotor type V-Shape Straight U-Shape Spoke Spoke+Straight
Optimal β [°] 39.4 36.4 42.4 42.4 51.5
Ld/Lq at 250 A [rms] and optimal β0.596 0.646 0.643 0.609 0.573
Ld/Lq at 250 A [rms] and β = 45.0° 0.604 0.664 0.642 0.604 0.596
© The Auth ors
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6 Hemsen et al. / SAE Int. J. Elect. Veh. / Volume 10, Issue 2, 2021
Spoke type. e U-Shape type provides less reluctance torque
and the Straight type even the least. is is in line with the
reluctance torque results shown in Figure 4. e dashed line
marks the 45°.
5.1.2. Lorentz and Overall Torquee other compo-
nent of the PMSM torque production besides reluctance
torque is the electromagnetic (or Lorentz) torque (Figure 5).
It represents the dominant factor at β = 0° and progressively
decreases towards zero at β = 90° as can beseen in the le
side of the summation in Equation 1.
With the information of the electromagnetic torque, the
overall torque production can bedetermined and is displayed
in Table 2.
5.2.  Power and Power
Stability
Figure 6 reports the power characteristic curves of each
analyzed design. It can beseen that they provide dierent
maximum power values as well as different extents of
decreasing power in the eld-weakening area.
In order to assess how well the maximum power can
bekept high in a eld-weakening operation, the speed range
between the maximum power and the point where the power
decreases below 70% of the maximum value is evaluated. is
value is called “70% power range” in the following and its unit
is in revolutions per minute (rpm). is method provides a
 FIGURE 4  Reluctance torque over the current angle (β) for the dierent rotor types.
© The Auth ors
 FIGURE 5  Electromagnetic and overall torque production of the dierent rotor types.
© The Auth ors
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Hemsen et al. / SAE Int. J. Elect. Veh. / Volume 10, Issue 2, 2021 7
rough estimation of the power output trend stability. e
obtained data are reported in Tab le 3.
As can be observed from the table, the Straight type,
followed by the U-Shape design, has the best power stability
characteristic since its curve does decrease rather slowly aer
the peak at rated speed. In contrast, the Spoke+Straight
conguration results to have the most unstable power char-
acteristic. However, in terms of peak power, the Spoke and
the Spoke+Straight type are most favorable.
5.3.  Noise
5.3.1. No-Load Air Gap Flux Density e noise
characteristic of a PMSM is strongly dependent on the air
gap ux distribution, i.e., the magnetic ux produced by the
PM that is passing through the air gap between the rotor and
stator (Figure 7). In fact, the ux density over rotor angle
contains a fundamental component, or rst harmonic, which
has a sinusoidal shape, and which is the only one responsible
for generating electromagnetic torque, and multiple other
odd harmonics that produce undesirable eects, such as
torque ripple, vibrations, acoustic noise, and losses.
It is visible in Figure 7 that the produced air gap ux is
very dierent for the investigated geometries. Here, the Spoke
type together with the Straight type provides the highest peak
air gap ux densities while the Spoke+Straight type provides
much lower ux densities but over a broad mechanical angle.
As said, it is important to consider also the odd harmonics
of a higher order, visible in the bar chart in Figure 8.
e harmonic content in the air gap ux density is e-
ciently resumed by the gure of merit “total harmonic distor-
tion,” THD (in %), which consists of the ratio between the sum
of the peak ux densities of all further harmonic components
ˆ
Bn
in T (nϵ{3, 5, 7, 9, 11}) and the rst harmonic peak magnetic
ux density
ˆ
B1
in T (Equation 4).
TH
DBB B
B
=++¼+
ˆˆ ˆ
ˆ
35 11
1
Eq . (4)
Because of the named disadvantages of the harmonics, a
lower THD results in smaller irregularities and unwanted
eects in the operational behavior of the EM.
e calculated THD according to Equation 4 is displayed
in Table 4. It can beobserved that the U-Shape and the Straight
type geometries have the least harmonic distortion while the
Spoke+Straight type has high harmonic contents. is corre-
sponds to observations that can bemade in Figure 7 where
the U-Shape and the Straight type seem to have the most
“sinusoidal-like” shape.
TABLE 2 Maximum torque output of each rotor type.
Rotor type V-Shape Straight U-Shape Spoke Spoke+Straight
Max. torque output [Nm] 405.3 385.8 3 67.2 416.7 393.5
© The Auth ors
 FIGURE 6  Power over speed for the dierent rotor designs.
© The Auth ors
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8 Hemsen et al. / SAE Int. J. Elect. Veh. / Volume 10, Issue 2, 2021
5.3.2. Cogging Torque and Torque RippleCog-
ging torque is the eect of reluctance at no-load conditions
due to the slotting of the stator. e permanent magnets try
to orientate in the axis with a stator tooth so that magnetic
resistance is minimized and, thus, produce a small torque.
Cogging torque is evaluated by multiple FEM calculations
with stepwise rotor rotation and no stator current. Torque
ripple on the other hand means the torque uctuations in the
base speed area with maximum stator current. It is produced
by the same eect as cogging torque but adds up to the regu-
lar torque output of the machine. Torque ripple is therefore
dened as the ratio of peak-to-peak value to the average val-
ue of the output torque.
For both eects, skewing of the rotor is not considered
in the calculations, which is oen done in reality in order to
lower both eects. e results for cogging torque and torque
ripple are shown in the following Table 5.
Combining both measures, it can be seen that the
U-Shape design here provides the best behavior while the
Spoke+Straight type has the worst.
5.4.  Critical Rotational Speed
due to Mechanical Stress
5.4.1. Methodology To nd the rotational speed at
which the material is exactly at its yield strength (critical
speed), several rotor speeds are simulated iteratively and the
critical speed is interpolated from the set.
e CAD models are exported from the electromagnetic
FEM program FEMAG and passed to the PDE Toolbox in
MATLAB in order to conduct all fur ther steps and to calculate
mechanical stress.
e following assumptions have been made:
Same material used (densities and elasticities) for
magnets and iron
Safety factor of 1.5 on the stated maximum stress in the
datasheet, reducing the allowed maximum stress by 50%
First of all, necessary dierential equations, which form
the basis of the PDE Toolbox, are set up by dening the
 FIGURE 7  Air gap flux density over the mechanical angle of two poles.
© The Auth ors
TABLE 3 Peak power and power stability for the dierent rotor types.
Rotor type V-Shape Straight U-Shape Spoke Spoke+Straight
Peak power [kW] 52.3 53.3 50.0 55.5 55.2
70% Power range [rpm] 4242 6909 5091 4970 3394
© The Auth ors
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Hemsen et al. / SAE Int. J. Elect. Veh. / Volume 10, Issue 2, 2021 9
elasticity tensor, the stiness matrices, and the volume force
densities. en the required boundary conditions are set.
Setting a rotor speed, displacements due to the occurring
centrifugal forces can becalculated, and the corresponding
stresses are derived from these displacements.
e critical rotor speed is then interpolated from a set of
rotor speeds and the maximum occurring stress in an element
using a second-degree polynomial (Figure 9).
e explained process of the program is shown Figure 10
in a owchart.
e results of the program are in the following example
shown for the V-Shape magnet design (Figure 11). The
maximum displacement is 13 nm, and the peak stress in the
iron bridge between the magnets is 233MPa.
5.4.2. EvaluationTable 6 shows the critical rotor speeds
of the considered rotor designs.
It is shown that the critical rotor speed of the
Spoke+Straight magnet design achieves the highest value. is
design can, by the distribution of stress to multiple locations
in the geometry, bewell suited for high-speed applications.
e Spoke type magnet achieves the lowest value of only 2319
rpm, whereas the other three geometries have a reasonable
critical speed between around 6000rpm and 9000rpm. e
critical speed of the Spoke-type rotor should beincreased in
order to beapplicable in automotive applications. is could
be achieved by increasing the iron bridges between the
magnets and air gap with the compromise of lowering the
torque output by the increased magnet leakage ux. e low
critical speed here results due to the fact that the initial
geometry optimization was only done with regard to electro-
magnetic performance, and the critical rotor speed was not
included. is should bechanged in a further investigation
of this kind.
5.5.  Eciency and Losses
e two main sources are the copper losses, which consist of
heat dissipation caused by the current injected in the stator
windings, and the core losses in the iron laminations, which
are further subdivided into stator yoke, stator teeth, and rotor
losses. Copper losses are directly dependent on the amount
of the owing current, which is, in turn, proportional to the
required output torque. us the copper losses are extremely
relevant at high torques in the constant torque region. Due to
 FIGURE 8  Harmonic content in the air gap flux density for the dierent rotor designs.
© The Auth ors
TABLE 4 THD of the air gap flux density of the considered geometries.
Rotor type V-Shape Straight U-Shape Spoke Spoke+Straight
THD 49.2% 41.2% 31.3% 59.1% 69.6%
© The Auth ors
TABLE 5 Cogging torque and torque ripple of the rotor types (no skewing considered).
Rotor type V-Shape Straight U-Shape Spoke Spoke+Straight
Cogging torque [Nm] 5.81 1.89 2.13 4.94 5.11
Torque ripple [%] 24.8 14.3 9.4 14.1 34.7
© The Auth ors
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10
Rotor speed [rpm]
10,000 12,000 14,000 16,000 18,000
Maximum
Critical
 FIGURE 9  Interpolation of critical speed from a set of 18 individual calculations.
© The Auth ors
 FIGURE 10  Applied process to calculate critical rotor speed.
© The Auth ors
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Hemsen et al. / SAE Int. J. Elect. Veh. / Volume 10, Issue 2, 2021 11
the same windings design and operating conditions, the
maxi mum copper losses are equal in a ll the investigated geom-
etries, but their allocation to the torque is dierent. For
example, the V-Shape and Straight type both have 14.86kW
maximum copper losses, but produce dierent torque at that
current level (405 Nm vs 384 Nm). So for a given operating
point of the EM in the base speed area (e.g., 50 Nm, 1000 rpm),
the V-Shape requires less current and, hence, produces fewer
copper losses than the Straight type.
e losses are calculated with the Jordan model, which
considers the eddy current losses Pe (in W) (Equation 5) and
hysteresis losses Ph (in W) (Equation 6).
Pk
fB
ee gap
=22
ˆ
Eq. (5)
Pk
fB
hhgap
=ˆ2
Eq. (6)
where ke and kh represent material-dependent coecients with
no unit. With the used iron material (see Table A .1 in the
Appendix), ke=0.22 and kh=9.5. f represents the fundamental
wave of the electrical frequency in hertz (Hz) and
ˆ
Bgap
the peak
air gap ux density in T. e nite element soware performs
a Fourier transformation of the ux density curve and calcu-
lates the losses for each frequency. For each nite element of
the machine geometry, the losses are independently ca lculated
and summed up to the overall losses.
Figure 12 shows the efficiency diagrams of the Spoke
type (left) and the Straight type (right). Between those
two rotors, the most differences in efficiency could
beobserved.
e results of the eciency evaluation show that the
main eciency dierences occur in the high-speed area,
towards which the eciency of the Spoke type drastically
drops, whereas the eciency of the U-Shape stays high. is
is expected since, in the base speed area, the copper losses
dominate, which are—as explained—almost equal. In the
high-speed area, in turn, the iron losses dominate, and the
ux shape strongly determines the amount of iron losses.
Since the Spoke type has an unfavorable ux shape with a
high THD value versus the U-Shape (cf. Section 5.2), the
iron losses are much higher at high speeds. e higher iron
losses result in a significant efficiency difference at
high speeds.
An overview of the losses and eciencies of all rotor ty pes
at dierent operating conditions is provided in Table 7.
e Spoke type and V-Shape have a slight advantage in
terms of eciency at high torques and low speeds, which
make them specically suitable for urban driving applica-
tions. On the other hand, the U-Shape shows a much better
efficiency at rotational speeds greater than 4000 rpm,
appearing as the most suitable candidate for extra-urban
driving environments.
 FIGURE 11  Maximum displacement (left) and von Mises stress (right) of the V-Shape at its critical rotor speed of 8367rpm.
© The Auth ors
TABLE 6 Comparison of the critical rotor speeds for the investigated rotor designs.
Rotor type V-Shape Straight U-Shape Spoke Spoke+Straight
Critical rotor speed 8366.84 6343.72 8808.67 2319.24 12,359.61
© The Auth ors
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12 Hemsen et al. / SAE Int. J. Elect. Veh. / Volume 10, Issue 2, 2021
5.6.  Real-Driving Energy
Consumption
For the energy consumption analysis in dierent driving
scenarios, a sophisticated Simulink model developed and
verified at the Institute for Automotive Engineering of
RWTH Aachen University is used. With the vehicle param-
eters (Table 8), the drive cycles (Fi g u re 14), and the herein
calculated eciency map, the energy consumption from the
battery of the vehicle can beevaluated, as shown in Figu re 13.
e vehicle specications employed in the simulation
process and shown in Ta ble 8 are derived mainly from the
electric light-duty vehicle employed in [9]. e battery is
derived from the 2013 Nissan Leaf 24kWh Li-ion battery, and
the specications of the electric motor correspond to the one
mentioned in Chapter 6. e ratio of the gearbox (including
dierential) was adapted so that, with the maximum rated
speed of the basic electric motor of 6000rpm [11], the vehicle
is able to drive 130 km/h.
Two driving cycles are simulated: the UDDS or FTP-72
and the HWFET. e UDDS represents urban driving with
23 start-stop cycles and an average speed of 31.5 km/h, whereas
the HWFET represents moderate highway driving with an
average speed of 77 km/h and a peak speed of 97 km/h with
a total duration of 765 s and a 16.45km route.
e results of the investigation can be seen in Table 9.
From the investigation on the vehicle energy consumption in
the two dierent scenarios, it can beobserved that with the
V-Shape rotor design, the vehicle has the best energ y consump-
tion in urban as well as in the highway scenario. However, it
is closely followed by the other three rotor designs, which have
a little more losses, but the dierence is negligible. e Spoke-
type rotor design has a dierent characteristic: it produces
much more losses in the urban scenario as well as in the
highway scenario and can eciency-wise beconsidered as the
worst geometry. Additionally, as stated in Section 5.4.2, the
allowed rotational speed of the Spoke type is theoretically not
sucient for the drive cycle. Improving the mechanical resil-
ience of the Spoke type would likely result in even bigger losses
and a bigger gap between the Spoke type and the other designs.
e evolution of cumulated energy consumption over the
cycle profile is displayed in Figure 15 below. For the
Efficency of Spoke-type EM
 FIGURE 12  Machines with the most significant eciency dierences. Left: Spoke type, Right: U-Shape.
© The Auth ors
TABLE 7 Losses and eciencies of the rotor types.
Rotor type V-Shape Straight U-Shape Spoke Spoke+Straight
Peak eciency [%] 95.7 95.9 95.8 95.4 95.6
Eciency in field weakening [%]
(6000 rpm, 50 Nm)
92.8 93.2 93.6 89.7 92.8
Eciency in base speed [%]
(1090 rpm, 300 Nm
85.7 83.0 82.1 85.5 83.7
Maximum copper losses [kW] 14.9
Maximum iron losses [kW] 1.2 0.99 0.85 2.5 0.96
© The Auth ors
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Hemsen et al. / SAE Int. J. Elect. Veh. / Volume 10, Issue 2, 2021 13
readability, only the best and worst geometries are shown, the
others lie in between.
e highest energy consumption of the Spoke-type EM,
as mentioned in Tabl e 9, is clearly visible here. It can
beobserved that the two curves diverge over the complete
cycle but that the divergence becomes more signicant in
segments with high speed, particularly, in the HWFET (begin-
ning in time 1370 second). is is in line with the ndings in
Chapter 7.4, where it was shown that the eciencies are most
dierent in the eld-weakening area where iron losses have a
high importance. In the base speed area, the eciencies do
not dier signicantly due to the identical stator and windings
for all rotor designs.
Figur e 16 below shows the operation points of the Spoke-
type EM during UDDS (le) and of the V-Shape EM during
HWFET (right). e size of the circles represents the operation
duration in that area. It becomes evident that the eld-weak-
ening eciency is more important for the HWFET than for
the UDDS cycle as the operation points lie at higher speeds.
Furthermore, the slight advantage in the eciency at high
torques and low rotational speeds shown by the Spoke-type
PMSM cannot beexploited and does not represent a factor,
since the maximum required torque in the analyzed cycles is
inferior to the 20% of the maximum EM torque. us the
Spoke-type motor does not possess any advantage with regard
to the energy consumption in the driving cycle simulation.
TABLE 8 Vehicle parameters for the drive cycle simulation.
Wheel radius 0.265 m
Vehicle mass 950 kg
Mass correction coecient 1.04
Rolling resistance coecient 0.011
Aerodynamic drag coecient 0.4
Vehicle frontal area 2.14 m2
Dierential gear ratio (fixed) 4.61
Inverter eciency (ideal) 100 %
Battery capacity 24 kWh
Battery charge and discharge eciency 95 %
Nominal battery voltage 360 V
Average auxiliary power during driving 250 W
© The Auth ors
 FIGURE 13  Process of calculation of the drive cycle energy consumption.
© The Auth ors
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14 Hemsen et al. / SAE Int. J. Elect. Veh. / Volume 10, Issue 2, 2021
e spared battery energy when employing the V-Shape
EM with respect to the Spoke-type EM ΔE (no unit) is calcu-
lated according to the following equation, where EVshape/spoke
represents the energy consumption during the cycle of the
respective type in J. ΔE results to 3.4% for the urban cycle,
3.9% for the hig hway cycle, and 3.7% for the combined cycle.
D
E
EE
E
Vshape spoke
spoke
=-
()
Eq. (7)
  Summaryand
Conclusion
The article presents a methodical approach to compare
dierent rotor designs in all their important characteristics.
Here, dierent magnet arrangements in t he rotor are compared
but the same method can beused to compare and optimize
magnet masses, iron bridges, or else. e seen eects of
dierent rotor designs are not only analyzed on the compo-
nent level but also assessed on the vehicle level by means of
longitudinal vehicle simulations. ereby it can beevaluated
how big the eect of dierent rotor designs is on the energy
consumption of a BEV.
It can beshown that the choice of the rotor does play a
role and that especially the Spoke-type rotor provides dierent
characteristics than the other shapes. is is due to the special
ux concentration in the air gap, producing very high torque
but also high THD and, therefore, high iron losses.
Tab le 10 provides an assessment of all investigated rotor
designs in terms of their characteristics, where the range is
from very good (“++”) over neutral (“o”) to very bad (“−−”).
e best geometry in its class receives the rating “++” whereas
the worst geometry receives “−−.” e other geometries
receive their rating according to t heir relative position bet ween
the best and the worst value. It should benoted here that low
losses are considered to beof high importance, being repre-
sented by the last three ratings and, thus, having relatively
high weight.
As can beseen, all types have their advantages and disad-
vantages without one design standing out very much.
Summing up the ratings of each design reveals the V-Shape
slightly leading the ranking.
In terms of overall eciency and energy consumption,
the V-Shape is the best due to its good efficiency in the
UDDS HWFET
Time [s]
Speed [km/h]
 FIGURE 14  Cycles to besimulated regarding energy consumption.
© The Auth ors
TABLE 9 Vehicle energy consumption from the traction battery including recuperation in the investigated cycles.
V-Shape Straight U-Shape Spoke Spoke+Straight
Vehicle energy consumption
urban [kWh/100 km]
8.83 8.91 8.91 9.14 8.92
Vehicle energy consumption
highway [kWh/100 km]
12.23 12.28 12.24 12.73 12.27
Vehicle energy consumption
mixed [kWh/100 km]
10.75 10.82 10.79 11.17 10.81
© The Auth ors
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15
C
V
Time [s]
 FIGURE 15  Cumulative energy consumption of the vehicle with V-Shape and. Spoke-type EM in UDDS and HWFET cycles.
© The Auth ors
EM speed [rpm] EM speed [rpm]
 FIGURE 16  Operation points of Spoke-type EM in UDDS (left) and of V-Shape EM in HWFET (right).
© The Auth ors
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16 Hemsen et al. / SAE Int. J. Elect. Veh. / Volume 10, Issue 2, 2021
low-speed area with still an acceptable efficiency at
higher speeds.
e Spoke type provides high power and torque and good
eciency at low speeds. In combination with the low critical
rotor speed, this type is particularly applicable in lower speed
applications and for high vehicle weights. However, when
shiing part of the material to other locations, for example,
as a straight magnet between the spokes as done here, the
centrifugal forces are absorbed better and the mechanical
stress is lowered. Here, the Spoke+Straight type even oers
the highest critical rotor speed of over 12,000rpm.
e U-Shape rotor leads to the best noise characteristic
among the investigated designs, but has lower torque and
power than the other types.
e Straight type is the most versatile rotor design, having
no very bad characteristic and a good overall rating. At the
same time, the design is the simplest one, meaning it can more
easily beoptimized, manufacturing is simpler, and costs li kely
a little lower than for the other designs.
It shall bealso noted here that each of the rotor designs
can possibly beoptimized to perform better or worse in each
of the investigated performance criteria (torque, power, NVH,
etc.). It may hence bepossible that through intensive multicri-
teria optimization like shown in [21, 22], the dierences
between the rotor designs get smaller, which would make the
specic selection of the rotor design according to the use-case
less importa nt. Such intensive multicriteria optimization could
not beperformed here, and hence, the quantication of the
described eect needs to beinvestigated further in the future.
Comparisons between dierent permanent magnet rotor
designs have been made in several previous researches and
studies like [9], [8], and [5], and their results mainly corre-
spond to the ndings here. All of the aforementioned refer-
ences indicate the V-Shape as the best of the designs. [8] states
that the Spoke type has the highest THD in its investigation
and that is also in line with results generated herein. However,
some of the results do not correspond to the previously
presented ones, which is due to the dierences in the geom-
etries. Even with the same magnet arrangements, the geom-
etries in the studies dier from those used here due to the
high number of design variables within each geometry.
Finally, it can beconcluded that the overlap of the gener-
ated results with the literature supports the validity of the
performed simulations. Despite virtual verication of the
simulation environment in previous applications (e.g., in [12]
and [13]), a comparison of the presented results against real
measurements on prototypes of the shown EM designs should
beconsidered in future studies.
Acknowledgments
Funded by the Deutsche Forschungsgemeinscha (DFG,
German Research Foundation) – GRK 1856.
Gefördert durch die Deutsche Forschungsgemeinscha
(DFG) – GRK1856.
e author thanks especially Adrian Herrmann B.Sc.
(RWTH Aachen University) having contributed to this
research and publication with great eort through his nal
thesis at the Institute for Automotive Engineering of RWTH
Aachen University.
Contact Information
For inquiries regarding this or related research please contact
jonas.hemsen@outlook.com
References
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TABLE 10 Overall assessment of the rotor designs.
Rotor type V-Shape Straight U-Shape Spoke Spoke+Straight
Torque + −− ++ o
Power o + −− ++ ++
Power stability o ++ + + −−
Noise + ++ o −−
Critical rotor speed oo−−* ++
Eciency at high speeds o + ++ −− o
Eciency at low speeds ++ −− ++ o
Real driving energy consumption ++ + + −− +
Sum of ratings (−− = 2; ++ = 2) 4 3 0 1 1
*Unacceptable low.
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Appendix
TABLE A.1 Motor data of modelled motor.
General
Stack length 80.6mm
Air gap width 0.73mm
Iron material (stator and rotor) Cogent Hi-Lite NO30
Iron sheet thickness 0.3mm
Magnet and copper temperature 60°C
Stator
Number of slots 48
Yoke radius RA 130mm
Inner radius RI 80.93mm
Slot height H33.5mm
Slot opening height H1 1mm
Slot opening height H2 0mm
Slot width SW 1.93mm
Slot upper radius R1 0.5mm
Slot lower radius R2 5.64mm
Tooth width TW 8.2mm
Rotor
Number of poles 8
Rotor outer radius 80.2mm
Rotor inner radius 55.5mm
Magnet mass 1.196kg
Magnet material BMN-42SH (NdFeB)
Relative permeability 1.05
Remanence flux density 1.17 T
Windings
Number of phases 3
Winding layers 1
Winding factor 0.9659
Turns per coil 9
Coil span 6
Copper fill factor 45%
Coil connection Series
Maximum rms phase voltage 159.2V
Maximum rms phase current 250 A
© The Auth ors
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18
 FIGURE A.1  V-shape geometry.
© The Auth ors
 FIGURE A.2  Straight-type geometry.
© The Auth ors
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19
 FIGURE A.3  Spoke-type geometry.
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 FIGURE A.4  Spoke+Straight type geometry.
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© 202 1 The Authors. Published by SAE International . This Open Access article is publish ed under the terms of the Creative Commons Attribution License (http://
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20 Hemsen et al. / SAE Int. J. Elect. Veh. / Volume 10, Issue 2, 2021
 FIGURE A.5  Multilayer U-shape geometry.
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... This makes the overall methodical approach flexible and adaptable to a variety of use cases. The design of electric machines and inverters is exemplarily presented in [18] and [19]. Currently, the methods can analytically generate PMSM designs based on torque and power requirements [cf. ...
... 20] and optimize these with the help of highfidelity FEM models. The implemented algorithms also allow the assessment and comparison of various motor technologies, e.g., magnet arrangements, as presented in [18]. Suitable inverters with different switch technologies (Si, SiC, GaN) can be designed and modeled for each motor [cf. ...
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The present research gives an overview of the process of designing and building prototypes of electric axles for heavy-duty vehicles at the Institute for Automotive Engineering (ika) of RWTH Aachen University. This overview starts with a brief presentation on the road transport and logistics industry. The expected growth of this market motivates - together with legislative regulations on tailpipe emissions - the development of electrically driven trucks. Thus, future trucks that have a powertrain containing one or more inverters, electric machines, and transmissions. A methodical approach to designing and evaluating electric powertrains is explained in the following. Within the developed methodology, powertrain concepts can be evaluated on the vehicle level in longitudinal simulations. By this approach, the energy demand of the vehicle may be derived and compared to different powertrain concepts for the exact vehicle. The presented approach was used to develop and build a prototype of an electric powertrain for a heavy-duty truck. The process and its results are presented, starting with a transmission synthesis followed by the validation of thermal simulations with measurement data of a developed prototype. The resulting axle comprises two gears in one transmission part and a fixed ratio in the other part. It is propelled by two electric machines, one with a lower power of 125 kW and one with a higher power of 250 kW, which can be used individually or combined. The paper closes with an outlook on current projects at ika concerning the electrification of heavy-duty trucks. The projects have broadened the field of research from focusing on the powertrain level to analyzing alternative power supplies such as overhead-line systems and developing innovative drive systems with purpose-designed chassis to break up historical boundaries of conventionally propelled trucks such as rigid axle bridges.
... In the following, the design of the gearbox is described in detail. The approach implemented within the holistic methodology for the dimensioning of the electric machine is described in detail in [14]. ...
... J. 2022, 13, x FOR PEER REVIEW 3 of 15 described in detail. The approach implemented within the holistic methodology for the dimensioning of the electric machine is described in detail in [14]. For the design of the gearbox, each parameter set of the holistic model is processed individually. ...
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