Halbach Array for an In-Wheel Traction Motor
I. Martinez Ocaña1, N. J. Baker1, B. C. Mecrow1, C. Hilton2, S. Brockway2
Abstract 1 - This paper compares a Halbach array to a
more conventional surface mounted permanent magnet
arrangement for an in wheel traction motor. Demagnetisation,
physical air-gap and torque capability at continuous and
overload operation is considered. Without increasing the
machine operating space, using one transition per pole was
found to increase rated torque by 5% and overload torque by
3%. A second comparison was done using 3 transitions per
pole and this topology was found to give an increase in the
overload torque of 4%. Finally, a novel trapezoidal Halbach
array arrangement has been proposed to reduce the
demagnetisation of the transition magnets and increase their
permeance coefficient.
performance [4]. This paper considers replacing the existing
surface mounted rotor topology with permanent magnets
arranged in a Halbach array.
Halbach arrays have previously been proposed as traction
motors for a solar powered electric vehicle in [5], [6] and
[7] and for aerospace traction in [8]. Both design and
demagnetisation of the permanent magnets is studied in the
latter.
This paper will investigate a rotor design using Halbach
array and compare predicted torque capability against the
surface mounted Reference Machine (RM). In addition the
effect of physical air-gap and demagnetization of the
topologies will be discussed.
Index Terms – Halbach array, In-wheel, Permanent
magnets, trapezoidal.
T
I.
II.
THE REFERENCE MACHINE
The reference design shown in Fig. 2 is an existing outer
rotor surface mounted permanent magnet machine [1]. This
machine has been manufactured and extensively tested both
on dynamometers and in road vehicles. Hence it is well
characterised. Per-unit values of torque are scaled to this
machine. The Reference Machine produces very high torque
density, but it is insightful to investigate whether other
topologies can be even more torque dense. Two critical
points of operation have been chosen for design
comparison: continuous steady state and short term
overload.
Dimensions of the proposed machines are constrained by
the stator inner diameter and rotor outer diameter of the
actual Reference Machine as well as the overall stack length
– all fixed by the wheel size. The stator design of the
proposed topologies has not been altered and only changes
in the rotor design are considered here. Design constraints
are shown in Table 1.
INTRODUCTION
he development of in-wheel motors has increased in
recent years as a way of providing direct drive
transmission in electric vehicles. By building the motor
directly in the wheel, classical automotive components such
as drive shafts, gears and differentials can be eliminated
with a potential increase in the reliability of the system, see
Fig. 1. Although the in-wheel motor increases the vehicle
unsprung mass, this causes minimal steering and handling
issues if the suspension system is designed to suit, whilst
the removal of other components gives overall efficiency,
weight and complexity gains. Control using true torque
vectoring at each wheel, electronic differential, traction
control and more efficient regeneration braking are inherent
and usually software controlled. In addition, the integration
of motor and inverter into the wheel also frees yet more
space in the vehicle to be used in other ways.
TABLE 1
DESIGN CONSTRAINS
Fig. 1:
320
Discontinuous DC voltage supply [V]
400
Base speed [rpm]
Top speed [rpm]
800
1600
The Reference Machine operates at a nominal speed of
800 rpm with a maximum speed of 1600 rpm. Maximum
torque at overload condition is double that at continuous
operation.
Protean integrated drive
This work is focused on the increase of torque density of
the in-wheel motor. Previous work on this machine has been
related to cost reduction [1], demagnetization analysis [2],
torque density improvement [3] and fault tolerant
III. ONE TRANSITION HALBACH ARRAY
In this section, a Halbach array model using one
transition magnet per pole is investigated. Following a
parametrized design study, the most promising designs have
been compared against the Reference Machine for different
air-gap lengths and at the two operating points,
corresponding to continuous operation (30Apk) and short
term overload (79Apk). Simulations have been performed in
This work has been supported by Protean Electric Ltd.
All FEA simulations have been done using the software JMAG Designer.
1
School of Engineering, Newcastle University, Newcastle upon Tyne,
United Kingdom
2
Protean Electric Limited, Farnham, Surrey, United Kingdom
978-1-5386-2477-7/18/$31.00 ©2018 IEEE
Continuous DC voltage supply [V]
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two dimensional FEA using an irreversible material so any
effect of demagnetisation of the magnets is included on the
torque predictions. For this initial study, the temperature of
the magnet material has been set to 20℃ to get an overall
impression of the torque capability of the Halbach array. In
addition the permanent magnet material mass has been kept
constant for all the machines. The Reference Machine uses
NdFeB magnets with an energy product higher than
40MGOe.
Fig. 4: Alteration of kw in the Halbach array design for different air-gaps
at 20℃, continuous operation
The demagnetisation shown indicates the percentage of
magnet material that is demagnetised by more than 1%.
This doesn’t mean that the whole area has completely lost
demagnetisation but that there might be smaller areas which
have.
Fig. 2: 2D model of the Reference Machine (RM)
Torque [p.u.]
In the Reference Machine, physical air-gap variation was
investigated by maintaining the permanent magnet height
and reducing the thickness of the rotor core back, hence
altering the air-gap without altering the volume of the
permanent magnets. In the Halbach configuration, the
permanent magnet height has been adjusted so the total
amount of magnet material is constant and equal to that in
the Reference Machine, regardless of air-gap length. The
width of the pole is determined by the parameter kw, as
defined in Fig. 3. This parameter was altered from 0.5 to
0.9. As values of kw less than 0.5 produce much poorer
performance, only values of kw > 0.5 were used.
Fig. 5:
Fig. 3:
Torque vs air-gap length for continuous operation at 80℃
Fig. 5 shows that, as expected for a kw = 0.7, higher rated
torque than the Reference Machine can be achieved at 80℃.
Although a Halbach array with a kw of 0.8 seem to obtain
higher torques than the Reference Machine at 20℃, due to
demagnetisation this is not met at realistic operating
conditions. All three models have the same magnet height,
however transition magnets for kw = 0.8 and kw = 0.9 are
quite small, which reduces the magnet operating point,
making it more susceptible to demagnetisation, which can
be seen in Fig. 6.
Pole pitch Halbach array
As shown in Fig. 4, using a Halbach array allows an
increase in the air-gap length of more than 20% whilst
giving the same rated torque as the original surface mounted
design. Continuous torque results take into account
demagnetisation and the anticipated operation temperature
of 80℃ for the magnets and are shown in Fig. 5
Demagnetisation simulations have also been undertaken at
125℃ for overload condition and they are compared in
terms of torque and demagnetised magnet area in Fig. 6 and
Fig. 7. The models include an irreversible material, hence
when the operation point of the magnet reaches the “knee”
on the BH curve, it recovers back in the recoil curve
(parallel to BH curve) and shows a loss in magnetisation.
Computed torque includes this non linearity of the material.
When simulating demagnetisation of the Reference
Machine, there was no loss in performance at continuous
operation for any air-gap. This indicates that the magnets
are working at a point which is adequate for this
temperature.
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3%
RM
k w = 0.7
2.5%
k w = 0.8
Demagnetised area [%]
Demagnetised area [%]
k w = 0.9
2%
1.5%
1%
0.5%
0%
Fig. 6:
1
1.2
1.4
1.6
Air gap [p.u.]
1.8
2
Fig. 8:
Demagnetised area vs air-gap length in overload at 125℃
Demagnetised area vs air-gap for continuous operation at 80℃
IV. THREE TRANSITION HALBACH ARRAY
Torque [p.u.]
An alternative to the single transition Halbach
configuration is the use of more transition magnets to
generate a more sinusoidal air-gap flux density as the
change in direction of magnetism within the magnets
occursa in a more gradual manner. As torque can be
expressed as:
Fig. 7:
(1)
In order to increase torque, as current loading (Â), axial
length (l), and rotor diameter (D) are fixed, only by
increasing the air-gap flux density (B̂ g) the torque can be
increased. Introducing more transitions increases the peak
flux density in the gap (B̂ g) as shown in Fig. 9. A Fourier
analysis reveals an increment of 8.8% in fundamental airgap flux density. As flux is better distributed, there is a
reduction in space harmonics, which creates a more
sinusoidal flux density distribution in the air-gap as seen in
Fig. 10.
Torque vs air-gap length in overload operation at 125℃
At overload condition, kw = 0.7 is still the topology that
can deliver the highest torque. According to Fig. 7, the
Halbach array topologies offer a better torque capability
than the Reference Machine at overload conditions.
In summary, the use of Halbach arrays could be
beneficial for either obtaining higher torque or maintaining
the torque developed by the Reference Machine but with an
increase in the air-gap, which is beneficial for estimating the
bearing tolerances and other mechanical aspects including
eccentricity and other manufacturing issues. On the other
hand these Halbach array topologies offer higher
demagnetisation than the Reference Machine, as can be
seen in Fig. 8. If no demagnetisation was occurring, higher
torques could be obtained with this topology.
Fig. 9:
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Flux density in the air-gap for Halbach topologies
Demagnetised area [%]
Flux density [T]
the equal segment model has a constant demagnetisation for
the increase of air-gap length. However the unequal
segment model has a better performance at air-gaps lower
than 1.4 p.u, as shown in Fig. 12. Both suffer less
demagnetisation than the one segment topology.
Introducing more transitions reduces the rate of change
between the segments direction of magnetisation (DOM).
With fewer opposing magnetic domains between the
segments the permeance coefficient is increased.
Fig. 10: Harmonic distribution of the Flux density in the gap for studied
topologies
For this topology two models were used. In the first
model, named the equal segment model, the pole-magnets
and transition magnets are the same size. In the second
model, termed, the unequal segment model, the transition
magnets are the same size but the pole magnets are larger,
as defined in Fig. 11. By increasing the width of the pole
magnet, B̂ g can be increased further.
Fig. 12: Demagnetisation comparison in continuous operation at 80℃
Fig. 13 shows that in overload operation, however, the
unequal segment model has a lower demagnetisation than
the equal segment model due to the bigger size of the pole
magnet, which suffers less demagnetisation than the
transitions. In the equal segment model, pole and transitions
get demagnetised in a similar manner as they are all the
same size.
Fig. 11: Three transitions Halbach array topologies (equal segment model
on the left and unequal segment model on the right)
The results are compared in Table 2, which shows that
the use of three transitions with equal segment size is of no
benefit compared to the use of only one transition.
However, in the unequal segment model, higher torque is
obtained for both continuous and the overload condition.
TABLE 2
TORQUE INCREASE COMPARISON AGAINST RM
equal segment
model
Airgap
[p.u.]
1
1.2
1.4
1.6
1.8
2
Conti
nuous
Overl
oad
4%
4%
4%
4%
4%
4%
1%
1%
1%
0%
0%
0%
unequal
segment
model
Conti Over
nuous load
5%
5%
6%
6%
6%
6%
4%
4%
4%
4%
4%
4%
One transition
kw = 0.7
Conti
nuous
Over
load
5%
5%
5%
5%
5%
5%
3%
4%
4%
4%
3%
3%
Fig. 13: Demagnetisation comparison in overload operation at 125℃
V.
OVERCOMING DEMAGNETISATION
One of the main concerns with Halbach array is the high
demagnetisation due to the proximity of magnets with
different polarities, hence other alternatives need to be
investigated. Demagnetisation occurs due to the low
operating point of the magnet with some areas working
below the “knee point”. When the magnet works below this
position, it cannot recover its remanence to the original
The amount of permanent magnet material that is
demagnetised is reduced by the use of three transitions. The
magnets work at a higher operational point, further away
from the “knee” of the BH curve. At continuous operation,
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value, losing magnetisation. To try and resolve this issue, a
new topology using trapezoidal magnets is investigated.
The use of trapezoidal magnets in a Halbach array is not
a new concept in itself, as it has been used before in other
applications such as “fridge magnets” and linear actuators
[9]. However, according to the literature, it has not
previously been used in the rotor of a PMSM.
By using trapezoidal magnets with a certain wall angle,
more areas of the transition magnet work with a higher
permeance coefficient, i.e. at higher operational points and
hence less demagnetisation could occur.
Fig. 14: Two poles trapezoidal Halbach array
Fig. 14 shows a linear set of pole pairs consisting of
trapezoidal magnets arranged in a Halbach array. Each pole
magnet is separated by one transition magnet, where the
angle between magnet walls is β and the angle of the change
in direction of magnetisation across a wall is αc. The angle
αc will depend on the number of transitions per pole and can
be found using (2), being ns the number of segments per
pole (pole and transitions). When using one transition, 2
segments are used, hence αc = 90°.
(2)
Fig. 15: Flux density in square Halbach array (top) and trapezoidal
(bottom) Bknee = 0.3T in a linearized model
Demagnetised area [%]
If the direction of magnetisation of transition and pole
magnets approaches the magnet wall with the same angle,
the magnet will be working at a higher operating point. The
angle β required to satisfy this requirement can be
calculated using (3). In this one transition example, β will
have a value of β = 90°.
(3)
Demagnetised area [%]
The magnet material used in the Reference Machine has
the “knee point” at 0.3T when operating at 125℃. Fig. 15
shows the flux density in a square Halbach array and in a
trapezoidal Halbach array. The area in purple shows where
the flux density is below the knee point, and hence the area
affected by demagnetisation. As it is shown, trapezoidal
magnets have a much smaller section working below the
knee point.
To study this behaviour in the actual geometry, the
trapezoidal geometry has been compared to the kw = 0.7
single transition model and a model using kw = 0.5.
Although kw = 0.5 couldn’t give the desired torque as shown
previously, it represents a rotor with same size square pole
and transition magnets. The magnet walls have been
constrained to the adequate β angle in the trapezoidal
topology. In addition, these models are compared against
the Reference Machine in Fig. 16 and Fig. 17. A
comparison with the 3 transition was intended to be done,
however, due to the geometrical constraint a model using 3
transitions and trapezoidal magnets is not physically
possible. As the number of transitions increases, the angle β
increases as well, making it impossible to keep the same
permanent magnet weight.
Fig. 16: Demagnetisation area comparison at continuous operation (top)
and overload (bottom)
Demagnetisation results in Fig. 16 show that the
trapezoidal
magnet
configuration
offers
lower
demagnetisation than the square magnet and the rectangular
pole one transition topology at rated current. At overload
the trapezoidal has the lowest demagnetisation of all
machines.
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VI. CONCLUSION
Torque [p.u.]
Torque [p.u.]
For a fixed volume of permanent magnet material,
compared to the surface mounted machine, an increase in
torque of 5% at continuous operation or 3% at overload can
be achieved by using a single transition magnet Halbach
array. Alternatively the same torque can be produced with a
20% air-gap increase, allowing for better tolerances for
mechanical constraints.
Using a three transitions Halbach array leads to very
similar torque achievements, with a 5% torque increase in
continuous operation and 4% in overload by having bigger
pole than transition magnets. If increasing the torque is not
intended, then again the air-gap distance can be increased
by 20% while maintaining the torque for both topologies.
A method has been introduced to reduce demagnetisation
in Halbach arrays using trapezoidal magnets. By reducing
the incident direction of magnetisation angle against the
segments sides, this increases the permeance coefficient of
the magnet and hence its operational point, having less area
under the “knee” of the BH curve. This greatly reduces the
overall demagnetised area both in continuous operation and
overload, but doesn’t gives any significant improvements in
torque.
The topologies compared in this paper have been
proposed for a very specific application with high
geometrical constraints. Future work could be done using
this topologies in a different application and with different
working conditions.
For this application the use of a Halbach array with a kw =
0.7 or the unequal segment model are good alternatives to
the Reference Machine. Although both topologies suffer
from demagnetisation, the produced torque is still higher
than that of the Reference Machine.
Fig. 17: Torque comparison at continuous operation (top) and overload
(bottom)
VII.
[1]
[2]
[3]
Fig. 18: Demagnetisation in square magnets (top) vs trapezoidal magnets
(bottom) at overload condition
[4]
In terms of torque development, the trapezoidal magnet
configuration does not produce as much torque as the
square magnet topology, as seen in Fig. 17, as it has a lower
peak gap flux density (B̂ g).
[5]
[6]
The use of trapezoidal magnets in a Halbach array can´t
give the same torque performance as using rectangular
magnets in the adequate height to length ratio. However, the
permanent magnet works in a much more secure
environment when high fields or high temperatures occur.
This trapezoidal configuration allows a more distributed
permance across the magnet, resulting in using more
effective the magnet material. The comparison in Fig. 18
clearly shows the demagnetised area in the square magnets
with kw = 0.5, which reaches almost 10% of the total
permanent magnet area, while this demagnetisation is less
than 1% for the trapezoidal Halbach array.
[7]
[8]
[9]
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VIII.
BIOGRAPHIES
Iago Martinez Ocaña received the B.Eng. (Hons) in Electrical and
Electronic Engineering in Glyndwr University, Wrexham, UK, in 2013 and
the Technical Industrial Engineering in Industrial Electronics in Alcalá de
236
Henares University, Alcalá de Henares, Spain, in the same year. He
received as well the M.Sc in Electrical Power in Newcastle University in
2014. He is currently pursuing the Ph.D. degree with the Electrical Power
group at Newcastle University, Newcastle upon Tyne, UK. He has been
working as an electromagnetic design engineer and has been involved in
the Innovate UK project A.E.M.T.A. designing actuators for aerospace
applications. His current research interests include in-wheel motors,
permanent magnet machines and permanent magnet materials and
assemblies.
Nick J. Baker received the M.Eng. degree in mechanical engineering from
the University of Birmingham, Birmingham, U.K., in 1999, and the Ph.D.
degree in electrical machine design from Durham University, Durham,
U.K., in 2003. He is currently a Lecturer with the Electrical Power Group,
Newcastle University, Newcastle upon Tyne, U.K. He is a Machine
Designer with research projects across the automotive, aerospace, and
renewable energy sectors.
Barrie Mecrow is Professor of Electrical Power Engineering at Newcastle
University, UK. His research interests include fault tolerant drives, high
performance PM machines and novel switched reluctance drives. He is
actively involved with industry in the aerospace, automotive and consumer
product sectors, who fund a large range of projects. Barrie commenced his
career as a turbo-generator design engineer with NEI Parsons, England. He
became a lecturer at the University of Newcastle in 1987 and a professor in
1998. In addition to his research interests he cares passionately about
provision of high quality electrical engineering education in UK
universities.
Chris Hilton is the Chief Technology Officer at Protean Electric having
previously held roles in the fields of communications electronics, satellite
navigation and particle physics research. He holds a PhD in physics from
the University of Manchester and a master's degree in mathematics from
the University of Cambridge, UK.
Simon Brockway is the Advanced Motor Research Manager at Protean
Electric Ltd. He has more than 30 years' experience in permanent magnet
electrical machine design and managing multi-disciplined engineering and
product development teams. Having graduated in 1985 with a BSc (Hons)
in Electrical & Electronic Engineering at Portsmouth Polytechnic he has
been a developer of in-wheel motor technology since the mid 1990's.
Apprentice trained he has experience in the servo, domestic appliance and
automotive sectors having worked in low and high volume manufacturing,
contractual research and start-up organisations.
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