Novel High-Speed, Lorentz-Type, Slotless Self-Bearing Motor

Novel High-Speed, Lorentz-Type, Slotless Self-
Bearing Motor
T.I. Baumgartner, A. Looser, C. Zwyssig, and J.W. Kolar
Power Electronic Systems Laboratory
ETH Zurich
CH-8092 Zurich, Switzerland
baumgartner@lem.ee.ethz.ch
Abstract — Active magnetic bearings are a preferred choice for
supporting rotors spinning at high-speed due to low friction
losses and no wear. However, the rotational speed in previous
bearing topologies has been limited by complex rotor
constructions, high rotor losses, or position control instabilities at
high speed. This paper presents a novel Lorentz-type, slotless
self-bearing motor concept which overcomes most limitations of
previously presented high-speed AMBs. An analytical model for
motor torque and bearing forces is presented and a design for
500 000 rpm is verified with FE simulations, showing
exceptionally low negative stiffness cross coupling. Finally, a
prototype system is described.
I. INTRODUCTION
Ultra-high-speed electrical drive systems are developed for
new emerging applications, such as generators/starters for
micro gas turbines, turbo-compressor systems, drills for medical
applications, and spindles for machining and optical
applications. Typically, the power ratings of these applications
range from a few watts to a few kilowatts, and the speeds from
a few tens of thousands of rpm up to a million rpm, which
results in machine rotor diameters in the Millimeter area [1].
The biggest remaining challenge is a bearing that can support
such rotors with low losses and a long lifetime. The active
magnetic bearing (AMB) is a preferred choice due to the
contactless operation which leads to low friction losses and no
wear, the ability to operate in vacuum, and the controllability
which allows for cancellation or damping of instabilities.
There are several feasibility studies and theoretical designs
for high-speed magnetic bearings, such as a 500 000 rpm
homopolar AMB concept in [2] and a comparison of long and
short AMB rotors in [3]. However, there are only few
publications with experimental results. [4] achieved a speed of
64 000 rpm with a heteropolar bearing and a homopolar
bearing in [5] ran at 120 000 rpm.
To the authors knowledge no AMB presented in literature
has achieved rotational speeds above 120 000 rpm, the biggest
challenges are the high rotor losses, the disintegration of the
rotor due to a complex rotor structure, and instabilities due to
high frequency excitation and limited controller bandwidth.
Therefore, in this paper, a novel slotless self-bearing motor
topology (Figure 1) is presented allowing for ultra-high speed
operation. It overcomes most of the limitations of previously
presented high-speed AMBs, which are usually due to the
bearing topology. The novel bearing is analyzed analytically,
and a design for 500 000 rpm is verified with FE simulations.
II. NOVEL SELF-BEARING MOTOR
The basic concept of a self-bearing (also called
bearingless) motor has been presented in 0 for a reluctance
motor and has been adopted for slotted permanent-magnet
motors in [7] and for a slice motor in [8]. There have been a
few attempts for high-speed self-bearing motors, and in [9] a
speed of 60 000 rpm has been achieved.
An early reference to a Lorentz-type bearing can be found
in [10], slotless Lorentz-type bearing prototypes have been
presented in [11] for positioning applications and in [12] for
mirrors in laser applications. [13] is the first to mention the
high-speed potential of a slotless self-bearing motor, although
the prototype presented rotates at only 5 000 rpm.
The magnetic bearing concept presented in this paper is
based on the electric machine concept presented in [14]. With
a different winding design, forces in x and y direction can be
generated beside the torque in direction of the z-axis. In order
to levitate a long rotor, two separate bearing windings
separated in z direction are required.
y
Motor winding
Bearing winding
Stator core
Air gap
Permanent magnet
r
θ
R 1
R Fw1
R Fw2
R 2
R 4
R 5
Sleeve
Figure 1. Machine cross-section and symbol definitions: diametrically
magnetized cylindrical permanent magnet rotor inside a slotless stator with
separate bearing and motor winding.
x
978-1-4244-5287-3/10/$26.00 ©2010 IEEE 3971

This concept has several advantages for high-speed
operation. The rotor consists of a diametrically magnetized,
two-pole ( p M = 1) cylindrical permanent magnet encased in a
nonmagnetic sleeve. Mechanically, this rotor construction
allows for highest rotational speeds even with large rotor
diameters. Furthermore, the slotless air-gap winding has
several advantages for high-speed operation: no slotting
harmonics in the air-gap field, which in other AMB topologies
lead to large eddy-current losses in the rotor, a constant
magnetic air-gap and a high rotational symmetry leading to
linear forces. With a thick winding the magnetic air-gap
between rotor magnet and stator iron can be made large such
that a very low negative stiffness results, which reduces the
position control complexity. Furthermore, a large magnetic
air-gap leads to a low inductivity, which allows for high
dynamics in current control which is required at high
rotational speeds. Finally, the magnetic flux density in the
stator iron will be low and therefore also the iron losses.
The motor winding for the torque generation has the same
number of pole-pairs ( pT = pM
) as the rotor, whereas the
bearing winding has to be pF
= pM
+ / − 1 according to [15].
In the concept presented here the pole-pair of the bearing
winding is chosen to be p F = 2 in order to achieve the lowest
possible fundamental frequency. The two windings can be
combined or separated as shown in Figure 1. In electric
machines the large stray fields in a slotless machine not
entering the stator iron are a disadvantage. This changes to an
advantage in the self-bearing motor as these stray fields add to
the bearing force. Due to that, if the windings are separated,
the bearing winding should be placed on the inner side where
the stray field is larger, and the torque winding should be
placed on the outer side where the moment arm is longer.
Beside the many advantages, there are also a few
drawbacks of the presented topology. As in all self-bearing
motors the bearing currents are depending on the rotor angle
for a constant force in one direction. Therefore, firstly the
rotor angle is required and secondly, the bearing currents show
a fundamental frequency depending on the rotational speed n,
in this topology ( pT
= pM
= 1 p 2 , F = ) it is n /60. This
leads to the requirement of high inverter dynamics, a fast
transformation between stationary and rotating reference
frames, and angle and current measurements with a high
accuracy and a bandwidth depending on the rotational
frequency. Furthermore, the achievable bearing forces are
small compared to other AMBs with the same rotor radius and
length. However, the limited force is not degrading the control
stability, as it comes along with a very low negative stiffness
as mentioned before. A further disadvantage is that the bearing
forces are applied in the axial center of the bearing winding,
penalizing the rotor dynamic design, ideally they should act on
each end of the rotor.
III. ANALYTICAL CALCULATIONS
The following discussion of the magnetic field is based on
the magnetostatic analytic field solution as in [16] and [14] for
a permanent magnet with pole-pair number p M = 1. In
cylindrical coordinates ( r, θ , z)
the magnetic field in the nonferromagnetic
region ( R1 < r < R4)
is given by
B
⎡
2
4
2 1 ⎛R
⎞
r = KB ⎢ + ⎥ cos − M
⎢⎣
⎜
⎝
⎤
r
⎟
⎠ ⎥⎦
( θ ϕ )
, (1)
⎡ 2
4
2 1 ⎛R
⎞ ⎤
Bθ =−KB
⎢ −⎜
⎥ sin ( θ −ϕM
)
r
⎟
⎢ ⎝ ⎠ ⎥
. (2)
⎣ ⎦
The constants K B2
and R 4 are defined according to [14]. ϕ M
is the pole orientation of the permanent magnet. It is assumed
that the axial component of the magnetic flux density B z is
very small and can therefore be neglected. This assumption is
valid when the active length of the motor L is large compared
to its diameter. Furthermore, it is assumed that the magnetic
field resulting from winding currents is small compared to the
permanent-magnet field and can be omitted as well. The
Lorentz-force and the torque density are given by
dFk
jk
B
dV = ×
, (3)
dM
k ⎛dFk
⎞
= a ×
dV
⎜
dV
⎟ , (4)
⎝ ⎠
where j k is the winding current density in z direction The
current density is constant over a winding segment k . a is the
local position vector. The total Lorentz-force and torque on the
rotor can be calculated by integration of the densities over the
volume of each winding segment and summation over all
segments as shown in (5) and (6).
K L/2
Rw2
θk,2
⎛dFk
⎞
F = ∑ ∫ ∫ ∫ ⎜ rdθ
drdz
dV
⎟
⎝ ⎠
k = 1 z=− L/2
r= Rw1 θ=
θk,1
K L/2
Rw2
θk
,2
⎛dM
k ⎞
M = ∑ ∫ ∫ ∫ ⎜ rdθ
drdz
dV
⎟
⎝ ⎠
k = 1 z=− L/2
r= Rw1 θ=
θk,1
A. Motor winding
In order to generate a motor torque on the rotor, a one
pole-pair, three-phase air-gap winding ( p T = 1, K = 6 ) is
considered. The winding has an inner radius R Tw1
and an
outer radius RTw2
and a copper filling factor k w . A
symmetrical three phase current is defined with a current
density amplitude ˆT j and a phase ϕ T . The force and torque
of this winding can be obtained by solving (5) and (6) in
Cartesian coordinates leading to
⎡0⎤
⎡ 0 ⎤
F
⎢
T 0
⎥ ⎢
⎥
=
⎢ ⎥
, MT = MT
⎢
0
⎥
, (7)
⎢⎣0⎥⎦ ⎢
⎣cos( ϕT
−ϕM
) ⎥
⎦
M ˆ
T = Lkw jT KB2( RTw2 −RTw1)
⋅
(8)
2 2 2
3 R + R + R R + R .
( 4 Tw1 Tw1 Tw2 Tw2)
B. Bearing winding
Radial bearing forces are generated by a two pole-pair,
three-phase winding ( p F = 2 K = 12 ). The winding has an
inner radius of R Fw1
and an outer radius of R Fw2
and a
copper filling factor k w . A symmetrical three phase current is
(5)
(6)
3972

defined with a current density amplitude ˆF j and a phase ϕ F .
The resulting torque and Lorentz force is given by
⎡ sin ( ϕF
−ϕM
) ⎤ ⎡0⎤
⎢ ⎥
FF = FF cos ( ϕF ϕM ) , M
⎢
F 0
⎥
⎢− − ⎥ =
⎢ ⎥
, (9)
⎢
⎣ 0 ⎥
⎦
⎢⎣0
⎥⎦
ˆ 2 ⎛ RFw2
⎞
FF = 3Lkw jF KB2 R4
ln ⎜ ⎟.
(10)
⎝ RFw1
⎠
This result indicates that the bearing force is linearly
dependent on the magnitude of the bearing current ˆF j . Its
direction is given by the angleϕ
F − ϕ M . Thus, the bearing
force can be controlled with a standard three phase inverter
when a good estimation of the angular position of the rotor is
available to the controller.
C. Negative stiffness
In this section the sensitivity of small rotor eccentricities is
examined. When the rotor is displaced radially, a reluctance
force dragging the rotor away from the centered position
occurs. This is due to the unsymmetrical field distribution at
the inner side of the iron core. This negative stiffness
dFx
kx
= (11)
dx
is defined similar to a spring constant. Due to the rotational
symmetry of the cross section k x = k y can be assumed. The
negative stiffness is determined with evaluating Maxwell
stress tensors in FEM field simulations.
D. Winding inductances
A major advantage of the proposed self-bearing motor is
the low winding inductances. Therefore, reactive power is
small and there is no need for high inverter dc link voltages to
achieve high current control dynamics as in other AMBs.
Contrariwise, an inverter topology and modulation has to be
chosen that allows for lowest inductances. The inductance
values given in Table I are calculated by means of magnetic
energy integration in FEM field simulations.
IV. WINDING OPTIMIZATION
Lorentz-force based force and torque generation is
primarily proportional to the winding currents and therefore
limited by the resulting copper losses [12]. Therefore, for a
given force and torque the minimization of the copper losses
P π ˆ2 2 2
Cu = w ( w2 w1)
2
Lk j R −
σ
R
(12)
cu
is desired. For the following optimization considerations an
approximate field solution
2
⎡ ⎤ Brem
R1
B2 = lim ⎢ lim KB2⎥
=
μ
2
r1→1
⎣μr5→∞
⎦ 2R4
K (13)
is used. It is assumed that the relative permeability of the back
iron μ r5
is considerably higher than in the air-gap, and that
the relative permeability of the permanent magnet μr1
is 1.
Realistic values are in the order of μ r5 = 20000 and
μ r1 = 1.05 (for amorphous iron and samarium–cobalt
permanent magnets). Thus, only very small field errors result
due to this approximation.
A. Motor winding optimization
Using (13), (8) can be simplified to
2
ˆ
BremR1
T w T 2 Tw2 Tw1
2R4
( )
M
= Lk j R −R
⋅
2 2 2
( R4 + RTw1+ RTw1RTw2 + RTw2)
3 .
(14)
Minimizing P Cu by varying the winding geometry R Tw1
and
R Tw2 for a given L , R 1 , R 4 , and a desired M T indicates that
all available space (namely the air-gap) shall be filled by the
torque winding. So ideally RTw1 = R2
and RTw2 = R4. In
practice this result is not applicable, because there has to be a
clearance between the rotor and the stator. Furthermore, a
radial bearing winding has to be integrated. This reduces the
space available for the motor winding.
B. Bearing winding optimization
Using the approximation in (13) the bearing force
magnitude is
3
ˆ 2 RFw2
F ⎛ ⎞
F = Lkw jF Brem
R1
ln ⎜ ⎟.
(15)
2
⎝ RFw1
⎠
This result indicates that the bearing force does not depend on
the inner radius of the back-iron. This is due to the fact that the
stray field B θ adds to the bearing force generation. Increasing
iron radius R 4 decreases the radial field B r but increases the
tangential stray field B θ . These two effects compensate each
other completely in the bearing force windings.
For a given given L , R 1 , R 4 , and a desired F F the copper
losses are proportional to
R
2
Fw2
( ) −
RFw1
RFw2
ln ( R )
1
P ~ F R
.
(16)
2 2
Cu F Fw 1 2
Fw1
Minimizing P Cu by varying R Fw2
and a constant R Fw1
leads
to
RFw2
= 2.2185 .
(17)
RFw1
Therefore. the bearing winding has minimal copper losses if
R Fw1 is chosen as small as possible and R Fw2
is chosen
according to (17). In contrary to the torque winding it is not
optimal to fill the entire air-gap with the force winding.
C. Joint bearing and motor winding optimization
In order to be able to use standard three phase inverters for
the motor and the bearing currents, a design is chosen with
separate torque and force windings. A key advantage of using
separate windings is the “decoupling” of force and torque
generation. Their associated currents can be controlled by
separate controllers. The bearing winding is placed as close as
possible to the rotor. The motor winding fills the rest of the
space between the bearing winding and the inner radius of the
back-iron ( RTw1 = RFw2
and RTw2 = R4).
3973

Optimization of the winding boundary R Fw2
is performed
by minimizing the sum of the copper losses in both windings
for a design torque and force. Figure 2 shows the resulting
copper losses for a given magnet and back-iron geometry, a
torque of 0.1 Nm/m and different force values. Values
exceeding a maximal allowable current density are excluded
from the figure.
V. VERIFICATION USING FEM
A. Centered rotor position
In order to verify the analytical model, force and torque
expressions (10) and (8) are compared to 2D-FEM simulations
for a centered rotor. Unlike in the analytical solution, field
contributions from the winding currents are included in these
force and torque calculation. Results shown in Figure 3 and
Figure 4 show a very good agreement between the analytic
solution and the numerical FEM results.
B. Eccentric rotor position
In contrary to the analytical model, FEM simulations allow
for an analysis of the characteristics of a proposed motor also
when the rotor is displaced from its centered position. For the
following calculations, the self-bearing motor design
presented in Table I is used. The resulting bearing forces are
presented in Figure 5, the resulting torque in Figure 6. The
reluctance force F R,
X is mainly linearly dependent on rotor
displacement. Furthermore, one can see that the maximal
reluctance force F R,
X is much smaller than the maximal
bearing forces available F F,
X . The bearing forces F F,
X ,
F F,
Y and the motor torque M T are almost constant over the
entire displacement range of the rotor. This simplifies motor
control considerably, because in a good approximation it can
be assumed that the Lorentz-force and torque to current
relationship is linear and independent of the rotor position.
When the rotor is centered, there is no cross-coupling between
force and torque winding. For large displacements a small
cross coupling can be observed. However, the maximal
possible cross coupling (shown in Figure 5 and Figure 6) is
much smaller than the rated forces and torques. Thus, bearing
and motor currents can be controlled independently of each
other.
Figure 7 depicts the radial negative stiffness per active
motor length versus the inner stator core radius for different
magnet radii. Stiffness values are calculated for a rotor
displacement of 0.1 mm. It can be seen that for decreasing
magnet radius and increasing inner stator core radius the
negative stiffness is decreasing.
VI. SELF-BEARING MOTOR DESIGN
A. Electromagnetic and mechanical layout
With the analytical design and optimization routines in section
III and IV a motor is designed for a rated speed of
500 000 rpm, a rated torque of 14.2 mNm and rated bearing
forces of 0.4 N per bearing winding. Two bearing windings
are attached to each other in z-direction. In contrary, the two
motor windings can be combined into one, which results in
three cable connections less. Similarly, the two back irons and
(P cu,F
+P cu,T
)/L (W/m)
12
10
8
6
4
2
F F
=10 N/m; M T
=0.1 Nm/m
F F
=15 N/m; M T
=0.1 Nm/m
F F
=20 N/m; M T
=0.1 Nm/m
F F
=25 N/m; M T
=0.1 Nm/m
0
5 6 7 8 9 10
R (mm) Fw2
Figure 2. Total copper loss optimization. Winding currents are limited to
2
j = 4A/mm . ( R 1 =3.5 mm, R Fw1
=4.25 mm, R 4 =15 mm)
F F
/L (N/m)
30
25
20
15
10
R1=2.5 mm
R1=3 mm
5
R1=3.5 mm
R1=4 mm
FEM Results
0
10 12 14 16 18 20
R4 (mm)
Figure 3. Comparison between analytic bearing force (lines) and numeric
2
FEM results (gray Xs). ( RFw1 = R1 + 0.75 mm , R Fw2 = 8mm,
j = 4A/mm )
M T
/L (Nm/m)
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
R1=2.5 mm
R1=3 mm
R1=3.5 mm
R1=4 mm
FEM Results
0
10 12 14 16 18 20
R4 (mm)
Figure 4. Comparison between analytic motor torque (lines) and numeric
2
FEM results (gray Xs). ( R Tw1
=8 mm, RTw2 = R4
, j = 4A/mm )
3974

the two permanent magnets are united in order to form one
workpiece each, lowering the manufacturing complexity. The
two bearing windings have to be kept separated as different
forces have to be applied in the two bearings. This results in
winding headers in between the two motors. Therefore, the
permanent magnet and the back iron have to be twice the
active length plus twice the bearing winding header length. A
CAD drawing of the self-bearing motor system is depicted in
Figure 8.
The force requirement results in an active length for the
bearing windings of 16 mm, the motor winding is twice this
length. The rated net current density is 2 A/mm 2 , with a
copper filling factor of 0.5 this results in a copper current
density of 4 A/mm 2 . With a 0.5 mm 2 wire for the bearing
winding and a 1 mm 2 wire for the motor winding this leads to
rated phase currents of 2 A for the bearing and 4 A for the
torque winding, respectively. The inner dimensions and
parameters can be found in Table I.
Beside the self-bearing motor itself, several further
components are required to form a fully functional prototype
system of a Lorentz-type, slotless self-bearing motor. The
following sections identify these subsystems, which are all
part of future research.
B. Axial bearing
This paper analyzes a self-bearing motor which can
generate torque in z-direction and forces in x- and y-direction.
However, for a fully functional system the position in z-axis
also has to be controlled actively, because the passive
stabilization is very low due to the large radial air-gap between
magnet and back iron.
For the prototype system to be built the axial stabilization
will be done with one externally pressurized axial air bearing
on each side of the rotor. Active axial magnetic bearings based
on windings using the existing field of the self-bearing motor
topology presented in this paper will be part of future research.
C. Position sensors
The radial position can be detected with commonly used
eddy current sensors. For a high bandwidth measurement with
a high resolution and a compact design a PCB based sensor
has found to be an ideal choice [17], [18]. Two such sensors
can be mounted on each axial end of the rotor.
The axial position does not have to be measured in the
prototype system due to the utilization of air bearings. In the
case of using an active axial magnetic bearing the position
detection can also be done with an eddy current sensor.
The angular position is required for the orientation of the
field of motor winding as well as the field of the bearing
winding. The angular position can be measured with hall
sensors detecting the permanent-magnet field, or with eddycurrent
sensors and an eccentric part of the rotor.
D. Power electronics and control
The two bearing as well as the motor windings are starconnected
three phase windings. Therefore, three three-phase
inverters are required to operate the self-bearing motor system.
This results in 18 semiconductors on power electronics side
and the according gate signals that have to be provided by the
control system. A standard active magnetic bearing and drive
F/L (N/m)
30
25
20
15
10
5
0
F F
(analytic)
F R,X
F F,X
F F,Y
F T,X
F T,Y
0 50 100 150 200 250 300 350 400
Rotor displacement on x-axis ( μm)
Figure 5. Bearing forces versus rotor displacement. FRX
, is the resultant
reluctance force due to the negative stiffness. F F,
X and F FY , are resulting
2
bearing forces in x and y-direction when a current desity of j F = 4A/mm is
applied with different phases. F T,
X and F TY , are the forces due to a torque
2
current density of j = 4A/mm .
M/L (Nm/m)
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
T
M T
(analytic)
M T
M F,X
M F,Y
-0.05
0 50 100 150 200 250 300 350 400
Rotor displacement on x-axis ( μm)
Figure 6. Motor torque versus rotor displacement. M T is the resulting torque
2
due to a torque current density of j T = 4A/mm . M F,
X and M FY , are due
2
to force current density of j = 4A/mm in different phases.
-k x
/L (kN/m/m)
50
45
40
35
30
25
20
15
10
5
F
R1=2.5 mm
R1=3 mm
R1=3.5 mm
R1=4 mm
0
10 12 14 16 18 20
R4 (mm)
Figure 7. Radial negative stiffness per active motor length versus inner stator
core radius for different magnet radii.
3975

TABLE I
SELF-BEARING MOTOR DESIGN
Symbol Quantity Value
Geometry
R1
Permanent magnet radius 3.5 mm
RFw1
Bearing winding inner radius 4.25 mm
RFw2 = RTw1
Bearing winding outer radius 8 mm
R4 = R Tw 2
Back-iron inner radius 15 mm
R5
Back-iron outer radius 20 mm
Material properties
Brem
Remanence flux density 1.1 T
Permanent magnet field properties
BˆM , iron Maximal magnetic field in back-iron 0.21 T
k x
Negative stiffness 262 N/m
Bearing winding properties
LF
Active length 16 mm
N F
Number of bearing winding turns 12
k I F
Force-current coefficient 0.20 N/A
LdF
, = LqF
,
Winding inductance 3.72 µH
Motor winding properties
LT
Active length 32 mm
N F
Number of motor winding turns 42
k I T
Torque-current coefficient 3.54 mNm/A
LdT
, = LqT
,
Winding inductance 90.5 µH
Figure 8. CAD drawing of the novel high-speed, lorentz-type, slotless
self-bearing motor.
with two times two windings (x- and y-direction on both
sides) for the bearings and a three-phase motor, where a total
of four full bridges and a single three-phase inverter is usually
implemented, requires 22 semiconductors and gate signals.
Therefore, the number of semiconductors and gate signals can
be reduced with the topology presented in this paper.
However, the drawback of the presented topology is that
all three-phase currents, in contrary to the common AMB also
the bearing currents, have a fundamental frequency equal to
the mechanical frequency of the rotor. Firstly, this requires
sufficiently low inductances of the windings in order to allow
a limited inverter dc link voltage. This is fulfilled according to
the self-bearing motor design in Table I. Secondly, it requires
a current controller capable of impressing such currents. With
a field-oriented controller this leads to the requirement of fast
coordinate transformations between stationary and rotating
reference frames.
VII. CONCLUSION
The Lorentz-type, slotless self-bearing motor presented in
this paper overcomes most limitations of previously presented
high-speed magnetic bearings. It has a simple and robust rotor
construction, low rotor losses, a very low negative stiffness
and low cross-coupling. The achievable bearing forces with
this concept are small compared to other AMBs with equal
rotor radius and length, but the negative stiffness is also very
small. This makes it an ideal choice for high-speed operation
where low external forces are applied to the rotor.
An analytical model for the torque and bearing forces has
been introduced and verified. It shows that the torque and
forces are almost independent of the displacement and linear
to the current, which simplifies position control considerably.
A motor design for 500 000 rpm leads to a torque of
14.2 mNm, bearing forces of 0.40 N per radial bearing and a
negative stiffness of 262 N/m for a net current density of
2 A/mm 2 . The prototype system to be built includes two
motors and allows for simplified manufacturing due to
unification of back iron, motor winding and permanent
magnet.
Further research will include the control of the presented
self-bearing motor, the power electronics, and the integration
of an active axial magnetic bearing.
REFERENCES
[1] C. Zwyssig, J.W. Kolar, S.D. Round, “Megaspeed Drive Systems:
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