Magnetic bearings used for the suspension of momentum wheels provide conclusive advantages: the low friction torques and the absence of abrasion allow the realization of lightweight high speed wheels with high angular momentum and energy storage capacity and virtually unlimited lifetime. The use of actively controlled bearings provides a magnetic gimballing capability by applying the external signals to the two servo loops controlling the rotational degrees of freedom. Thus, an attitude control system can be realized by using only one rotating mass for 3-axis active satellite stabilization

Sindlinger, R. S.

English

NASA Technical Reports Server

N79- 21 a.79 m-S
MAGNETIC BEARING MOMENTUM WHEELS
WITH MAGNETIC GIMBALLING CAPABILITY FOR
3-AXIS ACTIVE ATTITUDE CONTROL AND ENERGY STORAGE
by
Rainer S. Sindlinger
TELDIX GmbH, Heidelberg, Germany
ABSTRACT
-.%
Magnetic bearings used for the suspension of momentum wheels
provide conclusive advantages: the low friction torques and the
absence of abrasion allow the realization of lightweight high-
speed wheels with high angular momentum and energy storage capaci-
ty and virtually unlimited lifetime. The use of actively control-
led bearings provides a magnetic gimballing capability by ap-
plying external signals to the two servo loops controlling the
rotational degrees of freedom. Thus, an attitude control system
can be realized by using only one rotating mass for 3-axis active
satellite stabilization. In the future, an integrated energy
storage/attltude control system with one pair of counter-rotating
rotors could reduce considerably the mechanical complexity and
weight of conventional systems.
INTRODUCTION
The stringent attitude performance requirements of future
satellites can only be met by 3-axis body stabilization. Hereby, ......
the satellite's orientation is measured by the attitude control
system (ACS) with a set of optical, IR or RF sensors, and the
deviations from the desired attitude are transformed into ap-
propriate correction signals for the torque actuators. The most
common actuators are flywheels, i.e. reaction wheels or momentum
wheels.
For 3-axis active control, a set of three REACTION WHEELS
with mutually orthogonal axes can be used. Since external dis-
turbance torques are in the order of I0 -_ to 10 -5 Nm, an angular
momentum storage capacity of 0.2 to 5 Nms is sufficient.
With MOMENTUM WHEELS, active control is only possible in one
axis, and the remaining two axes are passively stabilized by gyro-
scopic effects. The angular momentum H required to maintain the
attitude to an accuracy of a_ at an external torque M over a time
interval T is • T
H _ _ M dt / A_
O
45
https://ntrs.nasa.gov/search.jsp?R=19790013208 2020-03-20T18:56:02+00:00Z
Typical valuers are in the order of 20 to 100 Nms for an
accuracy of _ _ 0.5".
If high angular accuracy is required, this passive stabili-
zation is possible within short time intervals only, and frequent
desaturations become necessary. Integration of the wheel into a
double gimbal system (DGS) allows to overcome this disadvantage.
At the same time, a DGSprovides the capability of rotating the
satellite, e.g. to correct the north-south error caused by in-
accurate positioning or to turn the antenna pointing vector.
Conventional wheels with sliding or ball bearings are re-
stricted to speeds below 5000 rpm due to their friction torque
and limited life caused by fatigue effects of the bearings and
aging of the lubricants. To prevent the lubricants from outgas-
sing, a housing is needed maintaining an internal pressure of
several hundred _bars.
MAGNETICBEARINGMOMENTUMWHEELS
During the last years, many efforts have been made to avoid
the shortcomings of conventional flywheels by use of non-
contacting bearings. Due to the absence of abrasion and their
very low friction torque, magnetic bearings are prime candidates
allowing the design of high-speed wheels with high angular mo-
mentum-to-mass and energy-to-mass ratios. Magnetic bearings are
insensitive to hard vacuum and therefore need no housing. The
lifetime is virtually unlimited and depends only on the relia-
bility of the associated electronics which can be considerably
increased by redundancy.
If appropriate materials are used, extreme velocities can be
realized, providing an energy storage capability which is com-
petitive to the best available batteries.
For the suspension of a rotating body, 5 degrees of freedom
must be stabilized: three translational ones along the X,Y,Zaxes,
and the rotational ones about the X and Y axes (see Figure I).
Generally, each degree of freedom can either be stabilized pas-
sively, i.e. by means of permanent magnets, or actively with
magnets controlled by a control loop. A complete passive sus-
pension is not possible and at least one degree of freedom must
be actively controlled [1S.
PASSIVE SUSPENSIONcan be realized either with repulsive
forces or with secondary forces yielded by attractive magnets.
Since only one control loop is required, mainly passive bearings
provide high reliability. Using the zero-power method [7] they
can operate even in a 1 g environment with low power consumption,
because the levitation of the rotor is done by forces generated
by permanent magnets.
46
However, the magnets must be very homogeneous; otherwise
considerable friction torque is generated by eddy currents and
hysteresis losses. The stiffness is limited yielding a certain
softness against external forces and torques. But the most severe
disadvantage is the absence of any internal damping, requiring
heavy and bulky dampers to prevent nutational and precessional
oscillations. In many cases, these dampers are heavier and more
voluminous than the bearings themselves. In the I g environment
these dampers can generate considerable drag torque causing ad-
ditional power consumption for the drive motor.
For ACTIVE SUSPENSION, two principles of operation can be
considered: In an ELECTROMAGNETICBEARING electromagnets on the
stator generate attractive forces on ferromagnetic parts of the
rotor. These forces are proportional to the square of the coil
current, thus the control loops must include linearizing networks.
Two magnets are required for each degree of freedom to yield posi-
tive and negative forces.
In the ELECTRODYNAMICBEARING, the forces are generated by
currents through electrical conductors on the stator, arranged
perpendicular to the magnetic flux provided by permanent magnets
fixed to the rotor. Since the forces are proportional to the
current, positive as well as negative forces can be obtained, and
the linearity facilitates the layout of the control loops. The
forces can be either parallel or orthogonal to the gap between
stator and rotor. Of course, the magnitude of the forces is much
lower than for the electromagnetic approach.
MOMENTUMWHEELWITH ELECTROMAGNETICBEARINGS
In the following, a 5-axis active magnetic bearing momentum
wheel (MBMW)is described. It was developed and built by Teldix
in cooperation with SEP in France under a contract of the COMSAT
and the German Space Organization DFVLR.
Two axial bearings AB, having the form of pot magnets,
stabilize the rotor in axial direction. They are controlled by
the axial sensors AS and a control electronics (see Figure 2).
The two radial bearings RB consist of four pairs of electro-
magnets each arranged in a plane and equally displaced by 90" as
shown in Figure 3. Radial translations are generated by currents
at the same side of the upper and lower bearing while torques
about the radial axes are provided by activation of opposite
sides. The control signals are obtained by addition or subtraction
of the outputs of a number of radial sensors RS.
Figure $ shows a block diagram of the translatory control
loops. Since the mass of the rotor provides a double integration,
proportional control would yield an oscillating system as it is
true for passive bearings. Therefore, a phase-lead network is
47
necessary to damp oscillations. An integrating control is added
to provide high statical stiffness. The frequency response of the
control loop is depicted in Figure 5.
At zero speed, the same control loop design could be used
for the rotatory degrees of freedom. At higher speeds, however,
the two control loops are coupled due to gyroscopic effects. As
shown in Figure 6, each variation of the input signal _ of the
X axis causes a disturbing torque MH_ on the Y axis via the di_-
ferenciating block H.s. It results in a change of the angle
about the Y axis which, in turn, generates the desired angle
by a disturbing torque MH_ about the X axis. Since H is pro-
portional to the rotational speed, the parameters of the control
loops vary in a very wide range, and a great bandwidth is re-
quired.
MAGNETICGIMBALLING CAPABILITY
The use of activemagnetic bearings for the rotatory degrees
of freedom provides the unique possibility of controlling the
attitude of the rotor. If the nominal values _o = 0 and _o = 0 in
Figure 5 are replaced by variable command signals _c and _c, the
rotor can be tilted by a defined angle about any radial axis. By
this tilting, the wheel is provided with a magnetic gimballing
capability.
Such a Magnetically Gimballed Momentum Wheel (NGNW)was de-
Veloped by Teldix on the basis of the MBNWdescribed above(Figure 7).
A gimballing angle range of ± 10 mrad is obtained by in-
creasing the gaps between stator and rotor from 0.3 to about
0.7 mm. At a nominal speed of n = 16,000 rpm, the wheel has an
angular momentum of H = 100 Nms, so that the storage capacity
about the perpendicular axes is ± I Nms. This is more than suf-
ficient to balance the periodic disturbance torques on the satel-
lite, and the attitude of the satellite can be controlled with an
accuracy of better than 0.01", depending only on the performance
of the attitude sensors. Furthermore, the MGMWcan be used as an
active nutation damper, thus superseding separate nutation
dampers for the satellite.
The magnetic gimballing needs practically no additional hard-
ware. The wider gaps increase the magnetic resistance of the
magnetic loops and, therefore, require a higher magnetic potential(i.e. a higher number of ampere-turns). Nevertheless, it was pos-
sible to reduce the weight from 14 kg to about 9 kg although ef-
fective emergency bearings and a caging mechanism, fixing the
rotor during launch, were added.
The electronics package for magnetic suspension and gimbal-
ling and for the motor commutation is integrated in thin film
hybrid technology and weighs about 3 kg. Thus, the total system
48
weight is about 12 kg. The power consumption at nominal operation
in orbit is expected to be about 10 to 15 watts. The brushless
and ironless d.c. motor/generator is able to provide the power
for magnetic suspension in case of primary power failure for up
to 20 minutes. Since the electronics is completely redundant,
a reliability of about 98 %, based on a 10-year mission, is
obtained.
ROTARYENERGYSTORAGESYSTEMS
The rotor of the wheel described so far was composed of a
momentum ring, a hub, and a disc connecting them. Of course_ this
is not the optimal shape for a momentumwheel rotor. In order to
obtain the highest possible momentum-to-mass ratio H/m, the total
mass should be arranged at the largest possible radius r, pro-
viding a thin-walled ring. The H/m ratio is then
-- ---- r
m
with _ being the allowed stresses, and p being the density of the
material [4]. If such a ring is rotated at a speed fully utilizing
the strength of the material, considerable kinetic energy can be
stored providing the opportunity of realizing the dual functions
of angular momentum and energy storage.
The energy-to-mass ratio of a thin-walled ring is
E
with v = m • r being the circumferential velocity. The specific
energy is, therefore, fully defined by the properties a and p of
the materials used for the rotor and independent of the ring
diameter. High-strength materials of low density are best suited
for energy storage systems, and since the stresses are mainly in
circumferential direction, fibre reinforced composites are prime
candidates for this application. In table I the energy density for
different materials is listed. The static value is the theoreti-
cal limit for the fibres only, while the values given for dynamic
loads take into account an energy storage cycling with the as-
sociated fatigue problems, and the weight for the matrix, which
does not contribute to the strength.
Table 1
E/m Ratio for Various Ring Materials
Material Energy-to-Mass Ratio _[Ws/g]
Static !Dynamic (10_ cycles)
Steel 250 200
Glass 670 370
Boron 610 425
Carbon 640 500
Kevlar 690 435
t
49
As can be seen, carbon fibre composites provide the highest
ratio
E Ws Wh
-- _ 500 m _ 140
m g kg
HIGH-SPEED RING WITH ELECTRODYNAMICBEARINGS
For such a ring, the dimensions and the mass of an electro-
magnetic bearing would be prohibitive, and the use of an electro-
dynamic bearing is to be preferred. The large ring surface allows
the use of comparatively large permanent magnets, and the stator
coils can be arranged on a ring inside the rotor.
Figure 8 shows a cross section of the bearing: On the rotor,
for instance, two permanent magnet rings with homogeneous radial
magnetizing in opposite directions are mounted. A soft iron ring
increases the flux density effective in the stator coils. The
radial and axial coils are arranged in areas where the axial and
radial component,respectively, ofthe magnetic field is predominant.
Therefore, the axial coils generate mainly axial forces while
radial forces are provided by the radial coils.
To form a complete bearing, the radial coils are divided into
four 90" segments providing forces along two perpendicular radial
axes. The tilting torques are yielded by segmented axial coils
excited in opposite directions. Any deviation from the nominal
rotor position is detected by a set of position sensors and
- using five control loops - balanced by forces generated in the
coils.
This bearing type provides high stiffness and excellent
oscillation damping. Due to the absence of any iron on the stator
and the uniform magnetizing on the rotor, the drag torque can be
kept extremely low even at very high speeds. The only braking
torques are caused by eddy currents in the magnets and the soft
iron ring, generated by the weak field of the ironless stator
coils. If the bearing must be able to support the rotor under 1 g,
however, about 15 to 25 % of the rotor mass is required for the
magnets. Otherwise, the stator coil currents would become in-
tolerably high.
Two counterrotating rings are necessary to realize an energy
storage system which is free of distortion torques. A vernier
magnetic gimballing of a few arc minutes is required to exactly
align the momentum vectors under all operational conditions. This
allows also to generate torques about all three satellite axes.
Therefore, the functions of energy storage and attitude control
"can be combined in one system.
A first experimental model of a high-speed ring was de-
veloped by Teldix under a DFVLR contract. Figure 9 shows the
complete unit. Although it was mainly designed as a momentum
5O
ring, it is able to:store about 45 Wh corresponding to a rotor .... :
energy density of 16 Wh/kg.
The total rotor mass is 3.8 kg including 0.6 kg for the
magnets. The bearings are able to provide forces of F a > 80
newtons in axial, and Fr > 70 newtons in radial direction, al-
lowing safe operation in each orientation under 1 g.
The maximum speed up to now was 15,000 rpm, corresponding to
an angular momentum of 105 Nms. The total weight is 8.6 kg, and
the dimensions are 290 mm diameter × 110 mm height. The volume is
7.2 1 with 4 1 available for the electronics in the interior of
the stator.
The motor provides a torque of 0.1Nm corresponding to a ........
power of 150 watts. The angular freedom for magnetic gimballing ..........
is _ 0.1 °, and the slew torque capacity is more than 2 Nm. The
behaviour of the gimballing loop was tested with a square wave
control signal input at a ring speed of 3000 rpm. In Figure 10
the resulting attitude angle of the ring is shown. As can be seen,
the commanded angle for the X axis is obtained with a reaction
time of less than 20 ms. In the orthogonal Y channel, only short
distortions are produced with no steady-state error.
CONCLUSION
Magnetic bearing technology allows to realize a 3-axis
active attitude control system with only one rotating part. This
is possible by using a momentum wheel with magnetic gimballing
capability as a torque actuator for all three body axes. Such a
wheel has been developed and will be qualified for space appli-
cations within the next two years.
Based on this technology, an integrated energy storage/at-
titude control system with one pair of counterrotating rings
could in the future considerably reduce the complexity and weight
of conventional systems.
REFERENCES
1. Earnshaw_ S.: On the Nature of Molecular Forces.
Trans. Cabridge Phil. Soc. 7, d842.
2. Sindlinger, R.S.: Magnetic Bearing Momentum Wheels with
Vernier Gimballing Capability for 3-axis Active Attitude
Control and Energy Storage.
IFAC Symposium "Automatic Control in Space",
Rottach-Egern/FRG, May 17-21, 1976
This paper is based in part on work performed under sponsorsh_ of _e _ternational Tele-
communications Satellite organization (_telsat). Any _ews expressed are not necessarily
those of _telsat.
51
i
.4.
.
.
o
Wehde, H.P. and Sindlinger, R;S.: Rare Earth-Cobalt Magnets,
Breakthrough to a new Generation of Drive Motors and Magnetic
Bearings for High-Speed Rotors. Second International Workshop
on Rare Earth-Cobalt Magnets, Dayton/0hio, 1976.
Stellbrink, K.: Anwendun_ faserverst_rkter Verbundwerkstoffe
fGr magnetisch gelagerte Schwungringe zur Satellitenstabili-
slerung und als Energiespeicher. DFVLR Report IB 454 75/_1975
Notti, J.E. et al.: Design and Testing of an Energy Flywheel
for an Integrated Power/Attitude Control System.
AIAA Paper No. 75 - 1107, 1975.
Anderson, W.W. et al.: The Annular Momentum Control Device
and potential Applications. NASA TN-D-7866, 1975.
Sabnls, A.V. et al.: A Magnetically Suspended Large Momentum
Wheel. J. Spacecraft, Vol. 12, No. 7, 1975.
Figure I: MBNW Coordinate System
Figure 2: Cross Section of the Magnetic Bearing Momentum Wheel
52
Figure 3" Magnetic Radial Bearing
sot
×0 Se, Control Ioop
fls)
Figure 4- Translational Control Loop
I Gain
\
" k
Phase
\-
Figure 5" Frequency Response of the Control Loop
53
Nle{_
f(s)
f(s)
j s2
MeB
Figure 6- Rotational Control Loops
iiiiii ..
Figure 7" Magnetically Gimballed Momentum Wheel
54
STATOR {
ROTOR
R A R A R COILS
_ PERMANENTMAGNETS
:S
SOFT IRON
CURRENTS
Figure 8" Basic Function of Electrodynamic Bearing
Figure 9: High-Speed Momentum Ring
commanded(x) Axis
orthogonal
B (Y) Axis
Figure 10- Magnetic Gimballing Angle
for Square Wave Command Signal
(vertical 0.4 mrad/Div. ; horizontal 50 ms/Div.)
55



Magnetic bearing momentum wheels with magnetic gimballing capability for 3-axis active attitude control and energy storage

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