Development of a Magnetic-Bearing Momentum Wheel for the AMSAT Phase 3-D Small Satellite

Michael SCHARFE (DK7UX)*, Karl MEINZER (DJ4ZC)*, Ralf ZIMMERMANN (DL1FDT)**

* AMSAT-Deutschland e.V., Holderstrauch 10, D-35041 Marburg, Germany
** Technical University of Darmstadt, Institute for Electro-Mechanical Constructions, Merckstr. 25, D-64283 Darmstadt, Germany

Presented at the International Symposium on Small Satellites,
Annecy, France 1996

ABSTRACT - The need for three-axis stabilisation of the Phase 3-D amateur radio small satellite led to the development of three magnetic-bearing momentum wheels. The main objectives for developing these wheels are low friction and a long lifetime. No lubrication is required and high momentum storage can be achieved through high rotational speeds. Moreover, the wheels will be operated in a momentum-bias mode, adding dynamic stiffness to the spacecraft against disturbing forces.

Each wheel provides a momentum storage capacity of 15 Nms at 3000 rpm. The mechanically simple construction of the wheels makes them competitive with conventional ball-bearing momentum wheels in terms of cost and physical properties. The actual wheel design consists of a two-axis, actively-controlled magnetic bearing with the associated control circuits, a brushless DC motor drive assembly and the rotor. This paper reviews the design principles of the wheel, presents magnetic FE-simulation results and compares them to the measured properties.

Contents



1 INTRODUCTION

Momentum wheels are frequently used for 3-axis attitude control on satellites, allowing the spacecraft to point its antennas at the Earth and the solar generator at the sun. For the AMSAT Phase 3-D mission, three momentum wheels will operate in a momentum bias mode at a nominal speed of 1000 rpm, giving the satellite dynamic stiffness. Changing wheel speeds can both reorient the spacecraft and compensate for disturbing forces such as solar pressure. The momentum of the wheels has to be dumped at a speed of 3000 rpm, which is achieved by generating an external torque at the perigee of the satellite orbit at a height of 4000 km. This is done with magnetorquers operating in the Earth magnetic field. A detailed description of the AMSAT Phase 3-D mission is given in [1].

Commercially available conventional ball-bearing momentum wheels for small satellites are not very attractive because ball-bearings inherently have a limited lifetime. Magnetic-bearing momentum wheels are not available with all the properties required for the intended mission. Therefore, the development of three suitable wheels with magnetic bearings at reasonable cost was initiated.

Early developments in the area of magnetic bearings for momentum wheels were started in 1972 by Studer [2, 3]. Parallel developments in ESA were done by Robinson in 1981 [4, 5] and influenced the first magnetic-bearing wheels in space on the French SPOT satellite in 1986 [6]. Today, several manufacturers offer momentum wheels with magnetic bearings for larger platforms. To our knowledge, there are no such wheels for satellites under 400 kg available.

Magnetic bearings in space applications offer high reliability, show no wear or abrasion and can be used in a high-vacuum environment without the need for lubrication. They show no stiction and have very low rotational losses. They are not susceptible to temperature changes and should be less expensive to produce than conventional ball-bearings due to less demanding manufacturing tolerances. These properies are appreciated for satellite momentum wheels, which have to operate at high rotational speeds in a vacuum for long periods of time.

2 THE MAGNETIC BEARING

2.1 Design Principles and Technologies

A completely passive and contactless magnetostatic bearing, stable in all 6 degrees of freedom (DOF), cannot be realised under normal conditions [7]. In practice, at least one axis has to be controlled actively by means of electromagnets. Earlier publications on magnetic-bearing wheels either control one, two or five DOF actively [6, 5, 8]. Table 1 compares these three options.

Number of actively controlled DOF Bearing Properties
1 (axial) Simple electronics, low power consumption but high axial dimensions, awkward mechanical construction; passive damping of radial oscillations difficult.
2 (both radial) High radial stiffness due to active contol, simple construction, low axial height.
5 Complex system, therefore less reliable than other options; offers vernier gimballing capability. Special precautions required for testing in 1g.
Table 1: Comparison between three optional magnetic bearing methods

Magnetic bearings can be realised by using attractive or repulsive forces. A better mass vs. stiffness ratio can be achieved by using the attractive force mode [9]. Preference was given to the 2 DOF option where the wheel is actively controlled along two orthogonal radial directions where axial movements and all other degrees of rotor freedom are passively controlled by means of permanent magnets, except for the rotor spin. The two radial axes are independently controlled by their control loops. This design principle generally results in a flatter geometry, using less volume and being suitable for panel mounting. Moreover, the 2 DOF actively controlled bearing allows a high momentum-to-mass ratio of the wheel as parts of the bearing contribute to the momentum storage capacity. For position detection, four field displacement type inductive sensors are mounted with 90 degrees angular spacing around the flywheel, facing the outside rim surface.

In the wheel design both permanent magnets and electromagnetic coils are used. Most of the DOF are passively controlled - this has the advantages of high reliability and low power consumption because the amount of electronics is reduced. The permanent magnets produce the main part of the magnetic flux in the magnetic circuit and the electromagnetic coils modulate this static bias flux, allowing the control of restoring forces on the wheel to keep it centered. This modulation is necessary to provide active control in the radial direction in the presence of imbalance or external forces. Another advantage is the linearised characteristic of force vs. current through the superposition of permanentmagnetic and electromagnetic fluxes [10]. Rare-earth permanent magnets were chosen because they offer a high energy density and have advantages in terms of mass and volume.

Figure 1: Schematic cross section view of the magnetic bearing.

Figure 1 shows a cross section view of the magnetic bearing. A bias flux is generated across the airgap, shown in paths A1 and A2, supporting the weight of the flywheel in the axial direction. If the wheel is not centered, the permanent magnets will create a destabilising force which pulls the wheel even further away from the center. The control system will detect this motion through position sensors at the wheel's outer diameter and generate a corrective flux B by sending current through the stator coils. In the air gap, this control flux B substracts and adds to the static fluxes A1 and A2 caused by the permanent magnets. By substracting flux at the narrow gap side and adding flux at the wide gap side, the magnetic bearing produces a net restoring force to centre the flywheel.

Figure 2: Drawing of the magnetic-bearing momentum wheel.

The actual wheel design is shown in Figure 2. The inertial mass is provided by the rotor assembly which also accommodates the permanent magnets for the brushless DC motor. These magnets are placed in a ``C`-shaped magnetic return ring, which in turn is housed inside the outer rim, thus adding to the inertial mass of the wheel. The rotor is made of aluminium and has holes on the upper side to reduce weight and allow angular inductive sensors to detect the position of the wheel relative to the motor coils. The latter are attached to the stator assembly and are not shown in Figure 2.

The inside diameter of the wheel consists of another ``C'-shaped magnetic return ring made of steel (1a) with a non-magnetic filling (1h) to act as a touchdown bearing in the radial direction. This emergency bearing will be used during launch and in case of a power failure. It prevents the return ring from touching the flux plates, thus maintaining a minimum air gap which is important to ensure lift-off of the bearing. The flux plates (3) and the return ring (1a) have tapered edges to increase the magnetic flux across the air gap and therefore improve the axial stiffness.

Figure 3: Expanded view of the stator assembly.

An expanded view of the stator assembly is given in Figure 3. The permanent magnets are situated between the fluxplates in a sandwich arrangement with a non-magnetic mounting structure. The fluxplates are made of cobalt-iron and all other magnetic flux-carrying parts are made of steel. The coils and coverplates are symmetrically arranged around the sandwich structure. The rotor assembly is mounted to the baseplate by means of a non-magnetic bolt with a nut and washer.

2.2 The Magnetic Finite-Element Simulation

For the development of the magnetic-bearing momentum wheel, the finite-element simulation software MAFIA was used. MAFIA's algorithms are based on the Finite Integration Technique (FIT) which is a theoretical basis for solving Maxwell's equations in integral form.

The magnetic finite element simulation allowed the rapid development of one engineering model of the momentum wheel within three months. Three flight versions with minor changes were built in nine further months. No ``trial-and-error` method with many breadboard models, long workshop and testing periods was necessary to validate the design. Properties like magnetic flux, force and stiffness parameters were obtained in a relatively short time from the simulations with much higher accuracy than with hand calculations. Most importantly, the function of the bearing design was validated in an early development state, where changes could be applied without great effort.


Figure 4: Simulated force-displacement characteristic in axial direction.

Figure 5: Simulated destabilising force of the permanent magnets in radial direction.

A critical issue in the design of the magnetic bearing was the magnetic flux saturation effect inside the steel parts. This effect is difficult to measure but can be simulated easily. A certain design optimisation with regard to mass, force current characteristic and stiffness was also done. Figures 4 and 5 show the axial force-displacement characteristic of the wheel and the destabilising force of the permanent magnets, respectively. Figure 4 proves that the wheel can carry its own weight in the 1g environment. With a rotor weight of 3.66 kg, the sag of the wheel is below 15% of the thickness of the flux plates in the air gap. This results in a good axial stiffness and is beneficial for damping oscillations caused by imbalances.

Figure 6: Magnetic field simulation in the airgap of the bearing; magneto-inductive force NI = 0 AW; wheel displacement of 0.7 mm in radial direction.

Figures 6 and 7 demonstrate the simulated operation of the bearing at lift-off: Figure 6 shows the magnetic flux density in the air gap, from 0 degrees to 360 degrees, without current in the stator coils. The wheel is off-centre by 0.7 mm and the magnetic flux density has risen to 1.38 T while the airgap has narrowed to 0.3 mm (at 180 degrees). At 0 degrees, where the gap has widened to 1.7 mm, the magnetic flux density has decreased to 0.46 T. This results in a net destabilising force of 232.2 N.

Figure 7: Magnetic field simulation in the airgap of the bearing; magneto-inductive force NI = 2400 AW; wheel displacement of 0.7 mm in radial direction.

In order to center the wheel again, a reverse force has to be applied. This is done by lowering the flux density in the narrow gap to 0.54 T (at 180 degrees) and increasing the flux density in the wide gap to 0.87 T (at 0 degrees) by sending current to generate a magneto-inductive force of 2400 AW through the coils. The wheel receives a net force of -86.7 N towards the centre of the bearing, shown in Figure 7.

Figure 8: Simulated force-current characteristic for different radial positions of the wheel.

Figure 8 shows the simulated force/current characteristic for different radial positions of the wheel. This diagram is important for the design of the control electronics because it allows the minimum current required to centre the wheel at different radial positions to be determined.

2.3 Control Engineering Aspects

The magnetic bearing requires active control in two radial axes because of the inherent instability in these directions. Four sensors are mounted to the baseplate to measure the distance to the rotor. These sensors are coils that change their inductance, using a 500 kHz carrier signal. They are very sturdy and insensitive to aging and the space environment.

Figure 9: Approximation of the control loop, one axis.

A simplified block diagram of the control loop for one axis is shown in Figure 9. The magnetic bearing coils were designed for high efficiency and thus their time constant is long compared to the characteristic frequency omega_o of the loop. To increase the stability of the loop, a local current loop is used to remove the coil pole from the characteristic equation, as shown in Figure 10.

Figure 10: Approximation with the current controller.

The real control system is more complex and compensates for cross-coupling effects between the two axes and undesired tilt modes. The control electronics actively damps these modes and makes the wheel unconditionally stable.

3 THE MOTOR ASSEMBLY

The wheel is driven by a three-phase brushless DC motor of the ``open-field` type. The motor coils are fixed to the baseplate by means of supports and the motor magnets are mounted inside the ``C'-shaped magnetic iron ring. When a current is applied to the motor coils, their magnetic field interacts with the magnetic field of the permanent magnets and a torque is applied, which accelerates or decelerates the wheel. The amount of torque can be controlled via the motor electronics.

Rare-earth magnets were used in this design as they were readily available at low cost and increase the motor performance substantially compared to ferrite magnets. The magnetic circuit of the motor assembly was optimised with the magnetic finite element simulation program MAFIA, thus optimising the amount of iron for the magnetic return ring without the danger of magnetic flux saturation. At the same time, the magnetic flux density could be increased, making the motor more efficient in terms of the torque-to-power ratio. Special care was taken to reduce the stray field outside the magnetic circuit which could otherwise induce eddy-current losses. The entire wheel design is kept as flat as possible and concentrates the motor mass closely at the rim so that it adds as much as possible to the moment of inertia.

The motor windings are embedded into two flat pieces of composite material which are separated by an angle of 180 degrees. This arrangement applies a symmetric torque and adds redundancy to the system. Three pairs of inductive field sensors located above the wheel provide the commutation signals. A number of holes is sequentially drilled into the upper part of the wheel structure, reducing the weight and generating field changes in the sensors. The sensor output signals are processed in the motor logic and connect the motor phases one at a time to the supply voltage. A motor controller keeps track of the wheel's total stored momentum thus simplifying the control of the spacecraft through the on-board computer software.

In practice, a maximum torque of 30 mNm was achieved. This allows the wheel to be accelerated from 0 to 3000 rpm within 8.5 minutes. As an option, the motor can be used as a generator to provide electric power for the magnetic bearing in case of a satellite power failure. The wheel is then decelerated safely to a rotation speed, where the mechanical safety bearing allows a safe touchdown between rotor and stator.

A motor controller keeps track of the wheel's total stored momentum and simplifies the control laws of the spacecraft's on-board computer software.

Table 2 summarises the main wheel and motor properties.

Wheel Diameter: 280 mm
Rotating mass: 3.66 kg
Moment of inertia: 0.049 kg m^2
Motor Principle: 3-phase brushless DC
Commutator sensors: Inductive field type
Maximum torque: 30 mNm !hline
Table 2: Summarised properties of the wheel and the motor.

4 PERFORMANCE OF THE WHEEL

General characteristics Momentum storage capacity: 15 Nms @ 3000 rpm
Dimensions of housing: 400 x 300 x 100 mm
slew rate on Phase 3-D: 6 degrees/min.
Nominal speed: 1000 rpm
Maximal speed: 3000 rpm
Magnetic bearing Type: Radial active, axial passive
Diameter: 100 mm
Nominal radial gap 1 mm
Axial stiffness: 80 N/mm, 95 N/mm simulated
Radial stiffness: 160 N/mm
Tilting stiffness: 0.4 Nm/rad
Touchdown bearing Mechanical gap: 0.3 mm, two phenolic touchdown rings in axial and radial direction.
Lubrication: Oil impregnation
Launch acceleration: Max. 5.5g
Power consumption Bearing: Max. 5 Watts, 0 - 3000 rpm
Motor: Max. 15 Watts @ 3000 rpm and full torque.
Mass Rotor: 3.66 kg
Stator: 2.5 kg
Cables, casing: ca. 2.5 kg
Electronics: 1 kg
Total: under 10 kg
Sensors Bearing: 4 in radial direction,
90 degrees angular spacing
Commutation: 6 above the wheel
Nutation: 4 below the wheel
All sensors are field displacement inductive sensors.
Table 3: Summarised performance characteristics.

A summary of the performance characteristics measured on the prototype model is given in Table 3. The three flight models are of the same design without significant differences in their properties. In future versions, the relatively moderate maximum wheel speed could increased, resulting in a gain in the angular momentum storage capacity. Angular momentum storage capacity is a function of mass (and its distribution), dimensions and speed. The maximum speed of the wheel to allow a safe touchdown is governed by the mechanical properties of the emergency bearing. With the motor in generator mode, the bearing can be supplied with power and the wheel slowed down smoothly until a lower rotation speed is reached. This overcomes the maximum speed limits set by the mechanical touchdown bearing.

Tests carried out on the wheel demonstrated that there are no critical rotation speeds in the full operating-speed range. No peaks in power consumption were noticed at particular speeds and no instabilities at any speed or wheel position in the Earth gravity environment were observed.

The power measurements were performed in the atmospheric environment. Future vacuum chamber tests are planned in the ESTEC labs to determine the eddy current losses, which are estimated to be a small fraction of the air-drag losses. In this way, the power consumption of the wheel in space can be determined. The wheel has a smooth shape (no spokes) and for in-air testing, all sensor holes were sealed with thin plastic foil. Moreover, the motor magnets are embedded into plastic to further reduce the air drag factor. With these precautions, a full operational checkout of the attitude control system of the spacecraft in air will be possible.

5 CONCLUSION

All objectives, which lead to the development of the magnetic-bearing momentum wheel, were fully met in a short timescale. The prototype of this design was found to operate reliably and consistently over long periods of time. For AMSAT, this momentum wheel represents a low cost solution to integrate 3-axis stabilisation technology into the Phase 3-D satellite and possible future AMSAT low-budget missions. The presented momentum wheel still leaves much potential for optimisation in terms of mass, volume and power consumption and can be seen as a first generation system.

6 ACKNOWLEDGEMENTS

The authors would like to thank the following people for their helpful inputs, organisational and technical support: Professors Bernhard Cramer and Wilmut Zschunke (University of Darmstadt), the technical staff at both Marburg and Darmstadt University, Mr Alan Robinson (ESA/ESTEC) and Mr Michael Bartsch (CST). We would also like to thank the German companies VAC GmbH (Hanau) for magnetic Materials, Hofmann (Pfungstadt) for balancing the wheels and CST (Darmstadt) for providing the magnetic finite-element simulation program MAFIA.

7 REFERENCES

[1]
Sperber, F.: AMSAT Phase 3-D - A 400 kg International Communication and Experimental Satellite in a High-Elliptical Orbit. International Symposium on Small Satellites, Annecy, France 1996.

[2]
Studer, A.: Magnetic Bearings for Instruments in the Space Environment. NASA TMX-66111, January 1972.

[3]
Studer, A.: Magnetic Bearings for Spacecraft. NASA Technical Memorandum 78046, Goddard Space Flight Center, Greenbelt, Maryland 1978.

[4]
Robinson, A.A.: Magnetic Bearings - the Ultimate Means of Support for Moving parts in Space. ESA Bulletin 26, May 1981.

[5]
Robinson, A.A.: A Leightweight, Low-Cost, Magnetic-Bearing Reaction Wheel for Satellite Attitude Control Applications. ESA Journal, Vol. 6, 1982.

[6]
Anstett, P., Souliac, M., Rouyer, C., Gauthier, M.: SPOT - The Very First Satellite to Use Magnetic Bearing Wheels. 33rd IAF Congress, Paris, France 1982.

[7]
Earnshaw, S.: On the nature of molecular forces which regulate the constitution of the limiferous ether. Trans. of the Cambridge Philosophical Society Vol. 7, 1842.

[8]
Bichler, U., Eckart,T.: A Gimballed Low Noise Momentum Wheel. 27th Aerospace Mechanisms Symposium, NASA Ames Research Center, May 1993.

[9]
Roland, J.P.: Magnetic Bearing Wheels for Very High Pointing Accuracy Satellite Missions. International Symposium on Magnetic Suspension Technology, Hampton, Virginia, 1991. NASA Conference Publication 3152.

[10]
Studer, P.A., Allaire, E.H., Sortore, C.K.: Low Power Magnetic Bearing Design for High Speed Rotating Machinery. International Symposium on Magnetic Suspension Technology, Hampton, Virginia, 1991. NASA Conference Publication 3152.