Reaction wheel

A reaction wheel is an actuator for controlling the position of a satellite . It usually consists of a motor , a flywheel mass rotated by it, and the control electronics for the motor speed.

Working principle

A reaction wheel brings by changes its rotational speed , a torque to the satellite on to it in the same axis but in the opposite direction to rotate ( action and reaction ). The total spin of the satellite system remains constant ( maintenance value ), in contrast to position control nozzles or magnetic coils , which change the spin of the system. Figuratively speaking, the angular momentum is only shifted back and forth between the satellite housing and the reaction wheel ( conservation of angular momentum ).

Difference to the twist wheel

Reaction wheels are not to be confused with spin wheels :

• A reaction wheel is normally at a standstill and is only brought to a corresponding speed to change the position of the satellite or to compensate for external disturbing torques. Typically there are several reaction wheels per satellite, which are aligned in different spatial directions.
  If the maximum speed of a reaction wheel is reached after several changes in position, it must be desaturated (stopped). For this purpose, position control nozzles or magnetic coils apply an external torque which counteracts that of the reaction wheel as it moves down. This ensures that the satellite retains its defined orientation in space despite the change in speed and does not turn into an undesired tumbling movement. The reaction wheel is then available again for changes in position.
• A twist wheel runs constantly at a high speed and thereby generates a stabilizing twist , i.e. This means that the reaction to disturbing torques perpendicular to the axis of rotation of the spin wheel is minimized. Therefore there is typically only one spin wheel (possibly two redundant ones ) per satellite. Spin wheels are used, for example, in classic spin-stabilized GEO satellites.

Arrangements

Reaction wheels in a tetrahedral arrangement

There are two main arrangements of reaction wheels used in space travel:

• In an axially decoupled system, a reaction wheel is used in each geometric main axis of the satellite, so a total of three. An example of the three-axis arrangement is the LAPAN-TUBSAT .
• In order to achieve redundancy, reaction wheels are installed in the tetrahedron arrangement, a total of four. This has the advantage that if a wheel fails, the system still remains fully functional. The disadvantage is the coupling of the individual wheels with one another: The rotation around a geometric axis of the satellite always results in a change in the speed of several reaction wheels. An example of the tetrahedral arrangement is the BIRD satellite.

Moment gyro

Control moment gyroscope (CMG) of the ISS

While with fixed reaction wheels, the three components of the angular momentum vector are changed individually, to set in Control Moment Gyroscope (CMG, gyro moment) direction and magnitude of this vector total of a, by the axis of the moment gyro is tilted. A constantly rotating impeller in a cardanic suspension is used for this purpose. H. a gyroscope . As an exception, the cardanic suspension is not free , but is adjusted by a motor in two orthogonal directions. The resulting reaction torque turns the spacecraft. The rotation around the axis of the impeller is controlled by changing the speed. This technology is used, for example, on the International Space Station .

Characteristics

A typical reaction wheel for a medium-sized commercial satellite is 20 to 30 cm in diameter, approximately 10 cm in height, and has a total mass of 5 to 10 kg. At a speed of approx. 5,000 rpm , it generates according to the formula

${\displaystyle L=J\,\omega }$

With

• the mass moment of inertia ${\displaystyle J}$
• the angular velocity ${\displaystyle \omega }$

an angular momentum of 20  Nm s . In contrast, the angular momentum of a spin wheel or a moment gyro (see above) is 500 Nms and more. ${\displaystyle L}$

A change in the angular momentum of the reaction wheel by changing causes an opposite rotation of the satellite around the axis of rotation of the flywheel. The orientation of the satellite can thus be controlled very precisely by making small changes in the rotation of the reaction wheel. ${\displaystyle \omega }$

The following applies to the torque generated : ${\displaystyle T}$

${\displaystyle T=J\,{\dot {\omega }}}$

with the angular acceleration . ${\displaystyle {\dot {\omega }}}$

The torque determines how quickly the rotation can be changed and the satellite can be tilted. The upper limit for the torque generated is typically 0.2 to 0.5  Nm .