Reaction Wheel Array Thermal Model

SWITCH TO API

Description

The Reaction Wheel Array Thermal Model is a specialized Thermal Model that is able to compute thermal power, and hence influence the temperature, of Reaction Wheels based on their current friction, wheel speeds and torque. The model assumes that all of the friction is converted to heat energy, as opposed to power, and that energy can be used to heat up the rest of the spacecraft or system that is attached.

This model must be attached to a Reaction Wheel Array component itself, and not the individual reaction wheels, as the calculations are done as a whole.

---

Example Use Cases

• Modelling the effects of friction on the reaction wheels, producing thermal energy in the process whilst slowing down the wheel speeds.
• Heating up spacecraft from reaction wheels, directly converting electrical power into residue heat energy.

---

Module Implementation

In the individual reaction wheels, they directly calculate the torque caused by the sum of the friction forces. This torque is known as the friction torque, ${\tau }_{\mathrm{net}}$. This can be calculated by:

$${\tau }_{\mathrm{net}}=-({\mu }_c+b\times |\omega |)$$

where ${\mu }_c$ is the Coulomb friction coefficient, $b$ is the viscous damping coefficient and $\omega$ is the current angular rate in radians per second.

Then, knowing the individual torques, the total power for thermal dissipation can be calculated as $P_{\mathrm{T}}$, using the sums of individual wheel powers:

$$P_T=\sum _{i=0}^n|{\omega }_i\times {\tau }_i|$$

where $i$ is the reaction wheel number, up to $n$ reaction wheels, ${\omega }_i$ is the angular rate of the reaction wheel and ${\tau }_i$ is the net torque of the reaction wheel, as calculated.

This updates the Power Generation property of the thermal model, which can be passed into the Thermal System for the calculation of the temperature and change in temperature based on the materials used.

---

Assumptions/Limitations

• All friction energy is converted directly to thermal energy and is not / cannot be captured back into electrical energy.
• Friction forces are accurate and specified by the user, with no calculations done in regard to the material of the reaction wheels.