Dynamic Friction in Reaction Wheel Model

[BriekArcsec]

I'm noticing some quite strange behaviour in the reaction wheel module when adding dynamic friction (Coulomb friction and viscous friction in particular). I would expect these types of friction to always reduce the RW's speed over time; however, for certain combinations of fCoulomb and cViscous, the exact opposite happens, and the energy of the system appears to increase (i.e. wheel speeds increase very noticeably).

To further investigate this, I modified the scenarioAttitudeFeedbackRW.py so that no active control is supplied (i.e. supplying an empty CmdTorqueBodyMsgPayload to rwMotorTorqueObj.vehControlInMsg). Then, I gave all of the three reaction wheels an initial speed of 200 rpm, and set the friction parameters as follows:

RW1.fCoulomb = 400 # [Nm]
RW2.fCoulomb = 400 # [Nm]
RW3.fCoulomb = 400 # [Nm]

RW1.cViscous = 0 # [Nm/(rad/s)]
RW2.cViscous = 0.00001 # [Nm/(rad/s)]
RW3.cViscous = 0.0001 # [Nm/(rad/s)]

In this manner, I investigated a number of scenarios. For example, when using the values as shown above (i.e. varying amounts of viscous friction), this results in the following wheel speeds:

This plot doesn't appear to make sense for a number of reasons:

• I don't think dynamic friction should result in increasing wheel speeds?
• An increase in viscous friction (RW3 > RW2 > RW) results in a higher increase in wheel speed ($\Omega_2$ > $\Omega_1$ > $\Omega_0$) - which again doesn't seem physical.
• Additionally, I find it odd that such a small amount of viscous friction has such a large effect. At speeds of 200-800 rpm, even RW3 should only experience an additional friction torque of 0.002-0.008 Nm, which seems negligible compared to the constant Coulomb friction of 400 Nm. Nevertheless, the observed differences in wheel speeds indicate a much larger discrepancy between the three wheels.

Another case was also investigated, where the friction parameters are set as follows:

RW1.fCoulomb = 0 # [Nm]
RW2.fCoulomb = 100 # [Nm]
RW3.fCoulomb = 200 # [Nm]

RW1.cViscous = 0.00001 # [Nm/(rad/s)]
RW2.cViscous = 0.00001 # [Nm/(rad/s)]
RW3.cViscous = 0.00001 # [Nm/(rad/s)]

Resulting in the following wheel speeds:

This seems to indicate that lower Coulomb friction (RW1 < RW2 < RW3) results in lower wheel speeds ($\Omega_0$ < $\Omega_1$ < $\Omega_2$). Again, I would expect to observe an opposite relation, with more friction causing the wheels to slow down more rapidly.

Additionally, the case for RW2 seems odd, since its wheel speed plot seems to indicate a state of equilibrium, which indicates a net torque of about zero. Nevertheless, a friction torque of around 100.002 Nm should be present at this velocity.

Am I looking at this problem in the wrong way? Or is there an inherent flaw in the way that Basilisk models this friction?