GP-B Post-Flight Analysis—Final Report - Gravity Probe B - Stanford ...

imbalance with non-spherical component of rotor shape (centrifugal bulging due to spin plus natural 10 nmlevel out-of-roundness terms) it is found that the gyroscope will tend to precess around the electrode axis withthe largest preload electric fieldDuring science data gathering, the suspension electric fields are reduced to the levels needed to meet thegyroscope centering and safety requirements which results in approximately 200 mV on the electrodes. Duringalignment, however, the electric fields are increased by a factor 300 over the science levels and explicitimbalances are introduced to increase the torques on the rotor by a factor of approximately 100 million over thenominal science levels.Using the SQUID output as a measure of the gyroscope’s orientation, a bang-bang control scheme is used toswitch the dominant preload between two electrode axes that are oriented at a 45 degree angle from the vehicleroll axis, the A and B electrode axes. Proper phasing of this signal allows the spin axis orientation to be movedfrom the post spin-up orientation — up to 500 arc-sec from the vehicle roll axis — to a final, specified,orientation within 10 arc-sec of the roll axis.Figure 9-15. Simulated (L) and actual (R) spin axis alignment tracks for Gyro 3 coarse alignmentFigure 9-15 (left) shows the trajectory of a gyro spin axis during the alignment process; the goal is the circle nearthe origin. With this system, alignment rates on the order of 3 arcsec/hr can be generated when driven by thehigh voltage amplifier using 50 V common mode on the electrode axes (coarse alignment mode), while rates of0.1 arc-sec/hr with a 8 V drive from the low voltage amplifiers (fine alignment mode); see Figure 9-16. Thespiral shape of the predicted trajectory is expected because a convenient, though sub-optimal, switching surfacewas used in the bang-bang controller: the pickup loop on the gyroscope parting plane.Figure 9-15 (right) shows the actual performance for the spin axis alignment of Gyro 3; note that the gyroscopefollows a similar curve to the prediction. All four gyroscopes were aligned successfully using this method.Gravity Probe B — Post Flight Analysis • Final Report March 2007 269