Output torque modeling of control moment gyros considering rolling element bearing induced disturbances

Control moment gyros (CMG) have been widely used in spacecraft attitude control and large angle slewing maneuvers over the years. Understanding and suppressing high-frequency disturbances in CMG's output torques is a crucial factor to achieving the desired level of payload performance. Output torque modeling of a single gimbal CMG (SGCMG) with nonlinear rolling bearing supports is conducted in this paper. Taking the installation errors and micro-vibrations of the flywheel into account, three axis output torques of a SGCMG are derived based on Newton-Euler approach and theorem of moment of momentum. Dynamic model is then constructed to obtain the micro-vibration responses of the rotary flywheel. Mass imbalances of the flywheel, flexibility of supporting structures and nonlinearity induced by one pair of angular contact ball bearings are considered in the dynamic model. Especially for the rolling bearing, an improved load distribution analysis is proposed to more accurately obtain the contact deformations and angles between the rolling balls and raceways. Various factors, including the preload condition, surface waviness, Hertz contact and elastohydrodynamic lubrication, are included in the analysis. The bearing restoring forces are then obtained through iteratively solving the load distribution equations at every time step. Dynamic tests on a typical SGCMG supported by angular contact ball bearings are conducted to verify the output torque model. The effects of flywheel dynamic/static eccentricities, inner/outer surface waviness amplitudes, bearing axial preload and installation skew angles on the dynamic output torques are discussed. The obtained results would be useful for the optimal design and vibration control of the SGCMG system.