Disturbances in reaction wheels; from measurement to modelling

Disturbances in reaction wheels have been long a crucial aspect for many scientific observation missions. An accurate and reliable disturbance model to understand and evaluate the influence of reaction wheel disturbances to the spacecraft is critically needed. Several reaction wheel disturbance models have been developed over time, using both empirical and theoretical approaches [1][2]. These models are able to capture the main features of disturbances such as ball bearing vibrations, unbalance of the rotor and the resonances of the structures. However, because the disturbance measurement equipment was limited in both stiffness and sensitivity, the empirical model output was not effective. In addition, the empirical model algorithm did not include structural resonances. This paper presents an improved disturbances measurement process and a reliable disturbance model by combining an empirical and a theoretical disturbance model. The empirical model is obtained from several wheel types (18Nms – 45Nms) at Moog-Bradford using a microvibration test based on a dedicated reaction wheel characterization table at ESA. With the state of the art micro-vibration test facility, the empirical data has a good accuracy to be used to derive an empirical model. The empirical model also includes the transmissibility of vibration sources through up to two wheel structural resonances in all six disturbance forces and moments. The theoretical disturbance model is derived from the equation of motion of a rigid rotor and disc supported by two ball bearings. This model formulates the static and dynamic unbalances of the wheel and the structural modes including gyroscopic effects of the rotor. Finally, the vibrations from ball bearings, which were obtained by the empirical model, are added to the theoretical model to form a combined disturbance model. The combined model is compared to the microvibration measurement results