Selection of electrodes geometry for contactless suspension of a conducting sphere

Electrostatically supported gyroscope (ESG) is the key component of long-term autonomous navigation system by virtue of its high precision. With the aid of the case rotation-dwell technology, the case-fixed drift of the ESG is largely averaged out and then the precision is mainly determined by the rotor roundness, electrodes geometry, suspension control law and circumstances stability. With the certain manufacturing limit and careful suspension system design, the factors of rotor roundness, circumstances stability and suspension fluctuation are already bounded to a certain level, so it is important to check the electrodes geometry to improve the performance of the ESG. In this paper, aiming to minimize the drift of gyroscope, the problem of determining the electrodes geometry is addressed with compromising suspension stiffness and practical realization. Firstly, a general drift model is put forward for arbitrary electrodes geometry and rotor attitude. It is found that the drift along the electrode axis vanishes when the rotor rotation axis coincides with this very electrode axis and the drift model turns to be simpler. Then, the effect of electrode shape on disturbing torque is analyzed with identical electrodes and isotropic stiffness. It is found that when the electrode shape is symmetrical about its geometry axis, the drift caused by cross-axis effect will be minimized and a simplest drift model can be potentially obtained with some sacrifices on suspension stiffness. Finally, two commonly used electrodes shape, hexahedral projection electrodes and spherical crown electrodes which respectively represents the potential maximal stiffness and the simplest form are compared with its drift magnitude, model cleanliness, suspension stiffness, disturbing torque, cross-axis effect and engineering realization. The result is useful in problem of electrode geometry selection.