Geometric error filtering performance of a cylindrical capacitive sensor (CCS) with circumferential gap

In measuring the radial error motion, geometric errors of the target rotor can be filtered effectively using a cylindrical capacitive sensor (CCS). Since the CCS consists of several sensor electrodes, there are circumferential gaps between sensor electrodes for electric insulation. However, CCSs, so far, have been analyzed ignoring the circumferential gaps. In this paper, the electric potential distribution and capacitance in the circumferential gap are investigated through FE (finite element) analysis. Based on the FE analysis, extra capacitance in the circumferential gap is represented by the equivalent length extension of the sensor electrode so that we can investigate the circumferential gap effect analytically. The circumferential gaps are shown to affect significantly the geometric error filtering performance of the CCS. In addition, the robust analysis shows that the four-segment CCS is more robust to the uncertainties of the circumferential gap than the eight-segment CCS. Finally, using the beat phenomenon of a magnetic bearing rotor system, an odd harmonic geometric error is verified experimentally to be filtered effectively by selecting a particular CCS geometry considering circumferential gaps.