Optimal multi-segment cylindrical capacitive sensor

This paper discusses a multi-segment cylindrical capacitive sensor (CCS) optimized to minimize the effects of geometric errors. Spindle error motion is a key index of performance in rotating machines. The CCS was developed as an alternative of probe-type sensors and applied to several rotating machine applications since the spindle error motion can be measured accurately without a significant effect of geometric errors. However, research on the CCS has so far focused on the case of two pairs of sensor units. Therefore, it is necessary to investigate the general case or multi-segment CCS for a better rejection of geometric errors. This work presents generalization of the previous CCS system down to a multi-segment CCS. We first introduce a multi-segment CCS that consists of equally spaced pairs of sensor units of the same angular size on the circumference, and derive a mathematical model of the measuring process with the multi-segment CCS. Theoretical analysis using the mathematical model shows that a multi-segment CCS with n pairs of sensor units can remove all harmonic errors except the (2nk - I)th and (2nk + I)th (k = 1, 2, 3....) harmonic errors. In addition, the angular size of the multi-segment CCS is optimized to minimize the effects of geometric errors through a minimum norm approach. The optimal multi-segment CCS with n pairs of sensor units has the largest sensor unit size among those which remove the (2n - I)th harmonic error, which is the lowest harmonic error that cannot be removed with n sensor unit pairs.