Optimal multi-segment cylindrical capacitive sensor

Abstract

This paper discusses a multi-segment cylindrical capacitive sensor (CCS)optimized to minimize the effects of geometric errors. Spindle error motion is akey index of performance in rotating machines. The CCS was developed as analternative of probe-type sensors and applied to several rotating machineapplications since the spindle error motion can be measured accurately without asignificant effect of geometric errors. However, research on the CCS has so farfocused on the case of two pairs of sensor units. Therefore, it is necessary toinvestigate the general case or multi-segment CCS for a better rejection ofgeometric errors. This work presents generalization of the previous CCSsystem down to a multi-segment CCS. We first introduce a multi-segmentCCS that consists of equally spaced pairs of sensor units of the sameangular size on the circumference, and derive a mathematical model ofthe measuring process with the multi-segment CCS. Theoretical analysisusing the mathematical model shows that a multi-segment CCS withnpairs of sensor units can remove all harmonic errors except the(2nk − 1)th and(2nk + 1)th(k = 1, 2, 3,...)harmonic errors. In addition, the angular size of the multi-segmentCCS is optimized to minimize the effects of geometric errors througha minimum norm approach. The optimal multi-segment CCS withn pairs ofsensor units has the largest sensor unit size among those which remove the(2n − 1)th harmonic error, which is the lowest harmonic error that cannot be removedwith nsensor unit pairs.