Nonlinear analysis of cylindrical capacitive sensor

A cylindrical capacitive sensor (CCS) is developed and applied to several rotating machinery applications due to its merit of accurately measuring the spindle error motion without a significant effort. So far, analysis and design were performed using a linearized approximate model of the CCS. This paper presents a nonlinear analysis of the CCS. First, a nonlinear mathematical model of the measuring process of the CCS is derived, and it is shown that the nonlinearity is affected not only by the rotor position but also by the angular size of the CCS. Second, odd harmonic errors are found to exist in the measured rotor displacement through a power series form derivation of the measuring process. Among various harmonic errors of the nonlinear gain, the third harmonic error is found to be largest one and this error can be removed by using an eight-segment CCS with 120° sensor angular size. Third, a nonlinear analysis of the effect of geometric errors is performed and the analysis result shows that the harmonic geometric error of a rotor is transmitted into different harmonic errors and its transmitability increases as the normalized eccentricity increases. The nonlinear analysis in this paper will give us useful information for the design and application of the CCS.