Modeling capacitance of capacitive transducer

Abstract

The modern circulating electrical machines used to produce electric power and act as drivers are wide spread in electric-power industry. One of the typical mechanical troubles electrical machines encounter is rotor eccentricity. It is usually accompanied by non-uniformity of air gap between stator and rotor and formation of additional magnetic fields in it which leads to deterioration of electromechanical features of electrical machines and increase in electric power loss. With a large displacement of the rotor, the rotor core starts to rub against the stator core. It is accompanied by fairing of cores and overheating. Severe overheat of rotor core can lead to rotor coil burning-out, and overheat of stator core is accompanied by accelerated thermal deterioration of insulation and a subsequent fault in its coil. This can lead to total damage of the machine. Nowadays, rotor eccentricity can be determined by using methods based on measuring values which are caused by additional magnetic fields. However, the sensitivity of the methods mentioned is limited by the need of considering the interferences due to variation of mains settings and loads. In this sense, capacitive sensors used as measuring capacitive transducers are known to be more perspective diagnostic means for determination of rotor eccentricity. However, there are no methods for calculation of parameters of such measuring transducers with complex geometry of electrodes. The current document features a simple method for calculation of a capacitive transducer with electrodes of various shapes. This method comprises modeling the transducer electro-statical field using nets method and calculation of capacitance based on the empirical formula proposed. As an example, the method efficacy is checked by determination of plate capacitor capacitance using the method proposed and classical formula. It was demonstrated that the modeling accuracy did not exceed 5%. The example included evaluating a capacitance for electrodes with toothed rotor of electrical machines and with different positions of capacitive transducer plates relative to rotor slot opening. This document also contains the principle of forming boundary conditions and electrostatic potential distribution patterns, and the calculation of capacitance.