Vibroconverter mathematical model based on the levitation effect

Abstract

Modern requirements for the safe operation of nuclear power plants dictate the need to introduce systems for early reactor plants state diagnosis. Vibrations have always been a threat to the safe nuclear power plants operation, therefore, solving the issues of improving the nuclear power plants vibronoise diagnostics accuracy, especially in the field of ultra-low frequencies, is an urgent task. The most promising way to solve the problem of flexible guides in electromechanical vibration transducers is the levitation effect, which makes it possible to completely eliminate mechanical contact and, accordingly, reduce the sensitivity threshold of the transducer. The article presents an analysis of existing vibration transducers and offers analogue and digital mathematical models of the magnetic levitation system, taking into account the influence of the electromagnetic force nonlinearity. The characteristics of such a nonlinear system are studied using the method of harmonic linearization, which makes it possible to obtain an equivalent linear system. At the same time, the third order terms of the electromagnetic force expansion in the Taylor series are taken into account, which made it possible to obtain a more accurate analogue the vibration transducer model. For the developed vibration transducer digital model, using the z-form method, a system function and the corresponding difference equation were obtained. Expressions and graphs of transient, pulse and frequency characteristics are derived for both analogue and digital vibration converter models, which allow us to conclude about the accuracy and adequacy of the developed digital model. Using obtained vibration transducer digital models will make it easier to model its operation and reasonably select the vibration transducer initial parameters.