Modeling of limiting states in the operation of electromechanical transducers

Mathematical support and software for computers, complexes and networks


Аuthors

Lisov A. A.*, Chernova T. A.**, Gorbunov M. S.***

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: 3141220@mail.ru
**e-mail: chernova3244@gmail.com
***e-mail: alfred.hammersmit@yandex.ru

Abstract

In actual operating conditions of electrical industry’s products the degrading changes of their properties should be accounted for. The object of research is various kinds of electromechanical converters, for which even a slight degradation of the properties leads to the serious technogenic aftermath. Methodological basics for solving such problems were considered and suggested; a number of regularities of degrading changes is established, and mathematical models were developed.

Analysis of the characteristic parameters changes allows the four most typical types of functions for describing these regularities: the entire rational functions or polynomials; fractional rational functions; exponential functions; function describing the saturation processes. For each dependence under consideration, examples of the limiting state attainment forecast and the residual resource calculation are given. Models’ building of degrading changes supposes tabulating the measured values and selection of such approximating function, which will provide the least mean square deviation from the tabular dependence. The best results in solving the problems of this kind is ensured by the method of least squares (OLS).

Analysis of considered functions degradation of processes’ descriptions allows establish the following: all functions have an initial value, known from the nameplate data on the device in service. Thus, it is expedient while the degradation changes analysis to study not the whole function, but only its degradation deviation. The initial value of the deviation function is zero, so its plot passes through the origin. When determining the number of approximating function parameters their number is reduced by one for the deflection function, therefore decreasing the order of normal OLS systems.

A practical tool for predicting the modes of functioning of electrical devices and estimating the residual resource has been developed, and a residual resource has been calculated for the degradation changes described by the dependencies of a different type. Prediction of residual resource is based on the solution of nonlinear equations, in which the degradation deviation function takes normative allowable values. The solution of the equation must be determined by limiting the value of the argument, as the moment of failure. Estimation of the residual resource of the device was performed based on the moment of failure.

Keywords:

an imitation-recurrent approach to the degradation processes of electrical devices modeling, method of least squares, types of non-linear functions of degradation change in the characteristic parameters, residual resource, attainment of the limiting state

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