Modeling of limiting states in the operation of electromechanical transducers

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

References

1. Goritskii V.M. Diagnostika metallov (Diagnostics of metals), Moscow, Metallurgizdat, 2004, 408 p.

2. Bugrov V.E., Vinogradova K.A. Optoelektronika svetodiodov (Optoelectronics of light-emitting diodes), Saint Petersburg, NIU ITMO, 2013, 174 p.

3. Kuzeev I.R., Bashirov M.G. Elektromagnitnaya diagnostika oborudovaniya neftekhimicheskikh i neftepererabatyvayushchikh proizvodstv (Electromagnetic diagnostics of equipment for petrochemical and oil refineries), Ufa, Ufimskii gosudarstvennyi neftyanoi tekhnicheskii universitet, 2001, 294 p.

4. Klunova S.M., Egorova T.A., Zhivukhina E.A. Biotekhnologiya (Biotechnology), Moscow, Akademija, 2010, 256 p.

5. Denisov V.V., Grachev V.A. Bezopasnost’ zhiznedeyatel’nosti. Zashchita naseleniya i territorii pri chrezvychainykh situatsiyakh (Life safety. Protection of the population and territories in emergencies), Moscow, MarT, 2007, 720 p.

6. Khil’chevskii V.V., Sitnikov A.E., Anan’evskii V.A. Nadezhnost’ truboprovodnoi pnevmogidroarmatury (Reliability of pipeline pneumatic hydraulic fittings), Moscow, Mashinostroenie, 1989, 208 p.

7. Bogdanov E.A. Osnovy tekhnicheskoi diagnostiki neftegazovogo oborudovaniya (Fundamentals of technical diagnostics of oil and gas equipment), Moscow, Vysshaya shkola, 2006, 279 p.

8. Dobrovol’skii G.V. Degradatsiya i okhrana pochv (Degradation and protection of soils), Moscow, Izd-vo MGU, 2002, 654 p.

9. Ivanov-Smolenskii A.V. Elektromagnitnye polya i protsessy v elektricheskikh mashinakh i ikh fizicheskoe modelirovanie (Electromagnetic fields and processes in electrical machines and their physical modeling), Moscow, Energoatomizdat, 1986, 304 р.

10. Kopylov I.P. Matematicheskoe modelirovanie elektricheskikh mashin (Mathematical modeling of electric machines), Moscow, Vysshaya shkola, 2001, 327 p.

11. Gol’dberg O.D., Gurin Ya.S., Sviridenko I.S. Proektirovanie elektricheskikh mashin (Designing electrical machines), Moscow, Vysshaya shkola, 2001, 431 p.

12. Gol’dberg O.D., Khelemskaya S.P. Nadezhnost’ elektricheskikh mashin (Reliability of electrical machines), Moscow, Akademiya, 2010, 288 p.

13. Zakovryashin A.I., Koshel’kova L.V. Trudy MAI, 2016, no. 89, available at: http://trudymai.ru/eng/published.php?ID=73384

14. Demidovich B.P., Maron I.A. Osnovy vychislitel’noi matematiki (Computational mathematics foundations), Moscow, Lan’, 2011, 664 p.

15. Lisov A.A., Chernova T.A., Gorbunov M.S. Vestnik Moskovskogo aviatsionnogo institute, 2017, vol. 24, no. 2, pp. 150-159.

16. Lisov A.A., Chernova T.A., Gorbunov M.S. Modelirovanie nelineinykh protsessov v elektrotekhnicheskikh ustroistvakh metodom naimen’shikh kvadratov (Modeling of nonlinear processes in electrical devices using the least squares method), Moscow, Infra-M, 2015, 120 p.

Download