ABOUT OF THE DYNAMICS OF FORCED OSCILLATIONS IN NONLINEAR SYSTEMS
The article discusses the issues of determining the effectiveness indicators of an electromagnetic vibration exciter in a dynamic mode of operation. It is established that this system is whole system of electrical and mechanical circuits. In this case, the mechanical part operates in the mode of forced vibrations. The oscillation parameters of the system, such as amplitude, frequency, and phase, largely depend on the parameters of the system load. For the analysis of this system, differential equations describing an electromagnetic vibration exciter have been compiled. For this purpose, the dependence L(x) of the inductance on the displacement is used. The dynamic modes of one of the ways of asynchronous excitation of an electromagnetic vibration exciter are investigated. The accuracy analysis and the evaluation of the results were performed by the Fisher criterion for the regression model. To analysis of transients in the electromagnetic vibration exciter, were used the software packages WinFact and MatLab to simulate and optimize dynamic systems. It is established that the system, depending on the initial conditions in the simulation, goes into one of two very different modes. In this case, the initial zero conditions switch the system into a “cyclic” mode, and in other, non-zero conditions, the system goes into an approximate cyclic mode, characterized by a higher speed of movement of the anchor. The parameters of the steady state cyclic movement are determined by the method of harmonic balance.
The obtained results allow us to describe autoparametric oscillations of the electric equivalent circuit. It has been established that the compilation of harmonic balance equations corresponding to a linear system helps simplify the solution of the task of determining the dynamics of forced oscillations. The expressions for determining the tractive force and the current flowing through the circuit are obtained, the wavelet spectra of vibration are constructed using the MatLab software package. As a result, for the mechanical part of a nonlinear system, in fact, it is necessary to solve only harmonic balance equation. The results show that this theoretical model allows a more qualitative and accurate assessment of the observed phenomenon. Based on this, the asymptotic conditions for solving the harmonic balance equations of a nonlinear system are determined. The expressions for the electromagnetic force acting on the anchor are obtained, the conditions for the harmonic balance of the mechanical part of the system are determined. The expressions obtained allow us to construct the amplitude-frequency characteristics of the electromagnetic vibration exciter. In conclusion, not only qualitative, but also quantitative estimates of the observed phenomena were obtained. It has been established that mechanical oscillations of a nonlinear system are insensitive to changes in the supply network and practically have a large amplitude with a constant frequency.
Атабеков Г.И. Теоретические основы электротехники. Линейные электрические цепи .СПб.: Лань, 2009. - 592 с.
Бессонов Л.А. Теоретические основы электротехники.Электрические цепи: учебник для вузов. 10-е изд. М.: Гардарики,2002.— 638 с.
МосколенкоВ.В. Электрический привод: учебник для студ. высш. учеб. Заведений / В.В.Москоленко. М.: Издательский центр «Академия», 2007.-368 с.
Джафаров С.Ф. Теория электромагнитного вибровозбудителя АГНА, Известия Высших Технических Заведений Азербайджана, Баку 2008, №4 (56), стр. 53- 59.
Lucien Le Cam (1986) Asymptotic Methods in Statistical Decision Theory: Pages 336 and 618–621 (von Mises and Bernstein).https://en.wikipedia.org/wiki/Fisher_information - cite_ref-3 Frieden&Gatenby (2013)
Джафаров С.Ф. «Вейвлет анализ динамики электромагнитного вибро-возбудителя» Известия высших технических учебных заведений Азербайджана. №5 2005
Jafarov S.F., Safarov R.S. “The simulation and estimation of the vibration machines efficiency parametrs” Interactive systems The problems of human-computer interaction . Proceedings of the international conference. Ulyanovsk 2003