Problems related to mathematical modeling of electromagnetic vibrators

The article deals with the problems of mathematical modeling of nonlinear electromagnetic vibrators. Based on the mathematical analysis of differential equations describing the oscillatory movements of electromagnetic exciters, the reasons for the discrepancy between mathematical experiments and experiments carried out on real objects are shown. With the help of theoretical analysis, a correct mathematical description of the physical action of a semiconductor diode in the power circuit of single-cycle electromagnetic vibrators is shown. Mathematical analysis of the excitation force showed that the equation describing electromagnetic excitation could be successfully taken into account in the right side of the equation describing mechanical vibrations, the right side of which describes the harmonic excitation force. The paper also shows a new simplified and accurate method for obtaining an important amplitude-frequency characteristic of nonlinear oscillatory systems with a discrete change in the excitation frequency. Mathematical experiments have shown that in the conditions of modern digital technology, vibration machines with two degrees of freedom should be considered as two-mass systems, and not as systems reduced to one mass, which was done to simplify calculations. When designing vibrators, taking into account technological loads or various dissipative forces acting on masses, it is very important that the mathematical model of the design scheme be considered as a two-mass system.