ANALYSIS OF STEADY-STATE HARMONIC ELECTRIC SKIN-EFFECT IN THE BYPASS OF THE CURVES OF EMDE

Abstract

Execution deep bar cage induction motors play an important role in the national economy, both in industry and in the agro-industrial complex. The intense electric skin effect that occurs in such slots performs direct work functions. Therefore, the reproduction of the corresponding elect­romagnetic phenomenon in the process of mathematical modeling should be performed with a sufficient accuracy for practice. Since in this case the current is distributed unevenly across the conductor, then such a concept of the theory of electric tracks as the ohmic resistance of the conductor loses its physical meaning. Appropriate solu­tions can be obtained only on the basis of the theory of a quasistationary electro­magnetic field. On this basis, we solved the problem in its general form. The resulting solutions are suitable for analysis of both transient and steady-state processes. Obtained with this boundary-value problem is suitable for analysis as of transient skin effect in the general case, and in the case of a deep rectangular slot of an electric machine is solved by numerical me­thods [18; 19].

As is shown by F. Emde, there is an analytical solution in the jumble of a jumbled sinusoidal current of a rectangular deep slot that lies in ferromagnetics. He proceeded from the power of the electromagnetic field. But the solution thus has the complex appearance that it was possible to offer it to the user only in a graphical form known as the "curves of Emde." At that time, the solution we have proposed, obtained by the value of the electric field strength vector on the surface of the conductor, is expressed by a simple hyperbolic function of a complex variable.

If the complex resistance of the conductor obtained by us, which includes both the ohmic and internal inductive supports, is decomposed into real and imaginary parts, then we can come to the result obtained by Emde.