Analytical Method for Investigating Nonlinear Magnetic Circuits of Measuring Transducers With a Standard Parameter Distribution Structure

The article proposes a new analytical method for investigating magnetic circuits with distributed parameters and nonlinear magnetic coupling. The method is based on introducing into the system of nonlinear differential equations of such circuits the condition that the second derivative of the magnetic flux with respect to the circuit length is equal to zero, as well as on assuming that one of the geometric parameters of the studied magnetic circuit – the value of the air gap between ferromagnetic cores, their thickness, width, or the linear value of the number of turns of the distributed excitation winding – is a function of the coordinate along the length of the circuit. The combination of these conditions makes it possible to significantly simplify the original system of equations and to obtain exact analytical expressions for the distribution of magnetic fluxes and magnetomotive forces along the magnetic circuit under investigation. The application of this method to magnetic circuits with a standard structure of parameter distribution and nonlinear magnetic coupling made it possible to derive analytical relationships for the air gap between long ferromagnetic cores, their width, and the linear value of the number of turns of the distributed excitation winding as functions of the coordinates along the length of the circuits. The obtained dependencies improve the linearity of the magnetic flux distribution in long ferromagnetic cores and, in some cases, allow maintaining the constancy of the magnetic field intensity between them, which is essential for ensuring the linearity of the static characteristics of many electromagnetic measuring transducers of electrical and non-electrical quantities.