Analytical model for the normal component of magnetic induction of a permanent magnets

Objectives . In a measuring system based on the inductive transmission of information from a moving structure to a stationary signal receiver, the signal carrying useful information about the parameters of the moving structure is formed by a magnetic system containing a permanent magnet mounted on the stationary part of the measuring system. The magnetic field of the permanent magnet (MFPM) determines the magnetic flux, and, consequently, the induction current in a conducting coil located on the moving structure. In order to theoretically justify the parameters of the measuring system including the optimization of its components, a simple and easy-to-use analytical model of the useful signal for determining the requirements for the mathematical description of the MFPM is required. The use of known solutions for developing an analytical model of the useful signal of the measuring system is complicated by the need to use inverse trigonometric functions or the results of numerical calculations. The present work sets out to obtain an exact solution to the problem of calculating the MFPM and on this basis to develop a simple, convenient analytical model of the normal component of the magnetic induction vector (NCMIV) of a permanent magnet used to develop an analytical model of the useful signal. Methods . The equivalent solenoid method was used along with mathematical analysis approaches. Results . An exact solution for calculating the normal component of the magnetic induction vector of the parallelepipedshaped permanent magnet was obtained. Based on this, a straightforward and easy-to-use analytical model of the NCMIV was developed, which closely approximates the formula derived for the exact solution. Conclusions. The developed analytical model of the NCMIV can be used for theoretical development of an analytical model of the useful signal of a measuring system with inductive transmission of information about the parameters of a moving structure to a stationary signal receiver.