Analytical model of a cylindrical linear module with permanent magnet based on approximation functions

The authors of the paper analyse and carry out simulation studies on a cylindrical linear “excitation coil – permanent magnet” module, which is an elementary component of many electromagnetic devices and linear permanent magnet (PM) electric motors. The geometric dimensions of the module and the winding data of the excitation coil correspond to the constructed prototype. The most important result of the work is demonstrating that it is possible to approximate the discrete function of the electromagnetic force acting on the runner, the flux linked with the excitation coil and the electromotive force of motion induced in the excitation coil using a modified Kloss function. The consequence of these approximations is conversion of the classical field-circuit model with Lookup Tables into a purely analytical model. Using this model, simulation studies of the oscillatory motion of the runner were carried out in the MATLAB Simulink environment, confirming the usefulness of the developed analytical model in the numerical analysis of dynamic states. The next part is dedicated to the experimental verification of the proposed analytical mathematical model. A laboratory setup with a high-speed camera was designed and built. A comparative analysis of the time curves obtained from measurement studies and simulation studies was conducted using the example of the damped oscillatory motion of the runner. The root mean square errors (RMSEs) were determined for various time intervals, relevant from the perspective of implementing the developed analytical mathematical model in control systems of different linear electromagnetic devices with permanent magnets.