Analytical calculation of the interaction magnetic force between cuboidal permanent magnets

Abstract

This paper represents an analytical method developed on the basis of the surface charge method in order to simplify the process of calculating the interaction of the magnetic fields of permanent magnets. A theoretical formulation is derived and solved numerically in order to predict the interaction between these permanent cuboidal magnets. The magnets used are identical in the sense that they are made of the same material, have the same magnetization along their axes of symmetry as well as having the same physical dimensions. Once analytical expressions were derived for calculating the interaction between the magnetic field of two permanent magnets, it was coded into MATLAB in order to carry out a numerical simulation for different situation under different parameters. The first numerical simulations were done for the interaction between two magnets and validated experimentally. This validates the expressions derived and allows for the simulation of much more complicated situation involving a larger number of magnets. A configuration of the magnets was required in order to produce a continuous translational motion along. In order for it to generate a continuous translational motion, slope of the resultant magnetic force acting on the magnet along the track has to be increasing along the length of the track. Once this increasing slope was achieved numerically, experimental validation was needed. Hence, a track was constructed according to configuration achieved using MATLAB and was found to produce the continuous translational motion just as predicted and needed. Next, a formula was derived and solved for the force calculation induced by the interaction of two magnetic fields. A test using the Universal Testing Machine (UTM) was used in order to verify the results achieved using the theoretical method mentioned. A graph was then draw comparing the results achieved between the theoretical and experimental method. This graph showed a similar trend between both curves with discrepancies between the points on the graph that lie within the limits of experimental accuracy. Once the force was calculated, only the velocity of the magnet was missing in order to calculate the power produced by this moving magnet, hence the average velocity for the magnet along the track was calculated.