Using the Coulombian Approach to Model 3-D Forces, Torques, and Stable Positions in a Master / Slave Permanent Magnet System

Previous research in master and slave systems has demonstrated the effectiveness of using permanent magnets to perform remote functions. Different approaches have been utilized by authors to model the force interactions between two or more magnets. Limiting aspects such as solution time or models with limited geometry inspired the use of a different method. The coulombian approach was used to model a master and slave system of neodymium magnets with complex 3-D orientation angles motivated by a previous prototype. The work demonstrated how the coulombian approach was applied to the master and slave system, how the force and torque interactions were calculated, and how stable positions were determined using the Newton-Raphson iterative method. Several methods for the distribution of point charges, which the coulombian approach relies on to simplify the modeling of magnets, were also demonstrated. The limitations of the model being able to provide accurate results versus computation time and separation distance between magnets was extensively explored. The model was shown to be capable of returning quick solutions for the force and torque interactions between permanent magnets and to also determine the position of a magnet needed to hold another magnet in a stable position. The results were confirmed experimentally and with an FEA package. The computation times were shown to have a large improvement over other methods even for separation distances where the magnets are in near contact. Point charge distribution methods were compared over a range of separation distances and for different numbers of point charges spread on the magnet pole surfaces. For cylindrical magnets, one method to distribute points uniformly on a disk surface performed better than the other methods. The minimum number of point charges needed for accuracy for the separation distance between the magnets was also explored, showing that the number of point charges needed for accuracy is low for small, minimum separation distance. The model was then used to provide analysis that was unavailable during the development of the motivating prototype. The analysis explored the difference between rotation schemes of the master magnet using only two degrees of freedom. A method was devised to determine how far apart magnets need to be separated for a master magnet to exert similar force and torques on a slave magnet using different rotation schemes. The change of the orientation of the controlling master magnet versus the change of the orientation of the slave magnet was also studied. The optimization of peak torque exertion on the slave magnet by the master magnet by varying the magnet geometries was also demonstrated