Abstract:The direct 3-dimensional (3D) method represents a mathematical assembling of the magnetic field of separate cuboidal magnets and vectors of a coil current density of a linear moving coil actuator within the global space. The mathematical description allows a variation of design parameters of the actuator and position of the coils with respect to the magnet array. The presented method describes the complete analytical derivation of the 3D magnetic field and coil current. Then a numerical integration is applied to obtain the forces and torques appearing in 6 degrees of freedom (DoF) actuator as the functions of the relative position of the coils with respect to the magnets in 3D space. The method and its governing equations are implemented as a rapid-design computational tool in Mathcad, and further the simulation results are experimentally verified.
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