This paper describes an analytical method to compute the planar and normal forces of an electromagnetic planar actuator. Fig. 1 presents a tri-dimensional view of an electromagnetic planar actuator. The actuator has a mover with two permanent magnets and a ferromagnetic stator covered by two orthogonal armature coils. The mover relies on a suspension system with linear bearings that enable bi-directional motion. The movement can take place along the x-axis and y-axis simultaneously. When the permanent magnets are located over excited coil phases, a planar magnetic propulsion force will be created on the mover and that drives the latter. The planar force is computed by means of Lorentz force. The intensity and direction of that force depend on the values of the active coil magneto motive force and the air gap flux density established by the permanent magnets. A normal force is also present as an attraction force between the mover and the armature core and depends on the magnetic flux density distribution produced by the permanent magnets and by the currents in the armature phases. The normal force was obtained by means of Maxwell Stress Tensor. The analytical models were validated by means of a Finite Element model and by experimental results. As the forces depend on the behaviour of the distribution of magnetic flux density, the authors developed an analytical method to preview such distribution. The planar actuator was divided into regions and boundaries in order to obtain the equations of the magnetic field and of the resulting forces. The magnetic field due to the permanent magnets is analysed separately from the magnetic field produced by the armature windings. The force that produces planar movement depends on the current density in the x and y phases and on the z-component of the flux density produced by the permanent magnets.
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