Hybrid FEM-analytical force and torque models of a reaction sphere actuator

This paper presents a hybrid FEM-analytical model for the magnetic flux density, the force and torque of a Reaction Sphere (RS) actuator for satellite attitude control. The RS is a permanent magnet synchronous spherical actuator whose rotor is magnetically levitated and can be accelerated about any desired axis. The spherical actuator is composed of an 8-pole permanent magnet spherical rotor and of a 20-coil stator. Due to the highly complex geometry of the spherical rotor, consisting of 8 bulk permanent magnet poles with truncated spherical shape adjusted on the back-iron structure with truncated octahedral shape, a pure analytical approach is not possible. Therefore, in this article we adopt a hybrid approach in which FEM or measured derived values are combined with other boundary conditions on a known analytical structure to derive expressions for the magnetic flux density, the force, and the torque. The Laplace equation is solved by exploiting powerful properties of spherical harmonic functions under rotation to derive closed-form linear expressions for all possible orientations of the rotor. The proposed models are experimentally validated using a developed laboratory prototype and with finite element simulations.