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In order to develop a new magnetic bearing set for a flywheel energy storage prototype, it was designed and simulated some configurations of Permanent Magnetic Bearings (PMB) and Superconducting Magnetic Bearings (SMB). The bearings were assembled with Nd-Fe-B permanent magnets and the simulations were carried out with the Finite Element Method (FEM). The PMB was designed to reduce the load on SMB and provide radial positioning of the whole set. SMB were designed with YBCO superconductors and an assembly of permanent magnets. Several configurations of permanent magnets were simulated, trying to maximize the magnetic flux gradient in direction orthogonal to the movement and flux density in the surface of the superconductors. Early experiments have shown an increasing stiffness and levitation force with increasing field gradient and intensity. It was also a goal to reduce the stray field outside the bearing. The levitation force of the SMB using a flux shapers configuration was measured and compared with FEM simulation, showing very good agreement. The simulation of a SMB using Halbach array configuration shows that it increases the levitation force and reduces the stray field.