PURPOSE: To limit rotation speed of a back-up bearing not beyond the designed maximum rotation speed of a rotation element after a magnetic bearing is failure and until the back-up bearing rotates at the same speed as the shaft for an assembly in which a rotation shaft is supported by the magnetic bearing having a back-up bearing.

CONSTITUTION: A back-up bearing 18 has one or more than one element(s), each of them is constituted by cylindrical rotation elements 20 supported on a single race or ball races 20 equipped with radical inner side race 22 and radical outer race 26. When a radical outer race is provided, it is secured to a base body 16, a dry bearing materials is secured to each race and the dry bearing material has a surface opposite to the shaft.