The present disclosure describes a mechanical backup bearing system arrangement to work in conjunction with non-contact magnetic bearings and capable of coping with thermal expansions of the bearing components during operations. Expansions or contractions of an inner or outer race of a bearing can be compensated using particular springs providing a low profile and a proper stiffness. An electric machine system includes a rotational portion and a stationary portion. The electric machine further includes a magnetic bearing configured to support the rotational portion to rotate within the stationary portion. A mechanical back-up bearing resides in a cavity between the rotational portion and the stationary portion. A flat spring is carried by the stationary portion and abutting the back-up bearing.