A touchdown bearing for supporting a rotor including: an inner race having a first inner circumferential surface; a self-lubricating insert having a second inner circumferential surface and affixed to the first inner circumferential surface, the second inner circumferential surface extending radially inward past at least a first portion of the first inner circumferential surface, an outer race located radially outward of the inner race; and a plurality of rolling elements configured radially between the inner and outer races to enable the outer race to rotate freely relative to the inner race.