An auxiliary bearing system may include an auxiliary bearing receiver housing and an inertia ring. The auxiliary bearing receiver housing may include an axial inner surface, a first radially extending surface, and a first arcuate surface extending therebetween. The inertia ring may include an axial outer surface, a second radially extending surface, and a second arcuate surface extending therebetween. The second arcuate surface may have a radial outer end adjacent the second radially extending surface and a radial inner end adjacent the axial outer surface. The inertia ring may define a first angle between the axis of rotation of the shaft and a first tangent at a first point on the second arcuate surface adjacent the radial outer end, and a second angle between the axis of rotation of the shaft and a second tangent at a second point on the second arcuate surface adjacent the radial inner end.