Bearing systems for high speed rotating shafts, such as turbocharger shafts, include a first ball bearing in one end of an elongated cylinder capable of carrying axial thrust in both directions and a second ball bearing in the opposite end of the elongated cylinder with its outer race slideably mounted in the cylinder against the biasing force of a preload spring. The second ball bearing is free to move axially with the shaft upon axial expansion of the shaft when exposed to high temperature. The inner races of the ball bearings are clamped to and rotate with the shaft as part of the rotating assembly.