Abstract: A tapered shaft retention apparatus is used with a shaft having a shoulder, a cylindrical surface, a smooth conically tapered surface, and an annular member such as an inner race of a bearing assembly mounted on the cylindrical surface. A sleeve is mounted on the shaft with an adjustment nut screwthreadably mounted thereon, and an internally tapered hub is mounted on the tapered surface in abutment with the nut with a preselected press fit. This assures the transmission of torque through the hub and positions the bearing assembly on the shaft. During assembly the hub is initially installed at an ambient temperature and the adjustment nut set at a preselected clearance therefrom, the hub is then removed and thermally expanded and reinstalled in abutment with the nut to establish the desired press fit.