Abstract: The assembly includes an outer race secured in one of the spindle bores in the revolving head of an automatic screw machine, and an inner race or sleeve which is adjustably secured to the associated work spindle. A plurality of roller bearing elements mounted in the outer race roll on the periphery of the sleeve to rotatably journal the forward end on the spindle in the head. The sleeve has a tapered, truncated-conical bore which mates with a complimentary taper formed on the outer periphery of the spindle. By rotating an adjusting nut on the spindle, the sleeve can be driven axially on the spindle in a direction which causes it to be slightly expanded radially to take up any undesirable radial play in the bearing assembly.