A spindle assembly (20) adapted to be mounted on the rotatable head (21) of a Davenport® multi-spindle automatic screw machine, broadly includes a one-piece outer spindle (38), a seal member (39), a front bearing assembly (40A, 40B, 40C), a front bearing retainer nut (41) forming with the seal member a tortuous passageway (85), a two-part spacer (37), a rear bearing assembly (44A, 44B), and a rear bearing retainer nut (45).