A bearing assembly lockable onto a shaft. The bearing assembly comprises a first tapered adapter defining a first axial bore for the receipt of the shaft which has an outer, annular tapered surface. There is a second tapered adapter defining a second axial bore for receipt of a sleeve portion of the first adapter. The second tapered adapter has an outer, annular tapered surface tapered at a taper angle opposite to that of the first tapered adapter such that the first and second tapered adapters co-operate to define an outer annular surface having a generally V-shaped configuration that tapers from spaced greater diameter outer ends to adjacent lesser diameter inner ends. The opposed tapered surfaces have a fixed limit in their axial travel toward each other along the shaft defined by engagement of the lesser diameter inner ends. When the tapered surfaces reach the end of their travel, the bearing supported on the tapered surfaces is tightened on the shaft with the correct clearances.