Abstract: An antifriction bearing (A) that enables a shaft (4) to rotate with minimum friction in a housing (2) includes a generally cylindrical outer race (46) located in an opening (12) in the housing, an inner race (48) located around the shaft, and rolling elements (50) arranged in rows between raceways on the outer and inner races. The outer race has a cylindrical exterior surface (56), whereas the opening in which the bearing is located has a flat wall (14, 16). A stabilizing block (C) may be attached to the outer race against its cylindrical surface, and this block lies along the flat surface of the housing opening to prevent the outer race from turning in the housing opening. A sensor module (B) is located within the environs of the bearing, and it contains a plurality of sensors (110, 112, 114) which produce signals that reflect conditions under which the bearing operates. Among the conditions monitored are speed, temperature and vibrations.