The invention relates to a turbomachine bearing support (1) supporting at least one bearing and extending according to a longitudinal principal axis of the turbomachine and comprising: a truncated part (11) having a diameter increasing from upstream to downstream; a flange part (12) which extends from the truncated part (11) as far as the bearing (5, 6) to which it is fixed by an axial flange (121), and having at its downstream end a radial internal flange (17) fixed to an oil inlet cover defining with the bearing (5, 6) an oil inlet container (170); oiled air clearance ducts (71) projecting downstream relative to the flange part (12) and on the oil inlet container (170) and to the other side upstream of the flange part (12) directly radially externally relative to the axial flange (121).