The combination comprising a machine element, a tubular member and a ring fastener for mounting the machine element in the circular bore of the tubular member, the ring fastener being in the form of a split annular ring member having confronting end faces, the ring member being of a diameter slightly greater than the diameter of a bore in the tubular member, each end face having a first axial portion extending generally parallel to the axis of the ring member and a second inclined portion extending at a predetermined angle to the axis of the ring member. The first and second portions of the end faces normally align and confront in the relaxed condition of the ring member and are displaceable axially relative to one another for insertion in the bore of the tubular member and after seating in the bore displaceable in an opposite axial direction by application of an axial force adjacent the axial end faces. The end faces coact and move from a partially overlapped position wherein the edge of the first surface of one end face confronts and engages the second surface of the other end face to a circumferentially aligned position resulting in the circumferential expansion of the ring such that a radially directed friction self-locking effect between the ring and the bore is achieved.