PURPOSE: To reduce a manufacturing cost and ensure easy assembly by providing screws or the like on a clamping sleeve and a clamping member for cooperation to rotate the clamping member with respect to the clamping sleeve in one unit with a first mechanical element for securing the first mechanical element to a second mechanical element.

CONSTITUTION: A first mechanical element is an inner ring of a ball bearing 1 assembled in a shaft 3 as a second mechanical element. The inner ring 2 includes a sleeve 4 having outer screw portions 5 at both ends and extending to the axial direction. The inner ring 2 and the sleeve 4 are formed of metal in one unit. A nut 6 as a clamping member is threaded to the sleeve 4 and, when the nut 6 is fastened, the sleeve 4 is fastened in the radial direction with wedging operation and friction-coupled with the shaft 3. In such a device for securing the mechanical element to the shaft, a manufacturing cost is reduced and east assembly is ensured.