Abstract: A method and device for machining the tappet collars of the inner rings of roller bearings by means of a frusto-conical cup wheel is proposed wherein such cup wheel is adjustable in the axial direction of the workpiece into engagement with the surface to be machined, is angularly adjustable about a remote axis perpendicular to the axis of the workpiece to provide for an adjustment in the inclination of the annular abrading surface of the cup wheel relative to the surface to be machined, and is supported for linear oscillating movement in a direction substantially parallel to the latter surface.