The invention relates to a hydrodynamic bearing system for the rotary bearing of a spindle motor particularly to drive the platter(s) in a hard disk drive having a stationary shaft, a bearing sleeve journaled to be rotatable about the axis of the shaft and a cover plate fixedly attached to the bearing sleeve to cover the bearing sleeve in the region of the free end of the shaft, the surfaces of the shaft, the bearing sleeve and the cover plate facing each other and spaced apart from each other by a bearing gap forming at least one radial bearing region and at least one axial bearing region.The invention is characterized in that the cover plate has a cylinder-shaped shoulder concentric to the axis and having a thread to receive a fastening screw which is rotatably accommodated in a recess in the end face of the shaft in such a way that the bearing gap continues between the inner surface of the recess and the outer surface of the shoulder.