158 the groove 157 is formed in a circular shape in the interior of the motor shaft 154 and the cross section of the groove 157 is rectangular the groove 157 is formed in a bevel shape in which there is provided an inner tapered surface 157 a as shown in fig3 the stop ring 158 is provided to correspond with the groove 157 and is inserted into the groove 157 the stop ring 158 has a certain thickness smaller than that of the groove 157 the stop ring 158 includes an opened center portion and is inserted into the interior of the groove 157 and has a diameter larger than that of the groove 157 for thereby being enlarged in the outer direction and has a cut outer portion in addition a bevel shape stop ring 158 has an outer surface 158 a tapered to correspond with the inner tapered surface 157 a namely the force applied to the outer portion of the stop ring 158 is converted into a force in an axial direction by the outer tapered surface 158 a and the inner tapered surface 157 a so that the stop ring 158 is closely contacted with the inner lock screw 156 of the groove 157 in the electronic power steering apparatus for a vehicle according to the present invention in a state that the ball nut 155 is inserted into the motor shaft 154 and the friction member 159 is engaged to one surface.