The tailstock center you have is designed for turning and drilling table lamps, with the workpiece supported with the point center in place, wind it in until the ring cuts in to the workpiece, remove the point center and wind the ring center back in to the groove. Using an 8mm long hole lamp auger drill half the length of the work piece then fit a drive / counter bore drive in to the headstock end, repeat step one with the tailstock center then drill the other end until the holes meet. With the lathe running slowly, grasp the workpiece and gently wind in the tailstock to bore the counter bore. Now turn the finished design with no fear of the hole bursting out of the side. Have fun (safely).
