METHOD AND APPARATUS FOR CUTTING AN ASPHERIC SURFACE ON A WORKPIECE

A lathe and a method of using the lathe are disclosed for forming an aspheric surface on a workpiece (12), in which the workpiece (12) is mounted to a holder (10) that is rotatably carried by the spindle (8), headstock (6) and bed of a lathe (4), with that spindle (8) and workpiece (12) being rotated about the axis (14) of the spindle (8) with the workpiece (12) being engaged by a forming tool (18) which forming tool is moved through an arcuate path about an axis (24) that is generally transverse to the spindle axis (14). The method and apparatus provide further for determining the time-varying angular position of the forming tool (18) along the arcuate path, for determining the time-varying angular position of a point on the workpiece (12) about the spindle axis (14) and for reciprocating the workpiece holder (10) and the workpiece (12) held thereby relative to the lathe headstock (6) and to the forming tool (18) in synchronization with the movement of the forming tool (18) and with the rotation of the workpiece (12) about the spindle axis (14) to form the desired contoured surface. Specified relationships are given for the movement of the workpiece holder (10) along the spindle axis (14) in relationship to the angle of rotation of the workpiece about its axis, the movement of the forming tool (18) and the radii of curvature desired.