Grinding of high-lead and gothic-arc profile ball-nuts with free quill-inclination

A method for gothic-arc ball-nut grinding is presented. The gothic-arc is a combined curve of two arcs with the same radius and shifted centers. Generally, gothic-arcs are manufactured by form grinding; the grinding wheel is formed into the gothic-arc and is tilted at the lead angle of the thread. In ball-nut grinding, which is internal grinding, interference between quill (wheel shaft) and internal surface of a workpiece limits the length of the ball-nut. In the presented method, the quill is tilted independently of the lead angle so as not to contact the internal surface of the workpiece. Instead, the wheel is formed into an optimum profile with which the nut obtains a gothic-arc profile. The procedure of finding the optimum wheel profile is presented. Grinding simulation showed that the gothic-arc thread is obtained accurately by the method, though a part of the thread surface is not a perfect gothic-arc. This method allows the use of large-diameter wheels to manufacture high-lead ball-nuts.