Thread Forms of Milled Worms: Progress Report No. 3 of the A.S.M.E. Special Research Committee on Worm Gears

Abstract

Abstract This paper is a continuation of the material on helicoidal sections given in the author’s paper on “Worm-Wheel Contact” presented before the Society in December, 1926. It covers the equations necessary to determine the thread form of milled and ground threads in various sections and also the sections of a helicoid formed by a straight-sided lathe tool, set toward the helix angle of a thread. This last helicoid is a convolute helicoid with the inclination of its generatrix in the opposite direction to that of the helix. As an example, the worm used in the drive AW-3 in Progress Report No. 2 of the A.S.M.E. Special Research Committee on Worm Gears has been analyzed and the coordinates of the thread form in an axial section have been determined when the thread is produced by a lathe tool, a 4-in.-diameter thread milling cutter, a 12-in.-diameter grinding wheel, and by the flat side of a grinding wheel which would produce an involute helicoid. This analysis shows that the form in the axial section of a thread produced by a lathe tool, tipped toward the helix angle, will be concave. That produced by a milling cutter may be concave, convex, or a form of double curvature, depending upon the diameter of the cutter, angle of thread, diameter and lead of screw, and depth of thread. The curvature increases with a reduction in thread angle and an increase in helix angle. The milled forms become more convex with an increase in the diameter of the cutter or grinding wheel. This paper is another attempt to introduce more mathematics in the machine shop to the end that we may know more definitely the conditions with which we are contending.