19.2 PITCH SURFACES AND GEAR RATIO

We recall that in the case of transformation of motions between crossed axes the relative motion is the screw one and the axodes are hyperboloids of revolution. There is nothing common to the pitch surfaces of a worm-gear drive and the axodes. The pitch surfaces are two cylinders with the same twist angle as that of the worm-gear drive. The purpose of application of such pitch surfaces is to provide by synthesis a main point of contact of the worm and the worm-gear surfaces, the same as the point of tangency of the crossed cylinders the pitch surfaces. Henceforth, we differentiate between ordinary pitch surfaces and operating pitch surfaces. In the case of ordinary pitch surfaces, the cross cylinders are the pitch cylinders of the worm and the worm-gear.

Figure 19.2.1(a) shows the operating pitch cylinders of the worm and the worm-gear. Axes z _f and z ₂ of these cylinders form the crossing angle ?, and their shortest distance is E [Figs. 19.2.1(a) and 19.2.1(b)]. Angle ? is measured clockwise from z _f to z ₂. The operating pitch cylinders are in tangency at point P. We assume that the worm is located above the worm-gear. The intersection of the respective cylinder with the surface of the worm thread and the worm-gear tooth surface represents a helix on the cylinder; the common tangent to both helices is t t; the unit...