Worm Pitch Diameter, Lead Angle, and Axial Pitch

Figure 19.3.1(a) shows the pitch diameter d _p of the worm ordinary pitch cylinder; p _ax is the axial distance between the neighboring threads of the worm, which is measured along the generatrix of the pitch cylinder. We designate with P _ax the ratio P _ax = ?/p _ax. The worm pitch diameter may be chosen as

Figure 19.3.1: Worm pitch cylinder (a) in 3D-space, and (b) developed on a plane.

The value of q depends on the number N ₁ of threads of the worm and the number N ₂ of gear teeth and may be picked up from a recommended set (7 ? q ? 25).

Let us develop the pitch cylinder on a plane [Fig. 19.3.1(b)]. The helix for each worm thread is represented by a straight line. The distance p _ax between the neighboring straight lines is

where N ₁ is the number of worm threads, and H is the lead. Considering as known r _p and P _ax, we can determine the lead angle on the pitch cylinder from the following equation [Fig. 19.3.1(b)]:

Lead Angle on Worm Operating Pitch Cylinder

The lead angles on the worm operating pitch cylinder and ordinary pitch cylinder are related as

where p = H/(2 ?) is the screw parameter. Equations (19.3.3) and (19.3.4) yield

where