thickness (CTN). The CTR is the thickness of the tooth

measured parallel to the gear's face, while the CTN is

measured at a right angle to the face of the tooth. The

When you cut a spur gear, you base selection of the

two dimensions are also related through the secant and

cutter on the gear's DP and on the NT to be cut. To cut

cosine functions. That is,

a helical gear, you must base cutter selection on the

helical gear's DP and on a hypothetical number of teeth

set at a right angle to the tooth path. This hypothetical

If we could open the gear on the pitch diameter

number of teeth takes into account the helix angle and

(PD), we would have a triangle we could use to solve

the lead of the helix, and is known as the number of teeth

for the lead (fig. 14-8, view A).

for cutter selection (NTCS). This hypothetical develop-

Figure 14-8, view B, shows a triangle; one leg is the

ment is based on the fact that the cutter follows an

real pitch circumference and the other is the lead. Notice

elliptical path as it cuts the teeth (fig. 14-9).

that the hypotenuse of the triangle is the tooth path and

The basic formula to determine the NTCS involves

has no numerical value.

multiplying the actual NT on the helical gear by the cube

To solve for the lead of a helical gear, when you

of the secant of the helix angle, or

know the RPD and the helix angle, simply change RPD

to RPC (real pitch circumference). To do that, multiply

RPD by 3.1416 (š) (fig. 14-8, view C), then use the

formula:

This formula is taken from the triangle in figure

14-9