Figure 14-9.--Helix cut with two different cutters.
Figure 14-8.--Formulation of a lead triangle and a helix angle.
Figure 14-10.--Formation of helical gear cutter selection.
thickness (CTN). The CTR is the thickness of the tooth
measured parallel to the gear's face, while the CTN is
Selecting a Helical Gear Cutter
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
NTCS = NT × sec
RPD by 3.1416 (š) (fig. 14-8, view C), then use the
formula:
This formula is taken from the triangle in figure
Lead = RPC × Cotangent
14-9