Figure 14-6.--Development of evenly spaced slots with an
not cut at an angle. One of these differences is shown in
the following example:
Figure 14-7.--Development of the helix angle.
You will need a 10-inch circular blank to cut 20
The lead of a helical gear is the longitudinal
one-quarter-inch wide slots spaced one-quarter
distance a point on the gear travels during one complete
of an inch apart parallel to the gear's axis of
revolution of the gear. During the gear manufacturing
rotation. But you will need a 10.6-inch circular
process, lead relates to the travel of the table.
blank to cut the same slots at an angle of 19°22´
The helix angle is the angle between a plane parallel
to the rotational axis of the workpiece and the helix line
Helical gears are measured at a right angle to the
generated on the workpiece. Use this angle to set the
milling machine table to cut the gear. Also use it to
tooth face in the same manner as spur gears with the
establish the relationships between the real dimensions
same diametral pitch.
and the normal dimensions on a helical gear.
DIMENSIONS OF A HELICAL GEAR,
Determining the Dimensions of a Helical Gear
REAL AND NORMAL
The RPD is the easiest helical gear dimension to
determine. Simply subtract twice the addendum from
Every helical gear contains a theoretical spur gear.
the ROD, or
Any gear element formula used to calculate a spur gear
dimension can also be used to determine an equivalent
RPD = ROD - 2 ADD
helical gear dimension. However, the helical gear
dimension is known as a normal dimension. For
To determine the other major dimensions, you must
example, the number of teeth (NT) on a helical gear is
relate real and normal dimensions trigonometrically
considered a normal dimension. Remember, though, all
through the helix angle. Then by knowing two of the
normal gear elements are calculated dimensions and
three components of the trigonometric relationship, you
therefore cannot be measured.
can determine the third component.
= Normal pitch diameter (NPD)
angle is the angle between the gear's axis of rotation and
the helix. In this view, the RPD and the NPD are related
Although most helical gear dimensions are normal
through the secant and cosine functions. That is,
dimensions, a few dimensions are real (measurable)
dimensions. Examples of real dimensions are the
outside diameter (OD), called the real outside diameter
(ROD), and the pitch diameter, called the real pitch
diameter (RPD). Two other real dimensions are the lead
mathematically shifted so we can compare the real
chordal thickness (CTR) and the normal chordal
and the helix angle