not cut at an angle. One of these differences is shown in

the following example:

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 axis of rotation (fig. 14-6).

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.

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

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.

Look at figure 14-7, view A, and recall that the helix

For example:

= *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

In figure 14-7, view B, the triangle has been

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

14-8

Integrated Publishing, Inc. |