T-48
6.1 Generation Of The Helical Tooth
The helical tooth form is involute in the plane of rotation and can be developed in a
manner similar to that of the spur gear. However, unlike the spur gear which can be
viewed essentially as two dimensional, the helical gear must be portrayed in three
dimensions to show changing axial features.
Referring to Figure 6-2, there is a base cylinder from which a taut plane is unwrapped,
analogous to the unwinding taut string of the spur gear in Figure 2-2. On the plane there
is a straight line AB, which when wrapped on the base cylinder has a helical trace AoBo.
As the taut plane is unwrapped, any point on the line AB can be visualized as tracing an
involute from the base cylinder. Thus, there is an infinite series of involutes generated by
line AB, all alike, but displaced in phase along a helix on the base cylinder.
Fig. 6-2 Generation of the Helical Tooth Profile
Again, a concept analogous to the spur gear tooth development is to imagine the taut
plane being wound from one base cylinder on to another as the base cylinders rotate in
opposite directions. The result is the generation of a pair of conjugate helical involutes. If
a reverse direction of rotation is assumed and a second tangent plane is arranged so that
it crosses the first, a complete involute helicoid tooth is formed.
6.2 Fundamentals Of Helical Teeth
In the plane of rotation, the helical gear tooth is involute and all of the relationships
governing spur gears apply to the helical. However, the axial twist of the teeth introduces
a helix angle. Since the helix angle varies from the base of the tooth to the outside radius,
the helix angle b is defined as the angle between the tangent to the helicoidal tooth at the
intersection of the pitch cylinder and the tooth profile, and an element of the pitch cylinder.
See Figure 6-3.
The direction of the helical twist is designated as either left or right. The direction is
defined by the right-hand rule.
For helical gears, there are two related pitches – one in the plane of rotation and the
other in a plane normal to the tooth. In addition, there is an axial pitch.
Referring to Figure 6-4, the two circular pitches are defined and related as follows:
pn = pt cosb = normal circular pitch
(6-1)
Twisted Solid Involute
Taut Plane
Base Cylinder
B
B0
A0
A
