T-49
Fig. 6-3 Definition of Helix Angle
The normal circular pitch is less than the transverse radial pitch, pt, in the plane of
rotation; the ratio between the two being equal to the cosine of the helix angle.
Consistent with this, the normal module is less than the transverse (radial) module.
Fig. 6-4 Relationship of Circular Pitches
Fig. 6-5 Axial Pitch of a Helical Gear
The axial pitch of a helical gear, px, is the distance between corresponding points of
adjacent teeth measured parallel to the gear's axis – see Figure 6-5. Axial pitch is related
to circular pitch by the expressions:
pn
px = pt cotb = ––––– = axial pitch
(6-2)
sinb
A helical gear such as shown in Figure 6-6 is a cylindrical gear in which the teeth
flank are helicoid. The helix angle in standard pitch circle cylinder is b, and the displacement
of one rotation is the lead, L.
The tooth profile of a helical gear is an involute curve from an axial view, or in the
plane perpendicular to the axis. The helical gear has two kinds of tooth profiles – one is
based on a normal system, the other is based on an axial system.
Circular pitch measured perpendicular to teeth is called normal circular pitch, pn. And
pn divided by p is then a normal module, mn.
pn
mn = –––
(6-3)
p
The tooth profile of a helical gear with applied normal module, mn, and normal pressure
angle an belongs to a normal system.
Element of Pitch
Cylinder (or
gear's axis)
Tangent to Helical Tooth
Pitch Cylinder
Helix
Angle
b
pt
pn
b
px
b
