T-57
The formulas of a standard helical rack are similar to those of Table 6-6 with only the normal
coefficient of profile shift xn =0. To mesh a helical gear to a helical rack, they must have the same
helix angle but with opposite hands.
The displacement of the helical rack, l, for one rotation of the mating gear is the product of the
radial pitch, pt, and number of teeth.
pmn
l = –––––z = ptz
(6-13)
cosb
According to the equations of Table 6-7, let radial pitch pt = 8 mm and displacement l = 160 mm. The
radial pitch and the displacement could be modified into integers, if the helix angle were chosen properly.
In the axial system, the linear displacement of the helical rack, l, for one turn of the helical gear
equals the integral multiple of radial pitch.
l = pzmt
(6-14)
SECTION 7 SCREW GEAR OR CROSSED HELICAL GEAR MESHES
These helical gears are also known as spiral gears. They are true helical gears and only differ
in their application for interconnecting skew shafts, such as in Figure 7-1. Screw gears can be
designed to connect shafts at any angle, but in most applications the shafts are at right angles.
7.1 Features
7.1.1 Helix Angle and
Hands
The helix angles need
not be the same. However,
their sum must equal the
shaft angle:
b1 + b2 = S (7-1)
where b1 and b2 are the re-
spective helix angles of the
two gears, and S is the shaft
angle (the acute angle be-
tween the two shafts when
viewed in a direction paral-
leling a common perpendicu-
lar between the shafts).
Except for very small
shaft angles, the helix hands
are the same.
7.1.2 Module
Because of the possibility of different helix angles for the gear pair, the radial modules may not
be the same. However, the normal modules must always be identical.
Fig. 7-1 Types of Helical Gear Meshes
NOTES:
1. Helical gears of the same hand operate at right
angles.
2. Helical gears of opposite hand operate on parallel
shafts.
3. Bearing location indicates the direction of thrust.
RIGHT-HAND
GEAR MESH
LEFT-HAND
GEAR MESH
OPPOSITE
HAND GEAR
MESH
DRIVER
DRIVER
DRIVER
DRIVER
DRIVER
DRIVER
LEFT-HAND
RIGHT-HAND
