Page 259 - Analysis and Design of Machine Elements

Wormgear Drives
9.1.3.3 The Number of Threads of Worm z and the Number of Wormgear Teeth z 237
1 2
Worms have a single thread, as in a typical screw, or multiple threads. The number of
threads in a worm is frequently referred as the number of starts. In practice, commonly
used numbers of starts are 1, 2, 4 or 6, which is usually selected according to the speed
ratio and efficiency. Similar to a spur or helical gear, the number of wormgear teeth z 2
is related to the speed ratio as z = iz .
1
2
9.1.3.4 Worm Lead Angle and Wormgear Helix Angle
Axial pitch p is the axial distance from a point on one thread to the corresponding
a
point on the adjacent thread. For proper meshing, the axial pitch of worm p must
a
be equal the transverse circular pitch of wormgear p in the central plane. The lead of
t
aworm p is the axial distance that a point on a worm would move as the worm is
z
rotated one revolution. For a multi-threaded worm, the worm lead is the product of
the number of thread and axial pitch, that is, p = z p , similar to a thread shown in
1 a
z
Figure 3.2b.
Lead angle is the angle between the tangent to the worm thread at reference
diameter and the plane normal to the worm axis. The worm lead angle must
∘
equal the wormgear helix angle with the same hand for a 90 shaft angle for
proper meshing [5]. The lead angle can be obtained from a simple triangle that
would be formed if the thread of worm is unwrapped from the reference cylinder,
which is similar to the calculation of thread lead angle illustrated in Figure 3.2b.
The relationship between lead angle ,lead p and worm reference diameter d are
z 1
expressed as
p z z p z m z 1
1 a
1
tan = = = = (9.5)
d 1 d 1 mq q
9.1.3.5 Profile Shift Coefficient x
Wormgears are cut by a straight hob with a radial feeding movement between the hob
and wormgear blank. To adapt to a predetermined centre distance, the hob can move
radially from its normal position towards or away from the wormgear, resulting the
reduction or enlargement of wormgear tooth dimensions [3]. The profile shift coefficient
is calculated by [4]

a d + d 2
1
x = − (9.6)
2
m 2m
9.1.3.6 Centre Distance a
As with a spur or helical gear, the reference diameter of a wormgear is related to its
module and number of teeth. Therefore, the centre distance is calculated by
1 1
a = (d + d + 2x m)= m(q + z + 2x ) (9.7)
2
1
2
2
2
2 2
Table 9.1 shows typical matching parameters common to wormgears and cylindrical
worms. More data can be found in references [6, 7].