T-80
B e c a u s e
t h e
t h e o r y
a n d
equations of these methods are so
complicated, they are beyond the
scope of this treatment. Usually, all
stock worm gears are produced with
crowning.
9.4 Self-Locking Of Worm Mesh
Self-locking is a unique characteristic of worm meshes that can be put to advantage.
It is the feature that a worm cannot be driven by the worm gear. It is very useful in the
design of some equipment, such as lifting, in that the drive can stop at any position
without concern that it can slip in reverse. However, in some situations it can be detrimental
if the system requires reverse sensitivity, such as a servomechanism.
Self-locking does not occur in all worm meshes, since it requires special conditions as
outlined here. In this analysis, only the driving force acting upon the tooth surfaces is
considered without any regard to losses due to bearing friction, lubricant agitation, etc.
The governing conditions are as follows:
Let Fu1 = tangential driving force of worm
Then, Fu1 = Fn (cosan sing – m cosg )
(9-6)
where:
an = normal pressure angle
g
= lead angle of worm
m
= coefficient of friction
Fn = normal driving force of worm
If Fu1 > 0 then there is no self-locking
effect at all. Therefore, Fu1 £ 0 is the
critical limit of self-locking.
Let an in Equation (9-6) be 20°, then
the condition:
Fu1 £ 0 will become:
(cos20° sing – mcosg) £ 0
Figure 9-11 shows the critical limit of self-locking for lead angle g and coefficient of
friction m. Practically, it is very hard to assess the exact value of coefficient of friction m.
Further, the bearing loss, lubricant agitation loss, etc. can add many side effects. Therefore,
it is not easy to establish precise self-locking conditions. However, it is true that the
smaller the lead angle g, the more likely the self-locking condition will occur.
0.20
0.15
0.10
0.05
0
0
3°
6°
9°
12°
Lead angle g
Fig. 9-11
The Critical Limit of Self-locking of
Lead Angle g and
Coefficient of Friction m
Fig. 9-10
The Value of Factor (k )
14°
15°
16°
17°
18°
19°
20°
21°
22°
23°
Axial Pressure Angle ax
0.6
0.55
0.5
0.45
0.4
0.35
k
