Worm and
wheel systems are no more and no less than crossed axle helical gear
system which has a drive wheel with a maximum of six teeth. Which is
called in this case a worm. The calculation of the reduction ratio is
exactly the same. As there are very few teeth on the drive wheel (worm),
it can be seen that the reduction ratios can be very high. This is
the major advantage of this system : With just two elements, it is
possible to considerably reduce the speed.
The
efficiency of such a system is not very good. It increases with the slope
angle of the tooth. There are high levels of friction, and part of the
kinetic energy is transformed into heat. In order to limit the friction
levels, the wheel is usually made out of bronze.
Lubrication either with grease or with oil is a
necessity.
HZPT proposes two different kinds of worm, bored or shaft mounted. The
difference is in the assembly. Its enough to pass a shaft through a
bored worm to get a shaft mounted version.
See worms
W, SW, SWH.
By reading
the formulas opposite one can see that the Helical angle is highly
significant in such a system. In effect, the diameter of the worm
and the HA are mathematically linked. In fact, in the case of a
breakage, the defective piece (normally the wheel) must be replaced
by an absolutely identical componant. Most of the time the piece
must be made to order. As well as that, the number of threads
(starts) on the worm influences the HA. This angle is linked to
the wheel angle, which must be designed for use with a 2,3, or 4
thread/start worm. 
Geometrical formulas for the worm : 
 Axial module : mx=mn/cos?/FONT>

 Axial pitch : px=mx


 pitch diameter : d=pz/tan?/FONT>

 external diameter : da=d+2mn

 root diameter: df=d2.5mn

Geometrical formulas for the wheel : 


 
Wheel M 
Worms 
Symbols 
Formulas 
Unit 
Outer
diameter 
D 
(2 x m) + d 
mm 
The
tangent to the lead angle

?/FONT> 
(m x Z) d 
 Pitch diameter 
d 
p x Z tan?/FONT> 
mm 
Center to center 
 d(wheel) + d(worm) 2 


Worm W and WH
Worm SW
and SWH

with bored
worm 
with shafted worm  Advantages, disadvantages and advice :
 Gives
very high reduction ratios
 Irreversible in certain circumstances
 Helical Angles must be equal
 The
direction of the lead angle must be the same for the wheel and for the
worm (to change direction by 90?
 Not
very efficient (from 40% to 70%) depending on the material and the
lubrication.

 