Page 263 - Analysis and Design of Machine Elements

Wormgear Drives
The tangential force acting on the worm F equals to the axial force on the wormgear 241
t1
∘
F a2 for the usual 90 shaft angle, that is,
2T 1
F = = F a2 (9.10)
t1
d 1
The radial force on the worm and wormgear are equal, directing to the centre of worm
and wormgear, respectively, separating the mating worm and wormgear.
F = F = F tan (9.11)
r1 r2 t2
The axial force acting on the worm F a1 equals to the tangential force on the wor-
∘
mgear F for the usual 90 shaft angle. The direction of axial force follows the Right- or
t2
Left-Hand Rule. The magnitude is calculated by
2T 2
F = F = (9.12)
a1 t2
d
2
Ignoring friction, the normal force can be regarded as acting on the pitch point in the
normal plane, expressed as
F a1 F t2 2T 2
F = = = (9.13)
n
cos cos n cos cos n d cos cos n
2
Because the output power P is less than the input power P due to power losses
2 1
caused by friction, the relation between the output power P and input power P can be
1
2
expressed as P = P ,where is transmission efficiency. This relation can be rewritten
1
2

as T = T . Thus, we have the relations between the input torque T and output
1
2
1
2
1
torque T as
2
T = T i (9.14)
1
2
9.2.3 Potential Failure Modes
Similar to previously discussed gearings, the principal failure modes in an enclosed
wormgear drive are fatigue pitting and tooth breakage. Both are observed mainly in
wormgears made of bronzes after extended service.
Different from previously discussed gearings where the motion of one tooth relative
to the mating tooth is primarily rolling, there is an inherently sliding motion between
worm threads and wormgear teeth, as illustrated in Figure 9.3. Therefore, friction and
wear play an important role in the performance of wormgear drives.
An enclosed worm gearing operating at a high speed or under a heavy load with
inadequate lubrication often shows a failure mode of scuffing. The high sliding velocity
between mating surfaces of worm and wormgear, combined with high pressure, will gen-
erate high temperature and consequently reduce the viscosity of lubricant. The thinned
oil film thickness due to reduced lubricant viscosity will result in the direct contact of
worm and wormgear teeth and eventually cause scuffing.
The principal failure modes for open wormgear drives are tooth wear and breakage.
Wear varies in a wide range depending on assembly, operation and lubrication. Inaccu-
rate assembly, frequent starting and stopping, insufficient lubrication, accelerate wear
process. Breakage can be observed mainly after severe wear. As a common scenario,
only the teeth of wormgear are broken.