Page 256 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
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T transmitted torque, N⋅mm helix angle, ∘
∘
t ambient air temperature, C lead angle, ∘
a
∘
t oil operating temperature, C efficiency
o
u teeth ratio, gear ratio 1 meshing efficiency
v pitch line velocity, m s −1 2 bearing efficiency
v s sliding velocity, m s −1 3 efficiency due to lubricating oil
x profile shift coefficient churning
Y Fa tooth form factor radius of curvature, mm
Y stress correction factor
Sa F bending stress, MPa
Y helix angle factor
[ ] allowable bending stress, MPa
F
Y contact ratio factor
[ ] ′ basic allowable bending stress,
[y] allowable deflection, mm F
MPa
z 1 number of thread of a worm contact stress, MPa
z 2 number of wormgear teeth H
z v2 virtual number teeth of a [ ] ′ allowable contact stress, MPa
H
wormgear [ ] basic allowable contact stress, MPa
H
∘
1/2
Z elastic coefficient, MPa , v equivalent friction angle,
E −1
−2 1/2
(N mm ) angular velocity, rad s
pressure angle, ∘
∘ Subscripts
a axial pressure angle,
n normal pressure angle, ∘ 1 worm
s heat transfer coefficient, 2 wormgear
W/(m 2 ∘ C) a axial plane

transverse pressure angle, ∘ t transverse plane
t
9.1 Introduction
9.1.1 Applications, Characteristics and Structures
Wormgear drives, or worm gearings, are used to transmit motion and power between
crossed shafts, usually at a right angle [1]. The drive consists of a worm and a wormgear.
The worm resembles a power screw thread on a high-speed shaft, driving the wormgear
whose appearance is similar to that of a helical gear. Wormgear drives are widely used
in machine tools and in automotive and many other machines.
Wormgear drives can achieve a high-speed ratio (i = 5–80) in a compact design. They
provide smooth and quite operation. However, the power transmission efficiency is usu-
ally less than 90%, which is far lower than other types of gear drives. This is due to the
frictional loss caused by sliding between meshing teeth surfaces. Sliding also makes it
necessary to use expensive antifriction materials for wormgears. Besides, self-locking
will occur if a lead angle is less than the equivalent friction angle.

9.1.2 Types of Wormgear Drives

According to the worm profile, there are three basic types of wormgear drives, that
is, cylindrical, toroidal and spiroid worm (or cone worm) gear drives, as shown in
Figure 9.1.