Page 215 - Analysis and Design of Machine Elements

Gear Drives
resolved into three orthogonal components, tangential force F , radial force F and axial 193
t
r
force F .
a
The tangential force F acts in the transverse plane and is at a tangent to the pitch circle
t
of the helical gear. It associates with power transmission and transmits torque from the
driving pinion to the driven gear. The tangential force can be derived from the nominal
torque as
2T 1
F = (8.43)
t
d 1
The radial force F acts towards the centre of gears. It tends to separate the driving
r
pinion and driven gear, and contributes to the shaft bending and bearing loads. It gives
F tan n
t
F = (8.44)
r
cos
The axial force F acts parallel to the axis of gear and causes an axial or thrust load that
a
must be resisted by bearings. Its direction can be determined by the Right- or Left-Hand
Rule. With the tangential force already known, the magnitude of axial force is computed
from
F = F tan (8.45)
a t
Since helical gears impose both radial and axial loads on supporting bearings, when
two or more helical gears are mounted on the same shaft, the hand of gears should be
properly selected so that the thrust loads produced by helical gears can counteract each

other.
From Figure 8.9, the normal force can be obtained from
F t F t
F = = (8.46)
n
cos cos n cos cos b
t
Figure 8.9 Force analysis of a helical gear.
α n
Fn
Fʹ
α t β b
β F r
F t F a

P
β
T 1
d 1