Page 205 - Analysis and Design of Machine Elements

Gear Drives
of a torque during rotation at a given speed. The relationship between the nominal 183
torque and the transmitted power is governed by
P 1
T = 9.55 × 10 6 (8.19)
1
n 1
If friction is neglected, the power transmitted by the pinion and gear are exactly the
same. Therefore, a reduction in the rotational speed of a gear will proportionally increase
the torque transmitted to the gear shaft.
Figure 8.3 shows a pinion rotates counterclockwise, transmitting a torque T .Assume
1
the force acts at the midpoint of face width. At pitch point P,anormal force F from
n
the driven gear exerts normally on the involute tooth profile of the pinion. Neglecting
friction, this force can be resolved into two components, that is, a tangential force F t
in the tangential direction and a radial force F in the radial direction. The tangential
r
force F is directly related to power transmission; therefore, this force is often called
t
transmitted force. By moment equilibrium about the axis of rotation, the magnitude of
tangential force F can be found from:
t
2T 1
F = (8.20)
t
d 1
The radial force F , which tends to separate the driving pinion and driven gear, is also
r
called separating force. It is calculated by
F = F tan (8.21)
r t
And the normal force F is
n
F t 2T 1
F = = (8.22)
n
cos d cos
1
The magnitude of forces on the pinion and gear are the same, except that they act
in the opposite directions. Therefore, Eqs. (8.20)–(8.22) can be used to compute forces
on either the pinion or the gear by appropriate substitution. Each tooth experiences
repeated loading during operation.
Figure 8.3 Force analysis of a spur gear.

F n
α

F t F r

P

T 1
d 1