(^700) „„„„„ A Textbook of Engineering Mechanics
34.7. VELOCITY RATIO OF A SIMPLE GEAR DRIVE
It is the ratio between the velocities of the driver and the follower or driven. Now consider a
simple gear drive as shown in Fig. 34.6.
Let N 1 = Speed of the driver,
T 1 = No. of teeth on the driver,
d 1 = Diameter of the pitch circle of the driver,
N 2 , T 2 , d 2 = Corresponding values for the follower, and
p= Pitch of the two wheels.
We know that the pitch of the driver
p=^1
1
d
T
π
...(i)
Similarly, pitch of the follower
p=^2
2
d
T
π ...(ii)
Since the pitch of both the wheels is the same, therefore equating (i) and (ii),
12
12
dd
TT
ππ

or
11
22
dT
dT

∴ Velocity ratio
211
122
.
NdT
NdT

34.8. POWER TRANSMITTED BY A SIMPLE GEAR
Consider a simple gear drive transmitting power, from one shaft to another.
Let F= Tangential force exerted by the driver (also called pressure
between the teeth) and
v= Peripheral velocity of the driver, at the pitch point,
∴ Power transmitted or work done
= Force × Distance = Fv
Example 34.1. In a spur gear arrangement, the driver has 100 teeth of 40 mm pitch. Find
the power, if it can transmit a tangential force of 100 N on the follower. Take speed of driver as
225 r.p.m.
Solution. Given: No. of teeth on driver (T) = 100; Pitch of the two wheels (p) = 40 mm;
Tangential force exerted by the driver (F) = 100 N and speed of the driver (N) = 225 r.p.m.
We know that circumference of the pitch circle
= 100 × 40 = 4000 mm = 4 m
∴ Velocity of driver at the pitch point
v=
4 × 225
=15m/s
60
and power transmitted by the gear,
P= F × v = 100 × 15 = 1500 N-m/s
= 1500 W = 1·5 kW Ans.