Mechanical Engineering Principles

204 MECHANICAL ENGINEERING PRINCIPLES

This shows that the movement ratio is independent
of the idler, only the direction of the follower being
altered.
Acompound gear trainis shown in Figure 18.6,
in which gear wheelsBandCare fixed to the same
shaft and henceNB=NC.
From equation (18.7),

NA

NB

=

TB

TA

i.e.NB=NA×

TA

TB

A

B

CD

Figure 18.6

Also,

ND

NC

=

TC

TD

i.e.ND=NC×

TC

TD

ButNB=NC,and

ND=NB×

TC

TD

therefore

ND=NA×

TA

TB

×

TC

TD

( 18. 8 )

For compound gear trains having, say, P gear
wheels,

NP=NA×

TA

TB

×

TC

TD

×

TE

TF

......×

TO

TP

from which,

movement ratio =

NA

NP

=

TB

TA

×

TD

TC

......×

TP

TO

Problem 7. A driver gear on a shaft of a

motor has 35 teeth and meshes with a

follower having 98 teeth. If the speed of the

motor is 1400 revolutions per minute, find

the speed of rotation of the follower.

From equation (18.7),

speed of driver

speed of follower

=

teeth on follower

teeth on driver

i.e.

1400

speed of follower

=

98

35

Hence, speed of follower=

1400 × 35

98

=500 rev/min

Problem 8. A compound gear train similar

to that shown in Figure 18.6 consists of a

driver gearA, having 40 teeth, engaging

with gearB, having 160 teeth. Attached to

the same shaft asB, gearChas 48 teeth and

meshes with gearDon the output shaft,

having 96 teeth. Determine (a) the movement

ratio of this gear system and (b) the

efficiency when the force ratio is 6.

(a) From equation (18.8), the speed ofD

=speed ofA×

TA

TB

×

TC

TD

From equation (18.7),movement ratio

=

speed ofA

speed ofD

=

TB

TA

×

TD

TC

=

160

40

×

96

48

= 8

(b) The efficiency of any simple machine is

force ratio

movement ratio

×100%

Thus,efficiency=

6

8

× 100 =75%

Now try the following exercise

Exercise 92 Further problems on gear

trains

1. The driver gear of a gear system has 28
   teeth and meshes with a follower gear hav-
   ing 168 teeth. Determine the movement
   ratio and the speed of the follower when
   the driver gear rotates at 60 revolutions per
   second. [6, 10 rev/s]