Gear Trains
Gear Trains
Introduction:
Sometimes, two or more gears are made to mesh with each other to transmit power
from one shaft to another. Such a combination is called gear train or train of toothed
wheels. The nature of the train used depends upon the velocity ratio required and the
relative position of the axes of shafts. A gear train may consist of spur, bevel or spiral
gears.
Types of Gear Trains:
Following are the different types of gear trains, depending upon the arrangement of
wheels:
1. Simple gear train,
2. Compound gear train,
3. Reverted gear train, and
4. Epicyclic gear train.
In the first three types of gear trains, the axes of the shafts over which the gears are
mounted are fixed relative to each other. But in case of epicyclic gear trains, the axes
of the shafts on which the gears are mounted may move relative to a fixed axis.
Simple Gear Train:
When there is only one gear on each shaft, as shown in Fig. 13.1, it is known as
simple gear train. The gears are represented by their pitch circles. When the distance
between the two shafts is small, the two gears 1 and 2 are made to mesh with each
other to transmit motion from one shaft to the other, as shown in Fig. 13.1 (a). Since
the gear 1 drives the gear 2, therefore gear 1 is called the driver and the gear 2 is
called the driven or follower. It may be noted that the motion of the driven gear is
opposite to the motion of driving gear.
Fig. 13.1. Simple gear train.
Let N1 = Speed of gear 1(or driver) in r.p.m.,
N2 = Speed of gear 2 (or driven or follower) in r.p.m.,
T1 = Number of teeth on gear 1, and
T2 = Number of teeth on gear 2.
Page 1 of 23
, Gear Trains
Since the speed ratio (or velocity ratio) of gear train is the ratio of the speed of the
driver to the speed of the driven or follower and ratio of speeds of any pair of gears in
mesh is the inverse of their number of teeth, therefore
It may be noted that ratio of the speed of the driven or follower to the speed of the
driver is known as train value of the gear train. Mathematically,
From above, we see that the train value is the reciprocal of speed ratio.
Sometimes, the distance between the two gears is large. The motion from one gear
to another, in such a case, may be transmitted by either of the following two methods :
1. By providing the large sized gear, or
2. By providing one or more intermediate gears.
A little consideration will show that the former method (i.e. providing large sized
gears) is very inconvenient and uneconomical method ; whereas the latter method (i.e.
providing one or more intermediate gear) is very convenient and economical.
It may be noted that when the number of intermediate gears are odd, the motion of
both the gears (i.e. driver and driven or follower) is like as shown in Fig. 13.1 (b).
But if the number of intermediate gears are even, the motion of the driven or
follower will be in the opposite direction of the driver as shown in Fig. 13.1 (c).
Now consider a simple train of gears with one intermediate gear as shown in Fig.
13.1 (b).
Let N1 = Speed of driver in r.p.m.,
N2 = Speed of intermediate gear in r.p.m.,
N3 = Speed of driven or follower in r.p.m.,
T1 = Number of teeth on driver,
T2 = Number of teeth on intermediate gear, and
T3 = Number of teeth on driven or follower.
Since the driving gear 1 is in mesh with the intermediate gear 2, therefore speed
ratio for these two gears is
…………(i)
Similarly, as the intermediate gear 2 is in mesh with the driven gear 3, therefore
speed ratio for these two gears is
…………(ii)
The speed ratio of the gear train as shown in Fig. 13.1 (b) is obtained by
multiplying the equations (i) and (ii).
or
i.e
Page 2 of 23
, Gear Trains
and
Similarly, it can be proved that the above equation holds good even if there are any
number of intermediate gears. From above, we see that the speed ratio and the train
value, in a simple train of gears, is independent of the size and number of intermediate
gears. These intermediate gears are called idle gears, as they do not affect the speed
ratio or train value of the system. The idle gears are used for the following two
purposes:
1. To connect gears where a large centre distance is required, and
2. To obtain the desired direction of motion of the driven gear (i.e. clockwise or
anticlockwise).
Compound Gear Train:
When there is more than one gear on a shaft, as shown in Fig. 13.2, it is called a
compound train of gear.
We have seen in previous section that the idle gears, in a simple train of gears do
not affect the speed ratio of the system. But these gears are useful in bridging over the
space between the driver and the driven. But whenever the distance between the
driver and the driven or follower has to be bridged over by intermediate gears and at
the same time a great ( or much less ) speed ratio is required, then the advantage of
intermediate gears is intensified by providing compound gears on intermediate shafts.
In this case, each intermediate shaft has two gears rigidly fixed to it so that they may
have the same speed. One of these two gears meshes with the driver and the other
with the driven or follower attached to the next shaft as shown in Fig.13.2.
Fig. 13.2. Compound gear train.
Page 3 of 23
Gear Trains
Introduction:
Sometimes, two or more gears are made to mesh with each other to transmit power
from one shaft to another. Such a combination is called gear train or train of toothed
wheels. The nature of the train used depends upon the velocity ratio required and the
relative position of the axes of shafts. A gear train may consist of spur, bevel or spiral
gears.
Types of Gear Trains:
Following are the different types of gear trains, depending upon the arrangement of
wheels:
1. Simple gear train,
2. Compound gear train,
3. Reverted gear train, and
4. Epicyclic gear train.
In the first three types of gear trains, the axes of the shafts over which the gears are
mounted are fixed relative to each other. But in case of epicyclic gear trains, the axes
of the shafts on which the gears are mounted may move relative to a fixed axis.
Simple Gear Train:
When there is only one gear on each shaft, as shown in Fig. 13.1, it is known as
simple gear train. The gears are represented by their pitch circles. When the distance
between the two shafts is small, the two gears 1 and 2 are made to mesh with each
other to transmit motion from one shaft to the other, as shown in Fig. 13.1 (a). Since
the gear 1 drives the gear 2, therefore gear 1 is called the driver and the gear 2 is
called the driven or follower. It may be noted that the motion of the driven gear is
opposite to the motion of driving gear.
Fig. 13.1. Simple gear train.
Let N1 = Speed of gear 1(or driver) in r.p.m.,
N2 = Speed of gear 2 (or driven or follower) in r.p.m.,
T1 = Number of teeth on gear 1, and
T2 = Number of teeth on gear 2.
Page 1 of 23
, Gear Trains
Since the speed ratio (or velocity ratio) of gear train is the ratio of the speed of the
driver to the speed of the driven or follower and ratio of speeds of any pair of gears in
mesh is the inverse of their number of teeth, therefore
It may be noted that ratio of the speed of the driven or follower to the speed of the
driver is known as train value of the gear train. Mathematically,
From above, we see that the train value is the reciprocal of speed ratio.
Sometimes, the distance between the two gears is large. The motion from one gear
to another, in such a case, may be transmitted by either of the following two methods :
1. By providing the large sized gear, or
2. By providing one or more intermediate gears.
A little consideration will show that the former method (i.e. providing large sized
gears) is very inconvenient and uneconomical method ; whereas the latter method (i.e.
providing one or more intermediate gear) is very convenient and economical.
It may be noted that when the number of intermediate gears are odd, the motion of
both the gears (i.e. driver and driven or follower) is like as shown in Fig. 13.1 (b).
But if the number of intermediate gears are even, the motion of the driven or
follower will be in the opposite direction of the driver as shown in Fig. 13.1 (c).
Now consider a simple train of gears with one intermediate gear as shown in Fig.
13.1 (b).
Let N1 = Speed of driver in r.p.m.,
N2 = Speed of intermediate gear in r.p.m.,
N3 = Speed of driven or follower in r.p.m.,
T1 = Number of teeth on driver,
T2 = Number of teeth on intermediate gear, and
T3 = Number of teeth on driven or follower.
Since the driving gear 1 is in mesh with the intermediate gear 2, therefore speed
ratio for these two gears is
…………(i)
Similarly, as the intermediate gear 2 is in mesh with the driven gear 3, therefore
speed ratio for these two gears is
…………(ii)
The speed ratio of the gear train as shown in Fig. 13.1 (b) is obtained by
multiplying the equations (i) and (ii).
or
i.e
Page 2 of 23
, Gear Trains
and
Similarly, it can be proved that the above equation holds good even if there are any
number of intermediate gears. From above, we see that the speed ratio and the train
value, in a simple train of gears, is independent of the size and number of intermediate
gears. These intermediate gears are called idle gears, as they do not affect the speed
ratio or train value of the system. The idle gears are used for the following two
purposes:
1. To connect gears where a large centre distance is required, and
2. To obtain the desired direction of motion of the driven gear (i.e. clockwise or
anticlockwise).
Compound Gear Train:
When there is more than one gear on a shaft, as shown in Fig. 13.2, it is called a
compound train of gear.
We have seen in previous section that the idle gears, in a simple train of gears do
not affect the speed ratio of the system. But these gears are useful in bridging over the
space between the driver and the driven. But whenever the distance between the
driver and the driven or follower has to be bridged over by intermediate gears and at
the same time a great ( or much less ) speed ratio is required, then the advantage of
intermediate gears is intensified by providing compound gears on intermediate shafts.
In this case, each intermediate shaft has two gears rigidly fixed to it so that they may
have the same speed. One of these two gears meshes with the driver and the other
with the driven or follower attached to the next shaft as shown in Fig.13.2.
Fig. 13.2. Compound gear train.
Page 3 of 23
