Gear trains

Gear trains

gear train :- some times, 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’.
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 train, 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.

1. simple gear train :-

When there is only one gear on each shaft, as shown in fig. 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. sinec the gear 1 drives the gear 2, therefore gear 1 is called the ‘driver ‘ and the gear 2 is called the ‘ driven’ or ‘ follower’.

2. compound gear train :-

                                              

When there are more then one gear on a shaft, as shown in fig, it is called a compound train of gear. In a compound train of gears, as shown in figure. The gear 1 is the driving gear mounted on shaft A, gears 2 and 3 are compound gears which are mounted on shaft B. the gears 4 and 5 are also compound gears which are mound on shaft C and the gear 6 is the driven gear mounted on shaft D.

3. reverted gear train :-

When the axes of the first gear (i.e., first driver) and the last gear (i.e., last driven) are co-axial, then the gear train is known as reverted gear trains shown in fig.
We see that gear 1 drivers the gear 2 in the opposite direction. Since the gears 2 and 3 are mounted on the same shaft, therefore they from a compound gear and the gear 3 will rotate in the same direction as that of gear 2. The gear 3 drives the gear 4 in the same direction as that of gear 1. Thus we see that in a reverted gear train, the motion of the first gear and the last gear is like.


4. Epicyclic gear train :-

Epicyclic gear train can be expressed, the axes of the shafts, over which the gears are mounted, may move relative to a fixed axis. A simple Epicyclic gear train is shown in figure. Where a gear A and the arm C have a common axis at 01 , about which they can rotate. The gear B meshes with gear A and has its axis on the arm at 02 , about which the gear B can rotate. If the arm is fixed, the gear train is simple and gear A can drive gear B or vice-versa, but if gear A is fixed and the arm is rotated about the axis of gear A .

Velocity ratio of epicyclic gear train :-
The following two methods may be used for finding out the velocity ratio of an epicyclic gear train.
1. Tabular method. 2. Algebraic method

                                        


1.Tabular method:-

Consider an epicyclic gear train as shown in figure.

TA= number of teeth on gear ‘A’, and TB = number of teeth on gear ‘B’. first of all, let us suppose that the arm is fixed. Therefore the axis of both the gears are also fixed relative to each other. When the gear ‘A’ makes one relative to each other. When the gear ‘A’ makes one revolution anticlockwise, the gear B will TA/ TB revolutions, clock wise. Assuming the anticlock wise rotation as positive and clock wise as negative, we may say that when gear A makes +1 revolution, then the gear B will make (-TA/ TB) revolutions. This statement of relative motion is entered in the first row of the table.
Secondly, if the gear A makes +x revolutions, then the gear B will make –x (TA/ TB) revolutions. This statement is entered in the second row of the table.
Thirdly, each element of an epicyclic train is given +y revolutions and entered in the third row. Finally, the motion of each element of the gear train is added up and entered in the fourth row.

2. algebraic method :-
In this method, the motion of each element of the epicyclic train relative to the arm is set down in the form of equations. The number of equations depends upon the number of elements in the gear train. But the two conditions are, usually, supplied in any epicyclic train viz, some elements is fixed and the other has specified motion. These two conditions are sufficient to slove all the equations, and hence to determine the motion of any element in the epicyclic gear train.
Let the cam C be fixed in an epicyclic gear train as shown in above epicyclic figure. Therefore speed of the gear A relative to the arm C.