Simple gear train: Definition, Formula, Examples, Advantages

The gear train is made up of several gears that are meshing together to attain the required gear ratio. Based on the arrangement it is classified as a simple gear train, compound gear train, epicyclic gear train, etc. In this article, we are discussing the simple gear train in detail.

What is a simple gear train?

Simple gear train is a type of gear train in which a single gear is mounted on each shaft. The speed ratio of a simple gear train depends only on the driven and driven gear.

The simple gear train consists of the following components:-

1] Driver gear:- It is the input gear mounted on the input shaft of a simple gear train to which the power is supplied.

2] Driven gear:- It is the output gear mounted on the output shaft of the simple gear train.

3] Idlers/intermediate gears:- The gears which do not affects the speed ratio of the gear train are known as idlers.
In a simple gear train, the idlers are used for the following purposes:-
1] To connect gears located at a large central distance.
2] To change the direction of rotation at the output shaft.

Simple gear train equation:

Speed ratio/ Gear ratio:-

The formula for the speed ratio (i) of the simple gear train is given by,

i = `\mathbf{\frac{N_{\text{Driver}}}{N_{\text{Driven}}}}` = `\mathbf{\frac{t_{\text{Driven}}}{t_{\text{Driver}}}}`

Where,
`N_{\text{Driver}}` = Speed of driver gear
`N_{\text{Driven}}` = Speed of driven gear
`t_{\text{Driven}}` = Number of teeths on driven gear
`t_{\text{Driver}}` = Number of teeths on driver gear

The speed ratio of the simple gear train never depends on idler gears.

Direction of motion:-

The relation between the direction of driving and driven gear is given by,

`\mathbf{Direction_{\text{Driven}}}` = `\mathbf{(-1)^{\text{(Number of idler +1)}}. Direction_{\text{Driver}}}`

Simple gear train advantages and disadvantages:

Advantages:-

1. The simple gear train can transfer large amounts of power without causing a slip.
2. It can transfer power with less central distance.
3. The desired direction of rotation can be achieved with the help of idlers.

Disadvantages:-

1. As, like a compound gear train, the simple gear train can’t give high gear ratios within less space.
2. It is more expensive than the chain drive or belt drive.
3. It requires proper lubrication.

Simple gear train examples:

1] Find the speed ratio and the direction of the driven shaft for the below simple gear train.

Given:-
`t_{\text{Driven}}` = 20
`t_{\text{Driver}}` = 60
Number of idlers = 2

Speed ratio:-

i = `\frac{t_{\text{Driver}}}{t_{\text{Driven}}}` = `\frac{60}{20}`

i = 3

This is the speed ratio for the above gear train.

Direction of motion:-

The relation between the direction of driving and driven gear is given by,

`Direction_{\text{driven}}` = `(-1)^{\text{(Number of idler +1)}}. Direction_{\text{driver}}`

`Direction_{\text{driven}}` = `(-1)^{2+1}. Direction_{\text{driver}}`

`Direction_{\text{driven}}` = `- Direction_{\text{driver}}`

It means that the driven gear rotates in the opposite direction of the driver gear.

As the driver gear rotates in a clockwise manner, thus the driven gear rotates in an anticlockwise direction.

2] A simple gear train consists of a driver gear, driven gear, with two idlers having a gear ratio of 3.5. Find the number of teeths on the driven gear if the driver gear has 30 teeth.

Given:-
i = 3.5
Number of idlers = 2
`t_{Driver}` = 30

The number of teeths on driven shaft is given by,

i = `\frac{t_{\text{Driven}}}{t_{\text{Driver}}}`

3.5 = `\frac{t_{\text{Driven}}}{30}`

`\mathbf{t_{\text{Driven}}}` = 105

Thus the driven gear has 105 teeth.

FAQs:

Read also:

• Simple and Compound gear train difference explained