# Compound gear train: Working, Diagram, Definition, Examples

The gear train is made up of a number of gears that work together to achieve the required speed ratio and the rotational direction. According to their configuration, the gear trains are categorized as simple gear trains, compound gear trains, reversed gear trains, etc.

Now in this article, we’ll look at one sort of gear train called a compound gear train.

Contents:

## What is a Compound gear train?

Compound gear train uses compound gears to obtain a higher gear ratio. It is a kind of gear train in which compound gears are mounted on one or more intermediate shafts. The compound gear consists of two or more gears of different sizes fixed together to rotate at the same speed.

The below figure shows the example of the compound gear train.

The compound gear train consists of the following components,

1] Input gear:- Input gear is the first gear mounted on the input shaft of the compound gear train to which the power is supplied.

2] Output gear:- Output gear is the last gear of the compound gear train that provides output power with required torque and RPM.

3] Compound gear:- Compound gear is one of the major components of the compound gear train, affecting the gear train’s gear ratio.

4] Idler:- The purpose of the idler gear in the compound gear train is to achieve a specific direction of rotation at the output shaft or to attain a particular center distance between input and output shafts.

The basic purpose of a compound gear train is to achieve a higher gear ratio within a limited space.

Because of the use of compound gears, the compound gear train can achieve higher gear ratios. Therefore the compound gear train has a broad range of applications in various sectors.

## How does a compound gear train work?

The compound gear train uses a compound gear consisting of two or more gears of different sizes that are mounted together on the same shaft.

As shown in the below figure, each gear of the compound gear forms a simple gear train with its adjacent meshing gear.

Thus for the above compound gear train, the total gear ratio can be given by,

i_{\text{total}} = i_{\text{(simple gear train, S1)}} \times i_{\text{(simple gear train, S2)}}

i_{\text{total}} = \frac{T_{2}}{T_{1}} \times \frac{T_{4}}{T_{3}

Due to the different number of teeth, the compound gear helps to affect the total gear ratio of the compound gear train.

The above equation can also rewrite as,

i_{\text{total}} = \frac{T_{2}}{T_{3}} \times \frac{T_{4}}{T_{1}

Hence in the above gear train, the compound gear affects the total gear ratio by the fraction, (\frac{T_{2}}{T_{3}})

This is how the compound gear train works to affect the gear ratio by the use of compound gear.

The following video clip will help you to visualize a working of a compound gear train.

## Compound gear train equation:

Following are the equations used to analyze the compound gear train:-

A] Gear ratio:-

The equation to find the gear ratio (speed ratio) of the compound gear train is given by,

OR

B] Direction of rotation:-

The following equation can give the relation between the direction of input and output gears.

Where, n = Number of intermediate shafts

## How to find gear ratio of compound gear train?

Following are the simple steps to find the gear ratio of the compound gear train:-

Step I: Identify drivers, followers (driven gear), and idlers:-

To find the gear ratio of the compound gear train, it is necessary to identify the role of each gear in the gear train.

The gear which drives another gear or helps to rotate the other gear is known as driver gear. In the above figure gear-1, gear-3 and gear-5 are the driver gears.

The gear which is driven by another gear or rotates with the help of another gear is known as a follower or driven gear. In the above figure, gear-2, gear-6, and gear-7 are the driven gears.

The single gear mounted on intermediate shafts is the idlers or the idle gear. These gears don’t affect the gear ratio of the compound gear train. In the above figure gear-4 acts as an idler gear.

Step II: Use the following formulas to find the gear ratio of the compound gear train:

a] Based on a number of teeth:
Based on the number of teeth, the gear ratio can be found by the use of the following equation.

𝑖 = \frac{\text{Product of the number of teeth on follower gears}}{\text{Product of the number of teeth on drivers}}

For the above gear train, the gear ratio is given by,

𝑖 = \frac{T_{2} \times T_{6} \times T_{7}}{T_{1} \times T_{3} \times T_{5}}

b] Based on the pitch circle diameter:
The equation of the gear ratio based on the pitch circle diameter of the gears is given by,

𝑖 = \frac{\text{Product of the pitch circle diameter of follower gears}}{\text{Product of the pitch circle diameter of driver gears}}

For the above gear train, the gear ratio is given by,

𝑖 = \frac{d_{2} \times d_{6} \times d_{7}}{d_{1} \times d_{3} \times d_{5}}

1. It is easy to obtain a higher gear ratio.
2. It uses a smaller size of gears thus it is more compact than the simple gear train.
3. The compound gear train can give higher speed reduction with less center distance between input and output shafts.
4. Higher efficiency of transmission with no slip.

1. The gearbox made using compound gears are heavy.
2. It has a noisy operation.
3. It requires proper cooling and lubrication.

## Compound gear train applications:

Following are the real-life examples of the compound gear train,

1] Watch/clock:- It uses a compound gear train to obtain different speed ratios to rotate the different hands of a clock at an accurate speed.

2] Lathe machine:- The lathe machine uses a compound gear train to obtain different speed ratios to rotate the spindle.

3] Milling machine:- The compound gear train used in a milling machine is used to control the movement of the bed.

4] Timing gear in the vehicle:- The compound gear train is also used in a valve timing mechanism to actuate the inlet and exhaust valves of the engine.

5] Radial drill machine:- Here the compound gear train is used to reduce the speed and to increase the torque output at the spindle.

## Compound gear train problems and solutions:

Solution:-

The Driver gears in the above gear train are: Gear-1, Gear-3 and Gear-4

The followers or the driven gears are: Gear-2, Gear-5, Gear-6

The formula of the speed ratio of the compound gear train is given by,

𝑖 = \frac{\text{Product of the number of teeth on follower gears}}{\text{Product of the number of teeth on drivers}}

𝑖 = \frac{T_{2} \times T_{5} \times T_{6}}{T_{1} \times T_{3} \times T_{4}}

𝑖 = \frac{40 \times 60 \times 30}{15 \times 20 \times 20}

Thus the gear ratio of the above gear train is 12.

Solution:-

Step I: Find gear ratio based on pitch circle diameter:
In the above gear train, the driver gears are: Gear-1 and Gear-3 and the follower gears are Gear-2 and Gear-4

The gear ratio of the compound gear train based on the pitch circle diameter is given by,

𝑖 = \frac{\text{Product of the pitch circle diameter of follower gears}}{\text{Product of the pitch circle diameter of driver gears}}

𝑖 = \frac{d_{2} \times d_{4}}{d_{1} \times d_{3}} = \frac{10 \times 12}{5 \times 4}

Step II: Number of teeth on 3rd gear:
The gear ratio of the compound gear train based on the number of teeth is given by,

𝑖 = \frac{\text{Product of the number of teeth on follower gears}}{\text{Product of the number of teeth on drivers}}

𝑖 = \frac{T_{2} \times T_{4}}{T_{1} \times T_{3}}

6 = \frac{40 \times 48}{20 \times T_{3}}

Thus the 3rd gear has 16 teeth.

FAQs:

1. Why Compound gear train is used?

The compound gear train is used to obtain the higher value of the gear ratio within limited space.

2. Why are compound gear trains better?

The compound gear train can obtain a higher gear ratio by using the smaller gears, this makes it better to use in various applications.

3. Why are compound gear trains better as compared to two gears alone?

The two gears alone are not able to achieve the higher gear ratio within compact space which can be possible by the use of the compound gear train, and hence the compound gear train is always better as compared to the two gears alone.

4. What is difference between compound gear train and reverted gear train explain?

In the reverted gear train, the input gear and the output gear are coaxial while in the compound gear train, the input and output gears are not coaxial.

Thus the compound gear train is the type of gear train that has a broad range of applications in industries and in our day-to-day life. In this article, we tried to provide ample of information about the compound gear train and we hope that this article has helped you to clearly understand the compound gear train.

If you like this article then check out our other articles related to the theory of machines and other categories as well.

Related article: Pratik is a Graduated Mechanical engineer. He enjoys sharing the engineering knowledge learned by him with people.