The objective of a **Gear Train** in machine tools is to transmit movement from one axis to another by means of gears to comply with a speed relationship between them.

The **Gear Train** is used on the lathe to make threads.

On milling machines, it has more applications, for example, differential indexing, linear indexing (racks), circular path milling, helical grooves, and spiral milling.

## The Gear Train must comply with a formula:

Where:**NA** is the Rotational speed of main shaft A.**NB** is the Rotational speed of main shaft B.**ZB** is the number of teeth on the gear on main shaft B.**ZA** is the number of teeth on the gear on main shaft A.

## Let’s see an example.

Find the gear wheels to set up the gear train and their arrangement in order to transmit motion from main shaft A which rotates at 500 RPM to main shaft B which must rotate at 200 RPM.

Known data:**NA** = 500 RPM**NB** = 200 RPM

So, applying the formula:

If the expression is simplified to the maximum, we have:

500/200 = 5/2

This is the solution.

You may also be interested in: Differential Indexing Using the Dividing Head

## Expanding possibilities…

In the set of gears available in the machine, be it the lathe or the milling machine, there are different sizes and therefore a number of teeth.

Then, with the obtained fraction 5/2, it must be amplified by multiplying by the same value both in the numerator and in the denominator until finding gear values that match those of the machine set.

Assuming the gear set contains values that are multiples of 5.

Then it is easy to multiply the fraction 5/2 10 times in both the numerator and the denominator like this:

The value **ZB = 50** is the sprocket that has 50 teeth and is located on main shaft B.

The value **ZA = 20** is the sprocket that has 20 teeth and is located on main shaft A.

Therefore, the transmission ratio is fulfilled:

The gear that transmits the main movement is called the **Driving Gear**, which in this case is ZA, which corresponds to main shaft A, and the gear that receives the movement from A, that is, gear B, is called the **Driven Gear** and corresponds to gear B.

If a toothed wheel (C) had to be inserted between the Driving Gear (A) and the driven gear (B), the driving ratio NA / NB = ZB / ZA is not affected.

Gear wheel C is also known as a gear or parasitic wheel.

## Types of Gear Trains

This concept refers to the number of driving and driven gears and two aspects are taken into account: the complexity of the relationship and the number of gears available in the machine.

Thus, the ZA / ZB ratio can be broken down into several factors, as follows:

Or also:

## Example:

If you multiply 10 times in the numerator and in the denominator you have:

If the numerator is broken down into 80 X 40 X 2 and the denominator y 35 X 20 X 1 and if finally 2 and 1 are multiplied 30 times, then:

This fulfills the transmission ratio:

And in addition, a **gear train** composed of six elements is obtained with this: three driving gears and three driven gears.

## How to build a Gear Train

- Verify which main shaft is the driver and therefore which main shaft is driven.
- With the previous point, the driving gears and the driven gears are now identified.
- The driving gears can be placed in any position as long as they keep their status as drivers and in the same way with the driven gears.
- Intermediate or parasitic gears do not alter the ratio but they do alter the final direction of rotation.
- If the number of shafts in the gear train is odd, the direction of rotation of the driven shaft will be equal to the direction of rotation of the drive shaft.
- If the number of shafts in the gear train is even, the direction of rotation of the driven shaft will be in the opposite direction to the direction of rotation of the drive shaft.

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