Gearing Systems : Gear Ratios

## Introduction to Gearing

The purpose of gearing is to covert rotational velocity into torque, or torque into rotational velocity depending on how the gears are setup. It however is the norm to convert rotational velocity into more torque. However, it is important to realize that it is always a tradeoff between the two. Power on the other hand will remain the same despite the gearing in an ideal situation where there aren't any energy losses such us friction. This is because power is a product of angular velocity and torque.

(1)

## Gear Ratio

From equation 1 the concept of a gear ratio can be derived. This means that if you know what your current torque and speed are, and have a certain torque you want to convert this to, you can use a gear ratio to determine the change in angular velocity to obtain this new torque. Refer to equation 2. Keep in mind this equation assumes that there is no loss in power through the gear train, meaning the gear train is 100% efficient, which is impossible in real life.

(2)

The above equation is not the only way to determine the gear ratio. Depending on what information you know at the time, there are different methods that can be used to determine the gear ratio. Refer to equation 3 for different methods to determine the gear ratio.

(3)

Notice from equation 3 there are different methods to determine the gear ratio. Also, from this equation, it can be seen that the size difference between the two gears can determine the gear ratio. This can be proven using statics by stating that the two gears are fixed. Refer to the example below.

## Example

For the image above the smaller gear is rotating at 1000 RPM and is produce a torque of 7 in-lb. Determine the torque of the larger gear using statics and by taking a gear ratio using the radius of the two gears. Also, how fast is the large gear rotating. Assume there is no loss in power.