Engineering Calculators

# Torque, Efficiency, Force And Power Calculations Of Spur Gears

For spur gear sets, there is a strict relation between torque and power. Also, power is transmitted between gear pairs with the acting forces between gear teeth. Efficiency is also a very important parameter when you are building up the gear system. These parameters are interrelated to each other and we will explain all of them in this article.

## Torque And Power Relation In Gear Sets

In gear systems, power is transmitted from pinion gear which is attached to the input shaft. And bigger gear takes the power to transmit it to the output shaft. In theory, the transmitted power is constant.

But you can adjust the moment or torques of different gear sets. There is also a strict relationship between torque and the RPM of gear. When you are using bigger output gears according to input gear, the output torque will be higher. But if you use a smaller output gear, the output torque will be lower.

But you must understand that when the diameter of output gear increases, torque increases but RPM decreases. RPM increases with the decreasing diameter of output gear also.

We stated that power is constant. So, when you divide the obtained torque with RPM, you will find out the power. But, to calculate the power and torque relations for a spur gear system, you must understand acting forces between gear teeth.

## Forces On Spur Gear Teeth Illustration of acting forces on spur gear tooth(Image Source: Robert L. Mott: Machine Elements In Mechanical Design).

Actually, there are three types of forces in theory between spur gear teeth pairs. These forces are; tangential force, radial force, and normal force.

### Tangential Forces In Spur Gear Teeth

The tangential force between spur gear pairs is the force that tangential to the pitch line. Power is completely transmitted with this force. You can find out tangential force if you divide the power to circumferential speed.

#### Tangential Force Calculator

Here we prepared a calculator to calculate the tangential force acting between spur gear pairs. You need to enter the ‘Pitch Line Velocity’ and ‘Power’ inside the brackets. Then hit the ‘Calculate!’ button to calculate the ‘Tangential Force’. If you want to do another calculation, click on the ‘Reset’ button, then re-enter all the parameters again.

You need to use proper sets of units to obtain correct results. For SI units, the pitch line velocity must be in the m/s. And power must be Joule. The obtained tangential force will be Newtons.

If you do not have proper sets of units, you can use the MB-Unit Converter tool to convert your units into another set of units.

### Radial And Normal Force In Spur Gear Teeth

To calculate radial and normal force, you need to know the pressure angle of the spur gear. And if you calculated the tangential force, you can calculate both radial and normal forces.

#### Radial And Tangential Force Calculator

The use of the calculator above to calculate radial and normal forces is very easy just like the previous calculator. The unit of the angle must be in degrees.

## Torque Calculation From The Data Above About Spur Gears

We stated the relation between torque and power. And you can easily calculate the torque of an individual gear if you know the power transmitted between gear sets and the diameter of this individual gear.

### Torque Calculator For An Individual Gear

Just enter the required information above. Again, you must enter the informations in correct units.

## Efficiency In Spur Gear Systems

Like all the other mechanical systems, spur gear systems have also efficiency in power transmission. Power is not transmitted fully between shafts through gears. For each gear pairs, there is a theoretical efficiency which is generally around 97-99%.

For gear trains, efficiencies between each gear pairs must be multiplied to find out the total power that is transmitted between input and output shafts.

For high power transmissions, this loss of power can appear as heat. Heat must be considered seriously. If it is required, some cooling systems must be built near the gear system. Because the lubrication and force transmission can be damaged because of the excessive heat generation because of the power loss.

## Conclusion

These parameters are the most important parameters to start the design of spur gear pairs.

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