Gears
A聽toothed wheel used with other gears to turn axles at different speeds. are wheels with toothed edges that rotate on an A bar, rod or shaft which passes through a wheel or gear. The wheel or gear will rotate around the axle. or shaft. The teeth of one gear fit into the teeth of another gear. This lets one gear turn the other, meaning one axle or shaft can be used to turn another shaft.
Rotation and transmission of forces by gears
As one gear turns, the other gear must also turn. Where the gears meet, the teeth must both move in the same direction. In the diagram, the teeth of both gears move upwards. This means that the gears rotate in opposite directions.
The forces acting on the teeth are identical for both gears, but their moments are different:
- If the driven gear is made larger is will rotate more slowly but with a greater moment. For example, a low gear ratio on a bike or car.
- If the driven gear is made smaller it will rotate more quickly but with a smaller moment. For example, a high gear ratio on a bike or car.
Example
A gear with a radius of 0.1 m is turned by a gear with a radius of 0.05 m. The moment of the smaller gear is 20 Nm. Calculate the moment of the larger gear.
First calculate the force on the teeth of the smaller gear.
Rearrange \(M = F \: d\) to find F:
\(F = \frac{M}{d}\)
\(F = 20 \div 0.05\)
\(F = 400~N\)
Use the answer above to calculate the moment of the larger gear:
\(M = F \: d\)
\(M = 400 \times 0.1\)
\(M = 40~Nm\)
Turning a gear that has double the radius doubles the turning effect - it is a 2脳 force multiplier.