Gear Ratio and Speed – JSS2 Basic Technology Lesson Note (Third Term)

Gear ratio compares the number of teeth on the driven gear with the number of teeth on the driver gear.

Behavioural objectives

By the end of the lesson, students should be able to:

1. define gear ratio and gear speed;
2. identify the driver gear and the driven gear in a pair of gears;
3. calculate the gear ratio of two gears;
4. calculate the gear ratio of a series of gears;
5. calculate the speed of a driven gear from the number of teeth and the speed of the driver gear.

What is a gear?

A gear is a wheel with teeth cut around its edge, used to transmit motion and force from one shaft to another.

• Driver gear: the gear that receives power first and turns the other gear. It is also called the input gear.
• Driven gear: the gear that is turned by the driver gear. It is also called the output gear.
• Meshing: the teeth of two gears fit into each other so that one can turn the other.
• Direction: two meshed gears turn in opposite directions.
• rpm: revolutions per minute, the unit used to measure how fast a gear spins.

What are common types of gear?

• Spur gear: straight teeth on parallel shafts, as in many simple machines.
• Bevel gear: angled teeth that change the direction of motion by 90 degrees, as in a hand drill.
• Worm gear: a screw-like gear that turns a toothed wheel and gives a large speed reduction.
• Rack and pinion: a small round gear that moves a flat toothed bar in a straight line.

What is gear ratio?

Gear ratio is the number of teeth on the driven gear divided by the number of teeth on the driver gear.

• It can also be written as the input speed relative to the output speed.
• It has no unit because it compares two numbers of the same kind.
• It is written as a ratio, for example 2:1.

Gear ratio = number of teeth on the driven gear ÷ number of teeth on the driver gear

Worked example 1

Calculate the gear ratio if a gear with 15 teeth is used to drive a gear with 30 teeth.

1. Driver gear = 15 teeth. Driven gear = 30 teeth.
2. Gear ratio = driven teeth ÷ driver teeth = 30 ÷ 15 = 2/1.
3. Gear ratio = 2:1.

What does the gear ratio tell you?

How do you find the ratio of a series of gears?

The ratio of a series of gears is found by multiplying the driven/driver ratio of each pair of gears.

• Work out the ratio of the first pair of gears.
• Work out the ratio of the next pair.
• Multiply the ratios together.
• A cluster gear is two gears fixed on one shaft, so both turn at the same speed.

Worked example 2

A 20-tooth driver gear drives a 24-tooth cluster gear. The second-speed cluster gear has 16 teeth and drives a 20-tooth second-speed driven gear. Find the gear ratio.

1. First pair: driven ÷ driver = 24/20 = 1.2.
2. Second pair: driven ÷ driver = 20/16 = 1.25.
3. Series ratio = 24/20 × 20/16 = 1.2 × 1.25 = 1.5.
4. Gear ratio = 1.5:1.

What is an idler gear?

• Idler gear: a gear placed between the driver and the driven gear.
• Effect on ratio: none, because its teeth cancel out in the calculation.
• Effect on direction: it makes the driven gear turn the same way as the driver gear.

What is gear speed?

Gear speed is how quickly a gear spins, usually measured in revolutions per minute (rpm).

• The speed of a gear is inversely proportional to its number of teeth.
• A gear with fewer teeth spins faster than a meshed gear with more teeth.
• A 5-tooth gear turns at twice the speed of a 10-tooth gear.

Teeth of driver × speed of driver = teeth of driven × speed of driven

Worked example 3

A gear has 20 teeth. Its speed of rotation is 10 rpm. The gear drives another gear with 10 teeth. Determine the speed of the 10-tooth gear.

Solution

1. 20 teeth × 10 rpm = 10 teeth × X rpm.
2. X rpm = (20 teeth × 10 rpm) ÷ 10 teeth.
3. X = 20 rpm.

Worked example 4

A driver gear with 12 teeth turns at 90 rpm. It drives a gear with 36 teeth. Find the speed of the driven gear and the gear ratio.

1. 12 × 90 = 36 × X.
2. X = 1080 ÷ 36 = 30 rpm.
3. Gear ratio = 36 ÷ 12 = 3:1.
4. The driven gear turns three times slower than the driver gear.

Evaluation

1. What is gear ratio?
2. Explain gear speed.
3. Calculate the gear ratio when a 10-tooth driver gear turns a 40-tooth driven gear.
4. A 30-tooth driver gear turns at 40 rpm and drives a 10-tooth gear. Find the speed of the driven gear.
5. A 10-tooth driver gear drives a 20-tooth cluster gear. A 10-tooth gear on the same shaft drives a 30-tooth driven gear. Find the gear ratio of the series.

Assignment

A driver gear with 24 teeth turns at 60 rpm and drives a gear with 8 teeth. Calculate the gear ratio and the speed of the driven gear, showing all your steps.