Gear ratio

The gear ratio is the relationship between the number of teeth on two gears that are meshed or two sprockets connected with a common roller chain, or the circumferences of two pulleys connected with a drive belt.

Related Topics:
Gear - Ratio - Sprocket - Roller chain - Circumference - Pulley - Belt

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

In the picture to the right, the smaller gear has thirteen teeth, while the second, larger gear has twenty-one teeth. The gear ratio is therefore 13/21 or 1/1.61 (also written as 1:1.61)

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

The first number in the ratio is usually the gear that power is applied to. In an automobile the first number is the gear receiving power from the engine.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

This means that for every one revolution of the smaller gear, the larger gear has made 1/1.61, or 0.62, revolutions. In practical terms, the larger gear turns more slowly.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Suppose the largest gear in the picture has 42 teeth, the gear ratio between the second and third gear then is; 21/42 = 1/2 and for every revolution of the smallest gear the largest gear has only turned 0.62/2 = 0.31 revolution, a total reduction of around 1:3.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Since the number of teeth is also proportional to the circumference of the gear wheel (the bigger the wheel the more teeth it has) the gear ratio can also be expressed as the relationship between the circumferences of both wheels (where d is the diameter of the smaller wheel and D is the diameter of the larger wheel):

Related Topics:
Proportional - Circumference - Diameter

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:gr = (pi imes d) / (pi imes D) = d/D

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Since the diameter is equal to twice the radius;

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

:gr = d / D = (2 imes r) /( 2 imes R) = r / R

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

as well.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

But keep in mind that counting the teeth derives the exact gear ratio, regardless of any variations in the diameter measurement. In the picture, each time the 13 teeth of the smaller gear make a revolution, 13 teeth of the larger gear will have moved, i.e. made 13/21 of a revolution or 0.62 of a revolution.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

As long as the gears remain meshed, the accounting of teeth and revolutions will remain perfect. So for instance gears can be used to construct a clock in which the minute hand moves exactly sixty times faster than the hour hand, regardless of the overall accuracy of the watch.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Diameter measurements are useful for determining approximate gear ratios for non-gear linkages such as pulleys and belts. Smooth belts can slip, so even if exact pulley diameters are known quite exactly, the gear ratio may vary in operation, and may even depend on the load.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Belts can have teeth in them also and be coupled to gear-like pulleys. And of course drive chains have spaces that teeth fit into, like the chain in a motorcycle or bicycle. So again, exact accounting of teeth and revolutions can be applied with these machines. A belt with teeth, called the timing belt is used in internal combustion engines to exactly synchronize the movement of the camshaft, so that the valves open and close at the top of each cylinder at exactly the right time to the movement of each cylinder. From the time the car is driven off the lot, to the time the belt needs replacing some 150,000 kilometers later, it synchronizes the two shafts exactly. This belt is not to be confused with the smooth rubber fan belts.

Related Topics:
Timing belt - Fan belts

~ ~ ~ ~ ~ ~ ~ ~ ~ ~