Gears: An Introduction
Gears are a means of changing the rate of rotation of a machinery shaft. They can also change the direction of the axis of rotation and can change rotary motion to linear motion.
Unfortunately, mechanical engineers sometimes shy away from the use of gears and rely on the advent of electronic controls and the availability of toothed belts, since robust gears for high-speed and/or high-power machinery are often very complex to design. However, for dedicated, high-speed machinery such as an automobile transmission, gears are the optimal medium for low energy loss, high accuracy and low play.
Gears are of several categories, and can be combined in a multitude of ways, some of which are illustrated in the following figures.
Meshing Circular Spur Gears
Rack and Pinion Spur Gears
Circular Worm Gear and Mating Cylindrical Worm
Inside Spur Gear withMating Pinion Spur Gear
Gears have existed since the invention of rotating machinery. Because of their force-multiplying properties, early engineers used them for hoisting heavy loads such as building materials. The mechanical advantage of gears was also used for ship anchor hoists and catapult pre-tensioning.
Early gears were made from wood with cylindrical pegs for cogs and were often lubricated with animal fat grease. Gears were also used in wind and water wheel machinery for decreasing or increasing the provided rotational speed for application to pumps and other powered machines. An early gear arrangement used to power textile machinery is illustrated in the following figure. The rotational speed of a water or horse drawn wheel was typically too slow to use, so a set of wooden gears needed to be used to increase the speed to a usable level.
An 18th Century Application of Gears for Powering Textile MachineryThe industrial revolution in Britain in the eighteenth century saw an explosion in the use of metal gearing. A science of gear design and manufacture rapidly developed through the nineteenth century. Today, the most significant new gear developments are in the area of materials. Modern metallurgy has greatly increased the useful life of industrial and automotive gears, and consumer electronics has driven plastic gearing to new levels of lubricant-free reliability and quiet operation.
Nomenclature of Common Gears
Some intermesh terms of common gears are illustrated in the following two figures.
Nomenclature of Bevel Gears
Some terms commonly used for bevel gears are annotated in the following figure.
To obtain the gear ratio, TV = (output rate)/(input rate), of a compound gear train, an illustrated example is presented in this section.
The procedure is to start with the input, and to calculate how the angular velocity propagates through each successive intermeshing pair of gears based upon the number of teeth.
Consider a compound gear train below.
Suppose that the input gear speed (rotation rate) is 1600 rpm clockwise, i.e.,
The gear ratio between w1 and W2 is inversely proportional to the teeth numbers, n, i.e.,
Hence,
where the negative sign represents for counter-clockwise direction.
Similarly,
and
The final gear ratio TV can thus be obtained,
Epicyclic gear trains are powerful when used correctly, but are often misunderstood. Illustrated below is a typical epicyclic gear train. Notice how the planet gears roll on and revolve about the sun gear. The ring gear rolls on the planet gears. Such a gear configuration has useful applications, but the overall gear ratio is quite difficult to intuitively calculate. Please select "Epicyclic Ratio Calc'n" to learn about an effective yet simple method for calculating the overall gear ratio.
Gears are a means of changing the rate of rotation of a machinery shaft. They can also change the direction of the axis of rotation and can change rotary motion to linear motion.
Unfortunately, mechanical engineers sometimes shy away from the use of gears and rely on the advent of electronic controls and the availability of toothed belts, since robust gears for high-speed and/or high-power machinery are often very complex to design. However, for dedicated, high-speed machinery such as an automobile transmission, gears are the optimal medium for low energy loss, high accuracy and low play.
Gears are of several categories, and can be combined in a multitude of ways, some of which are illustrated in the following figures.
Meshing Circular Spur Gears
Rack and Pinion Spur Gears
Circular Worm Gear and Mating Cylindrical Worm
Inside Spur Gear withMating Pinion Spur Gear
Gears have existed since the invention of rotating machinery. Because of their force-multiplying properties, early engineers used them for hoisting heavy loads such as building materials. The mechanical advantage of gears was also used for ship anchor hoists and catapult pre-tensioning.
Early gears were made from wood with cylindrical pegs for cogs and were often lubricated with animal fat grease. Gears were also used in wind and water wheel machinery for decreasing or increasing the provided rotational speed for application to pumps and other powered machines. An early gear arrangement used to power textile machinery is illustrated in the following figure. The rotational speed of a water or horse drawn wheel was typically too slow to use, so a set of wooden gears needed to be used to increase the speed to a usable level.
An 18th Century Application of Gears for Powering Textile Machinery
Some intermesh terms of common gears are illustrated in the following two figures.Some terms commonly used for bevel gears are annotated in the following figure.
To obtain the gear ratio, TV = (output rate)/(input rate), of a compound gear train, an illustrated example is presented in this section.
The procedure is to start with the input, and to calculate how the angular velocity propagates through each successive intermeshing pair of gears based upon the number of teeth.
Consider a compound gear train below.
Suppose that the input gear speed (rotation rate) is 1600 rpm clockwise, i.e.,
The gear ratio between w1 and W2 is inversely proportional to the teeth numbers, n, i.e.,
Hence,
where the negative sign represents for counter-clockwise direction.
Similarly,
and
The final gear ratio TV can thus be obtained,
Epicyclic gear trains are powerful when used correctly, but are often misunderstood. Illustrated below is a typical epicyclic gear train. Notice how the planet gears roll on and revolve about the sun gear. The ring gear rolls on the planet gears. Such a gear configuration has useful applications, but the overall gear ratio is quite difficult to intuitively calculate. Please select "Epicyclic Ratio Calc'n" to learn about an effective yet simple method for calculating the overall gear ratio.
Distributed by Abu-Iyad
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