Gear Ratio 8.1.1

[Michelle Benitone]

Gearteeth are designed to ensure the pitch circles of engaging gears roll on each other without slipping, providing a smooth transmission of rotation from one gear to the next.[2] Features of gears and gear trains include:

The transmission of rotation between contacting toothed wheels can be traced back to the Antikythera mechanism of Greece and the south-pointing chariot of China. Illustrations by the Renaissance scientist Georgius Agricola show gear trains with cylindrical teeth. The implementation of the involute tooth yielded a standard gear design that provides a constant speed ratio.

In addition, consider that in order to mesh smoothly and turn without slipping, these two gears A and B must have compatible teeth. Given the same tooth and gap widths, they also must have the same circular pitch p \displaystyle p , which means

In other words, the [angular] speed ratio is inversely proportional to the radius of the pitch circle and the number of teeth of gear A, and directly proportional to the same values for gear B.

The gear ratio also determines the transmitted torque. The torque ratio T R A B \displaystyle \mathrm TR _AB of the gear train is defined as the ratio of its output torque to its input torque. Using the principle of virtual work, the gear train's torque ratio is equal to the gear ratio, or speed ratio, of the gear train. Again, assume we have two gears A and B, with subscripts designating each gear and gear A serving as the input gear.

For this analysis, consider a gear train that has one degree of freedom, which means the angular rotation of all the gears in the gear train are defined by the angle of the input gear. The input torque T A \displaystyle T_A acting on the input gear A is transformed by the gear train into the output torque T B \displaystyle T_B exerted by the output gear B.

Assuming the gears are rigid and there are no losses in the engagement of the gear teeth, then the principle of virtual work can be used to analyze the static equilibrium of the gear train. Because there is a single degree of freedom, the angle θ of the input gear completely determines the angle of the output gear and serves as the generalized coordinate of the gear train.

A hunting gear set is a set of gears where the gear teeth counts are relatively prime on each gear in an interfacing pair. Since the number of teeth on each gear have no common factors, then any tooth on one of the gears will come into contact with every tooth on the other gear before encountering the same tooth again. This results in less wear and longer life of the mechanical parts.A non-hunting gear set is one where the teeth counts are insufficiently prime. In this case, some particular gear teeth will come into contact with particular opposing gear teeth more times than others, resulting in more wear on some teeth than others.[6]

The simplest example of a gear train has two gears. The input gear (also known as the drive gear or driver) transmits power to the output gear (also known as the driven gear). The input gear will typically be connected to a power source, such as a motor or engine. In such an example, the output of torque and rotational speed from the output (driven) gear depend on the ratio of the dimensions of the two gears or the ratio of the tooth counts.

In a sequence of gears chained together, the ratio depends only on the number of teeth on the first and last gear. The intermediate gears, regardless of their size, do not alter the overall gear ratio of the chain. However, the addition of each intermediate gear reverses the direction of rotation of the final gear.

An intermediate gear which does not drive a shaft to perform any work is called an idler gear. Sometimes, a single idler gear is used to reverse the direction, in which case it may be referred to as a reverse idler. For instance, the typical automobile manual transmission engages reverse gear by means of inserting a reverse idler between two gears.

Idler gears can also transmit rotation among distant shafts in situations where it would be impractical to simply make the distant gears larger to bring them together. Not only do larger gears occupy more space, the mass and rotational inertia (moment of inertia) of a gear is proportional to the square of its radius. Instead of idler gears, a toothed belt or chain can be used to transmit torque over distance.

If a simple gear train has three gears, such that the input gear A meshes with an intermediate gear I which in turn meshes with the output gear B, then the pitch circle of the intermediate gear rolls without slipping on both the pitch circles of the input and output gears. This yields the two relations

Notice that this gear ratio is exactly the same as for the case when the gears A and B engage directly. The intermediate gear provides spacing but does not affect the gear ratio. For this reason it is called an idler gear. The same gear ratio is obtained for a sequence of idler gears and hence an idler gear is used to provide the same direction to rotate the driver and driven gear. If the driver gear moves in the clockwise direction, then the driven gear also moves in the clockwise direction with the help of the idler gear.

In the photo, assume the smallest gear (Gear A, in the lower right corner) is connected to the motor, which makes it the drive gear or input gear. The somewhat larger gear in the middle (Gear I) is called an idler gear. It is not connected directly to either the motor or the output shaft and only transmits power between the input and output gears. There is a third gear (Gear B) partially shown in the upper-right corner of the photo. Assuming that gear is connected to the machine's output shaft, it is the output or driven gear.

A double reduction gear set comprises two pairs of gears, each individually single reductions, in series. In the diagram, the red and blue gears give the first stage of reduction and the orange and green gears give the second stage of reduction. The total reduction is the product of the first stage of reduction and the second stage of reduction.

It is essential to have two coupled gears, of different sizes, on the intermediate layshaft. If a single intermediate gear was used, the overall ratio would be simply that between the first and final gears, the intermediate gear would only act as an idler gear: it would reverse the direction of rotation, but not change the ratio.

Special gears called sprockets can be coupled together with chains, as on bicycles and some motorcycles. Alternatively, belts can have teeth in them also and be coupled to gear-like pulleys. Again, exact accounting of teeth and revolutions can be applied with these machines.

For example, a belt with teeth, called the timing belt, is used in some internal combustion engines to synchronize the movement of the camshaft with that of the crankshaft, so that the valves open and close at the top of each cylinder at exactly the right time relative to the movement of each piston. A chain, called a timing chain, is used on some automobiles for this purpose, while in others, the camshaft and crankshaft are coupled directly together through meshed gears. Regardless of which form of drive is employed, the crankshaft-to-camshaft gear ratio is always 2:1 on four-stroke engines, which means that for every two revolutions of the crankshaft the camshaft will rotate once.

For internal combustion engine (ICE) vehicles, gearing is typically employed in the transmission, which contains a number of different sets of gears that can be changed to allow a wide range of vehicle speeds while operating the ICE within a narrower range of speeds, optimizing efficiency, power, and torque. Because electric vehicles instead use one or more electric traction motor(s) which generally have a broader range of operating speeds, they are typically equipped with a single-ratio reduction gear set instead.

The second common gear set in almost all motor vehicles is the differential, which contains the final drive to and often provides additional speed reduction at the wheels. Moreover, the differential contains gearing that splits torque equally[citation needed] between the two wheels while permitting them to have different speeds when traveling in a curved path.

The transmission and final drive might be separate and connected by a driveshaft, or they might be combined into one unit called a transaxle. The gear ratios in transmission and final drive are important because different gear ratios will change the characteristics of a vehicle's performance.

In 1st gear, the engine makes 2.97 revolutions for every revolution of the transmission's output. In 4th gear, the gear ratio of 1:1 means that the engine and the transmission's output rotate at the same speed, referred to as the "direct drive" ratio. 5th and 6th gears are known as overdrive gears, in which the output of the transmission is revolving faster than the engine's output.

The Corvette above is equipped with a differential that has a final drive ratio (or axle ratio) of 3.42:1, meaning that for every 3.42 revolutions of the transmission's output, the wheels make one revolution. The differential ratio multiplies with the transmission ratio, so in 1st gear, the engine makes 10.16 (= 2.97 3.42) revolutions for every revolution of the wheels.

The car's tires can almost be thought of as a third type of gearing. This car is equipped with 295/35-18 tires, which have a circumference of 82.1 inches. This means that for every complete revolution of the wheel, the car travels 82.1 inches (209 cm). If the Corvette had larger tires, it would travel farther with each revolution of the wheel, which would be like a higher gear. If the car had smaller tires, it would be like a lower gear.

For example, it is possible to determine the distance the car will travel for one revolution of the engine by dividing the circumference of the tire by the combined gear ratio of the transmission and differential.

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