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Differential (mechanical device)

From Wikipedia, the free encyclopedia
A differential is a device, usually, but not necessarily, employing gears, which is connected to the outside world by three shafts, chains, or similar, through which it transmits torque and rotation. The gears or other components make the three shafts rotate in such a way that a=pb+qc, where a, b, and c are the angular velocities of the three shafts, and p and q are constants. Often, but not always, p and q are equal, so a is proportional to the sum (or average) of b and c. Except in some special-purpose differentials, there are no other limitations on the rotational speeds of the shafts, apart from the usual mechanical/engineering limits. Any of the shafts can be used to input rotation, and the other(s) to output it. See animation of a simple differential in which p and q are equal. The shaft rotating at speed a is at the bottom-right of the image.
In automobiles and other wheeled vehicles, a differential is the usual way to allow the driving roadwheels to rotate at different speeds. This is necessary when the vehicle turns, making the wheel that is travelling around the outside of the turning curve roll farther and faster than the other. The engine is connected to the shaft rotating at angular velocity a. The driving wheels are connected to the other two shafts, and p and q are equal. If the engine is running at a constant speed, the rotational speed of each driving wheel can vary, but the sum (or average) of the two wheels' speeds can not change. An increase in the speed of one wheel must be balanced by an equal decrease in the speed of the other. (If one wheel is rotating backward, which is possible in very tight turns, its speed should be counted as negative.)
It may seem illogical that the speed of one input shaft can determine the speeds of two output shafts, which are allowed to vary. Logically, the number of inputs should be at least as great as the number of outputs. However, the system has another constraint. Under normal conditions (i.e only small tyre slip), the ratio of the speeds of the two driving wheels equals the ratio of the radii of the paths around which the two wheels are rolling, which is determined by the track-width of the vehicle (the distance between the driving wheels) and the radius of the turn. Thus the system does not have one input and two independent outputs. It has two inputs and two outputs.
A different automotive application of differentials is in epicyclic gearing. A gearbox is constructed out of several differentials. In each differential, one shaft is connected to the engine (through a clutch or functionally similar device), another to the driving wheels (through another differential as described above), and the third shaft can be braked so its angular velocity is zero. (The braked component may not be a shaft, but something that plays an equivalent role.) When one shaft is braked, the gear ratio between the engine and wheels is determined by the value(s) of p and/or q for that differential, which reflect the numbers of teeth on its gears. Several differentials, with different gear ratios, are permanently connected in parallel with each other, but only one of them has one shaft braked so it can not rotate, so only that differential transmits power from the engine to the wheels. (If the transmission is in "neutral" or "park", none of the shafts is braked.) Shifting gears simply involves releasing the braked shaft of one differential and braking the appropriate shaft on another. This is a much simpler operation to do automatically than engaging and disengaging gears in a conventional gearbox. Epicyclic gearing is almost always used in automatic transmissions, and is nowadays also used in some hybrid and electric vehicles.
Non-automotive uses of differentials include performing analog arithmetic. Two of the differential's three shafts are made to rotate through angles that represent (are proportional to) two numbers, and the angle of the third shaft's rotation represents the sum or difference of the two input numbers. An equation clock that used a differential for addition, made in 1720, is the earliest device definitely known to have used a differential for any purpose.[1] In the 20th Century, large assemblies of many differentials were used as analog computers, calculating, for example, the direction in which a gun should be aimed. However, the development of electronic digital computers has made these uses of differentials obsolete.[2] Practically all the differentials that are now made are used in automobiles and similar vehicles. This article therefore emphasizes automotive uses of differentials.


Purpose
A vehicle's wheels rotate at different speeds, mainly when turning corners. The differential is designed to drive a pair of wheels while allowing them to rotate at different speeds. In vehicles without a differential, such as karts, both driving wheels are forced to rotate at the same speed, usually on a common axle driven by a simple chain-drive mechanism. When cornering, the inner wheel needs to travel a shorter distance than the outer wheel, so with no differential, the result is the inner wheel spinning and/or the outer wheel dragging, and this results in difficult and unpredictable handling, damage to tires and roads, and strain on (or possible failure of) the entire drivetrain.
Functional description
Input torque is applied to the ring gear (blue), which turns the entire carrier (blue). The carrier is connected to both sun gears (red and yellow) only through the planet gear (green). Torque is transmitted to the sun gears through the planet gear. The planet gear revolves around the axis of the carrier, driving the sun gears. If the resistance at both wheels is equal, the planet gear revolves without spinning about its own axis, and both wheels turn at the same rate.
If the left sun gear (red) encounters resistance, the planet gear (green) spins as well as revolving, allowing the left sun gear to slow down, with an equal speeding up of the right sun gear (yellow).

The following description of a differential applies to a "traditional" rear-wheel-drive car or truck with an "open" or limited slip differential combined with a reduction gearset using bevel gears (these are not strictly necessary - see spur-gear differential):
Torque is supplied from the engine, via the transmission, to a drive shaft (British term: 'propeller shaft', commonly and informally abbreviated to 'prop-shaft'), which runs to the final drive unit that contains the differential. A spiral bevel pinion gear takes its drive from the end of the propeller shaft, and is encased within the housing of the final drive unit. This meshes with the large spiral bevelring gear, known as the crown wheel. The crown wheel and pinion may mesh in hypoid orientation, not shown. The crown wheel gear is attached to the differential carrier or cage, which contains the 'sun' and 'planet' wheels or gears, which are a cluster of four opposed bevel gears in perpendicular plane, so each bevel gear meshes with two neighbours, and rotates counter to the third, that it faces and does not mesh with. The two sun wheel gears are aligned on the same axis as the crown wheel gear, and drive the axlehalf shafts connected to the vehicle's driven wheels. The other two planet gears are aligned on a perpendicular axis which changes orientation with the ring gear's rotation. In the two figures shown above, only one planet gear (green) is illustrated, however, most automotive applications contain two opposing planet gears. Other differential designs employ different numbers of planet gears, depending on durability requirements. As the differential carrier rotates, the changing axis orientation of the planet gears imparts the motion of the ring gear to the motion of the sun gears by pushing on them rather than turning against them (that is, the same teeth stay in the same mesh or contact position), but because the planet gears are not restricted from turning against each other, withinthat motion, the sun gears can counter-rotate relative to the ring gear and to each other under the same force (in which case the same teeth do not stay in contact).
Thus, for example, if the car is making a turn to the right, the main crown wheel may make 10 full rotations. During that time, the left wheel will make more rotations because it has further to travel, and the right wheel will make fewer rotations as it has less distance to travel. The sun gears (which drive the axle half-shafts) will rotate in opposite directions relative to the ring gear by, say, 2 full turns each (4 full turns relative to each other), resulting in the left wheel making 12 rotations, and the right wheel making 8 rotations.
The rotation of the crown wheel gear is always the average of the rotations of the side sun gears. This is why, if the driven roadwheels are lifted clear of the ground with the engine off, and the drive shaft is held (say leaving the transmission 'in gear', preventing the ring gear from turning inside the differential), manually rotating one driven roadwheel causes the opposite roadwheel to rotate in the opposite direction by the same amount.
When the vehicle is traveling in a straight line, there will be no differential movement of the planetary system of gears other than the minute movements necessary to compensate for slight differences in wheel diameter, undulations in the road (which make for a longer or shorter wheel path), etc.


For more explanations, see the videos here :
History of the differential, Simple explanations but striking our memories.
Around The Corner (1937) How Differential Steering Works

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