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A differential is a gear train with three
drive shaft A drive shaft, driveshaft, driving shaft, tailshaft ( Australian English), propeller shaft (prop shaft), or Cardan shaft (after Girolamo Cardano) is a component for transmitting mechanical power and torque and rotation, usually used to conne ...
s that has the property that the rotational speed of one shaft is the average of the speeds of the others, or a fixed multiple of that average.


Functional description

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): Thus, for example, if the car is making a turn to the right, the main ring gear may make 10 full rotations. During that time, the left wheel will make more rotations because it has farther 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 at different speeds relative to the ring gear (one faster, one slower) 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 ring 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.


Applications

With
automobile A car or automobile is a motor vehicle with wheels. Most definitions of ''cars'' say that they run primarily on roads, seat one to eight people, have four wheels, and mainly transport people instead of goods. The year 1886 is regarded ...
s and other wheeled vehicles, the differential allows the outer drive wheel to rotate faster than the inner drive wheel during a turn. This is necessary when the vehicle turns, making the wheel that is traveling around the outside of the turning curve roll farther and faster than the other. The average of the rotational speed of the two driving wheels equals the input rotational speed of the drive shaft. An increase in the speed of one wheel is balanced by a decrease in the speed of the other. When used in this way, a differential couples the longitudinal input propeller shaft to the pinion, which in turn drives the transverse ring gear of the differential. This also usually works as reduction gearing. On rear wheel drive vehicles the differential may connect to half-shafts inside an axle housing, or drive shafts that connect to the rear driving wheels. Front wheel drive vehicles tend to have the engine crankshaft and the gearbox shafts transverse, and with the pinion on the end of the counter-shaft of the gearbox and the differential enclosed in the same housing as the gearbox. There are individual drive-shafts to each wheel. A differential consists of one input (the drive shaft) and two outputs, which are connected to the two drive wheels; however the rotations of the drive wheels are coupled to each other by their connection to the roadway. Under normal conditions, with small tyre slip, the ratio of the speeds of the two driving wheels is defined by the ratio of the radii of the paths around which the two wheels are rolling, which in turn is determined by the track-width of the vehicle (the distance between the driving wheels) and the radius of the turn. Non-automotive uses of differentials include performing analog
arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...
. 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. The earliest known use of a differential gear is in the
Antikythera mechanism The Antikythera mechanism ( ) is an Ancient Greek hand-powered orrery, described as the oldest example of an analogue computer used to predict astronomical positions and eclipses decades in advance. It could also be used to track the four-y ...
, circa 80 BCE, which used a differential gear to control a small sphere representing the moon from the difference between the sun and moon position pointers. The ball was painted black and white in hemispheres, and graphically showed the phase of the moon at a particular point in time. An
equation clock An equation clock is a mechanical clock which includes a mechanism that simulates the equation of time, so that the user can read or calculate solar time, as would be shown by a sundial. The first accurate clocks, controlled by pendulums, were ...
that used a differential for addition was made in 1720. 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.


History

There are many claims to the invention of the differential gear, but it is possible that it was known, at least in some places, in ancient times. ''Confirmed'' historical milestones of the differential include: * 100 BCE–70 BCE: The
Antikythera mechanism The Antikythera mechanism ( ) is an Ancient Greek hand-powered orrery, described as the oldest example of an analogue computer used to predict astronomical positions and eclipses decades in advance. It could also be used to track the four-y ...
has been dated to this period. It was discovered in 1902 on a shipwreck by sponge divers, and modern research suggests that it used a differential gear to determine the angle between the ecliptic positions of the Sun and Moon, and thus the phase of the Moon.Presentation given to the NHRF in Athens, 6 March 2007 – M. T. Wright * c. 250 CE: Chinese engineer Ma Jun creates the first well-documented south-pointing chariot, a precursor to the compass. Its mechanism of action is unclear, though some 20th century engineers put forward the argument that it used a differential gear. * 1720: Joseph Williamson uses a differential gear in a clock. * 1810:
Rudolph Ackermann Rudolph Ackermann (20 April 1764 in Schneeberg, Electorate of Saxony – 30 March 1834 in Finchley, London) was an Anglo-German bookseller, inventor, lithographer, publisher and businessman. Biography He attended the Latin school in Stollbe ...
of Germany invents a four-wheel steering system for carriages, which some later writers mistakenly report as a differential. * 1827: modern automotive differential patented by watchmaker Onésiphore Pecqueur (1792–1852) of the '' Conservatoire National des Arts et Métiers'' in
France France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pac ...
for use on a steam wagon. * 1832: Richard Roberts of England patents "gear of compensation", a differential for road locomotives. * 1874: Aveling and Porter of
Rochester, Kent Rochester ( ) is a town in the unitary authority of Medway, in Kent, England. It is at the lowest bridging point of the River Medway, about from London. The town forms a conurbation with neighbouring towns Chatham, Rainham, Strood and Gil ...
list a crane locomotive in their catalogue fitted with their patent differential gear on the rear axle. * 1876: James Starley of
Coventry Coventry ( or ) is a city in the West Midlands, England. It is on the River Sherbourne. Coventry has been a large settlement for centuries, although it was not founded and given its city status until the Middle Ages. The city is governed b ...
invents chain-drive differential for use on
bicycle A bicycle, also called a pedal cycle, bike or cycle, is a human-powered or motor-powered assisted, pedal-driven, single-track vehicle, having two wheels attached to a frame, one behind the other. A is called a cyclist, or bicyclist. B ...
s; invention later used on automobiles by
Karl Benz Carl Friedrich Benz (; 25 November 1844 – 4 April 1929), sometimes also Karl Friedrich Benz, was a German engine designer and automotive engineer. His Benz Patent Motorcar from 1885 is considered the first practical modern automobile and fi ...
. * 1897: first use of differential on an Australian steam car by
David Shearer David James Shearer (born 28 July 1957) is a New Zealand United Nations worker and politician. He was a member of the New Zealand Parliament for the Labour Party from 2009 to 2016, serving as Leader of the Opposition from 2011 to 2013. Shear ...
* 1958: Vernon Gleasman patents the Torsen dual-drive differential, a type of
limited-slip differential A limited-slip differential (LSD) is a type of differential that allows its two output shafts to rotate at different speeds but limits the maximum difference between the two shafts. Limited-slip differentials are often known by the generic tr ...
that relies solely on the action of gearing, instead of a combination of clutches and gears.


Epicyclic differential

An epicyclic differential can use
epicyclic gearing An epicyclic gear train (also known as a planetary gearset) consists of two gears mounted so that the center of one gear revolves around the center of the other. A carrier connects the centers of the two gears and rotates the planet and sun gea ...
to split and apportion
torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...
asymmetrically between the front and rear axles. An epicyclic differential is at the heart of the Toyota Prius automotive drive train, where it interconnects the engine, motor-generators, and the drive wheels (which have a second differential for splitting torque as usual). It has the advantage of being relatively compact along the length of its axis (that is, the sun gear shaft). Epicyclic gears are also called planetary gears because the axes of the planet gears revolve around the common axis of the sun and ring gears that they mesh with and roll between. In the image, the yellow shaft carries the sun gear which is almost hidden. The blue gears are called planet gears and the pink gear is the ring gear or annulus. Ring gears are also used in starter motors.


Spur-gear differential

A spur-gear differential has two equal-sized spur gears, one for each half-shaft, with a space between them. Instead of the Bevel gear, also known as a miter gear, assembly (the "spider") at the centre of the differential, there is a rotating carrier on the same axis as the two shafts. Torque from a prime mover or transmission, such as the drive shaft of a car, rotates this carrier. Mounted in this carrier are one or more pairs of identical gears, generally longer than their diameters, and typically smaller than the spur gears on the individual half-shafts. Each pinion pair rotates freely on pins supported by the carrier. Furthermore, the pinion pairs are displaced axially, such that they mesh only for the part of their length between the two spur gears, and rotate in opposite directions. The remaining length of a given pinion meshes with the nearer spur gear on its axle. Therefore, each pinion couples that spur gear to the other pinion, and in turn, the other spur gear, so that when the drive shaft rotates the carrier, its relationship to the gears for the individual wheel axles is the same as that in a bevel-gear differential. A spur gear differential is constructed from two identical coaxial epicyclic gear trains assembled with a single carrier such that their planet gears are engaged. This forms a
planetary gear train An epicyclic gear train (also known as a planetary gearset) consists of two gears mounted so that the center of one gear revolves around the center of the other. A carrier connects the centers of the two gears and rotates the planet and sun gea ...
with a fixed carrier train ratio ''R = -1''. In this case, the fundamental formula for the planetary gear train yields, \frac=-1, or \omega_c = \frac(\omega_s + \omega_a). Thus, the angular velocity of the carrier of a spur gear differential is the average of the angular velocities of the sun and ''annular gears''.


Automotive applications

A vehicle with two drive wheels has the problem that when it turns a corner the drive wheels must rotate at different speeds to maintain traction. The automotive 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 An axle or axletree is a central shaft for a rotating wheel or gear. On wheeled vehicles, the axle may be fixed to the wheels, rotating with them, or fixed to the vehicle, with the wheels rotating around the axle. In the former case, beari ...
driven by a simple chain-drive mechanism. When cornering, the inner wheel travels a shorter distance than the outer wheel, so without a differential either the inner wheel rotates too quickly or the outer wheel rotates too slowly, which results in difficult and unpredictable handling, damage to
tire A tire (American English) or tyre (British English) is a ring-shaped component that surrounds a Rim (wheel), wheel's rim to transfer a vehicle's load from the axle through the wheel to the ground and to provide Traction (engineering), t ...
s and roads, and strain on (or possible failure of) the drivetrain. In rear-wheel drive automobiles the central drive shaft (or prop shaft) engages the differential through a hypoid gear (ring and pinion). The ring gear is mounted on the carrier of the planetary chain that forms the differential. This hypoid gear is a bevel gear that changes the direction of the drive rotation.


Loss of traction

One undesirable side effect of an open differential is that it can limit traction under less than ideal conditions. The amount of traction required to propel the vehicle at any given moment depends on the load at that instant—how heavy the vehicle is, how much drag and friction there is, the gradient of the road, the vehicle's momentum, and so on. The torque applied to each driving wheel is the result of the
engine An engine or motor is a machine designed to convert one or more forms of energy into mechanical energy. Available energy sources include potential energy (e.g. energy of the Earth's gravitational field as exploited in hydroelectric power ...
, transmission and drive axle applying a twisting force against the resistance of the traction at that roadwheel. In lower gears, and thus at lower speeds, and unless the load is exceptionally high, the drivetrain can supply as much torque as necessary, so the limiting factor becomes the traction under each wheel. It is therefore convenient to define traction as the amount of force that can be transmitted between the
tire A tire (American English) or tyre (British English) is a ring-shaped component that surrounds a Rim (wheel), wheel's rim to transfer a vehicle's load from the axle through the wheel to the ground and to provide Traction (engineering), t ...
and the road surface before the wheel starts to slip. If the torque applied to one of the drive wheels exceeds the threshold of traction, then that wheel will spin, and thus provide torque only at the other driven wheel equal to the sliding friction at the slipping wheel. The reduced net traction may still be enough to propel the vehicle slowly. An open (non-locking or otherwise traction-aided) differential always supplies close to equal torque to each side. To illustrate how this can limit torque applied to the driving wheels, imagine a simple
rear-wheel drive Rear-wheel drive (RWD) is a form of engine and transmission layout used in motor vehicles, in which the engine drives the rear wheels only. Until the late 20th century, rear-wheel drive was the most common configuration for cars. Most rear-wheel ...
vehicle, with one rear roadwheel on asphalt with good grip, and the other on a patch of slippery ice. It takes very little torque to spin the side on slippery ice, and because a differential splits torque equally to each side, the torque that is applied to the side that is on asphalt is limited to this amount. Based on the load, gradient, etc., the vehicle requires a certain amount of torque applied to the drive wheels to move forward. Since an open differential limits total torque applied to both drive wheels to the amount used by the lower traction wheel multiplied by two, when one wheel is on a slippery surface, the total torque applied to the driving wheels may be lower than the minimum torque required for vehicle propulsion.


Active differentials

The Volkswagen Golf GTI Mk7 in Performance trim has an electronically controlled front-axle transverse differential lock, also known as VAQ. The 2016 Ford Focus RS has a different type of differential setup. This essentially gives each wheel its own differential. This allows torque vectoring and can send power to any wheel that needs it.


Enthusiast interest

Drifting is a popular motorsport style that has its origins in the mountains of Japan. This style of driving is known for sliding a car through a corner without leaving the road surface. To easily get the car into a slide the driver can use a
limited-slip differential A limited-slip differential (LSD) is a type of differential that allows its two output shafts to rotate at different speeds but limits the maximum difference between the two shafts. Limited-slip differentials are often known by the generic tr ...
or a locked differential. A limited-slip differential limits the difference in rotational speed of the output shafts, preventing wheelspin on one side from causing the other wheel to lose all torque. Since the inside wheel of the car is going a shorter distance than the outside wheel, this causes slippage in a tight turn. This slippage is what makes it easier to slide the car around a turn.


Non-automotive applications

Chinese south-pointing chariots may also have been very early applications of differentials. The chariot had a pointer which constantly pointed to the south, no matter how the chariot turned as it travelled. It could therefore be used as a type of
compass A compass is a device that shows the cardinal directions used for navigation and geographic orientation. It commonly consists of a magnetized needle or other element, such as a compass card or compass rose, which can pivot to align itself with ...
. It is widely thought that a differential mechanism responded to any difference between the speeds of rotation of the two wheels of the chariot, and turned the pointer appropriately. However, the mechanism was not precise enough, and, after a few miles of travel, the dial could have very well been pointing in the completely opposite direction. The earliest definitely verified use of a differential was in a clock made by Joseph Williamson in 1720. It employed a differential to add the equation of time to
local mean time Local mean time (LMT) is a form of solar time that corrects the variations of local apparent time, forming a uniform time scale at a specific longitude. This measurement of time was used for everyday use during the 19th century before time zone ...
, as determined by the clock mechanism, to produce solar time, which would have been the same as the reading of a
sundial A sundial is a horological device that tells the time of day (referred to as civil time in modern usage) when direct sunlight shines by the apparent position of the Sun in the sky. In the narrowest sense of the word, it consists of a f ...
. During the 18th Century, sundials were considered to show the "correct" time, so an ordinary clock would frequently have to be readjusted, even if it worked perfectly, because of seasonal variations in the equation of time. Williamson's and other
equation clock An equation clock is a mechanical clock which includes a mechanism that simulates the equation of time, so that the user can read or calculate solar time, as would be shown by a sundial. The first accurate clocks, controlled by pendulums, were ...
s showed sundial time without needing readjustment. Nowadays, we consider clocks to be "correct" and sundials usually incorrect, so many sundials carry instructions about how to use their readings to obtain clock time. In the first half of the twentieth century, mechanical analog computers, called differential analyzers, were constructed that used differential gear trains to perform
addition Addition (usually signified by the plus symbol ) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or '' sum'' ...
and subtraction. The U.S. Navy Mk.1 gun fire control computer used about 160 differentials of the bevel-gear type. A differential gear train can be used to allow a difference between two input axles. Mills often used such gears to apply torque in the required axis. Differentials are also used in this way in watchmaking to link two separate regulating systems with the aim of averaging out errors.
Greubel Forsey Greubel Forsey is a Swiss watchmaking company specializing in complicated, high-end timepieces. It was launched in 2004 by Robert Greubel and Stephen Forsey and is based in La Chaux-de-Fonds, Switzerland. Greubel Forsey makes timepieces with mul ...
use a differential to link two double
tourbillon In horology, a tourbillon (; " whirlwind") is an addition to the mechanics of a watch escapement to increase accuracy. It was developed around 1795 and patented by the Swiss-French watchmaker Abraham-Louis Breguet on June 26, 1801. In a tourb ...
systems in their Quadruple Differential Tourbillon.


See also

*
Anti-lock braking system An anti-lock braking system (ABS) is a safety anti-skid braking system used on aircraft and on land vehicles, such as cars, motorcycles, trucks, and buses. ABS operates by preventing the wheels from locking up during braking, thereby maint ...
*
Ball differential A ball differential is a type of differential typically used on radio-controlled cars. It differs from a geared differential by using several small ball bearings rotating between two plates, instead of bevel gears. History The first ball diff ...
*
Equation clock An equation clock is a mechanical clock which includes a mechanism that simulates the equation of time, so that the user can read or calculate solar time, as would be shown by a sundial. The first accurate clocks, controlled by pendulums, were ...
* *
Locking differential A locking differential is a mechanical component, commonly used in vehicles, designed to overcome the chief limitation of a standard open differential by essentially "locking" both wheels on an axle together as if on a common shaft. This forces ...
* Traction control system * Whippletree


References


External links


A video of a 3D model of an open differential

''Popular Science'', May 1946, ''How Your Car Turns Corners''
a large article with numerous illustrations on how differentials work {{Powertrain Articles containing video clips Auto parts Automotive transmission technologies Gears Mechanisms (engineering) Vehicle technology