![Transmission diagram](https://upload.wikimedia.org/wikipedia/commons/2/27/Transmission_diagram.JPG)
A differential is a
gear train
A gear train is a mechanical system formed by mounting gears on a frame so the teeth of the gears engage.
Gear teeth are designed to ensure the pitch circles of engaging gears roll on each other without slipping, providing a smooth transmission ...
with three
drive shafts that has the property that the
rotational speed
Rotational frequency (also known as rotational speed or rate of rotation) of an object rotating around an axis is the frequency of rotation of the object. Its unit is revolution per minute (rpm), cycle per second (cps), etc.
The symbol fo ...
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
![BAUMA 2004 ZF Differentialgetriebe](https://upload.wikimedia.org/wikipedia/commons/a/ad/BAUMA_2004_ZF_Differentialgetriebe.jpg)
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 regarde ...
s and other wheeled vehicles, the differential allows the outer
drive wheel
A drive wheel is a wheel of a motor vehicle that transmits force, transforming torque into tractive force from the tires to the road, causing the vehicle to move. The powertrain delivers enough torque to the wheel to overcome stationary for ...
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
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 connect ...
to the
pinion, which in turn drives the transverse
ring gear
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 ...
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
Analog or analogue may refer to:
Computing and electronics
* Analog signal, in which information is encoded in a continuous variable
** Analog device, an apparatus that operates on analog signals
*** Analog electronics, circuits which use 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. 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-yea ...
, 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 pa ...
that used a differential for addition was made in 1720. In the 20th Century, large assemblies of many differentials were used as
analog computer
An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities (''analog signals'') to model the problem being solved. In ...
s, 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-yea ...
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
The south-pointing chariot (or carriage) was an ancient Chinese two-wheeled vehicle that carried a movable pointer to indicate the south, no matter how the chariot turned. Usually, the pointer took the form of a doll or figure with an outstretch ...
, 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 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
A music school is an educational institution specialized in the study, training, and research of music. Such an institution can also be known as a school of music, music academy, music faculty, college of music, music department (of a larger ins ...
'' in
France
France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of overseas regions and territories in the Americas and the Atlantic, Pacific and Indian Oceans. Its metropolitan area ...
for use on a
steam wagon
A steam wagon (or steam lorry, steam waggon or steamtruck) is a steam-powered truck for carrying freight. It was the earliest form of lorry (truck) and came in two basic forms: ''overtype'' and ''undertype'', the distinction being the position ...
.
* 1832:
Richard Roberts of England patents "gear of compensation", a differential for
road locomotives.
* 1874:
Aveling and Porter
Aveling and Porter was a British agricultural engine and steamroller (road roller) manufacturer. Thomas Aveling and Richard Thomas Porter entered into partnership in 1862, and developed a steam engine three years later in 1865. By the ear ...
of
Rochester, Kent list a crane locomotive in their catalogue fitted with their patent differential gear on the rear axle.
* 1876:
James Starley
James Starley (21 April 1830 – 17 June 1881) was an English inventor and father of the bicycle industry. He was one of the most innovative and successful builders of bicycles and tricycles. His inventions include the differential gear and t ...
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
bicycles; 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 fir ...
.
* 1897: first use of differential on an Australian
steam car
A steam car is a car (automobile) propelled by a steam engine. A steam engine is an external combustion engine (ECE) in which the fuel is combusted outside of the engine, unlike an internal combustion engine (ICE) in which fuel is combusted ins ...
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.
Shea ...
* 1958:
Vernon Gleasman patents the
Torsen
Torsen Torque-Sensing (full name Torsen traction) is a type of limited-slip differential used in automobiles.
It was invented by American Vernon Gleasman and manufactured by the Gleason Corporation. Torsen is a portmanteau of Torque-Sensing. ''TO ...
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 t ...
that relies solely on the action of gearing, instead of a combination of clutches and gears.
Epicyclic differential
![Epicyclic gear ratios](https://upload.wikimedia.org/wikipedia/commons/d/d5/Epicyclic_gear_ratios.png)
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
The is a car built by Toyota which has a hybrid drivetrain, combining an internal combustion engine with an electric motor. Initially offered as a four-door sedan, it has been produced only as a five-door liftback since 2003.
In 2007, ...
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
![Spur gear differential (Manual of Driving and Maintenance)](https://upload.wikimedia.org/wikipedia/commons/7/75/Spur_gear_differential_%28Manual_of_Driving_and_Maintenance%29.jpg)
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
Bevel gears are gears where the axes of the two shafts intersect and the tooth-bearing faces of the gears themselves are conically shaped. Bevel gears are most often mounted on shafts that are 90 degrees apart, but can be designed to work at othe ...
, 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
Prime mover may refer to:
Philosophy
*Unmoved mover, a concept in Aristotle's writings
Engineering
* Prime mover (engine), motor, a machine that converts various other forms of energy (chemical, electrical, fluid pressure/flow, etc) into energy ...
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,
or
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
![Differential (Manual of Driving and Maintenance)](https://upload.wikimedia.org/wikipedia/commons/3/3b/Differential_%28Manual_of_Driving_and_Maintenance%29.jpg)
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
kart
Kart racing or karting is a road racing variant of motorsport with open-wheel, four-wheeled vehicles known as go-karts or shifter karts. They are usually raced on scaled-down circuits, although some professional kart races are also held on ...
s, 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 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 wheel's rim to transfer a vehicle's load from the axle through the wheel to the ground and to provide traction on the surface over which t ...
s and roads, and strain on (or possible failure of) the
drivetrain
A drivetrain (also frequently spelled as drive train or sometimes drive-train) is the group of components that deliver mechanical power from the prime mover to the driven components. In automotive engineering, the drivetrain is the components o ...
.
![Sprocket35b](https://upload.wikimedia.org/wikipedia/commons/d/d1/Sprocket35b.jpg)
In rear-wheel drive automobiles the central drive shaft (or prop shaft) engages the differential through a
hypoid gear
A spiral bevel gear is a bevel gear with helical teeth. The main application of this is in a vehicle differential, where the direction of drive from the drive shaft must be turned 90 degrees to drive the wheels. The helical design produces less ...
(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 wheel's rim to transfer a vehicle's load from the axle through the wheel to the ground and to provide traction on the surface over which 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
The Ford Focus is a compact car (C-segment in Europe) manufactured by Ford Motor Company since 1998. It was created under Alexander Trotman's Ford 2000 plan, which aimed to globalize model development and sell one compact vehicle worldwide. The ...
RS has a different type of differential setup. This essentially gives each wheel its own differential. This allows
torque vectoring
Torque vectoring is a technology employed in automobile differentials that has the ability to vary the torque to each half-shaft with an electronic system; or in rail vehicles which achieve the same using individually motored wheels. This method ...
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 t ...
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
![20-TallyTakeupDrive](https://upload.wikimedia.org/wikipedia/commons/4/4f/20-TallyTakeupDrive.JPG)
Chinese
south-pointing chariot
The south-pointing chariot (or carriage) was an ancient Chinese two-wheeled vehicle that carried a movable pointer to indicate the south, no matter how the chariot turned. Usually, the pointer took the form of a doll or figure with an outstretch ...
s 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 wit ...
. 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
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in F ...
to
local mean time, as determined by the clock mechanism, to produce
solar time
Solar time is a calculation of the passage of time based on the position of the Sun in the sky. The fundamental unit of solar time is the day, based on the synodic rotation period. Two types of solar time are apparent solar time (sundial ti ...
, which would have been the same as the reading of a
sundial. 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 pa ...
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 computer
An analog computer or analogue computer is a type of computer that uses the continuous variation aspect of physical phenomena such as electrical, mechanical, or hydraulic quantities (''analog signals'') to model the problem being solved. In ...
s, called
differential analyzer
The differential analyser is a mechanical analogue computer designed to solve differential equations by integration, using wheel-and-disc mechanisms to perform the integration. It was one of the first advanced computing devices to be used operat ...
s, were constructed that used differential gear trains to perform
addition 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
Mills is the plural form of mill, but may also refer to:
As a name
* Mills (surname), a common family name of English or Gaelic origin
* Mills (given name)
*Mills, a fictional British secret agent in a trilogy by writer Manning O'Brine
Places Uni ...
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 tourbill ...
systems in their Quadruple Differential Tourbillon.
See also
*
Anti-lock braking system
*
Ball differential
*
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 pa ...
*
*
Locking differential
*
Traction control system
A traction control system (TCS), also known as ASR (from german: Antriebsschlupfregelung, lit=drive slippage regulation), is typically (but not necessarily) a secondary function of the electronic stability control (ESC) on production motor vehicle ...
*
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