Differential (mechanical device): Difference between revisions

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{{Short description|Type of simple planetary gear train}}

: ''This article deals with the concept of a differential in [[mechanics]]. For other meanings of "differential" see [[differential]].''

{{Use Oxford spelling|date=July 2024}}

{{Use dmy dates|date=July 2024}}

{{More citations needed|date=July 2015}}

{{Multiple image

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| image1 = BAUMA 2004 ZF Differentialgetriebe.jpg

| caption1 = Differential unit for a [[rear-wheel drive]] car, built by [[ZF Friedrichshafen|ZF]] {{circa|2004}}

| image2 = 20-TallyTakeupDrive.JPG

| caption2 = Differential gears (in yellow) in a [[punched tape]] reader, built by [[Tally (company)|Tally]] c. 1962

}}

A '''differential''' is a [[gear train]] with three [[drive shaft]]s that has the property that the [[rotational speed]] of one shaft is the average of the speeds of the others. A common use of differentials is in [[motor vehicle]]s, to allow the wheels at each end of a [[drive axle]] to rotate at different speeds while cornering. Other uses include clocks and [[Analog computer|analogue computers]].

Differentials can also provide a gear ratio between the input and output shafts (called the "axle ratio" or "diff ratio"). For example, many differentials in motor vehicles provide a gearing reduction by having fewer teeth on the [[pinion]] than the [[ring gear]].

==History==

[[Image:Differential free.png|frame|In this differential, input torque is applied to the ring gear (blue). The pinion gear (green) applies power to both side gears (red and yellow), which in turn may drive the left and right wheels. If both wheels turn at the same rate, the pinion gear does not rotate.]]

Milestones in the design or use of differentials include:

[[Image:Differential locked.png|frame|If the left side gear (red) encounters resistance or is immobile, the pinion gear (green) rotates about the left side gear, in turn applying extra rotation to the right side gear (yellow).]]

* 100 BCE–70 BCE: The [[Antikythera mechanism]] has been dated to this period. It was discovered in 1902 on a shipwreck by [[Sponge diving|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.<ref name="Wright-Reconsidered">{{cite journal |last=Wright |first=M. T. |date=2007 |title=The Antikythera Mechanism Reconsidered |journal=Interdisciplinary Science Reviews |volume=32 |number=1 |pages=27–43 |doi=10.1179/030801807X163670 |bibcode=2007ISRv...32...27W |s2cid=54663891 |url=http://fsoso.free.fr/antikythera/DOCS/TheAntikytheraMechanismReconsidered.pdf |access-date=8 June 2023 }}</ref>{{clarify|Please provide a quote to support that this mechanism is a predecessor to the modern differential devices|date=February 2023}}

* {{circa|250 CE}}: Chinese engineer [[Ma Jun (mechanical 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.<ref>{{cite journal |last=Needham |first=Joseph |author-link=Joseph Needham |date=1986 |journal=Science and Civilization in China |title=<!--We need the title of the article.--> |volume=4 Part 2 |pages=296–306 |___location=Taipei |publisher=Caves Books }}{{Title missing|date=January 2023}}</ref>{{clarify|Please provide a quote to support that this mechanism is a predecessor to the modern differential devices|date=February 2023}}

* 1810: [[Rudolph Ackermann]] of Germany invents a four-wheel steering system for carriages, which some later writers mistakenly report as a differential.

* 1823: [[Aza Arnold]] develops a differential drive train for use in [[Cotton-spinning machinery|cotton-spinning]]. The design quickly spreads across the United States and into the United Kingdom.<ref>{{Cite book |last=Mitman |first=Carl W. |date=1947 |editor-last=Johnson |editor-first=Allen |url=https://archive.org/details/dictionaryofamer01ilamer |title=Dictionary of American Biography |chapter=Arnold, Aza |publisher=[[Charles Scribner's Sons]], [[American Council of Learned Societies]] |volume=1 |pages=361–362 |___location=New York }}</ref>

* 1827: Modern automotive differential patented by watchmaker [[Onésiphore Pecqueur]] (1792–1852) of the ''[[Conservatoire National des Arts et Métiers]]'' in [[France]] for use on a [[steam wagon]].<ref>{{cite web|url=http://www.gmcanada.com/inm/gmcanada/english/about/OverviewHist/hist_auto.html |title=History of the Automobile |publisher=General Motors Canada |access-date=9 January 2011 }}</ref>

* 1874: [[Aveling and Porter]] of [[Rochester, Kent]] list a crane locomotive in their catalogue fitted with their patent differential gear on the rear axle.<ref>{{cite book |last=Preston |first=J.M. |title=Aveling & Porter, Ltd. Rochester |publisher=North Kent Books |date=1987 |isbn=0-948305-03-7 |pages=13–14 }}</ref>

* 1876: [[James Starley]] of [[Coventry]] invents chain-drive differential for use on [[bicycle]]s; invention later used on automobiles by [[Karl Benz]].

* 1897: While building his Australian [[steam car]], [[David Shearer (engineer)|David Shearer]] made the first use of a differential in a motor vehicle.<ref>{{cite web |title=David Shearer's Steam Car at Mannum in 1897 – Australia's First – with World-First Differential |url=https://adelaideaz.com/articles/david-shearer-s-steam--car--at-mannum-1897--australia-s-first---with--world-first-differential- |website=AdelaideAZ.com |access-date=27 February 2023 }}</ref>

* 1958: Vernon Gleasman patents the [[Torsen]] [[limited-slip differential]].<ref>{{cite web |title=Inventor Of Automotive Technologies – Vernon Gleasman's Legacy |url=https://www.theautochannel.com/news/2004/11/19/285488.html |website=TheAutoChannel.com |access-date=27 August 2023 }}</ref>

== Use in wheeled vehicles ==

In an [[automobile]] and other wheeled vehicles, a '''differential''' is a device, usually consisting of [[gear]]s, for supplying equal [[torque]] to the driving [[wheel]]s, even as they rotate at different speeds.

=== Purpose ===

[[File:Around the Corner (1937) 24fps selection.webm|thumb|1937 film about how differentials function]]

During cornering, the outer wheels of a vehicle must travel further than the inner wheels (since they are on a larger radius). This is easily accommodated when [[stub axle|the wheels are not connected]], however it becomes more difficult for the [[drive wheel]]s, since both wheels are connected to the engine (usually via a transmission). Some vehicles (for example [[go-kart]]s and [[tram]]s) use axles without a differential, thus relying on wheel slip when cornering. However, for improved cornering abilities, many vehicles use a differential, which allows the two wheels to rotate at different speeds.

In some vehicles such as [[Kart racing|kart]]s, torque is simply applied evenly to all driving wheels using a simple driveshaft. This works well enough when travelling in a straight line, but when changing direction the outer wheel needs to travel farther than the inner wheel. Hence, the simple solution results in the inner wheel spinning. For general road use, such a method would result in too much damage to both the [[tire]] and [[road]] surface.

Differentials are typically composed of a gear mechanism in which a ''ring'' gear receives input power, which is transferred to two ''side'' gears by means of usually two opposing central [[pinion]] gears on a common shaft. The pinion gear(s) are mounted to a ''cage'' which is affixed to the ring gear. When the ring gear and cage rotate, the pinion gears drive the side gears; the pinion gears are free to rotate about their own axis when either of the side gears meets resistance.

The purpose of a differential is to transfer the engine's power to the wheels while still allowing the wheels to rotate at different speeds when required. An illustration of the operating principle for a ring-and-pinion differential is shown below.

In a motor vehicle, the two side gears may be used to transfer power to the left and right wheels. When the vehicle turns a corner, or one of the wheels encounters resistance, the pinion gears rotate around the side with the most resistance; this rotation drives the other side gear with additional speed.

{{gallery |mode=nolines |width=400 |align= left | File:Differential free.png |'''Differential operation while driving in a straight line:'''<br />Input torque is applied to the ring gear (purple), which rotates the carrier (purple) at the same speed. When the resistance from both wheels is the same, the planet gear (green) doesn't rotate on its axis (although the gear and its pin are orbiting due to being attached to the carrier). This causes the sun gears (red and yellow) to rotate at the same speed, resulting in the car's wheels also rotating at the same speed.

The most basic differential described above, known as an open differential, suffers from one important problem, however. In an automobile, if one wheel begins to slip while the other maintains traction, the slipping wheel will receive most of the power. This means that if one wheel is spinning on ice while the other is still in contact with the pavement, acceleration of the [[driveshaft]] will only cause the slipping wheel to spin faster and very little power will reach the wheel with good traction. Similarly, if one wheel is lifted off the ground, nearly all the power will go to the wheel that is off the ground; not a hopeful prospect for off-road vehicles. Such a loss of traction is sometimes called "diffing out."

| File:Differential locked-2.png |'''Differential operation while turning left:'''<br />Input torque is applied to the ring gear (purple), which rotates the carrier (purple) at the same speed. The left sun gear (red) provides more resistance than the right sun gear (yellow), which causes the planet gear (green) to rotate anti-clockwise. This produces slower rotation in the left sun gear and faster rotation in the right sun gear, resulting in the car's right wheel turning faster (and thus travelling farther) than the left wheel.}}

Differential mechanisms possess two [[degrees of freedom]] (DOF), and the state of the mechanism depends on two constraints. In a vehicle, the first constraint is the motor, and the second is the frictional kinematic chain between the two wheels and the ground. When the two wheels slip on the ground, the second constraint becomes weaker or disappears. The differential also becomes undetermined and transmits less or no power. For control and recovery of the second constraint, various mechanisms are used.

{{clear left}}

=== Ring-and-pinion design ===

One solution to this problem is the [[limited slip differential]] (LSD), one of the most common of which is the clutch-type LSD. With this differential, each of the side gears has a clutch which limits the speed difference between the two wheels. Another solution is the locking differential, which employs a mechanism for allowing the pinion gear(s) to be locked, causing both wheels to turn at the same speed regardless of which has more traction; this is equivalent to removing the differential entirely.

[[File:Transmission diagram.JPG|thumb|left|Illustration of a ring-and-pinion differential for a rear-wheel drive vehicle]]

[[File:Differential (Manual of Driving and Maintenance).jpg|thumb|Schematic diagram of a ring-and pinion differential]]

A relatively simple design of differential is used in [[rear-wheel drive]] vehicles, whereby a [[ring gear]] is driven by a [[pinion]] gear connected to the transmission. The functions of this design are to change the axis of rotation by 90 degrees (from the propshaft to the half-shafts) and provide a reduction in the [[gear ratio]].

A [[four-wheel-drive]] vehicle will have at least two differentials (one for each pair of wheels) and possibly a center differential to apportion power between the front and rear axles. Vehicles without a center differential should not be driven on dry, paved roads in all wheel drive mode, as small differences in rotational speed between the front and rear of the vehicle cause a torque to be applied across the [[transmission (mechanics)|transmission]]. This phenomenon is known as "wind-up" and can cause damage to the transmission. On loose surfaces these differences are absorbed by the slippage of the road surface.

The components of the ring-and-pinion differential shown in the schematic diagram on the right are: 1. Output shafts ([[axle]]s) 2. Drive gear 3. Output gears 4. Planetary gears 5. Carrier 6. Input gear 7. Input shaft ([[driveshaft]])

A differential gear train can also be used to give the difference between two input axles. The oldest known example of a differential, in the [[Antikythera mechanism]], used such a train to produce the difference between two inputs, one input related to the position of the [[sun]] on the [[zodiac]], and the other input related to the position of the [[moon]] on the zodiac. The output of the differential gave a quantity related to the moon's [[phase]].

{{clear right}}

=== Epicyclic design ===

==Active differential==

<!--"Epicyclic differential" redirects here.-->

A relatively new technology is the electronically-controlled active differential. A computer uses inputs from multiple sensors, including [[yaw]] rate, steering angle, and lateral acceleration and adjusts the distribution of torque to compensate for undesirable handling behaviors like [[understeer]]. Active differentials are common in the [[World Rally Championship]], though they may be eliminated in coming years.

[[File:Epicyclic gear ratios.png|thumb|Diagram of an [[epicyclic gearing]] system]]

An '''epicyclic differential''' uses [[epicyclic gearing]] to send certain proportions of [[torque]] to the front axle and the rear axle in an [[all-wheel drive]] vehicle.{{citation needed|date=March 2023}} An advantage of the epicyclic design is its relatively compact width (when viewed along the axis of its input shaft).{{citation needed|date=March 2023}}

The first use of this technology on a production automobile was [[Honda]]'s [[1997]] ''Active Torque Transfer System'' on the [[Honda Prelude|Prelude ''SH'']]. This "differential" was actually a [[planetary gear]]set placed next to an open front differential, not an integrated system. Fully integrated active differentials are used on the [[2005]] [[MR layout|MR]] [[Ferrari F430]] and on all four wheels in the [[Acura RL]].

{{clear right}}

The second constraint of the differential is passive – it is actuated by the friction kinematics chain through the ground. The difference in torque on the tires (caused by turns or bumpy ground) drives the second [[DOF]],(overcoming the torque of inner friction) to equalise the driving torque on the tires. The sensitivity of the differential depends on the inner friction through the second [[DOF]]. All of the differentials (so called “active” and “passive”) use clutches and brakes for restricting the second [[DOF]], so all suffer from the same disadvantage – decreased sensibility to a dynamically changing environment. The sensibility of the computer controlled differential is also limited by the time delay caused by sensors and the response time of the actuators.

=== HistorySpur-gear design ===

[[File:Spur gear differential (Manual of Driving and Maintenance).jpg|thumb|Spur-gear differential]]

There are many claims to the invention of the differential gear, but it is likely that it was known, at least in some places, in ancient times. Here are some of the milestones in the history of this device.

A spur-gear differential has equal-sized spur gears at each end, each of which is connected to an output shaft.<ref name="Sergeant Clutch">{{cite web |title=What Is a Spur Gear Differential? |url=http://www.sergeantclutchdiscounttransmission.com/DifferentialPartsSanAntonio.html |website=SergeantClutchDiscountTransmission.com |access-date=27 March 2023 }}</ref> The input torque (i.e. from the engine or transmission) is applied to the differential via the rotating carrier.<ref name="Sergeant Clutch" /> Pinion pairs are located within the carrier and rotate freely on pins supported by the carrier. The pinion pairs only mesh 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. Each pinion connects the associated spur gear to the other spur gear (via the other pinion). As the carrier is rotated (by the input torque), the relationship between the speeds of the input (i.e. the carrier) and that of the output shafts is the same as other types of open differentials.

*[[2634 BC]] according to legend - [[South Pointing Chariot]] used by the Yellow Emperor [[Huang Di]] in [[China]].

*[[1st century BC]] - [[Antikythera mechanism]] contains a planar differential.

*[[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 des Arts et Métiers]] in [[France]] for use on a steam car. [Sources: Britannica Online and [http://www.gmcanada.com/inm/gmcanada/english/about/OverviewHist/hist_auto.html]]

*[[1832]] - [[Richard Roberts]] of England patents 'gear of compensation', a differential for road locomotives.

*[[1876]] - [[James Starley]] of [[Coventry]] invents chain-drive differential for use on [[bicycle]]s; invention later used on automobiles by [[Carl Benz]].

*[[1897]] - first use of differential on an Australian steam car by [[David Shearer]].

Uses of spur-gear differentials include the [[Oldsmobile Toronado]] American front-wheel drive car.<ref name="Sergeant Clutch" />{{explain|reason=Additional referenced examples are needed.|date=March 2023}}

== External links ==

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* An excellent explanation of how differentials work, with explanatory animations, is available at [http://auto.howstuffworks.com/differential.htm How Stuff Works].

=== Locking differentials ===

[[Category:Automotive transmission technologies]]

{{Main|Locking differential}}

[[Category:Mechanics]]

''Locking differentials'' have the ability 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 both wheels to turn in unison, regardless of the traction (or lack thereof) available to either wheel individually. When this function is not required, the differential can be "unlocked" to function as a regular open differential.

[[de:Differentialgetriebe]]

[[es:Diferencial (automóvil)]]

Locking differentials are mostly used on off-road vehicles, to overcome low-grip and variable grip surfaces.

[[fr:différentiel]]

[[it:Differenziale (meccanica)]]

=== Limited-slip differentials ===

[[nl:Differentieel (werktuigbouwkunde)]]

{{Main|Limited-slip differential}}

[[no:Differensial]]

An undesirable side-effect of a regular ("open") differential is that it can send most of the power to the wheel with the lesser traction (grip).<ref>{{cite book |last=Bonnick |first=Allan |date=2001 |url=https://books.google.com/books?id=odUZ0O_OWZwC&pg=PA22 |title=Automotive Computer Controlled Systems |isbn=9780750650892 |page=22 |publisher=Elsevier Science & Technology Books }}</ref><ref>{{cite book |last=Bonnick |first=Allan |date=2008 |url=https://books.google.com/books?id=78HoZb-ohbIC&pg=PA123 |title=Automotive Science and Mathematics |isbn=9780750685221 |page=123 |publisher=Butterworth-Heinemann }}</ref> In situation when one wheel has reduced grip (e.g. due to cornering forces or a low-grip surface under one wheel), an open differential can cause [[wheelspin]] in the tyre with less grip, while the tyre with more grip receives very little power to propel the vehicle forward.<ref>{{cite web |last=Chocholek |first=S. E. |date=1988 |url=http://zhome.com/ZCMnL/tech/Torsen/Torsen.htm |title=The Development of a Differential for the Improvement of Traction Control }}</ref>

In order to avoid this situation, various designs of ''limited-slip differentials'' are used to limit the difference in power sent to each of the wheels.

=== Torque vectoring ===

{{main|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. In the case of automobiles, it is used to augment the stability or cornering ability of the vehicle.

== Other uses ==

{{More citations needed section|date=March 2023}}

[[File:ChartDriveDetail.JPG|thumb|upright|Planetary differential used to drive a [[chart recorder]] c. 1961. The motors drive the Sun and annular gears, while the output is taken from the planet gear carrier. This gives 3 different speeds depending on which motors are on.]]

Non-automotive uses of differentials include performing [[Analog signal|analogue]] [[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, c. 80&nbsp;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.<ref name="Wright-Reconsidered" /> An [[equation clock]] that used a differential for addition was made in 1720. In the 20th century, large assemblies of many differentials were used as [[Analog computer|analogue computers]], calculating, for example, the direction in which a gun should be aimed.<ref>{{cite AV media |title=Basic Mechanisms in Fire Control Computers, Part 1, Shafts Gears Cams and Differentials, posted as 'U.S. Navy Vintage Fire Control Computers' |medium=Training Film |url=https://www.youtube.com/watch?v=mQhmmTX5f9Y&list=PLF1A5EC36E8EDF711 |archive-url=https://ghostarchive.org/varchive/youtube/20211118/mQhmmTX5f9Y| archive-date=18 November 2021 |url-status=live |date=1953 |time=37 seconds |publisher=U.S. Navy |id=MN-6783a |access-date=20 September 2021 }}{{cbignore}}</ref>

===Compass-like devices===

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]]. 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 be pointing in the wrong direction.

===Clocks===

The earliest 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]], as determined by the clock mechanism, to produce [[solar time]], 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 clocks 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.

===Analogue computers===

[[Differential analyzer|Differential analysers]], a type of mechanical analogue computer, were used from approximately 1900 to 1950. These devices used differential gear trains to perform addition and subtraction.

===Vehicle suspension===

The Mars rovers ''[[Spirit (rover)|Spirit]]'' and ''[[Opportunity (rover)|Opportunity]]'' (both launched in 2004) used differential gears in their [[rocker-bogie]] suspensions to keep the rover body balanced as the wheels on the left and right move up and down over uneven terrain.<ref>{{cite web |title=Rover Wheels |url=https://mars.nasa.gov/mer/mission/rover/wheels-and-legs/ |website=Mars.NASA.gov |access-date=18 January 2023 }}</ref> The ''[[Curiosity (rover)|Curiosity]]'' and ''[[Perseverance (rover)|Perseverance]]'' rovers used a differential bar instead of gears to perform the same function.<ref>{{cite web |title=Curiosity Mobility System, Labeled |url=https://www.planetary.org/space-images/curiosity-mobility-system |website=Planetary.org |access-date=18 January 2023 }}</ref>

==See also==

* [[Anti-lock braking system]]

* [[Ball differential]]

* [[Drifting (motorsport)]]

* [[List of auto parts]]

* {{Section link|Hermann Aron|Electricity meters}}

* [[Traction control system]]

* [[Whippletree (mechanism)|Whippletree]]

==References==

{{Reflist}}

==Further reading==

* [https://books.google.com/books?id=kiEDAAAAMBAJ&pg=PA76 ''Popular Science'', May 1946, ''How Your Car Turns Corners''], a large article with numerous illustrations on how differentials work

==External links==

{{Commons category|Automobile differentials}}

* [https://www.youtube.com/watch?v=vBm-SzO3ggE A video of a 3D model of an open differential]

{{Gears}}

{{Powertrain}}

[[Category:Articles containing video clips]]

[[Category:Auto parts]]

[[Category:Automotive transmission technologies]]

[[Category:Gears]]

[[Category:Mechanisms (engineering)]]

[[Category:Vehicle technology]]