Differential (mechanical device)

Differential unit for a rear-wheel drive car, built by ZF circa 2004

Differential gears (in yellow) in a punched tape reader, built by Tally circa 1962

A differential is a gear train with three drive shafts 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.

Purposes

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):

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.

With automobiles 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. 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, 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 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

Milestones in the design or use of differentials include:

• 100 BCE–70 BCE: The Antikythera mechanism 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.
• 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 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 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 list a crane locomotive in their catalogue fitted with their patent differential gear on the rear axle.
• 1876: James Starley of Coventry invents chain-drive differential for use on bicycles; invention later used on automobiles by Karl Benz.
• 1897: While building his Australian steam car, David Shearer made the first use of a differential in a motor vehicle.
• 1958: Vernon Gleasman patents the Torsen limited-slip differential, a design which solely uses gears (without any clutches, unlike many other types of limited-slip differentials).

Use in wheeled vehicles

A cutaway drawing of a car's rear axle, showing the crown wheel and pinion of the final drive, and the smaller differential gears

Automotive differential: The drive gear 2 is mounted on the carrier 5 which supports the planetary bevel gears 4 which engage the driven bevel gears 3 attached to the axles 1.

"Around the Corner" (1937), a Jam Handy film made for Chevrolet explaining how an open differential works

Hypoid gear pair that connects an automotive drive shaft to a differential

Many wheeled vehicles use a differential on the driven axle, in order to improve the vehicle's cornering ability. However some vehicles (for example go-karts and trams use axles without a differential, thus relying on wheel slip when cornering.

Ring and pinion design

A relative 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 changes the axis of rotation by 90 degrees (from the propshaft to the half-shafts) and provide a reduction in the gear ratio.

Epicyclic design

Epicyclic gearing is used here to apportion torque asymmetrically. The input shaft is the green hollow one, the yellow is the low torque output, and the pink is the high torque output. The force applied in the yellow and the pink gears is the same, but since the arm of the pink one is 2× to 3× as big, the torque will be 2× to 3× as high.

An epicyclic differential can use epicyclic gearing to split and apportion torque 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).

Spur-gear design

A spur-gear differential constructed by engaging the planet gears of two co-axial epicyclic gear trains. The casing is the carrier for this planetary gear train.

Uses of spur-gear differentials include for centre differentials (used to distribute torque between the front and rear axles of an all-wheel drive vehicle) and in the Oldsmobile Toronado front-wheel drive car.

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.

Locking differentials

Main article: Locking differential

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.

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

Limited-slip differentials

Main article: Limited-slip differential

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). 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.

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 article: 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

Planetary differential used to drive a chart recorder circa 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.

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 have very well been pointing in the completely opposite 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 analyzers, a type of mechanical analog computer, were used from approximately 1900 to 1950. These devices 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.

Vehicle suspension

The Mars rovers Spirit and 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. The Curiosity and Perseverance rovers used a differential bar instead of gears to perform the same function.

See also

• Anti-lock braking system
• Ball differential
• Drifting (motorsport)
• Hermann Aron § Electricity meters
• Traction control system
• Whippletree

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