Automotif Engine A differential is a particular type of simple planetary gear train that has the property that the angular velocity of its carrier is the average of the angular velocities of its sun and annular gears. This is accomplished by packaging the gear train so it has a fixed carrier train ratio R = -1, which means the gears corresponding to the sun and annular gears are the same size. This can be done by engaging the planet gears of two identical and coaxial epicyclic gear trains to form a spur gear differential. Another approach is to use bevel gears mfor the sun and annular gears and a bevel gear as the planet, which is known as a bevel gear differential.
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.
When used in this way, a differential couples the input shaft (or prop shaft) to the Pinion, which in turn runs on the Crown wheel of the differential. This also works as reduction gearing to give the ratio. On rear wheel drive vehicles the differential may connect to half-shafts inside an axle casing or drive shafts that connect to the rear driving wheels. Front wheel drive vehicles tend to have the pinion on the end of the main-shaft of the gearbox and the differential is enclosed in the same casing as the gearbox. They have individual drive-shafts to each wheel. Older 4x4 vehicles and tractors usually have a solid front axle, the modern way can be a separate differential and drive shaft arrangement for the front.
A differential consists of one input, the drive shaft, and
two outputs which are the two drive wheels, however the rotation of the drive
wheels are coupled 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. See also the
Chinese South-pointing chariot 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. However, the development of
electronic digital computers has made these uses of differentials obsolete.
Military uses may still exist. See Electromagnetic pulse. Practically all the
differentials that are now made are used in automobiles and similar vehicles. |
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Differential. The drive shaft enters from
the front and the driven axles run left and right.
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Differential Rebuild and differential defenition 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. Some historical milestones of the differential include: 1050 BC–771 BC: The Book of Song (which itself was written between 502 and 557 A.D.) makes the assertion that the south-pointing chariot, which may have used a differential gear, was invented during the Western Zhou Dynasty in China.[citation needed] 100 BC–70 BC: 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 30 BC–20 BC: Differential gear systems possibly used in China 227–239 AD: Despite doubts from fellow ministers at court, Ma Jun from the Kingdom of Wei in China invents the first historically verifiable south-pointing chariot, which provided cardinal direction as a non-magnetic, mechanized compass. Some such chariots may have used differential gears.
658, 666 AD: two Chinese Buddhist monks and engineers create south-pointing chariots for Emperor Tenji of Japan.
1027, 1107 AD: Documented Chinese reproductions of the south-pointing chariot by Yan Su and then Wu Deren, which described in detail the mechanical functions and gear ratios of the device much more so than earlier Chinese records.
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 des Arts et Métiers in France for use on a steam cart. (Sources: Britannica Online and),
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: first use of differential on an Australian steam car by David Shearer.
1958: Vernon Gleasman patents the Torsen dual-drive differential, a type of limited slip differential 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 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).
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.
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,
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 30 BC–20 BC: Differential gear systems possibly used in China 227–239 AD: Despite doubts from fellow ministers at court, Ma Jun from the Kingdom of Wei in China invents the first historically verifiable south-pointing chariot, which provided cardinal direction as a non-magnetic, mechanized compass. Some such chariots may have used differential gears.
658, 666 AD: two Chinese Buddhist monks and engineers create south-pointing chariots for Emperor Tenji of Japan.
1027, 1107 AD: Documented Chinese reproductions of the south-pointing chariot by Yan Su and then Wu Deren, which described in detail the mechanical functions and gear ratios of the device much more so than earlier Chinese records.
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 des Arts et Métiers in France for use on a steam cart. (Sources: Britannica Online and),
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: first use of differential on an Australian steam car by David Shearer.
1958: Vernon Gleasman patents the Torsen dual-drive differential, a type of limited slip differential 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 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).
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.
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,
History
Automotif Engine Spur-gear differential.This is another type of differential that was used in some early automobiles, more recently the Oldsmobile Toronado as well as other non-automotive applications. It consists of spur gears only.
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 pinions, 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 with a fixed carrier train ratio R = -1.
In this case, the fundamental formula for the planetary gear train yields
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.
In discussing the spur gear differential, the use of the term annular gear is a convenient way to distinguish the sun gears of the two epicyclic gear trains. The second sun gear serves the same purpose as the annular gear of a simple planetary gear train, but clearly does not have the internal gear mate that is typical of an annular gear.
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. 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 complete 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, 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.
In the first half of the twentieth century, mechanical analog computers, called differential analyzers, 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 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 use a differential to link two double tourbillon systems in their Quadruple Differential Tourbillon.
Application to vehicles
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 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 fast or the outer wheel drags, which results in difficult and unpredictable handling, damage to tires and roads, and strain on (or possible failure of) the entire drivetrain.
In rear-wheel drive automobiles the central drive shaft (or prop shaft) engages the differential through a hypoid gear(crown-wheel and pinion) the crown-wheel 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.
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 with a fixed carrier train ratio R = -1.
In this case, the fundamental formula for the planetary gear train yields
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.
In discussing the spur gear differential, the use of the term annular gear is a convenient way to distinguish the sun gears of the two epicyclic gear trains. The second sun gear serves the same purpose as the annular gear of a simple planetary gear train, but clearly does not have the internal gear mate that is typical of an annular gear.
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. 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 complete 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, 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.
In the first half of the twentieth century, mechanical analog computers, called differential analyzers, 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 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 use a differential to link two double tourbillon systems in their Quadruple Differential Tourbillon.
Application to vehicles
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 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 fast or the outer wheel drags, which results in difficult and unpredictable handling, damage to tires and roads, and strain on (or possible failure of) the entire drivetrain.
In rear-wheel drive automobiles the central drive shaft (or prop shaft) engages the differential through a hypoid gear(crown-wheel and pinion) the crown-wheel 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.
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