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By

VARUN K R
DEPARTMENT OF MECHANICAL ENGINEERING
CITY ENGINEERING COLLEGE



ABSTRACT

A differential is an important component which has a rack and a pinion, which allows the automobile to take turn by transmitting the power equally on both sides. Otherwise the tendency of the inner wheel taking a turn will have a slower rotation and the outer wheel should rotate faster. Differential actually helps the inner wheel to rotate at slow pace and the other wheel at a fast pace. This mechanism can happen because of the arrangement of rack and pinion which is shown in the diagram above. Thus the pinion gets the transmission from the propeller shaft & with the tolerance effect, has the tendency to transfer the torque to the rack. This rack & pinion is housed in a pumpkin shape, which is called as housing. This housing is connected with a spindle at both the ends namely the left and the right side. When the automobile is taking a turn, for example to the right side, the tendency is that the inner wheel will take a smaller radius and has to go slow, where as the outer wheel has to rotate fast & with a bigger radius. So at this point in time, the shaft like thing which is called as spindle towards the right side gets engaged, hence bringing in a slow rotation. The outer wheel naturally rotates at its actual speed because it is free from the spindle engagement. This process becomes reverse, when it comes to taking a left turn and the whole process repeats.

The pinion is engaged to the rack with certain amount of tolerance to avoid the tight fit, which has the characteristics of a intolerance limit and for obvious reasons, the friction is more and also has the chances of a fracture. To avoid the same, lubricant is poured in the housing, hence enabling the reduction in heat dissipation which is created during friction.

INTRODUCTION
A differential is a mechanical device which allows a flexible division of drive between wheels to allow cornering.

Differential is a mechanical device which transmits the power through three rotating shaft which makes the automobile turn without traction

The differential has three jobs:
 To aim the engine power at the wheels

 To act as the final gear reduction in the vehicle, slowing the rotational speed of the transmission one final time before it hits the wheels

 To transmit the power to the wheels while allowing them to rotate at different speeds (This is the one that earned the differential its name.)

HISTORY
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.
 1050 BC-771 BC: The Book of Song claimed the South Pointing Chariot, which uses a differential gear, was invented during the Western Zhou Dynasty in China.

 200-100 BC - The Antikythera mechanism: The device is remarkable for the level of miniaturization and for the complexity of its parts, which is comparable to that of 18th century clocks. It has over 30 gears, although Michael Wright (see below) has suggested as many as 72 gears, with teeth formed through equilateral triangles, In Greece.

 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.

 58, 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.

 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 bicycles; invention later used on automobiles by Karl Benz.

 1897 - first use of differential on an Australian steam car by David Shearer.

 1913 - Packard introduces the spiral-gear differential, which cuts gear noise.

 1926 - Packard introduces the hypoid differential, which enables the propeller shaft and its hump in the interior of the car to be lowered.

 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.

Need for differential
Car wheels spin at different speeds, especially when turning. You can see from the animation that each wheel travels a different distance through the turn, and that the inside wheels travel a shorter distance than the outside wheels. Since speed is equal to the distance traveled divided by the time it takes to go that distance, the wheels that travel a shorter distance travel at a lower speed. Also note that the front wheels travel a different distance than the rear wheels.
For the non-driven wheels on your car -- the front wheels on a rear-wheel drive car, the back wheels on a front-wheel drive car -- this is not an issue. There is no connection between them, so they spin independently. But the driven wheels are linked together so that a single engine and transmission can turn both wheels. If your car did not have a differential, the wheels would have to be locked together, forced to spin at the same speed. This would make turning difficult and hard on your car: For the car to be able to turn, one tire would have to slip. With modern tires and concrete roads, a great deal of force is required to make a tire slip. That force would have to be transmitted through the axle from one wheel to another, putting a heavy strain on the axle components.

PRINCIPLE OF DIFFERENTIAL
Consider the simplest differential called an open differential shown in fig. To the crown wheel of the final drive is attached a cage which carries a ‘cross pin’. Two sun gears mesh with the two or four planet pinions. Axel half-shafts are splined to each of these sun gears. The crown wheel is free to rotate on the half-shaft as shown.
When the vehicle is going straight the cage and the inner gears rotate as a single unit and the two half shafts revolve at the same speed. In this situation there is no relative movement among the various differential gears. When the vehicle is taking a turn, assume that the cage is stationary. Then turning one sun gear will cause the other to rotate in the opposite direction. i.e., if left sun gear rotates ‘n’ times in a particular time, the right sun gear will also rotate ‘n’ times in the same period but, in the opposite direction. This rotation is super imposed on the normal wheel speed when the vehicle is taking a turn.
The torque from the final drive is divided between the two half-shafts. As the planet pinions are free to rotate on the cross-pin or the spider arm, they cannot apply different torque to the teeth on one side from the one on the other side. Therefore, they act as a balance and divide the torque equally between the two wheels on the axel, even when their speeds are different.

PURPOSE

A vehicle's wheels rotate at different speeds, mainly when turning corners. The differential is designed to drive a pair of wheels with equal torque, whilst 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 needs to travel a shorter distance than the outer wheel, so with no differential, the result is the inner wheel spinning and/or the outer wheel dragging, and this results in difficult and unpredictable handling, damage to tires and roads, and strain on (or possible failure of) the entire drive train.

FUNCTIONAL DESCRIPTION

A cutaway drawing of a car's rear axle, showing the crown wheel and pinion of the final drive, and the smaller differential gears
The following description of a differential applies to a "traditional" rear-wheel-drive car or truck:
Torque is supplied from the engine, via the transmission, to a drive shaft (British term: 'propeller shaft', commonly and informally abbreviated to 'prop-shaft'), which runs to the final drive unit and contains the differential. A spiral bevel pinion gear takes its drive from the end of the propeller shaft, and is encased within the housing of the final drive unit. This meshes with the large spiral bevel ring gear, known as the crown wheel. The crown wheel and pinion may mesh in hypoid orientation, not shown. The crown wheel gear is attached to the differential carrier or cage, which contains the 'sun' and 'planet' wheels or gears, which are a cluster of four opposed bevel gears in perpendicular plane, so each bevel gear meshes with two neighbours, and rotates counter to the third, that it faces and does not mesh with. The two sun wheel gears are aligned on the same axis as the crown wheel gear, and drive the axle half shafts connected to the vehicle's driven wheels. The other two planet gears are aligned on a perpendicular axis which changes orientation with the ring gear's rotation. In the two figures shown above, only one planet gear (green) is illustrated, however, most automotive applications contain two opposing planet gears.


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Other differential designs employ different numbers of planet gears, depending on durability requirements. As the differential carrier rotates, the changing axis orientation of the planet gears imparts the motion of the ring gear to the motion of the sun gears by pushing on them rather than turning against them (that is, the same teeth stay in the same mesh or contact position), but because the planet gears are not restricted from turning against each other, within that motion, the sun gears can counter-rotate relative to the ring gear and to each other under the same force (in which case the same teeth do not stay in contact).
Thus, for example, if the car is making a turn to the right, the main crown wheel may make 10 full rotations. During that time, the left wheel will make more rotations because it has further 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 in opposite directions relative to the ring gear 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 crown wheel 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.
When the vehicle is traveling in a straight line, there will be no differential movement of the planetary system of gears other than the minute movements necessary to compensate for slight differences in wheel diameter, undulations in the road (which make for a longer or shorter wheel path), etc.

DIFFERENTIALS AND TRACTION
The open differential always applies the same amount of torque to each wheel. There are two factors that determine how much torque can be applied to the wheels: equipment and traction. In dry conditions, when there is plenty of traction, the amount of torque applied to the wheels is limited by the engine and gearing; in a low traction situation, such as when driving on ice, the amount of torque is limited to the greatest amount that will not cause a wheel to slip under those conditions. So, even though a car may be able to produce more torque, there needs to be enough traction to transmit that torque to the ground. If you give the car more gas after the wheels start to slip, the wheels will just spin faster.

On Thin Ice
If you've ever driven on ice, you may know of a trick that makes acceleration easier: If you start out in second gear, or even third gear, instead of first, because of the gearing in the transmission you will have less torque available to the wheels. This will make it easier to accelerate without spinning the wheels.
Now what happens if one of the drive wheels has good traction, and the other one is on ice? This is where the problem with open differentials comes in.
Remember that the open differential always applies the same torque to both wheels, and the maximum amount of torque is limited to the greatest amount that will not make the wheels slip. It doesn't take much torque to make a tire slip on ice. And when the wheel with good traction is only getting the very small amount of torque that can be applied to the wheel with less traction, your car isn't going to move very much.


Off Road
Another time open differentials might get you into trouble is when you are driving off-road. If you have a four-wheel drive truck, or an SUV, with an open differential on both the front and the back, you could get stuck. Now, remember -- as we mentioned on the previous page, the open differential always applies the same torque to both wheels. If one of the front tires and one of the back tires comes off the ground, they will just spin helplessly in the air, and you won't be able to move at all.
The solution to these problems is the limited slip differential (LSD), sometimes called positraction. Limited slip differentials use various mechanisms to allow normal differential action when going around turns. When a wheel slips, they allow more torque to be transferred to the non-slipping wheel.
The next few sections will detail some of the different types of limited slip differentials, including the clutch-type LSD, the viscous coupling, locking differential and Torsen differential

LOSS OF TRACTION

One undesirable side effect of a conventional differential is that it can reduce overall torque - the rotational force which propels the vehicle. The amount of torque 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. For the purpose of this article, we will refer to this amount of torque as the "threshold torque".
The torque applied to each driving roadwheel is a result of the engine and transmission applying a twisting force against the resistance of the traction at that roadwheel. Unless the load is exceptionally high, the engine and transmission can usually supply as much torque as necessary, so the limiting factor is usually the traction under each wheel. It is therefore convenient to define traction as the amount of torque that can be generated between the tire and the road surface, before the wheel starts to slip. If the total traction under all the driven wheels exceeds the threshold torque, the vehicle will be driven forward; if not, then one or more wheels will simply spin.
To illustrate how a differential can limit overall torque, imagine a simple rear-wheel drive vehicle, with one rear roadwheel on asphalt with good grip, and the other on a patch of slippery ice. With the load, gradient, etc., the vehicle requires, say, 2,000 newton metres (1,480 ft•lbf) of torque to move forward (i.e. the threshold torque). Let us further assume that the non-spinning traction on the ice equates to 400 N•m (300 ft•lbf), and the asphalt to 3,000 N•m (2,210 ft•lbf).
If the two roadwheels were driven without a differential, each roadwheel would be supplied with an equal amount of torque, and would push against the road surface as hard as possible. The roadwheel on ice would quickly reach the limit of traction(400 Nm), but would be unable to spin because the other roadwheel has good traction. The traction of the asphalt plus the small extra traction from the ice exceeds the threshold requirement, so the vehicle will be propelled forward.

With a differential, however, as soon as the "ice wheel" reaches 400 Nm, it will start to spin, and then develop less traction ~300 Nm. The planetary gears inside the differential carrier will start to rotate because the "asphalt wheel" encounters greater resistance. Instead of driving the asphalt wheel with more force, the differential will still symmetrically split the total amount of available torque equally. ~300 Nm is sufficient to make the ice wheel to spin, but the equal amount of ~300 Nm is not enough to turn the asphalt wheel. Since the asphalt wheel remains stationary, the spinning ice wheel will rotate twice as fast as before. As the actual torque on both roadwheels is the same - the amount is determined by the lesser traction of the ice wheel. So both wheels will get 300 Nm each. Since 600 Nm is less than the required threshold torque of 2000 Nm, the vehicle will not be able to utilise the output from the engine, and will not move.An observer will simply see one stationary roadwheel on one side of the vehicle, and one spinning roadwheel on the opposite side. It will not be obvious that both wheels are generating the same torque (i.e. both wheels are in fact pushing equally, despite the difference in rotational speed). This has led to a widely held misconception that a vehicle with a differential is really only "one-wheel-drive". In fact, a normal differential always allows the transmission of equal torque to both driven roadwheels; unless it is a specific type of differential, such as locking, torque-biasing, or limited slip type.
A proposed way to distribute the power to the wheels, is to use the concept of gearless differential, of which a review has been reported by Provatidis [2], but the various configurations seem to correspond either to the "sliding pins and cams" type, such as the ZF B-70 available for early VWs, or are a variation of the ball differential.

TRACTION-AIDING DEVICES

There are various devices for getting more usable traction from vehicles with differentials.
• One solution is the limited slip differential (LSD), the most well-known of which is the clutch-type LSD. With this differential, the side gears are coupled to the carrier via a multi-disc clutch which allows extra torque to be sent to the wheel with high resistance than available at the other driven roadwheel when the limit of friction is reached at that other wheel. Below the limit of friction more torque goes to the slower (inside) wheel. If there is no load on one wheel then no torque goes to the other so the LSD provides no torque except for spring loading, but some extra effect can be obtained by partially applying the vehicle's parking brake when one roadwheel is spinning, as this can provide some resistance there to increase the overall torque, and allow the other driven roadwheel to move the vehicle. This only works where the handbrake acts on the driven wheels, as in the traditional rear-wheel drive layout. Naturally, the handbrake should be released as soon as the vehicle is moving again.
• A locking differential, such as ones using differential gears in normal use but using air or electrically controlled mechanical system, which when locked allow no difference in speed between the two wheels on the axle. They employ a mechanism for allowing the planetary gears to be locked relative to each other, causing both wheels to turn at the same speed regardless of which has more traction; this is equivalent to effectively bypassing the differential gears entirely. Other locking systems may not even use differential gears but instead drive one wheel or both depending on torque value and direction.
• A high-friction 'Automatic Torque Biasing' (ATB) differential, such as the Torsen differential, where the friction is between the gear teeth rather than at added clutches. This applies more torque to the driven roadwheel with highest resistance (grip or traction) than is available at the other driven roadwheel when the limit of friction is reached at that other wheel.

• When tested with the wheels off the ground, if one wheel is rotated with the differential case held, the other wheel will still rotate in the opposite direction as for an open differential but there with be some frictional losses and the torque will be distributed at other than 50/50. Although marketed as being "torque-sensing", it functions the same as a limited slip differential.
• A very high-friction differential, such as the ZF "sliding pins and cams" type, so that there is locking from very high internal friction. When tested with the wheels off the ground with torque applied to one wheel it will lock, but it is still possible for the differential action to occur in use, albeit with considerable frictional losses, and with the road loads at each wheel in opposite directions rather than the same (acting with a "locking and releasing" action rather than a distributed torque).
• An additional function of the conventional electronic traction control systems usually use the anti-lock braking system (ABS) roadwheel speed sensors to detect a spinning roadwheel, and apply the brake to that wheel. This progressively raises the reaction torque at that roadwheel, and the differential compensates by transmitting more torque through the other roadwheel - the one with better traction. In Volkswagen Group vehicles, this specific function is called 'Electronic Differential Lock' (EDL).

• In a four-wheel drive vehicle, a viscous coupling unit can replace a centre differential entirely, or be used to limit slip in a conventional 'open' differential. It works on the principle of allowing the two output shafts to counter-rotate relative to each other, by way of a system of slotted plates that operate within a viscous fluid, often silicone. The fluid allows slow relative movements of the shafts, such as those caused by cornering, but will strongly resist high-speed movements, such as those caused by a single wheel spinning. This system is similar to a limited slip differential.

A four-wheel drive (4WD) vehicle will have at least two differentials (one in each axle for each pair of driven roadwheels), and possibly a centre differential to apportion torque between the front and rear axles. In some cases (e.g. Lancia Delta Integrale, Porsche 964 Carrera 4 of 1989 [2]) the centre differential is an epicyclic differential (see below) to divide the torque asymmetrically, but at a fixed rate between the front and rear axle. Other methods utilise an 'Automatic Torque Biasing' (ATB) centre differential, such as a Torsen - which is what Audi use in their quattro cars (with longitudinal engines).
4WD vehicles without a centre differential should not be driven on dry, paved roads in four-wheel drive mode, as small differences in rotational speed between the front and rear wheels cause a torque to be applied across the transmission.
This phenomenon is known as "wind-up", and can cause considerable damage to the transmission or drive train. On loose surfaces these differences are absorbed by the tire slippage on the road surface.
A transfer case may also incorporate a centre differential, allowing the drive shafts to spin at different speeds. This permits the four-wheel drive vehicle to drive on paved surfaces without experiencing "wind-up".

DIFFERENTIAL TYPES

The different types of differentials are,
• OPEN DIFFERENTIALS
• LIMITED SLIP DIFFERENTIALS

The other types of limited slip differentials are,
• Clutch type LSD
• Viscous Coupling type LSD
• Locking type LSD
• Torsen type LSD

ADVANTAGES

• Predictable power distribution on dry surfaces
• Easy to drive and handle
• Simplicity of design
• Lower maintenance costs


DISADVANTAGES

• Poor off-road handling
• Unpredictable power distribution on lower friction surfaces, such as sand or mud
• Does not work if one of the wheels in the set is suspended in the air.

APPLICATIONS OF TORSEN DIFFERENTIALS

• Torsen differentials are used in off-road and high performance all-wheel drive vehicles.
• Torsens can also be handy on icy or dirt roads


CONCLUSION

Differential being an important component of any automobile which transmits the power to the rear wheel is being used by many of the premier companies would help the companies in terms of its economical growth and viable for most of the automobiles. There are cases where two differentials are used in cases like military trucks which are generally called tandem axles, generally used to carry heavy loads. Needless to say, since its time of invention to the present date, there has been little scope for its replacement.

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