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 limited slip differential full report
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ABSTRACT

In automotive mechanics, a Differential is an arrangement of gears that transmits power from the engine to a pair of driving wheels, dividing the force equally between them but permitting them to follow paths of different lengths, as when turning a corner or traversing an uneven road. The differential allows the driven wheels to rotate at the same speed while on a straight road; it allows the outer wheel to rotate faster (proportionately) than the inner wheel, while taking a curve or traveling on an uneven surface. In other words, the differential is a device that splits the engine torque two ways, allowing each output to spin at a different speed.

The conventional differential, which is also called an 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 an automobile may be able to produce more torque, there needs to be enough traction to transmit that torque to the ground. 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. The wheel with less traction, which is the wheel on the ice, begins to slip. This is because the wheel with good traction is only getting the very small amount of torque that can be applied to the wheel with less traction. The limited slip differential employs a pair of clutches which limits the slipping way of wheels with less traction.

1. INTRODUCTION
What is a Differential? The differential is a device that splits the engine torque in two ways, allowing each output to spin at a different speed. A differential allows the driven wheels to rotate at the same speed while on a straight road; it allows the outer wheel to rotate faster than the inner wheel, while taking a curve or traveling on an uneven surface.
The differential is aimed at performing the following three main functions;
1) To aim the engine power at the wheels.
2) 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.
3) 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.).
2. NEED FOR DIFFERENTIAL
The wheels of vehicles spin at different speeds, especially when turning. 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 the front wheels travel a different distance than the rear wheels. The following figure shows the different path followed by front and back wheels while at a curve.
For the non-driven wheels on the vehicle -- the front wheels on a rear-wheel drive vehicle, the back wheels on a front-wheel drive vehicle -- 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 the vehicle does
not have a differential, the wheels would be locked together, forced to spin at the same speed. This would make turning difficult and hard on the vehicle: For the vehicle 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. So to avoid all these problems a differential is introduced in between the driven wheels.
3. OPEN DIFFERENTIAL
Differentials are found on all modern cars and trucks, and also in many all-wheel-drive (full-time four wheel drive) vehicles. These all-wheel-drive vehicles need a differential between each set of drive wheels, and they need one between the front and the back wheels as well, because the front wheels travel a different distance through a turn than the rear wheels. Part-time four-wheel-drive systems don't have a differential between the front and rear wheels; instead, they are locked together so that the front and rear wheels have to turn at the same average speed. This is why these vehicles are hard to turn on concrete when the four-wheel-drive system is engaged.
The conventional differential used nowadays is called the Open Differential. It has got a ring gear, two side gears and a pair of spider gears.
When a vehicle is driving straight down the road, both drive wheels are spinning at the same speed. The input pinion is turning the ring gear and cage, and none of the pinions within the cage are rotating -- both side gears are effectively locked to the cage.
When a car makes a turn, the wheels must spin at different speeds. To achieve this action, the pinions in the cage start to spin as the car begins to turn, allowing the wheels to move at different speeds. The result is that the inside wheel spins slower than the cage, while the outside wheel spins faster.
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 vehicle may be able to produce more torque, there needs to be enough traction to transmit that torque to the ground. If we increase the throttle after the wheels start to slip, the wheels will just spin faster.
The real problem comes when one of the driven wheels has a good traction and the other is having less traction (For e.g. when one wheel is on ice). 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, the vehicle isn't going to move very much.
Another time open differentials might get us into trouble is when we are driving off-road. If we have a four-wheel drive truck, or an SUV, with an open differential on both the front and the back, we could get stuck. Now, remember -- as we mentioned earlier, 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 we won't be able to move at all.
4. LIMITED SLIP DIFFERENTIAL
The problems caused by a an open differential can be solved by employing a limited slip differential (LSD), sometimes called positraction, in between the driven wheels. 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.
According to the different mechanisms used limited slip differential can classified into the following three types :
1) Clutch type LSD
2) Viscous Coupling
3) Worm & Worm Wheel LSD
1. CLUTCH TYPE LSD
The clutch-type LSD is probably the most common version of the limited slip differential. This type of LSD has all of the same components as an open differential, but it adds a spring pack and a set of clutches. The spring pack pushes the side gears against the clutches, which are attached to the cage. This creates additional resistance. This resistance is always present and is called Preload.
Both side gears spin with the cage when both wheels are moving at the same speed, and the clutches aren't really needed -- the only time the clutches step in is when something happens to make one wheel spin faster than the other, as in a turn. The clutches fight this behavior, wanting both wheels to go the same speed. If one wheel wants to spin faster than the other, it must first overpower the additional resistance offered by the clutch (preload). The stiffness of the springs combined with the friction of the clutch determines how much torque it takes to overpower it. Traction and preload have to be high enough to keep tires from spinning but low enough to still allow tires to rotate at different speeds in a turn.
Limited Slip Differential
Let us consider a practical example to understand the working more clearly. Consider a vehicle up on a hoist, engine running, both rear tires are rotating slowly. Let us say 20 revolutions per minute. If we can carefully grab one tire, it would take very little force to slow down that tire. Let us say (probably not the right number, but just for arguments sake) it would take 50N to slow down the tire. Let us say the tire slows down from 20 rpm to 10 rpm (20-10). We can notice that the opposite tire will start rotating faster - it will go 30 rpm (20+10). This is because: Since the differential always splits rpm equally when conditions are equal (it split 40 rpm into 20/20 when resistance was equal) - it will split rpm proportional when conditions change (if one side goes 10 rpm faster - the other side will go 10 rpm slower). Let us say it would take us 100N of force to completely stop the tire (0 rpm) then the opposite tire will speed up to 40 rpm (20+20). Now get a second person and have him/her grab the rotating tire. Even though they won't be able to stop it - they will be able to slow it down. Let us say he applies 50N of force and the tire slows down from 40 rpm to 30 rpm (40-10). The moment he applies 50N and
the tire slows down, we will experience an increase of force coming from the tire we are holding. The force will increase by 50N (exactly the force the other person applies to the rotating tire) and since 150N are too much for us to hold - the tire will start rotating again.
Getting back to the situation in which one drive wheel is on the ice and the other one has good traction: With this limited slip differential, even though the wheel on the ice is not able to transmit much torque to the ground, the other wheel will still get the torque it needs to move. The torque supplied to the wheel not on the ice is equal to the amount of torque it takes to overpower the clutches. The result is that you can move forward, although still not with the full power of the vehicle.
2. Viscous Coupling
Viscous Coupling is a special kind of limited slip differential which does not involve any gears to transfer power between the wheels. The viscous coupling is often found in all-wheel-drive vehicles. It is commonly used to link the back wheels to the front wheels so that when one set of wheels starts to slip, torque will be transferred to the other set.
The viscous coupling has two sets of plates inside a sealed housing that is filled with a thick fluid. One set of plates is connected to each output shaft. Under normal conditions, both sets of plates and the viscous fluid spin at the same speed. When one set of wheels tries to spin faster, perhaps because it is slipping, the set of plates corresponding to those wheels spins faster than the other. The viscous fluid, stuck between the plates, tries to catch up with the faster disks, dragging the slower disks along. This transfers more torque to the slower moving wheels -- the wheels that are not slipping.
When a car is turning, the difference in speed between the wheels is not as large as when one wheel is slipping. The faster the plates are spinning relative to each other, the more torque the viscous coupling transfers. The coupling does not interfere with turns because the amount of torque transferred during a turn is so small. However, this also highlights a disadvantage of the viscous coupling: No torque transfer will occur until a wheel actually starts slipping.
A simple experiment with an egg will help explain the behavior of the viscous coupling. If you set an egg on the kitchen table, the shell and the yolk are both stationary. If you suddenly spin the egg, the shell will be moving at a faster speed than the yolk for a second, but the yolk will quickly catch up. To prove that the yolk is spinning, once you have the egg spinning quickly stop it and then let go -- the egg will start to spin again (unless it is hard boiled). In this experiment, we used the friction between the shell and the yolk to apply force to the yolk, speeding it up. When we stopped the shell, that friction -- between the still-moving yolk and the shell -- applied force to the shell, causing it to speed up. In a
viscous coupling, the force is applied between the fluid and the sets of plates in the same way as between the yolk and the shell. Despite of the marginal increase in traction the clutch type limited slip differential fails in serious off-road conditions. For such conditions we use a Worm and Wheel Limited Slip Differential.
3. Worm and Wheel Limited Slip Differential (Torsen)
The worm and wheel LSD unit simply replaces the spider gears and ring gear carrier in an open differential. Basically the worm and gear differential uses a principle of machines; a worm gear can turn a worm wheel, but the worm wheel is not capable of turning the worm gear. The reason for this is the pitch of the gears. Like a very steep ramp that is easy to slide down but impossible to climb up, the pitch of the average worm gear is such that the worm wheel can't spin it. The word Torsen comes from torque sensing.
This can be altered. If the pitch of the teeth were altered, so that our worm gear become more like a barber pole, then our worm wheel could spin our worm gear because the gear ratio is not so extreme. It would be like a push-type screwdriver or drill. In concept the differential is really two differentials in one. As the carrier is turned by the ring gear, it forces the worm wheels to rotate with it. Because the wheel is unable to turn the worm gear, this transfers power to axle shaft. However, the worm wheels of each side are connected via the spur gears. It is these spur gears that provide the differential action.
In a corner when differential action is required the inside axle slows, slowing the worm gear to which it is attached. This in turn twists the worm wheels in which it is contact. As these worm wheels twist they turn the spur gear. The spur gears are mated in such a manner that they turn each other in opposite directions. So, as the inside spur gear slows, it speeds up the outside spur gear which in turn twists the outside worm wheel. Normally, twisting the worm wheel has not affect upon the worm gear. Like the twist drill, the worm wheel and worm gear angles are cut to allow a certain amount of this twisting of the worm wheel to turn the worm gear. Thus as the inside axle slows it forces the outside axle to increase its speed by a like amount. The result is perfect differentiation while maintaining power to both wheels.
Because of the carefully selected gear angles, there is some resistance to all this motion. It is this resistance that creates the limited slip nature of this diff. By changing gear angles, the ratio of differential action can be changed. The following figures explain the constructional details.
Worm and Wheel LSD
When one wheel looses traction, a conventional differential would allow the wheel with the least traction to spin or increase its RPM level relative to opposite wheel. Like before this increase in axle shaft speed twists that wheel's worm wheel, which turns its spur gear. However the spur gear in mesh with spur of the opposite axle shaft and attempts to slow it. But, the opposite axle is in good contact with the pavement, and thus resists being slowed by the axle shaft with the loss of traction. Hence the spur gear of the axle shaft with good tractions will resist being turned by the spur gear of the axle without traction. This prevents the wheel with the loss of traction to increase it speed relative to opposite wheel. Power
is automatically distributed proportionally to both wheels reflecting the amount of traction available at each wheel. Nowadays the torsen differentials are available with a differential lock. Heavy duty off-road situations ask for three (center differential & front and rear axle differentials) manually and independently lockable differentials. The side gears are locked together pneumatically or hydraulically using locking pins. After the lock is engaged, no matter what happens, both sides turn at the same speed, and if one side offers lots of resistance, and the other none, then effectively all the "usable" or "useful" torque goes to the side where there is resistance. It's getting 100% of the available torque. The side with no traction doesn't need torque to spin helplessly.
When you go to drive around a corner, both tires are forced to turn the same speed. Either one drags while the other spins a little, or probably the outside matches the ground speed (as the weight transfers) and the inside tire spins on the pavement (shorter distance to travel, but it's spinning as fast as the outside tire which has farther to go in the same time). Either way it tends to make the vehicle want to go straight all the time. This puts the axles under heavy pressure which causes them to break. So it requires a trained and experienced driver to operate them properly. Untrained use may cause more harm than good. Improper use on pavement may cause death or injury. Improper use off-road may cause component failure or severe difficulties to maneuver the vehicle. Ideally, differentials should be (manually) locked before traction is lost and wheels start spinning. They need to be switched off immediately after passing through a tough off-road section.
5. CONCLUSION
The limited slip differential enables us to take turns at greater speeds compared to an open differential. It also prevents the slipping of wheels to a great extent. Nowadays LSDâ„¢s are available with a differential lock that locks both the side gears using a built in stud. As a result, equal torque is applied to all the driven wheels as long as the lock is engaged, enabling quicker starts and stability.
6. REFERENCE
1) http://www.howstuffworks.com
2) http://www.efunda.com
3) http://www.popularscience.com
4) Jack Erjavec, Automotive Technology.
5) Govindan K.R., Automobile Engineering.
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