In automotive applications, a limited slip differential (LSD) is a modified or derived type of differential gear arrangement that allows for some difference in rotational velocity of the output shafts, but does not allow the difference in speed to increase beyond a preset amount. In an automobile, such limited slip differentials are sometimes used in place of a standard differential, where they convey certain dynamic advantages, at the expense of greater complexity.
The main advantage of a limited slip differential is found by considering the case of a standard differential where one wheel has no contact with the ground at all. In such a case, the contacting wheel will remain stationary, and the non-contacting wheel will rotate at twice its intended velocity – the torque transmitted will be zero and the vehicle will remain stationary. In everyday use on typical roads, such a situation is very unlikely, and so a normal differential suffices. For more demanding use however, such as driving off-road, or for high performance vehicles, such a state of affairs is undesirable, and the LSD can be employed to deal with it. By limiting the velocity difference between a pair of driven wheels, useful torque can be transmitted as long as there is some friction available on at least one of the wheels.
Two main types of LSD have been generally used – torque sensitive (geared or clutch-based) and speed sensitive (viscous/pump and clutch pack). The latter is gaining ground especially in modern all-wheel drive vehicles, and generally requires less maintenance than the mechanical type.
The use of the word mechanical implies that the limited slip differential is engaged or not due to interaction between two (or more) mechanical parts. This category includes clutch and helical limited slip differentials. For road racing, many prefer a helical limited slip differential, because it does not lock the two output shafts to spin at the same rate, but rather biases torque to the wheel with more grip by up to 80%.
Clutch Type - Driveshaft Torque ActivatedEdit
The clutch type LSD responds to driveshaft torque. The more driveshaft input torque present, the harder the clutches are pressed together, and thus the more closely the drive wheels are coupled to each other.
With no / little input torque (trailing throttle / gearbox in neutral / main clutch depressed) the drive wheels are still coupled somewhat as the clutches are always in contact to some degree, producing friction. The amount of preload (hence static coupling) on the clutches is determined by the general condition (wear) of the clutches and by how tightly they are shimmed.
Broadly speaking, there are three input torque states - load, no load, & over run. Under load, as previously stated, the coupling is proportional to the input torque. With no load, the coupling is reduced to the static coupling. The behaviour on over run (particularly sudden throttle release) determines whether the LSD is 1 way, 1.5 way, or 2 way.
If there is no additional coupling on over run, the LSD is 1 way. This is a safer LSD, as soon as the driver lifts the throttle, the LSD unlocks and behaves somewhat like a conventional open diff. This is also the best for FWD cars, as it allows the car to turn in on throttle release, instead of ploughing forward. 
If the LSD increases coupling in the same way regardless of whether the input torque is forwards or reverse, it is a 2 way diff. Some drifters prefer this type as the LSD behaves the same regardless of their erratic throttle input, and lets them keep the wheels spinning all the way through a corner. An inexperienced driver can easily spin the car when using a 2 way LSD if they lift the throttle suddenly, expecting the car to settle like a conventional open diff.
If the LSD behaves somewhere inbetween these two extremes, it is a 1.5 way diff, which is a compromise between sportiness and safety.
Clutch LSDs are frequently noisy, clunky, & expensive, which makes them unlikely to be installed on a passenger car these days. However their response speed and coupling strength is the best of the commonly available LSDs. They are also the only commonly available LSD able to stand up to extreme motorsport abuse. The Salisbury type ofmultidisc LSD works very well. It does cause some entry understeer - but not a lot - and it is very smooth, progressive and easy to drive.
The latest version of this basic design, introduced in the late 1990s on the Jeep Grand Cherokee (Spicer sourced) uses a small hydraulic pump, driven by the difference in axle speed, to apply more lockup pressure, similar to the action of an automatic transmission clutch pack. Later Dodge Vipers have also used this system with only moderate success.
The clutch type has a stack of thin clutch discs, half of which are coupled to one of the drive shafts, the other half of which are coupled to the spider gear carrier. The clutch stacks may be present on both drive shafts, or on only one. If on only one, the remaining drive shaft is linked to the clutched drive shaft through the spider gears. If the clutched drive shaft cannot move relative to the spider carrier, then the other drive shaft also cannot move, thus they are locked.
The spider gears mount on an cross shaped internal member which rests in angled cutouts forming cammed ramps. The cammed ramps in the casing are not necessarily symmetrical. If the ramps are symmetrical, the LSD is 2 way. If they are saw toothed (i.e. one side of the ramp is vertical), the LSD is 1 way. If both sides are sloped, but are assymmetric, the LSD is 1.5 way.
As the input torque of the driveshaft tries to turn the diff centre, internal pressure rings (adjoining the clutch stack) are forced sideways by the spider gear mount trying to climb the ramp, which compresses the clutch stack. The more the clutch stack is compressed, the more coupled the wheels are. The mating of the vertical ramp surfaces in a 1 way LSD on over run produces no cam effect and no corresponding clutch stack compression.
Another variator is the "cone type", which is preloaded by a strong spring. These are generally less effective in high torque situations (drag racing, etc.) but better in low-torque conditions (ice, snow) where there may not be enough torque to apply any clutch pressure in the clutch-pack type, especially if somewhat worn.
The break-in of clutch LSDs is quite critical. Manufacturers give detailed instructions on how to break the diff in.  If these are not followed, the LSD may be permanently harmed, in that it may engage and disengage erratically, due to irregularities on and damage to the clutch surfaces. Essentially the LSD must be worked hard to remove manufacturing imperfections, then the now metal-laden oil changed immediately following.
Servicing consists of changing the oil after hard sessions, also to remove metal particles, and eventually replacing the clutches, or the centre. In any case the oil should should be changed regularly (as opposed to the open diff, where the oil could be left unchanged for several hundred thousand kilometres).
Solid spools connect both wheels so that they both turn at the same speed. While this is ideal for straight line acceleration, upon turning the inside wheel drags, causing the car to understeer.
The Detroit Locker is not an LSD, but a locking differential. Most often found in off road trucks, the Detroit Locker isn't suitable for racing. "The Detroit Locker is violent and unpredictable in operation and because of this it is simply not possible to place the car precisely where you want it on the racetrack or ot apply the throttle as early as the tires will allow on corner exit. Given any kind of choice at all, no one in their right mind uses a Detroit Locker." - Carroll Smith
Geared, torque-sensing mechanical differentials utilize planetary gears to "sense" torque on one shaft. The most famous version is the Torsen differential invented by Vernon Gleasom in 1958, then sold to Gleason Corporation, who started marketing it in 1982. Geared LSDs are less prone to wear than the clutch type, but the high number of parts, and their stress risers, limits their torque handling capability. As such it is not suitable for racing. Technically, these are really torque-biasing diffs, not true LSDs. It requires at least one wheel to grip or else it acts as an open differential (it doesn't work when both tires are slipping).
"The worm and wheel is a very inefficient gear configuration at high speeds and it generates a lot of heat - which is destructive and wastes power. It has never been very successful , possibly because of a lack of development and possibly because the concepts is just too complex and too inefficient to succeed...while they have performed well, have failed early. Gleason engineers certainly have the expertise and the faciities to solve the metallurgy problems." - Carroll Smith, Engineer to Win
The viscous type is generally simpler, and relies on the properties of a dilatant fluid - that is, one which thickens when subject to shear. Silicone-based oils are often used. Here, a chamber of fluid rotates with the normal motion of the output shafts, but a differential motion causes paddles or vanes to move through the fluid. The greater the speed of the vanes, the more resistance the fluid will put up to oppose this motion. In contrast to the mechanical type, the limiting action is much softer and more proportional to the slip, so for the average driver is generally much easier to cope with.
The gerotor pump uses the housing to drive the outer side of the pump and one axle shaft to drive the other. When there is differential wheel rotation, the pump pressurizes its working fluid into the clutch pack area to provide a clamp load for frictional resistance to differentiation for a torque transfer to the higher traction wheel. The pump based systems have a lower and upper limits on applied pressure, and internal damping to avoid hysteris. The newest gerotor pump bases system has computer regulated output for more versatility and no oscillation
Viscous LSDs are less efficient than mechanical types, that is, they "lose" some power. They do not stand up well to abuse, particularly any sustained load which overheats the silicone results in sudden permanent loss of the LSD effect. They do have the virtue of failing gracefully, reverting to semi-open diff behaviour, without the graunching of metal particles / fragmented clutches. The silicone oil is factory sealed in a separate chamber from the gear oil surrounding the rest of the diff. This is not serviceable and when the diff's behaviour deteriorates, the VLSD centre is replaced. 
Since the 1958 introduction of Chrysler's "Sure Grip" (Spicer sourced clutch type LSD) many manufacturers began to apply brand names to their LSD units. The most famous of these was Chevrolet's "Positraction". Since then, Positraction (often shortened to "positrac" or merely "posi") has become a genericized trademark for LSDs.
Other factory names for LSD's include
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