A limited-slip differential (LSD) is a type of differential gear train that for on-road use allows its two output shafts to rotate at different speeds, but limits the maximum difference between the two shafts to enforce a minimum of traction, unlike the open differential that allows one wheel to stand still while all power is applied to the other wheel, or a locking differential that locks them together.
Limited-slip differentials are often known by the generic trademark Positraction, a brand name owned by General Motors and originally used for its Chevrolet branded vehicles.
Early history In 1932, Ferdinand Porsche designed the P-Wagen Grand Prix racing car, later adopted for Auto Union racing cars. The high power of the supercharged V16 design caused one of the rear wheels to experience excessive wheel spin at any speed up to . In 1935, Porsche commissioned the engineering firm ZF to design a limited-slip differential to improve performance. The ZF "sliding pins and cams" became available,The Motor Vehicle K.Newton W.Steeds T.K.Garrett Ninth Edition pp549-550 and one example was the Type B-70 used during the Second World War in the military VWs (Kübelwagen and Schwimmwagen), although technically this was not a limited-slip differential, but a system composed of two freewheels, which sent the whole of the engine power to the slower-turning of the two wheels.
Limited-slip differentials were widely introduced by U.S. automakers in the late 1950s and were marketed under a wide variety of trademarked names. In early 1956, Packard introduced a clutch-type limited-slip differential under the Twin Traction trademark, promoting it as an aid for driving in severe winter weather. In 1957, General Motors (GM) introduced a competing system for Chevrolet branded vehicles under the Positraction name. Within a few years, other American automotive brands introduced similar systems under a variety of names, including Safe-T-Track for GM's Pontiac brand and Anti Spin for its Oldsmobile brand, while the Ford Motor Company introduced Traction-Lok for Ford vehicles and Directed Power for its Lincoln cars. Chrysler purchased Power-Lok units from Dana Incorporated and Spin-Resistant units from Borg-Warner, marketing both under the Sure-Grip name on Chrysler, Dodge, and Plymouth vehicles. Limited-slip differentials became very popular and sought after during the muscle car era in the 1960s and 1970s. Despite the myriad marketing names used by competing brands, the popularity of Chevrolet vehicles resulted in Positraction becoming a generic trademark in the U.S. for limited-slip differentials generally.
Characteristics The main advantage of a limited-slip differential is demonstrated by considering the case of a standard (or "open") differential in off-roading or snow situations where one wheel begins to slip. In such a case with a standard differential, the slipping or non-contacting wheel will receive the majority of the power (in the form of low-torque, high-rpm rotation), while the contacting wheel will remain stationary with respect to the ground. The torque transmitted by an open differential will always be equal at both wheels; if one tire is on a slippery surface, the supplied torque will easily overcome the available traction at a very low number. For example, the right tire might begin to spin as soon as of torque is placed on it, since it is on an icy surface. Since the same amount of torque is always felt at both wheels, regardless of the speed at which they are turning, this means that the wheel with traction cannot receive more than of torque either, which is far less than is required to move the vehicle. Meanwhile, the tire on the slippery surface will simply spin, absorbing all of the actual power output (which is a function of torque provided over the course of revolutions), even though both wheels are provided the same (very low) amount of torque. In this situation, a limited-slip differential prevents excessive power from being allocated to one wheel, and so keeps both wheels in powered rotation.
The advantages of LSD in high-power, rear-wheel drive automobiles were demonstrated during the United States "Muscle-Car" era from the mid-1960s through the early 1970s. Cars of this era normally were rear-wheel drive and did not feature independent suspension for the rear tires (but instead used a live axle). With a live axle, when high torque is applied through the differential, the traction on the right rear tire is lower as the axle naturally wants to turn with the torsion of the drive shaft (but is held stationary by being mounted to the vehicle frame). This coined the terms "one wheel peel" or "one tire fire". As such, "Muscle-Cars" with LSD or "posi" (positraction) had a distinct advantage to their wheel-spinning counterparts.
Mechanical limited-slip differentials are considered essential to perform a proper drift.
Basic principle of operation Both limited-slip differentials and open differentials have a gear train that allows the output shafts to spin at different speeds while holding the sum of their speeds proportional to that of the input shaft.
Automotive limited-slip differentials have some type of mechanism that applies a torque (internal to the differential) that resists the relative motion of the output shafts. In simple terms, this means they have some mechanism which resists a speed difference between the outputs, by creating a resisting torque between either the two outputs, or the outputs and the differential housing. There are many mechanisms used to create this resisting torque. Types of limited-slip differential typically are named from the type of the resisting mechanism. Examples include viscous and clutch-based LSDs. The amount of limiting torque provided by these mechanisms varies by design.
A limited-slip differential has a more complex torque-split and should be considered in the case when the outputs are spinning the same speed and when spinning at different speeds. The torque difference between the two axles is called Trq d . (In this work it is called Trq f for torque friction). Trq d is the difference in torque delivered to the left and right wheel. The magnitude of Trq d comes from the slip-limiting mechanism in the differential and may be a function of input torque (as in the case of a gear differential), or the difference in the output speeds (as in the case of a viscous differential).
The torque delivered to the outputs is: Trq 1 = ½ Trq in + ½ Trq d for the slower output Trq 2 = ½ Trq in – ½ Trq d for the faster output
When traveling in a straight line, where one wheel starts to slip (and spin faster than the wheel with traction), torque is reduced to the slipping wheel (Trq 2 ) and provided to the slower wheel (Trq 1 ).
In the case when the vehicle is turning and neither wheel is slipping, the inside wheel will be turning slower than the outside wheel. In this case the inside wheel will receive more torque than the outside wheel, which can result in understeer.
When both wheels are spinning at the same speed, the torque distribution to each wheel is: Trq (1 or 2) = ½ Trq in ±(½ Trq d ) while Trq 1 +Trq 2 =Trq in .
This means the maximum torque to either wheel is statically indeterminate but is in the range of ½ Trq in ±( ½ Trq d ).
Types Several types of LSD are commonly used in passenger cars. Fixed value Torque sensitive Speed sensitive Electronically controlled
Fixed value
In this differential the maximum torque difference between the two outputs, Trq d , is a fixed value at all times regardless of torque input to the differential or speed difference between the two outputs. Typically this differential used spring-loaded clutch assemblies.
Torque sensitivity (HLSD)
These limited-slip differentials use helical gears, clutches or cones (an alternative type of clutch) where the engagement force of the gears or clutch is a function of the input torque applied to the differential (as the engine applies more torque the gears or clutches grip harder and Trq d increases).
Torque sensing LSDs respond to driveshaft torque, so that the more driveshaft input torque present, the harder the clutches, cones or gears are pressed together, and thus the more closely the drive wheels are coupled to each other. Some include spring loading to provide some small torque so that with little or no input torque (trailing throttle/gearbox in neutral/main clutch depressed) the drive wheels are minimally coupled. The amount of preload (hence static coupling) on the clutches or cones is affected by the general condition (wear) and by how tightly they are loaded.
Clutch, cone-type, or plate LSD 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. In a cone type the clutches are replaced by a pair of cones which are pressed together achieving the same effect.
One method for creating the clamping force is the use of a cam-ramp assembly such as used in a Salisbury/ramp style LSD. The spider gears mount on the pinion cross shaft which rests in angled cutouts forming cammed ramps. The cammed ramps 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 asymmetric, the LSD is 1.5 way.
An alternative is to use the natural separation force of the gear teeth to load the clutch. An example is the center differential of the 2011 Audi Quattro RS 5.
As the input torque of the driveshaft tries to turn the differential center, internal pressure rings (adjoining the clutch stack) are forced sideways by the pinion cross shaft 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 (80–85° in practice to avoid chipping) surfaces in a one-way LSD on overrun produces no cam effect or corresponding clutch stack compression.
2-Way, 1-Way, 1.5-Way There are three input torque states: load, no load, and over run. During load conditions, as previously stated, the coupling is proportional to the input torque. With no load, the coupling is reduced to the static coupling. The behavior on over run (particularly sudden throttle release) determines whether the LSD is 1 way, 1.5 way, or 2 way.
A 2-way differential will have the same limiting torque Trq d in both the forward and reverse directions. This means the differential will provide some level of limiting action under engine braking. The early Packard Twin Traction unit is designed to function in this manner, which was promoted to provide a different benefit: if one rear drive wheel momentarily leaves the ground when it hits a bump with the differential under load, the airborne wheel will not spin freely and cause the vehicle to break traction when the spinning wheel touches the ground again.
A 1-way differential will provide its limiting action in only one direction. When torque is applied in the opposite direction it behaves like an open differential. In the case of a FWD car it is argued to be safer than a 2-way differential. The argument is if there is no additional coupling on over run, i.e. a 1-way LSD as soon as the driver lifts the throttle, the LSD unlocks and behaves somewhat like a conventional open differential. This is also the best for FWD cars, as it allows the car to turn in on throttle release, instead of ploughing forward.