In 1932, Ferdinand Porsche designed a Grand Prix racing car for the Auto Union company. The high power of the design caused one of the rear wheels to experience excessive wheel spin at any speed up to 100 mph (160 km/h). In 1935, Porsche commissioned the engineering firm ZF to design a limited-slip differential that would perform better. The ZF "sliding pins and cams" became available, and one example was the Type B-70 for early VWs.
The main advantage of a limited-slip differential is shown by considering the case of a standard (or "open") differential in off-roading situations where one wheel has no contact with the ground. In such a case, with a standard differential, the non-contacting wheel will receive 100% of the power while the contacting wheel will remain stationary. The torque transmitted will be equal at both wheels; therefore, will not exceed the threshold of torque needed to move the wheel with grip. In this situation, a limited-slip differential prevents 100% of the power from being allocated to one wheel, and thereby keeping both wheels in powered rotation.
Basic principle of operation
Automotive limited-slip differentials all contain a few basic elements. First, all have a gear train that, like an open differential, allows the outputs to spin at different speeds while holding the average speed of the two outputs to be equal to the input speed.
Second, all have some sort 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. The type of limited-slip differential typically gets its name from the design of this resisting mechanism. Examples include viscous and clutch-based LSDs. The amount of limiting torque provided by these mechanisms varies by design and is discussed later in the article.
Torque split during operation
An open differential has a fixed torque split between the input and outputs. In most cases the relationship is:
Trq out_1 = Trq out_2 , where 1 and 2 are typically the left and right drive wheels.
Trq in = Trq out_1 + Trq out_2 .
Thus the wheels always see the same torque even when spinning at different speeds, including the case where one is stationary. Note, the torque split can be unequal, though 50:50 is typical.
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 ).
Several types of LSD are commonly used on passenger cars.
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.
This category includes helical gear limited-slip differentials and clutch, cone (an alternative type of clutch) where the engagement force of the clutch is a function of the input torque applied to the differential (as the engine applies more torque the clutches grip harder and Trq d increases).
ZF LSD – clutch stack visible on left
ZF LSD – spider pinion shaft ramps visible
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 are affected by the general condition (wear) and by how tightly they are loaded.
Clutch, cone-type 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. (See the discussion of 2, 1.5 and 1 way below)
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-, 1-, and 1.5-way LSD
Broadly speaking, there are three input torque states: load, no load, and overrun. 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 overrun (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 under engine braking.
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 overrun, 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.
A 1.5-way differential refers to one where the forward and reverse limiting torques, Trq d_fwd, d_rev , are different but neither is zero as in the case of the 1-way LSD. This type of differential is common in racing cars where a strong limiting torque can aid stability under engine braking.