A limited-slip differential (LSD) is a type of differential that allows its two output shafts to rotate at different speeds but limits the maximum difference between the two shafts.
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.
Early history
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 160 km/h (100 mph). In 1935, Porsche commissioned the engineering firm ZF to design a limited-slip differential to improve performance.[citation needed] The ZF "sliding pins and cams" became available,[1] 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.[2]
Benefits
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 70 N⋅m (50 lb⋅ft) 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 70 Nm 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 time), 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, ensuring that the traction will not be limited to the wheel which can handle the minimum amount of power.
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" (posi-traction) had a distinct advantage to their wheel-spinning counterparts.
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 .[3] (In this work it is called Trq ffor torque friction[4]). 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.[4]
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 ).
| This article uses material from the Wikipedia article Metasyntactic variable, which is released under the Creative Commons Attribution-ShareAlike 3.0 Unported License. |