With a normal "open" differential, power flows from the pinion gear on the driveshaft and through the ring gear on the outside of the diff carrier. The carrier is like a hollow cylinder, with a set of pinion gears on the inside. These pinion gears -- which ride on spindles poking inward from the inside of the carrier -- engage the axle gears. As long as both of the axles are spinning at the same speed, the pinion gears remain stationary and split the power 50/50 to the axle gears. But if one axle starts spinning faster than the other, the pinion gears will rotate about the slower-spinning gear and route all of the engine's power to the faster-spinning axle gear.
The traditional open differential is like a 1980s office drone: it shows up, does its job to the minimum required specifications and then goes home. The limited-slip differential is like that obnoxious IT guy down the hall, justifying its attitude and flaws by doing what the open differential cannot. At the end of the day, which one you choose depends primarily upon what you expect and what you're willing to tolerate to get it.
Limited Slip Differentials
The problem with an open differential is that it will always send engine power to faster-spinning wheel -- exactly what you don't want. Any differential that either completely or partially locks the axles together is a type of "limited slip," and there are all kinds out there. The one you're probably most familiar with uses a set of clutches to lock the axles together. The clutch-type diff engages whenever there's a difference in torque between the driveshaft and ring gear, which means under either acceleration or deceleration. A one-way LSD locks only under acceleration, and a two-way locks under both acceleration and deceleration. A "1.5-way" diff locks fully under acceleration, but only partially under deceleration.
Clutch-Type Pros and Cons
The clutch-type LSD is a time-tested design capable of hypothetically maintaining a perfect 50/50 power split. Of course, torque-splitting capacity depends upon the strength and size of the clutches, but it can be done. The clutch-type diff is perfect for drag and top-speed racers, but it's not the most progressive design. You'll definitely know when the clutches engage while cornering, because the car will immediately go from neutral handling to understeer, or "push." Under braking, sudden engagement can cause both wheels to lose traction, causing that axle to lose traction and slide; that's why most clutch-type road racers prefer the 1.5-way LSD. On the positive side, that sudden and violent traction loss can be a good thing if you're trying to rotate the car, as you would when drifting or rally racing.
Torque Biasing Differentials
Also known as the "Quaiffe" or "torque vectoring" diff, the TBD is a different animal entirely from the clutch-type. A TBD is architecturally identical to an open diff, but uses spiral or "helical" cut pinion gears. When one wheel starts rotating faster than the other, the spiral-cut gears sort of jam against the case and axle gears. This jamming increases resistance inside of the differential, not truly locking the axles together but helping the otherwise open diff act a bit less open. Thus, the TBD doesn't "limit slip" so much as it continues to send a bit of power to the slower-spinning wheel.
TBD Pros and Cons
Because it's essentially an open diff, the TBD is a smoother and more transparent mechanism than even the subtlest of clutch-types. While the TBD's torque splitting capability is fairly limited --typically about 80/20 to the clutch-type's hypothetical 50/50 -- its inherent progressiveness often pays dividends on the road course and in the real world. The Quaiffe may tend to push a bit more than an open diff, but it depends on the application. In some cases, the extra power to the outside wheel will actually help to rotate the car, or at the very least keep it neutral while cornering. You will sacrifice a bit of straight-line traction relative to the clutch-type, but you'll still have more than you would with an open diff.
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