Torsen (full name Torsen traction) is a type of limited-slip differential used in automobiles.
The Torsen differential is a purely mechanical device;built from gears only. It does not have clutches that can wear out. It doesn't require LSD specific oil either, it will run happily on regular gear oil. The famous "jack up and spin one wheel" test does not work for a Torsen LSD - the axle code really is the only way to identify it without opening it up.

The Torsen (from Torque Sensing) works as an open differential when the amount of torque going to each wheel is equal. As soon as one wheel starts to lose traction, the difference in torque causes the gears in the Torsen differential to bind together. The design of the gears in the differential determines the torque bias ratio. For instance, if a particular Torsen differential is designed with a 5:1 bias ratio, it is capable of applying up to five times more torque to the wheel that has good traction.
These devices are often used in high-performance all-wheel-drive vehicles. Like the viscous coupling, they are often used to transfer power between the front and rear wheels. In this application, the Torsen is superior to the viscous coupling because it transfers torque to the stable wheels before the actual slipping occurs.
However, if one set of wheels loses traction completely, the Torsen differential will be unable to supply any torque to the other set of wheels. The bias ratio determines how much torque can be transferred, and five times zero is zero.
It's all based on one principle - that a worm gear cannot backdrive its worm. See what I mean?
Then skip to the next paragraph, because I will now explain roughly what a worm is.
Picture a gear with very fine teeth, the size of bolt threads. Now add a bolt, and have its threads hook up with the gear teeth. Hold the bolt steady and spin it. It will drive the gear, right? Okay, now try turning the gear. It'll seem locked - you will not succeed in making it spin the bolt. That's the principle of a worm gear. The amount of "back-drive" possible depends on the "spiral angle" of the worm, which is near zero in this (bolt) example. The driven gear is normally angle cut to match the worm's spiral angle (for good contact between gear teeth and worm).
A Torsen LSD consists of three pairs of worms, like a normal diff has 2 or 4 pinion gears. The worms in each pair are connected by normal straight cut gears, and the worms themselves drive the side gears. (note : in a normal diff one pinion gear drives both side gears. In a torsen diff, they are driven by a pair of worms, one for each side gear)
Now if one wheel is losing traction, it will try to spin faster than the other. To make this possible, the worms will have to spin. Now because the worms will resist being driven by the side gears, speed difference between the wheels is limited : we got an LSD!
Uhhh...okay...but I don't get it...can I see a picture?
Sure. Here's two. Click to enlarge to 640x480 :
<img src="//fcache1.pakwheels.com/original/4X/d/c/a/dca6e1788cdb1d32c3530bf4c1167a72c0b7e197.jpg" width="640" height="480"><br/> <img src="//fcache1.pakwheels.com/original/4X/2/f/3/2f3bdc5502a660401bb9462e1866558d9ed432f7.jpg" width="640" height="480"><br/>
You can see one pair of worms on these pictures. There are two more pairs of worms, each pair is connected by small straight cut gears on each end. Straight cut? But aren't straight cut gears really noisy?
Yes they are, but only when spinning! If both wheels turn at the same speed (like they do 99% of the time during normal driving), the worms just sit there, just like the pinions in a normal diff.
Also note the worms have a quite steep "spiral angle". If they didn't, the LSD would be much tighter.
Torsen differentials improve your car's ability to turn. With an open differential, a car will deliver power to the wheel that has the easiest time of it - this means the wheel with the least grip. You might assume this means when one wheel is in mud or sand while the other on pavement, but this also occurs in turns. The inside wheel is always naturally easier to spin.
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However, when you're turning, it's best to have the force on the outside wheel. The outside wheel has leverage and it will "push" the weight of the car in the direction it's facing. The inside wheel has less grip (because the car tilts and puts its weight on the outside wheel), and can only pull, with far less leverage. This results in drastically reduced high-power or sudden turning capability, especially in front-wheel drive vehicles, though rear-wheel drive suffers from an open differential as well.
A normal limited slip would simply activate whenever one wheel is spinning slower than the other.
A Torsen differential isn't a real limited slip because if you place one wheel on slick ice and the other on dry pavement, the one on ice will still spin itself silly. The torsen is a gear-based differential, the gears are cut in a helical fashion (at angles). When a car turns, the gears press against each other and slide into place, distributing the torque in the best way possible for the turn. This makes it particularly good for front-wheel drive cars, which have a tendency to spin the inside wheel too much and "understeer". A Torsen won't get rid of understeer, but it will make turns much sharper.
Types
There are currently three types of Torsen differentials.
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Torsens in front and/or rear axles
When attempting to turn with a torque sensitive differential, the outer wheel will need to rotate quicker relative to the differential, and the inner wheel will rotate slower than the differential. Friction in the differential will oppose motion, and that will work to slow the faster side and speed up the slower/inner side. This leads to asymmetric torque distributions in drive wheels, matching the TBR. Cornering in this manner will reduce the torque applied to the outer tire, leading to possibly greater cornering power, unless the inner wheel is overpowered (which is easier to do than with an open differential). When the inner tire (which has less traction due to weight transfer from lateral acceleration) is overpowered, it angularly accelerates up to the outer wheel speed (small percent wheel spin) and the differential locks, and if the traction difference does not exceed the TBR, the outer wheel will then have a higher torque applied to it. If the traction difference exceeds the TBR, the outer tire gets the tractive torque of the inner wheel multiplied by the TBR, and the remaining applied torque to the differential contributes to wheel spin up.
When a Torsen differential is employed, the slower-moving wheel always receives more torque than the faster-moving wheel. The Torsen T-2R RaceMaster is the only Torsen to have a preload clutch. So, even if a wheel is airborne, torque is applied to the other side. If one wheel were raised in the air, the regular Torsen units would act like an open differential, and no torque would be transferred to the other wheel. This is where the parking brake "trick" can help out. If the parking brake is applied, assuming that the parking brake applies even resistance to each side, then the drag to the airborne side is 'multiplied' through the differential, and TBR times the drag torque is applied to the other side. So, the ground side would see (TBR X drag torque) minus drag torque, and hopefully that can help restore progress either forward/backwards. In Hummer/HMMWV applications, there are both front and rear Torsen differentials, so the use of the main brakes will operate this "trick" on both axles simultaneously.
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