Through a bunch of years, I've read numerous articles about differentials, and thought about how they behave under different circumstances. (This is basically a disclaimer explaining that I can't pinpoint any specific source for what I'm about to say...)

My understanding of differentials is this:

Open differentials apply equal TORQUE to each axleshaft.

Limited slip differentials attempt to equalize the SPEED of the axleshafts.


This may not seem to make sense at first, especially the statement regarding open differentials. Lemme try to explain, and show that real-world behavior supports this.

Take a vehicle with an open differential. Let's say one wheel is on ice, and the other is on dry pavement. When you step on the accelerator, the wheel on ice spins and the wheel on pavement does little or nothing. This is the "equal torque" part of open differentials at work. It takes very little torque to spin the wheel on ice. So, the speed of the wheel on ice goes up, since it's not providing much resistance. Meanwhile, the wheel on pavement is doing nothing. Ever been told to apply the parking brake in such a case? It often works, and here's why: Applying the parking brake adds resistance to the spinning action of the wheel on ice. This resistance must be overcome, by more torque. If the drive torque to the wheel on ice increases because you applied the brake, the drive torque to the wheel on pavement also increases. It may well increase to the point that the wheel on pavement will now move the vehicle forward. It's not necessary to bring the spinning wheel to a standstill, only to provide enough resistance (and resulting torque to both wheels) to over come whatever may be trying to hold the vehicle still.

Now, you may be thinking "yeah, but the brakes are also holding the wheel on pavement back." That's true, but here's the catch: the spinning wheel is producing more friction from the brakes than the stationary wheel. So, the added torque applied due to brake resistance on the spinning wheel is greater than the brake resistance on the stationary wheel. If this difference is great enough, the vehicle can move.

Now, let's look at limited slip differentials. I said earlier that they try to equalize wheel SPEED. Go around a corner in a vehicle with a limited slip differential, and the wheels don't slide, do they? (unless it's a VERY tight limited slip unit) That's not because the unit isn't trying to hold wheel speed equal, it's because it has only a limited ability to do so, and turning a corner exceeds that ability. Hence, it lets the wheels turn at different speeds until the vehicle is pointed straight again. Ok, let's put this vehicle in the same situation as the other one. One wheel is on ice, and the other is on pavement. You step on the accelerator, and the vehicle probably moves forward. This is because the limited slip unit can apply more torque (to a limit) to the wheel with traction in it's attempt to keep speeds equal. Assuming you apply enough power to overcome whatever is trying to hold the vehicle in place (maybe just inertia) and the limited slip unit is capable of enough torque biasing in favor of the wheel with traction, the vehicle will move.

It is possible to overpower a limited slip unit, causing one wheel to rotate at a different speed than the other. Let's say you have the aforementioned vehicle in the aforementioned situation, but there's a big travel trailer with 4 flat tires hooked to the vehicle. Now there's a bunch of resistance that must be overcome to move the vehicle. To do this, the limited slip unit must be capable of biasing the torque to the wheel with traction much more than was required to move the unencumbered vehicle. If the limited slip unit is not capable of biasing enough torque to the wheel with traction, the wheel without traction will spin anyway, and the vehicle will remain stationary. Additionally, doing this will cause the limited slip unit to wear out very fast, as its clutches are slipping constantly in this situation. When it wears out, it will cease functioning as a torque biasing device, and will behave exactly as an open differential.

Note: The factory limited slip units in our dodge diesel trucks often require application of the parking brake to begin working. This is not because they are not true limited slip units, but rather is because the type of unit in these is not a simple clutch setup. It involves a worm gear that progressively biases more and more torque as the situation requires, but it apparently is designed such that a little initial resistance from the spinning wheel is needed to activate the unit. I don't know the mechanics of why this is the case, only that it is. Once activated by using the parking brake, it will then proceed to supply much more torque to the wheel with traction than an open unit would with the parking brake applied.