Diffs are pretty odd devices and can be difficult to understand. It's frequently a source of great confusion for developers too, ranking right up there with tire modelling, so don't feel bad if they go over your head. It took me a long time to get my head around this subject too.
Here's a map showing how a limited slip differential operates, taken from Milliken's "Race Car Vehicle Dynamics."
Much of the confusion comes about due to the desire to visualize the engine input torque creating the locking torque in the diff, then wanting to know how that torque is then fed to the wheels. In reality, at least mathematically speaking, the engine torque input is not really a variable to be looking at here.
Looking at this graph, instead of thinking about torque going outward to the wheels from the engine, flip it around and imagine the reaction torque from the road coming into the tires. (Huh? :razz
The fact of the matter is you won't know how much torque is going to each tire from the engine while the car is cornering unless you know the slip ratios and weight transfer.
The engine is trying to turn the wheels forward (positive torque). At the same time, however, the tire rubber being stretched is trying to slow the tire back down by twisting in the opposite direction (negative torque). Let's just call this negative torque the "road reaction torque." This is the tire and road interaction that is fighting the engine.
Whether or not the differential remains locked depends on what the two road reaction torques are coming in from the left and right tires. With a given percentage locking factor, there is a constant ratio that can't be exceeded between the left and right sides (except when operating within the preload area. More on that later.) In this particular graph the ratio is 2.90:1. I don't recall what percentage locking factor that is, but it's not important.
We'll accelerate hard in a left hand turn. We have a healthy amount of weight transfer to the right side tire so the forward traction force is greater on the right than it is on the left. This also means that our road reaction torque (the negative torque reaction) is higher on the right than the left.
Looking at point A on the chart, we have 500 lb-ft torque on the right side and 250 lb-ft on the left (really they should be negative values, but this map is symmetrical so I'll just stick with positive numbers). That ratio is 500/250 or 2:1. This is lower than our 2.90:1 torque bias ratio, so the diff remains locked. This can be verified on the graph by seeing that point A is inside a shaded area. Any time you're in the shaded area the diff is either locked or will become locked soon. For now just consider it locked so we can ignore transient phases that don't last very long anyway.
If we suddenly increased weight transfer to the outside tire, the forward force at the outside (RH) tire will rise and the forward force at the inside (LH) tire will drop. We might find ourselves at point C, with RH=750 ft-lb and LH = 200, where we are outside of the shaded area.
Here's where the differential magic happens. We're outside of the shaded area so our diff begins slipping and the wheels begin rotating at different speeds. This means that the slip ratios at the tires change. It turns out that the slip ratios will adjust themselves in such a way as to move us down to point B. The diff is not locked, but the outside tire will not produce any more than 2.90 times the force that the inside tire is producing.
Mathematically we started with RH = 750 and LH = 200, a ratio of 750/200 = 3.75:1. Our differential only allows the outside tire to produce 2.90 times whatever torque the inside tire produces. The differential slips and the outside tire slows down just enough to arrive at a new slip ratio that produces 2.90 times whatever the inside tire was doing (LH = 200).
The RH torque becomes 2.90 * 200 = 580 lb-ft.
Ok, next chart:
Here we see the forward forces at the tires as we accelerate in a left hand turn. An open differential is similar to our LSD except it has a torque bias ratio of 1:1 instead of 2.90:1. What this means is that the outside tire can produce no more than the inside tire can. The forward forces remain the same. If you increase weight transfer and cause the inside tire to reduce force, the outside tire force will drop right along with it. This is because the differential action changes the slip ratios at the tires "just right" to maintain this force ratio of 1:1.
The second diagram is a limited slip diff with a torque bias ratio of 2:1. The wheels remain locked together or the differential slips in a way that makes sure that the outside tire can produce no more than 2 times the force that the inside tire produces. If the torque bias ratio is 5:1, it can make 5 times the force, etc.. The locking percentage maps to this torque bias ratio.
Ok, so what about preload?
Let's go back to the first diagram. The differential map. Without that preload area, at very low traction forces (low throttle), the ratio of forces can still only be 2.90:1. Preload allows the torque bias ratio to become much greater in low throttle or light coasting/braking situations, such as when you are approaching the apex of a corner and maintaining more or less a constant speed.
Point D shows RH = 750 and LH = 50 (or so). With a torque bias ratio of 2.90 the differential would slip and produce RH = 50 * 2.9 = 145 lb-ft while LH remains unchanged as always. However, with that preload area there we can have a constant torque difference exist without the torque bias ratio sticking its head into our business. The preload here is just under 250 lb-ft. This is where the preload crosses each axis (just a bit to the left of point E). In this particular case we move to Point E right at the edge of the preload shaded area where our outside tire produces 300 lb-ft of torque. Note that the inside tire is only producing 50 (6:1 ratio), but the preload allows us to have this big torque on the outside tire anyway. The preload is 250, and indeed in this case the outside tire produces 50 + 250 = 300 lb-ft of torque.
So long as the torque difference between the left/right tires is less than 250 lb-ft the axle will remain locked, regardless of the ratio of the forces. I.e., LH = 10 and RH = 200 gives a torque *difference* of 200-10=190 lb-ft, with a torque *ratio* of 20:1. The preload wins since our preload torque is 250 lb-ft and our axle remains locked
What's important here is that preload is not effecting the differential operation at all except in these situations where there isn't very much throttle or braking being used. Anything beyond that and the locking torque from torque bias ratio will win. The triangular shapes devour the preload area underneath it. They are not cumulative. You have a torque ratio between the tires as well as a torque difference. Locking percentage is equated with torque ratio while preload is linked to torque difference.
Back to the other diagram showing the axles: The third picture shows a light throttle situation without any preload. The outside force can grow no larger than 2 times whatever the inside tire force is. However, if we add in some preload, the difference can be 250 lb-ft (or whatever our preload setting is), regardless of the ratio that would result from that. The fourth picture shows the outside tire force growing considerably, well in excess of the 2:1 ratio allowed by the torque bias ratio.
As we feed in more power and the torque *difference* between the tires grows larger than 250 lb-ft (our preload setting), then the 2:1 ratio kicks in and the outside force will not go over 2 times whatever the inside tire force is. So when you're on the throttle or brake really hard while cornering, the preload is not having any effect at all.
What I suggest you guys do is try the forces view looking down on the car from the top, then drive in circles at the car park to see the forward forces and how they change with locking percentage and preload. With no locking percentage (torque bias ratio of 1:1), and 250 lb-ft preload, the outside tire will not produce any more than 250 lb-ft of whatever the inside tire is producing. I don't know if there is a preload setting on the open diff, but essentially it's just a constant torque trying to speed up one wheel and slow down the other. Once the forces get large the torque bias ratio effect overpowers that. It's one or the other.