OK. Glad we've got that far in agreement.

One point. Right at the beginning of the post I stated that the stacks were designed so as the reaction torque increased, the force binding the clutch & plate stack on that axle also increased. And you agreed on that point. I guess it was implied that the inverse was also true.

***

Now, I am writing the following description based on a 1-way differential just for simplicity.

***

Coming up to the curve, you let off the gas and finish braking. As you take your foot off the brake you turn into the corner.

There is no reaction torque on the axles at this point. There is minimal reaction to the differential behavior as the clutch-plate stack preload is not a significant force. Behavior is the same as an open diff, practically speaking.

As you come around the corner and approach the apex you begin to apply throttle. The engine transfers torque to the carrier and the spider gears transfer torque to the axle side gears.

The tires do not have the same amount of traction. Due to the outside wheel bearing more of the weight of the vehicle, reaction torque increases and the stack on that axle binds. The inside wheel is unweighted and so the reaction torque decreases.

The carrier is spinning, pushing the spider gears which are pushing the side gears. As I accelerate the reactive torque on the outer axle increases, which increases the force on the outer stack, which increases the rotational friction with the spinning carrier.

As we stated earlier, the torque at each axle is equal to the resistance of that wheel to rotate, i.e. reaction torque. So the differential and spider gears are transferring more torque to the outside axle, having more traction and thus more reaction torque than the inside axle.

***

Now, I am willing to say that this is gray area for me. Can we really treat the inside of a spinning carrier as a stationary object? With respect to forward motion, the wheel on the outside is pushing past a carrier spinning with 200 lb-ft of torque but not quite not as fast as forward motion, while the inside axle is being pushed only by the spider gears and nominal friction from the stack.

 

It does seem that we are in some agreement on the wheels turning the same speed case. At least we agree that so long as the wheels are spinning the same speed torque can shift instantly. As I said, that’s like having a spool which can instantly shift 100% of the torque to either wheel except in our case only say 30% of the torque can shift. We don’t seem to agree on the moving case as you still feel that the wheel with the most grip gets the added torque regardless of which wheel is actually spinning faster. This isn’t the case as my first post showed.

 

Which is why I said originally that you don't really understand how they work.

It isn't a balanced force inside. You insist it *always* is. Hence the disagreement. You can do all the math you want and make any claim you wish, but when your basic premise is wrong, everything you create from that is wrong.

And your math completely ignores any forces except torque coming from the engine. That isn't how I learned physics. Physics models are a limited set of forces. No matter what the model says, the physical world trumps all. And any physics model is going to deviate from the real world by varying degrees. The most accurate model is still less than accurate, it is only an approximation. It is a mistake to pretend a model IS the thing.

You cannot ignore the forces acting against the movement of the wheel and claim your model is accurate. I don't care who you think agrees with you.

 

My basic premiss isn't wrong at all. I didn't address the trivial case where both wheels spin at the same speed until later on the first page. In the very first case I was talking about a car in a corner. Sure a LSD is great for drag racing but I was talking about the advantages of a e-LSD for cornering and it's affect on the car's handling. Since you didn't explicitly say you were talking about the straight line case and I had the cornering case in my head we were already in disagreement regarding context. I agree with you in context of a straight line case. The problem is I don't know that you as of yet understand the case where we aren't trying to go straight.

If you think my math ignores the torque coming from the engine you need to reread what I said. T_diff (the torque into the diff) = T_left + T_right (the output torques). If the left wheel is the slower of the two wheels: T_left = 1/2 T_spider + T_clutch ; T_right= 1/2 T_spider - T_clutch. To add a bit more math, if we assume we have a pure torque sensing diff, T_clutch = k*T_spider where k is a constant that relates torque into the spider gears with the clamping force thus locking torque of the diff clutches. This description assumes relative wheel motion. This is just a restatement of what I have already said. Note that the ONLY forces (well torques in this case) external to the diff are the input T_diff and the outputs T_left and T_right (which I didn't explicitly label in the past). The T_clutches and the rest can all be calculated from knowing those three external torques.

More importantly, the math shows that the slower of the two driven wheels will get more torque. BTW, I've always said the load on the spider gears is balanced. I said the clamping FORCES on the clutches are balanced. I clarified that the T_clutch torques are equal but opposite in direction when we have relative wheel motion. They are simply less than T_clutch (the maximum static T in this case) when both wheels spin at the same speed. You seem to feel these series of claims are wrong but you have yet to illustrate why.

 

Nunco,

I think it's a good idea to rehash were this discussion came from. I had made a comment about the advantages of an e-LSD vs traditional LSD for handling. I offered a description which basically mirrored what I've said here. When you are cornering and neither wheel is freely slipping the slower wheel gets more torque thus creating an understeer moment about the rear axle.

I believe you were thinking about the straight line case when you suggested that I was wrong. Your actual phrasing was less complementary thus put me on the defensive. Because I was considering the cornering case that is where I focused my arguments while I presume you were thinking mostly about the straight line case. This might have lead to some of the initial misunderstandings. My descriptions of cornering torques have been consistent but I did have to amend my statements to make it clear that I was discussing the cornering case and in the straight line, wheels turning the same speed case, much of what you said was extrinsically true (eg the diff transfers up to the bias ratio of torque between the two wheels and the wheel with the most grip gets the most torque so long as both are spinning at the same speed).

Where our discussion has diverged is the cornering case. I have explained the torque distribution and why it occurs for the cornering case. I have explained mechanically why the slower wheel gets more torque and why the amount of torque could be velocity based or input torque to the diff based. I have offered a number of both simple and complex explanations why the slower wheel gets more torque. I have also explained how this holds true even when the inside wheel slips (ie it becomes the faster wheel!). I explained why this would lead to a transition from under to over steer.

Correct me if I'm wrong but I believe you currently do not buy the claim that the slower wheel gets more torque when we have a difference in wheel speeds. You also, I believe, feel that because the slower wheel gets the torque this would make a torque sensing diff a speed sensing diff. If this is the case perhaps this is where we should focus the discussion. I could believe that others would confuse such maters and I think it's great to try to clarify the operation of these diffs for others.

 

Those Elises, Caymans and 911s you see without LSD are because those cars have enough weight over the rear wheels that traction is not as much of an issue as on FF and FR.

 

After years of autocross, this can only be applied in certain situations. Autocross is a very unique motorsport, with extremely quick transitions and emphasis on rotational ability. In this case, an LSD will certainly be beneficial, especially since low speed corners are where you lose time, and autocross is ALL low speed corners.

When you are talking about high speed sweepers and serious full throttle application, the behavior of the car is going to be different.

 

I wouldn't disagree with that but I thought it was also because the manufacture decided the car drove/felt better with the open diff. I'm sure in some cases the car was slower due to the lack of a LSD but it also likely felt better in other cases.

 

Cheaper to make the car without LSD, plain and simple. If you ask the manufacturer, I'm *sure* they'll have a good reason other than that (like: "but it *feels* better without lsd"), but that's the bottom line.

Used to be able to get an LSD on the lowliest BMW 318i, now you have to get an M-car to get an LSD
Same w/ Porsche. You can no longer get an LSD on a base 911, you have to get a 911S.

Shenanigans!

 

I feel that I have less experience with diffs than either of you, but I will say that in the miata that I track regularly, and have tracked with both an open and torsen style lsd. That in a street based race car, that does not have extremely fancy electronics, you want some form of LSD. As for your friend driving the Miata on street tires, he wasn't going fast enough. On a bone stock Miata, on bad A/S tires, or on star specs, I could easily spin the inside tire while tracking. Same result on the Star specs and coilovers. Same result on R-comps and coilovers. Then I put in a torsen style LSD and like magic, no more wheel spin. Since, and immediately after I picked up 2-3 seconds a lap on a sub one mile course.

I am not saying that an LSD is better in EVERY situation, but I would say that it is better for RACING, on a road car based race car. There is a reason that every Spec-Miata driver there is either has or wants a LSD in their car.