Hahaha, I'm surprised it took this long to degenerate into name calling.

 

But I would rather nunco simply explain where my explanations fail and what the correct interpretations should be.
In all seriousness I put together the original post to try to give people more insight into what happens in their car. I don't mind at all when people challenge me to justify what I say. Nunco did just that early on. I was considering primarily cornering where we really WANT the left and right wheels to spin at different speeds. I hadn't put as much though into properly describing the straight line case where both wheels spin at the same speed. Still, if someone is going to say I'm wrong it is best for the knowledge of me and the forum when we are told exactly why I am wrong (not just saying I didn't agree with some marketing material or I didn't address some point) but say these forces aren't equal because X or these torques are only equal under the following conditions etc.

 

You restate your claims every other time you post. And modify and correct and refine. Which is fine. I know my understanding and ability to put it into words has changed over time. My basic theory is the same, but the ability to couch it in terms another human can understand has improved, I think. You know it's complex, so let's both not act like any difficulty expressing it is a sign of mental frailty.

You keep coming back to wheel speed differences being a fundamental factor in the operation of an LSD. This I disagree with as a sweeping generalization. It is true in some designs, but not in the Torsen type or clutch types.

I also disagree that the clutch stacks on both sides are always in equilibrium. They only are as long as both wheels have equal traction. In my understanding.

 

Read the Torsen article again. In the mathematical representation of the Torsen, relative wheel speeds are not mentioned at all. The discussion is limited to forces and torques.

While I trust the paper to describe the Torsen accurately, I do not refer to it as a adequate reference for a clutch type lsd. But I can try to describe the clutch type using some of their language. I'm freely cribbing from it, but it's not copy-paste.

Engine torque applied to the ring gear is roughly equal to the sum of reaction torques of the axles. In other words, the amount of torque from the engine will equal the resistance of the wheels to rotate. Mash the gas on ice, and both tires will spin but very little torque is being sent to the wheels - the engine is essentially spinning as freely as the wheels and not actually producing much torque.

And we can further break it down to the torque at each axle is equal to the resistance of that wheel to rotate, i.e. reaction torque.

The engine torque is transferred to the axles via the ring gear bolted to the differential housing and the spider gears.

Gear trains generate friction opposing rotation of the train in proportion to the torque being carried by the train. Since all of the engine torque being transferred to the axles is carried by the spider gears, reaction torque which opposes the rotation of the spider gears is proportional to the engine torque which is transferred to the drive wheels. Thus the transfer of torque between the drive wheels is resisted in proportion to the transfer of torque between the engine and drive axles.

All of the frictional forces generated within the differential, and all of the resulting resistant torques which oppose the transfer of torque between axles are proportional to the torque being conveyed by the differential.

In a clutch type differential, there is a stack of metal plates and clutches. These are splined to the carrier and axle, respectively. They transfer torque from the carrier to the axles. They have a spring preload, and are constructed so as the amount of resistant torque at that axle increases, so does a pressure that binds the stack together and increases rotational friction. So a clutch type lsd has an additional way to transfer torque to the axles - the plate and clutch stacks.

The stack has an initial preload which provides a degree of locking behavior, in the event one wheel is on ice for example. The reaction torque is low on one side, and if there was no preload, the differential would behave just like an open diff in the same situation.

In an open differential, the amount of torque applied to both wheels is the same. And we have agreed that the torque applied to the ring gear is the same as the sum of the reaction torque at the wheels. With one wheel on ice, there is little to no reaction torque, and therefore little to no transfer of torque from the engine to the differential housing. Hence you won't go anywhere very fast. The amount of torque an engine can transfer to an open differential is the amount of reaction torque of the wheel with least traction.

The preload on the stacks in our lsd provides frictional resistance to differential action in this case. The reaction torque on the icy side is not zero. The other wheel is on dry pavement and so has an even higher reaction torque. We know that the amount of torque delivered by the engine is equal to the sum of the reaction torque of the wheels, so unlike the open diff, here the engine is actually able to deliver torque to the differential and it is transferred to the axles via the spider gears, according to the amuont of reaction torque at each axle.

(It appears to me that in this special case the clutch-type lsd behaves much like an e-diff that brakes the wheel with less traction, transferring torque to the other axle.)

Now in the case of straight line travel, our lsd behaves identically to an open diff as long as both axles have an equal amount of reaction torque.

When one wheel goes over a sandy patch, the reaction torque decreases at that axle. And as the amount of torque delivered to the axle is roughly equal to the reaction torque, the stack on that side relaxes. Since the reaction torque on the other axle is higher, and the amount of torque that can be transferred to an axle is roughly equal to the reaction torque, the differential transfers more torque to the wheel on clear pavement. Since at the time this occurred the engine was accelerating and transferring 200 lb-ft, now that the amount of torque that could be transferred to one wheel has dropped and we know the total amount of torque that can be transferred to the differential is the sum of reaction torques of the axles, either the engine has to instantly cease applying torque or the wheel with the higher reaction torque will see an increase in applied torque, and consequently an increase in reaction torque. Assuming there is sufficient traction on the "good" side to support this increased load, there is a corresponding increase in reaction torque.

And our clutch-plate stacks are configured to bind together and increase rotational friction when reaction torque increases.

This limits the differential action and prevents the "loose" wheel from spinning by more firmly binding the axle side gear to the spinning carrier.

The result is that the torque the engine can transfer to the carrier is higher than if the diff were open. Rather than being the amount of reaction torque the wheel with least traction can provide, it is the sum of the reaction torque of both wheels.

 

What have I changed? Where did I change a claim? The only change has been a clarification of the case where the wheels are spinning at the same speed. You have had to modify your theory because you weren't sure about the torque distribution of an open diff. Have you at least reached a conclusion on that point? I agree this stuff isn't easy to express but if you claim my descriptions are wrong you better be able to say why.

I come back to the wheel speed being fundamental because it is. I started this thread talking about a LSD's behavior in a turn. That means wheels speeds are not equal thus very important. You are correct that I didn't address the case where wheel speeds are identical AND the differences in left and right traction are such that the diff can maintain equal speeds at both wheels. I later clarified that point. Please tell me what happens in a LSD when you turn. What is the torque distribution and why.

This is a mischaracterization of what I am saying. You are suggesting that I am claiming the difference in wheel speeds is important. No, it is the DIRECTION that's important. If you push a box on the floor the direction of friction is the opposite of the direction of travel. If we assume simple coulomb friction (what we are taught in high school) then how fast you push the box doesn't change the force of friction. If the box weights 100N and mu=0.5 then the Ffriction = 50N regardless of how fast you push the box.

Here is how that relates to the diff. Assuming a given clamping force on a clutch (that clamping force could be fixed via springs or based on loads through the diff eg a torque sensing diff) the torque required to twist the clutch is T_clutch. Any torque less than T_clutch won't move the output with respect to the diff housing. Any torque greater than T_clutch will but that greater torque will now be resisted by T_clutch. So will T_clutch be clockwise (we'll call that faster than the diff) or counter clockwise (call that slower than the diff)? Well that can be answered by looking at the speeds of the wheels. If the wheel is spinning faster the T_clutch will be in the reverse direction. That means it will try to slow the wheel. Note that we don't care about how fast thus this is not a speed sensing case we only care about direction. Do not confuse relative direction with velocity. The box didn't care how fast I pushed, only what direction. The same is true with the diff clutches.

 

There are actually several different clutch-style LSD's out there. I'm sure they don't all work precisely the same way.

The one you posted a link to uses a spring preload, but I'm not going to bet money it operates precisely like my description above. It is a reasonably common clutch-type for race cars, but I don't know how much use it sees in production cars. I simply don't know, I'm not saying it is an uncommon style. But most of the clutch-types I've seen mount the spider gears on the carrier, not floating between two plates.

 

Hey, you are entitled to change or clarify. It's better than sticking with a poorly worded statement or not addressing an important point just to seem consistent.

I wanted to start with the behavior in a straight line before discussing behavior in a turn because, again, if there is confusion in a straight line, it won't get better when discussing behavior in a turn.

And if I am going to have to word my points in your language, you have to cut me some slack on terminology. I'm not writing a textbook or a whitepaper, and I haven't had the benefit of a peer review process so I'm bound to misconstrue something even if I have the concept right. Obviously if I am mistaken on a concept the lack of a common language won't help resolve things.

Do you see why I might find some of your posts confusing if not needlessly opaque? I'm not being overly critical, just pointing out that one is entitled to clarify and refine how one expresses an idea. It's for the best. It's just frustrating for me to dispute a point, have you claim I am not understanding you, then for you to restate the point of contention yet again in the same words. I'm not sure anymore who is misunderstanding who, you know?

And I don't know that we can freely use "pushing a box" in place of "turning a wheel." You can apply thrust to a box on the floor and it will move, but if there is no resistance to turning the bolt your torque wrench will never read 100 ft-lbs.

 

Sure thing. Understand that while the Torsen uses a very different mechanism to generate it's internal frictions at a black box system ends up working basically the same as a clutch pack diff. The differences are small (wear, what happens during the transition from off to on the power etc) but the fundamental point that when there is relative wheel motion the wheel spinning faster will get less torque holds true.

This is the same for a ramp style clutch pack. The locking torque is a function of the input torque. If one wheel is on ice then then there isn't enough resistance to cause the ramps to press on the clutches thus virtually no locking torque.

Same as with a ramp type clutch system. Basically the equivalent of the spiders incorporate clutching surfaces. It's hard to verbally separate the forces so I chose to describe things using a clutch pack diff.

IF our clutch diff has a spring preload mechanism then yes, we can deliver T_output=T_clutch assuming one wheel is on ice. The clamping force on the clutch packs is still equal since that clamping force is F_springs+F_spiders_spreading_force. The springs are often placed between the same clutch clamping plates as the spiders. One side of the spring pushes on the left clutch, the other on the right clutch. Net result the springs clamp each clutch evenly. The forces clamping the clutches are equal because they always come from the same place, the spider gears. In the ramp versions it's equal wedging (do you disagree?). In the spreading of the gear case it's equal because the spiders apply forces equally.

Agreed though this is the trivial case where an open diff, a LSD and a spool all act the same.

You have basically described the case when both wheels are spinning at the same speeds and are on a surface with sufficient traction that both wheels will spin at the same speed. I discussed this on April 3rd. Tell me about the case when we are going around a corner.

 

You are correct, they don't all work the same way. However, they can be distilled down to a few basic ideas. The T-clutch comes from the clamping force applied to teh clutches. That force comes from springs, the spiders and or both. T_clutch is proportional to the clamping forces on the clutch plates. That clamping force is F_springs+F_spiders. By F_spiders I mean the force either of the spreading of the gears or of the ramp system.

 

True, as many times as you have made me say the same things and in trying to pick different terms AND in taking my quotes out of context it could be confusing. Again, in every case I have said the same critical thing, when you have relative motion it's the direction of motion with respect to the diff housing. So if one wheel is slower (ie a speed difference) we care. If you look at it from the point of view of the diff housing it's just a relative motion (forward or back). Note that I have more than once said even a tiny difference in speed (ie just defining a direction) is what we care about.

Perhaps you should ask what I mean or ask do I mean A or B rather than stating that I am claiming X. You said I am claiming a Torsen is speed sensing. No, the clamping torque is torque sensing. However, in a turn the faster wheel gets less torque. I didn't say how much faster or that the distribution of torque is based the RPM difference. Like the box on the floor, the clamping force simply resists movement. The faster outside wheel moves forward with respect to the diff so the clutch tries to resist (a backwards torque). It doesn't mater if the RPM difference is small or large.

Perhaps instead of pushing the box we should talk about turning the box or moving a rusty gate. Would that make it easier for you to see?