Now I really have to start to wonder if you will ever get this.
No, they don't. The SAE paper on page 6 uses T_r (Torque ring gear I would assume) and notes the assumption of a 1:1 final drive. On page 582 of the IEEE paper (582 is the journal page number) you will see the same thing. T_diff is the torque into what would be the open diff portion of the drive or T_spider as I called it. The schematic diagrams make that clear.

Let's hit a really simple point... The net result of the clutch pack is that it effectively works on both wheel. The actual diff they used as an example has ONLY 1 clutch pack and that is attached to only one output. In their picture the clutch is attached to the right wheel. Are you actually claiming the left wheel has nothing to act like a clutch? The paper says that the clutch effectively acts on both wheels. If you finished reading the math part you would see that they prove that the equations you copied (SAE paper, eq 10, 11) result in the equations I mentioned (SAE paper, eq 14 and 15).
That is basically what they got but we must note that in the case of a turn the direction of T_CT_rr and T_CT_lr will be opposite in direction so that that would change the sign for one of your equations. Also, they effectively showed that even if the clutches work only on one output the torque, thanks to the connection provided by the spider gears is evenly applied to both axles.

Note that the papers EXPLICITLY state that torque is transferred to the slower wheel. Do you still disagree with this point?

The magnitude of T_CR_ is based on how tightly the clutches are bound. The way that torque is added to the diff is based on equations that are equivalent to my own.

Do understand you can claim that because I have only limited professional experience in this area that perhaps I might not understand these things. However, you are now claiming that Eaton Corp engineers who are designing vehicle control systems don't understand how a diff works. It is understood that what ever torque the system outputs is resisted by the tires and what ever they are sitting on. BTW, did you notice in the IEEE paper these guys were doing computer simulations of the vehicles. Do you think they were just making that stuff up or something?

In that case you didn't have a good physics professor. However, I think it's more likely your physics proof would understand the math and would accept it just as the controls and engineering professors who would have peer reviewed those submissions did before allowing them to be published.

Are you serious? Look most of the time even with a LSD we aren't asking so much of our tires that the inside tire would slip even when it gets more torque. The fact is they showed the same thing I did. When you turn with a LSD the inside (slower) tire gets more torque.

Well then you are 100% wrong. The papers and I both said understeer moment (a yaw moment applied to the chassis). This yaw moment will occur basically every time a car with a LSD turns and the math proves it. The net effect on the vehicle is small in most cases. Then again in most cases (ie when we aren't driving hard) all those things that we find important like good weight distribution, low polar moment of inertial, etc don't mater. At parking lot speeds I may not notice these various forces and I don't notice the difference between the FWD of a base A4 vs the RWD of a BMW. That doesn't mean that these forces don't exist. Most of the time AWD is pointless extra weight. Like a LSD we want it for the marginal conditions.

That is grasping. The IEEE paper was a 2006 paper looking at control strategies for AWD systems based around one type of component set. The descriptions of the rear LSD diff are sound.

So now you are saying the people who design the cars are clueless? What issue would I concede? My descriptions match those of engineers who work for Eaton and are interested in initially simulating and later testing vehicle control systems. How can you possibly think they don't have a reasonable back ground for this sort of paper? How can you possibly think they don't also have real world experience? What would I concede? I have offered counter explanations to every claim you have made. I have provided 4 sources, two from peer reviewed journals, saying the same thing I have said. Why would I suddenly agree that your explanations which I have disagreed with in detail are now suddenly correct?



Nunco, I think it's time we ask a very important question. What is your technical background? Are you degreed in the field. If not what alternative background do you have in the field? I've run across some talented non-degreed engineers so a lack of a formal degree is not a sign someone would be clueless.

 

Nunco,

I had a chance to review this thread with the engineer I know who designs diffs. He didn't see anything to question in what I was saying. As I said he was working with the Indy car teams in the 1980s as they were adopting Torsen 1 diffs. He suggested something that I hadn't though to say earlier. When looking at slide 9 you rightly point out that we need to consider both the torque into the diff as well as the reaction torque the group applies to the wheels. That is true. Consider that the reaction torque at the group is somewhat like the slipping of the plates in the clutch. Up to a given force the tires basically don't slip. When the papers talk about a high mu surface they mean something along the lines of dry pavement or more technically they mean that the torque applied by the tires to the ground isn't so great as to cause outright wheel slippage. We may see a change in slip angles and the like but the tires aren't outright slipping. So a "high" mu surface could be wet pavement if the applied power isn't too high or dry pavement with more applied power. So long as we aren't in a state where wheels are slipping the reaction torque from the ground is equal but opposite the torque sent out through the axle shafts. This was implicit in the information presented in slide 9. Perhaps that clears up why the papers didn't talk about reaction torques.

In cases where a wheel is slipping it still applies torque to the ground though it changes some of the other parameters because it changes the relative speeds of the diff and the two outputs.

While my engineer friend does not deal with AWD cars on a regular basis he has done prototype work for GM as well as many race teams. He doesn't see any issues with the basic descriptions in the papers though he didn't verify the details.

 

See, here's my issue with the papers. Nobody spends the money on a limited slip for it's behavior when one isn't putting enough power to the wheels to cause any slipping on wet pavement. If one says "this is how an LSD works," I am expecting discussion of how it copes with traction differences and wheel slippage. When the model ignores any case where a wheel is slipping, it ignores the reason people find an LSD to be superior to an open diff.

IOW, a model that demonstrates LSD behavior in conditions where there would be no wheel slipping even with an open diff is useless for explaining how an LSD operates. Because implied in the phrase "how an LSD works" is the assumption that we are talking about it's behavior when an open diff would be smoking one tire and going nowhere fast.

I realize that it is easier to describe the behavior when things are simple - equal traction for both wheels. But that doesn't represent the value of an LSD in real-world usage. One cannot claim to know how an LSD works if one's understanding is limited to the behavior when the engine isn't applying enough torque to the rear differential to overpower at least one tire with an open diff.

Again, it's the behavior of the LSD when an open diff would be spinning that is of interest to people who value the abilities of an LSD design.

And in fairness, there are a number of LSD designs, so one cannot accurately model one particular design using physics notation and apply that to all designs. On the other hand, one can come up with a general high level description that applies in limited degrees to all LSD designs, with caveats for specific variants. Rather than see a slew of engineering papers selling a particular design, I'd like to see a discussion of the behavior of an LSD in a case where an open differential would be a liability.

One of the papers you posted stated a fact that I found to be true - there is little available technical literature on the LSD, of any design. That doesn't mean there is nobody in the world who understands the behavior, just nobody who took the time to write a technical paper for publication. I would think a person would have to be very narrow-minded and sure of themselves to suggest that unless one has written a technical paper for academic publication, one has no clue how something works.

 

But the characteristics of the diff while we are on the edge of slipping are very important for vehicle dynamics. Take cornering and understeer. The rear wheels may have sufficient grip during a corner but do the fronts? Have you overloaded the front wheel to the point where the understeer moment caused by the rear axle is a factor in the car's handling? I had that with my car. That is the behavior people are talking about when they say a LSD causes understeer.

My topic how a LSD works was perfectly named. I talked about how the forces/torques flow through the diff. Exactly how that affects the car is very complex. Limiting the conversation to the case where one wheel is already slipping is only half the story. There is a range where the LSD could hurt performance with respect to an open diff. Part of properly selecting a LSD is dealing with that trade off. I believe the GTR article talked about that to some degree.

No one is ignoring the advantages of the open diff but the fact that I have had to explain the torque flow through a LSD illustrates that many people don't understand what is really happening inside of he diff.

First, let's not say equal traction. We are talking about sufficient traction. For instance, one wheel on grass, one on pavement isn't equal traction but if I am light on the gas both tires have sufficient traction and I don't spin the tires. Second, when we add cornering into the mix the traction needs of both wheels aren't equal. Third, I didn't limit the conversation just to the non-slipping case. Even the papers were more than just the straight and level case. They were talking about he affect of the LSD on slip angles. That means they had to be near the limits of the tires. You also have overlooked the affect that the rear axle has on the steering of the car. That is why I have talked about understeer caused by a LSD. I have also talked about the transitional period when we go from a largely non-slipping state to a slipping state.

And ironically the LSD will spin the inside tire more readily (ie with less torque into the diff) than the open diff. The difference is what happens next (well and how the behavior before the rear tires slipped was affecting the front wheels).

Actually just about all LSDs (all fully mechanical and some electronically controlled models) can be modeled using the equations I, and the paper, discussed. Basically all with have some sort of resistive torque that tries to keep the two wheels spinning at the same speed. The magnitude of that torque could be fixed, a function of torque into the diff, a function of the difference in output shaft speeds, or even computer controlled (multi-factored). In all cases what the mechanism does is try to equalize the output speeds of the diff by applying a resistive torque. In ALL cases that means the slower wheel gets more torque. That is a fundamental. ANY time there is a speed difference the slower wheel gets more torque.

I would agree with that. My engineer friend who worked in Indy likely hasn't published any engineering papers on diff design. That doesn't mean he doesn't know what he's talking about. Good thing no one suggested that the lack of an academic publication means one doesn't know the subject. However, it does add creditability in absence of other information. You have been, generally politely, critical of my explanations. My explanations are consistent with both enthusiasts-technical publications (the GT-R book which was presumably written with input from Nissan engineers) and academic publications written in conjunction with engineers who specialize in the area.

 

My point was that three of the papers you linked discussed a hydraulic device that operates differently than most limited slip differentials. They gave a short overview of how a "typical" limited slip works in order to highlight how theirs was superior. I'm not sure a discussion of how "this" is better than "that" provides an accurate and complete description of "that." Or that it even attempts to do so. So it would be a mistake to take them as such.

I just don't understand why you continually refer back to the behavior when no tire will slip. I mean, we call the device a "limited slip differential," because it limits the amount a wheel can slip. So discussion restricted to cases where there is no slipping does not address the device's intent.

 

The part that is different than a normal LSD is how we decide how much clamping torque the diff will have at any point in time. Once we know how much clamping force we are applying to the clutch we can know now much locking torque the diff has. Since that clamping torque controlled by a computer we could make this eLSD behave like a torque sensing diff, a viscous diff or even a plain old spring diff. Again, it doesn't mater after with respect to how that torque affects the total behavior of the car. BTW, their diff actually has the exact same behavior as the typical (ie sends more torque to the slower wheel). The only difference is they can command the clamping of the clutch rather than leaving it up to purely mechanical means.

I refer back to the no slip condition because it represents the marginal case. It can represent the case where the front wheels are having trouble overcoming the action of the diff (understeer). It also lets us know what happens right at the time the inside tire starts to slip (quick increase in torque to the outside wheel that is already near it's traction limit in many cases) etc. At some point we have to have a transition from neither wheel slipping to at least one slipping. That is the region we operate the car in when we are running at 9/10ths and above.

BTW, I also have discussed the slipping case. That was the easy one where the slipping wheel ends up spinning faster than the wheel with grip. Since the wheel with grip is now the slower wheel it gets more torque.

 

What?!?

You need to stop. You have no idea what you are talking about, and the more you type the more it becomes apparent. You can read and quote all the papers you want, at the end of the day you really don't understand the subject. You are supremely unqualified to lecture anyone on this topic. This last post of yours made that obvious.

 

Nunco, I really think the tables are the other way around. I think you don't know what you are talking about. Respectfully, I think you are clinging to an idea that you don't truly understand. I have the opinions of others backing what I am saying. I have an expert in the field who agrees with me. I may be unqualified to lecture on this topic but that would have more to do with my inability to communicate with you than any lack of understanding of the material.

You are always free to discuss, in detail, where my theories are wrong. Notice that I have often posted paragraph by paragraph replies to your posts. I also took the time to create illustrations to help with the explanation. I also put together math equations. You have disagreed with me but you haven't provided any substantive counter explanation. You are free to try but in the past when I have noted where I disagree with your previous explanations you haven't offered detailed replies.

I suspect with my last post you simply don't understand what I am saying. That is fine but it would be good if you would point out the detail you disagree with so we could argue that specific point. Again, in this case my explanations agree with the guy I know, with the author of the GT-R book, with the authors of the papers I cited and with the math I have posted. You are the only one in the other camp. I welcome the conversation and you have forced me to think so if you have detailed areas where you disagree please feel free to posts them. I'm pretty sure you are the only one who has read this and thinks that I'm off base.

 

You cannot disregard the reaction torque in a model of a torque-sensing LSD. That is one of the fundamental forces that affects their operation. Your claim that you understand how they work is contradicted by your theory that the model does not need to account for the rotational resistance at the wheel.

Both clutch type and helical gear types use the difference in reaction torque to trigger the differential action. The fact that you deny this highlights the limitations of your understanding. You need to accept that in order for Torsen types, as an example, to function the wheels have to have some traction to provide a resistance against which the differential internals deliver the limited slip capability. If we ignore reaction torques, no model in the world could explain how a Torsen can possibly work. Yet it does.

The same goes for the clutch types. In designs where the spider gears are mounted to the carrier, the greater reaction torque on one side is what binds those clutches to the carrier and axle and transfers more torque to the wheel that isn't slipping, i.e. the wheel with most traction. You CANNOT accurately model their behavior on a road using a model where the wheels are in the air. If you try to design a model where reaction torque is ignored, you have a fundamental failing with the model. It will not reflect the actual behavior.

Your refusal to considering the resistance to rotation as a factor, much less as the most relevant factor, is why I say you haven't the slightest understanding of how these devices function.

You are not ignorant. But on this subject you are at a loss. Why in the world, in a model of a device designed to react to the differences in reaction torque from axle to axle, would you insist that we could ignore reaction torque entirely?

 

But I've never disregarded it. The torque into the diff equals the torque applied to both wheels. If the torque applied to the left wheel drops then the torque into the diff has to drop or the diff has to spin up as physics tells us. Everything I have said assumes some level of throttle modulation. So my model has ALWAYS accounted for resistance at the wheels. Torque in = Torque left+ Torque right. What's the reaction torque at the right wheel? Torque right. What's it equal to? Torque in - Torque left.

Your comment about the difference in reaction torques isn't quite right. The locking torque is a function of the torque into the diff. That of course is a function of who much traction we have. We can't put 300 lbft into a diff if the left wheel can only apply 100 and the right can only apply 50. However, in that case we can put in 150 lbft.

I think you are confusing things when you say What do you mean by differential action? Do you mean the locking torque such as the clamping of the clutch plates? Do you mean the relative motion of the left and right wheel? I don't think you mean the relative motion which is what I would call differential action. We both know that a Torsen with one wheel on ice will have plenty of differential action as the wheel on ice spins basically freely while the other wheel is motionless.

I think you mean the locking torque is a result of the difference in reaction torque which wouldn't be true. The difference in torque applied to the two wheels doesn't determine how hard the clutches are clamped. The input toque to the diff (or if you wish, the sum of the left and right reaction torques) determines the clamping force. It doesn't mater have fast or slow the relative wheel speeds happen to be.

I'm not sure about this comment In many clutch diffs the clamping force for the clutches comes from a wedge system that applies clamping pressure equally to each wheel. However, even if we put a clutch on only one side the equations in the papers I quoted show why did doesn't mater to the diff. IF we have relative wheel motion then the torque the clutches apply to the left and right wheels is equal. The direction will be opposite and the total to each wheel follows the equations I previously stated. I think you are suggesting that the clutches may not act with equal magnitude on each wheel. This is incorrect. If the left clutch only reacted to the left wheel then the Eaton diff which has only one clutch would only work on one wheel.

I have always considered it. Now that I have explicitly stated it (In = Left out + right out) are you willing to try to understand the rest of what I and several experts have said? Perhaps I should rephrase that question. I have linked to several sources on the subject. Do you agree that they agree that we can assume they are right? Do you think what I'm saying disagrees with them? If so, why?