LSD Types and Yaw Behavior

[johnc]

From Mark Ortiz's latest newsletter. I actually called him on this issue and he asked if he could make it a question/answer for his newsletter.

 

DIFFERENTIALS AND YAW CONTROL

 

I've been reading some statements on various Internet message boards (yeah, I know) regarding how a Quaife or Torsen type of differential adds some level of yaw control to a RWD vehicle above and beyond what a CLSD provides. Given that many CLSDs are adjustable for preload and lockup percentage, what additional (if any) yaw control will an automatic torque biasing differential provide?

Maybe a more direct question is: Can a passive differential of any type provide any yaw control beyond the inputs from a driver's right foot?

 

The quick answer is: no, a passive differential cannot provide yaw control, in the sense that we usually use the term nowadays. However, more loosely, the action of passive diffs does affect the car's yaw behavior, and the driver's ability to control the car's yaw behavior, so semantically maybe there's some sort of case for calling that yaw control. That's a stretch, though.

 

For readers less familiar with these devices, CLSD stands for clutch limited slip differential. CLSD designs commonly used in road racing have split differential carriers that can spread apart slightly when the carrier applies torque to the pinion shafts. This spreading is used to load packs of clutch plates on either side of the diff which create a locking effect. The amount of spreading force per unit of drive torque depends on the angle of flats on the pinion shaft, which bear against corresponding ramps on the carrier halves. There is one set of flats and ramps for forward torque, and another set for reverse torque. By selecting components with different ramp angles, the unit's properties can be varied for propulsion torque and deceleration torque independently. Additionally, the clutch packs can be preloaded to provide an initial locking torque which is always present, even when no torque is being applied by the engine.

 

A Torsen or Gleason-type differential uses worm gears rather than clutch discs to produce locking torque. Normally only one set of worm gears is available, so Torsens are less tunable than CLSD's. We can normally preload the gears to some extent, although the preload tends to be highly wear-

 

sensitive. One interesting difference is that reverse torque in a Gleason will actually relieve the preload and reduce locking torque, at least up to some value, whereas with a CLSD, preload adds locking torque in all conditions. "Automatic torque-biasing differential" is another term for a worm-gear LSD.

 

Actually, all limited-slip diffs bias torque automatically. The torque to the output shafts is allowed to differ by an amount less than or equal to whatever locking torque the mechanism creates. Whenever the torque bias, or difference, is less than the locking torque, both shafts are forced to turn at the same speed. Any time the shafts are turning at different speeds, their torque differs by the locking torque.

 

By contrast, with an open differential, the torque to both shafts is always identical, and their speeds can differ freely. It is also possible to design open diffs that split torque unequally, in a fixed ratio. These designs are commonly used for center diffs in all-wheel-drive systems, sometimes in combination with an active or passive locking mechanism. Open diffs in a front or rear axle are always 50/50.

 

Yaw is rotation of the car about a vertical axis: change in the direction the car is pointing. Strictly, then, yaw control would be anything that controls such motion – the primary mechanism for this being the car's steering. However, in current usage, yaw control means active, computer-controlled creation of yaw moments, intended to augment the driver's control of the vehicle over and above that provided by the steering. Usually, this is done by selectively applying one or more of the brakes.

 

The propulsion or retardation thrusts from the tires create yaw moments. If we have two equal propulsion thrusts from the rear wheels, and the car's c.g. is exactly centered right to left, the two yaw moments exactly cancel each other, and there is no net yaw moment from propulsion. If the c.g. is not exactly centered, the rear tire thrust forces have unequal moment arms about the rearward inertia force acting at the c.g., and there is a yaw moment toward the heavy side. However, when the c.g. offset is small, this yaw moment is likewise small.

 

When there are unequal thrusts from the rear tires, and the c.g. is centered laterally or nearly so, we get a yaw moment away from the greater thrust. For example, if there is more thrust on the right, the car tends to turn left.

 

We noted earlier that a limited-slip diff allows the rear wheel torques to differ by the amount of the locking torque. So when the rear wheels have unequal grip, there is a yaw moment away from the side with more grip. The greater the locking torque, the greater this yaw moment can be.

 

If the road surface has dramatically and erratically varying grip levels – for example, randomly distributed patches of snow, ice, and bare pavement – and the diff has a lot of locking torque, under power the car will tend to erratically snake right and left. Absent any computerized yaw control, the driver will have to make constant corrections with the steering to keep the car pointed in the desired direction. With an open diff, the car will have better directional stability. Unfortunately, it will also

 

have less available propulsive thrust.

 

When the rear tires have unequal amounts of grip, we face an inescapable tradeoff: thrust versus stability. No device or control strategy can give us both at once. Either we let the thrust of the drive wheels be unequal, to let the wheel with greater grip take advantage of its grip, and accept the resulting yaw moment, or we restrict that thrust to make it more equal to the lesser thrust, and gain yaw stability at a price in propulsion.

 

Even if we have a computer controlling the brakes and/or diff, the requirements for traction control and yaw control inescapably conflict. To achieve traction control, we need to brake the wheel with less grip. To achieve yaw control, we need to brake the wheel with greater grip. If we do both at once, we are merely turning fuel into heat and brake pad dust. The one thing we can do with computer control that we cannot do otherwise is to set some limits on the car's yaw behavior, below which the system functions to optimize thrust, and above which it changes character and optimizes stability instead.

 

The differential with the most driver-friendly properties, the one that makes it easiest for the driver to control the car's yaw behavior, is a completely open diff. Comparing limited-slips, the one that comes closest to this will be the one that has the smallest locking torque, under the conditions being examined. In general, worm gear diffs have less locking torque than clutch pack diffs, although this depends on the specifics of the units being compared. If the worm gear diff locks less, a car equipped with it will be more stable in yaw under power, and will therefore feel more like a car with computerized yaw control. However, the same car with more locking torque will be able to put more power to the road and will therefore be faster, provided the driver can keep it pointed straight.

 

So it is defensible to say that, in general, worm gear diffs provide a measure of yaw control, over what we have with CLSD's. However, this comes at a price in speed, and it is due to the worm gear diff acting more like an open diff than a CLSD does. If the worm gear unit does not provide less locking torque, it also does not provide greater yaw stability. And it is really not correct to suggest that either alternative is fully equivalent to computerized yaw control.

[BRAAP]

From Mark Ortiz's latest newsletter. I actually called him on this issue and he asked if he could make it a question/answer for his newsletter.

 

 

DIFFERENTIALS AND YAW CONTROL

……

 

The differential with the most driver-friendly properties, the one that makes it easiest for the driver to control the car's yaw behavior, is a completely open diff. Comparing limited-slips, the one that comes closest to this will be the one that has the smallest locking torque, under the conditions being examined. In general, worm gear diffs have less locking torque than clutch pack diffs, although this depends on the specifics of the units being compared. If the worm gear diff locks less, a car equipped with it will be more stable in yaw under power, and will therefore feel more like a car with computerized yaw control. However, the same car with more locking torque will be able to put more power to the road and will therefore be faster, provided the driver can keep it pointed straight.

 

So it is defensible to say that, in general, worm gear diffs provide a measure of yaw control, over what we have with CLSD's. However, this comes at a price in speed, and it is due to the worm gear diff acting more like an open diff than a CLSD does. If the worm gear unit does not provide less locking torque, it also does not provide greater yaw stability. And it is really not correct to suggest that either alternative is fully equivalent to computerized yaw control.

 

That entire post covers and clears up so many other threads.

 

The last two paragraphs are an excellent summation for those in the process of designing/building their high performance sports car.

 

Thank you John for sharing and if you talk to Mark, be sure to extend thanks to him as well.

[Flexicoker]

I'm not sure if I agree with this entirely... I was under the impression that an ATB differential could bias torque up to its torque ratio, without significantly affecting differentiation, and therefore cause no power-on understeer. This was, in my opinion, its advantage over the CLSD. The tradeoff is that an ATB will support less of a bias ratio than a CLSD, and therefore will require a suspension setup that will keep the inside rear planted. On the other hand, the CLSD will support a much higher bias ratio, but at the expense of power-on understeer (or steady state understeer depending on the amount of pre-load), which requires a suspension tuned to allow steady-state oversteer to counteract.

 

Mark treats the ATB as a high ramp angle/low to no preload CLSD, which I believe is incorrect. I could be mistake though...

[johnc]

When the rear tires have unequal amounts of grip, we face an inescapable tradeoff: thrust versus stability. No device or control strategy can give us both at once. Either we let the thrust of the drive wheels be unequal, to let the wheel with greater grip take advantage of its grip, and accept the resulting yaw moment, or we restrict that thrust to make it more equal to the lesser thrust, and gain yaw stability at a price in propulsion.

 

I think this is where he's making the distinction. In a turn you always have unequal amounts of grip available from the tire (outside tire has more grip due to lateral load transfer). The ATB sacrifices ultimate thrust to gain yaw stability and coincidentally not cause understeer.

[JMortensen]

I'm not sure I'm very impressed with this article either. Even though I prefer the CLSD and frequently argue for it I think he sells the HLSD short. The arguments that I've heard from proponents of the HLSD is that it allows for better turn in as flexicoker mentions. The other common one is that the HLSD eats up less hp in it's operation as it doesn't tend to "overlock" the wheels and drag the inside around corners to the same degree as a CLSD. Ortiz seems to assume that the HLSD will always spin the inside tire and be slower than the CLSD even though it is possible to tune around that tendency via a lower rear roll stiffness, wider rear tires, lower tire pressures, etc. On a fast course with no tight turns and the car set up so that it doesn't spin the inside tire, one would expect the HLSD to have an advantage all else being equal. At an autox or a road course with tight turns or where the car gets light and might have more of a tendency to spin the inside, one would expect the CLSD to have an advantage. Beyond all that, what does the function of the diff have to do with simulating computerized yaw control? The question had me asking why someone would ask that question.

[johnc]

The question had me asking why someone would ask that question.

 

Uuuuhhh, I asked the question and it wasn't about computerized yaw control. Mark just went in that terminology direction with his response. I was interested in how differential types can affect yaw and I guess using the term "control" translated to computerized control systems in Mark's head.

 

In my experience the HLSD can provide easier and better handling (turn in, power out) then a high lockup percent CLSD and can result in faster race lap times because its easier to drive fast. But my experiences also show that high lockup percent CLSD (even a spool) can ultimately turn faster qualifying lap times if a fast single lap is the goal.

 

Again, from my experiences, if heat generated is a measurement of power used in a diff, then the order is spool, CLSD, then Quaife putting the most heat into the diff fluid.

[JMortensen]

Uuuuhhh, I asked the question and it wasn't about computerized yaw control. Mark just went in that terminology direction with his response. I was interested in how differential types can affect yaw and I guess using the term "control" translated to computerized control systems in Mark's head.

I see that now. It just struck me as an odd thing to compare the LSDs to the computerized yaw control and it stuck in my head, and I guess I somehow got confused there.

 

In my experience the HLSD can provide easier and better handling (turn in, power out) then a high lockup percent CLSD and can result in faster race lap times because its easier to drive fast. But my experiences also show that high lockup percent CLSD (even a spool) can ultimately turn faster qualifying lap times if a fast single lap is the goal.

I guess I'd need to see more to buy this argument. At least in theory I would think it was as I said before; if the car was set up so that it didn't spin the inside tire, the HLSD should have no disadvantage in that regard, and it's smoother handing and less drag from the tires should be an advantage.

 

Again, from my experiences, if heat generated is a measurement of power used in a diff, then the order is spool, CLSD, then Quaife putting the most heat into the diff fluid.

This idea assumes that the heat generated in the diff is where the hp is lost. Granted, that is where some hp is lost, but I was more referring to the tire/ground interface. Surely we can agree that dragging a tire across the road takes more power than rolling it.

[jt1]

I'm going way out on a limb and suggest that if you compared a spool and a quaife, the amount of extra heat the quaife transfers to the diff fluid, is equal to the amount of extra heat the spool puts in the tires. The spool wins the pole, the quaife wins the race.

 

jt

[thehelix112]

The arguments that I've heard from proponents of the HLSD is that it allows for better turn in as flexicoker mentions. The other common one is that the HLSD eats up less hp in it's operation as it doesn't tend to "overlock" the wheels and drag the inside around corners to the same degree as a CLSD.

 

Jon,

 

Correct me if I'm wrong, but Ortiz did say that you can alter the locking torque for decel and accel with CLSDs independently. So you could set it up for the track I think. On a short tight twisty (autox?) you would have high decel locking torque so the inside tyre dragging as you say creates a yaw moment into the corner, and hence improves turn-in.

 

I think the accel locking torque is always going to be setup depending on how the weight transfer affects the torque required to get longitudinal slip in the tyres.

 

I guess I'm confused why a HLSD in this situation would provide better turn-in? Maybe I'm misunderstanding something. Does the CLSD in decel locking try to turn the car out of the corner?

 

Dave

[JMortensen]

Correct me if I'm wrong, but Ortiz did say that you can alter the locking torque for decel and accel with CLSDs independently. So you could set it up for the track I think. On a short tight twisty (autox?) you would have high decel locking torque so the inside tyre dragging as you say creates a yaw moment into the corner, and hence improves turn-in.

The only way I know of to change accel vs decel lockup is to change the angle of the ramps or the shape of the cross pin so that it is more aggressive or less aggressive. While I'm sure that at the upper levels they are changing these things for a given track, for most of us we get something and run it, or maybe we have two different LSD choices, one more and one less aggressive.

 

As far as dragging the inside tire helping turn in, it would work that way if it was only the inside tire getting dragged. Instead on decel a 2 way LSD like Nissan made is locking both wheels together, and that makes it harder to turn in because the drive wheels want to go straight. A 1.5 way provides some lesser degree of lockup, and a 1 way only locks up on accel. I think most HLSDs are 1 way.

[thehelix112]

The only way I know of to change accel vs decel lockup is to change the angle of the ramps or the shape of the cross pin so that it is more aggressive or less aggressive. While I'm sure that at the upper levels they are changing these things for a given track, for most of us we get something and run it, or maybe we have two different LSD choices, one more and one less aggressive.

 

That makes sense, I just wanted to be sure I understood what was happening.

 

As far as dragging the inside tire helping turn in, it would work that way if it was only the inside tire getting dragged. Instead on decel a 2 way LSD like Nissan made is locking both wheels together, and that makes it harder to turn in because the drive wheels want to go straight. A 1.5 way provides some lesser degree of lockup, and a 1 way only locks up on accel. I think most HLSDs are 1 way.

 

That also makes sense. Cheers.

 

Dave

[kiwi303]

and VLSDs are not even covered, he mentions Open diffs are the easiest to drive, and a VLSD is effectively an open until a wheel slips and starts spinning at a high rotational difference to the other, much greater than just going round a corner.

 

so how does a viscous diff stack up as far as drivability vs performance compared to the helical and Clucth types

[logr]

I'm confused. I have an R200 S15 gear type LSD in a 240sx. I autox it. When I am powering out of a turn, does it provide drive to both tires at an equal force but different speeds or not? That is what I thought was the advantage to a HLSD. I am starting on a 240Z and am trying to decide on a LSD for it right now.

 

Viscous type provide only up to 25% lockup from what I understand so would be the easiest to drive but would also provide the least lockup.

[JMortensen]

I'm confused. I have an R200 S15 gear type LSD in a 240sx. I autox it. When I am powering out of a turn, does it provide drive to both tires at an equal force but different speeds or not? That is what I thought was the advantage to a HLSD. I am starting on a 240Z and am trying to decide on a LSD for it right now.

Your understanding of the HLSD is incorrect. These are also referred to as Automatic Torque Biasing differentials, because they put a different amount of torque (power) to one wheel or the other, based on the torque bias ratio. The downside to the ATB or HLSD diff is that when one side gets no traction, or when the car exceeds 4:1 or 5:1 or whatever the ratio that the diff can support is, then the inside wheel will spin.

 

This is all pretty tricky and there is a lot of dispute as to how they work. Wikipedia now has a page I see, but it also looks inconsistent: http://en.wikipedia.org/wiki/Torsen

 

From that page:

When a Torsen differential is employed, the slower-moving wheel always receives more torque than the faster-moving wheel.

One would think the exact opposite would happen, since the inside tire is the one that you don't want to spin, and it has less load on it so it would be far more likely to spin.

 

Contradiction:

If one wheel were raised in the air, the regular Torsens would act like an open differential and no torque would be transferred to the other wheel. This is where the parking brake 'trick' can help out. If the parking brake is applied, assuming that the parking brake applies even resistance to each side, the drag to the airborne side is 'multiplied' through the differential and TBR times the drag torque is applied to the other side.

Now I think they have it right. By applying the brake to the side that has minimal traction, the force is multiplied, and the opposite wheel (if this were in a corner this would be the outside wheel) gets the multiplied force from the diff.

 

As far as what LSD to buy, I think if you're autoxing the Z you should go with CLSD.

[Flexicoker]

This is an article written by my boss at Taylor Race Engineering. We are the only US motorsports importer for Quaife products, so obviously we like selling Quaife differentials. However, I think this article is written very objectively, and Craig is a really smart guy.

 

http://www.taylor-race.com/pdf/understanding_differentials.pdf

 

The reason autocrossers may have trouble with an ATB is due to caster, not weight transfer. Weight transfer is roughly a function of lateral acceleration, CG height, and track width. The problem with autocrossing is that the turning radius is typically far tighter than that of a road course, so with any significant amount of caster, you're taking a ton of force out of the inside rear-outside front cross weight, which is effectively lifting the tire. We run a Quaife ATB in our Formula SAE car, and we do have to tune the suspension to keep the rear tire planted. Once that is taken care of, we don't have any problems. Of course, this is in a purpose built racecar with a CG near the wheel centerline...

[johnc]

so how does a viscous diff stack up as far as drivability vs performance compared to the helical and Clucth types

 

Its very hard to compare VLSDs because there's such a huge variance between the VLSD units installed in vehicles. The stock VLSD in the 350Z is fine for street driving but basically useless for autocross and track use. They heat up and stop working. Conversely, there are some very high dollar ($5,000 and above) VLSDs that are the best you can get for very specific rally and road racing applications.

[JMortensen]

This is an article written by my boss at Taylor Race Engineering. We are the only US motorsports importer for Quaife products, so obviously we like selling Quaife differentials. However, I think this article is written very objectively, and Craig is a really smart guy.

 

http://www.taylor-race.com/pdf/understanding_differentials.pdf

 

The reason autocrossers may have trouble with an ATB is due to caster, not weight transfer. Weight transfer is roughly a function of lateral acceleration, CG height, and track width. The problem with autocrossing is that the turning radius is typically far tighter than that of a road course, so with any significant amount of caster, you're taking a ton of force out of the inside rear-outside front cross weight, which is effectively lifting the tire. We run a Quaife ATB in our Formula SAE car, and we do have to tune the suspension to keep the rear tire planted. Once that is taken care of, we don't have any problems. Of course, this is in a purpose built racecar with a CG near the wheel centerline...

That is a very nice .pdf and I'm sure it will come in very handy when this subject comes up again. It also backs up my point on the wiki page contradiction. While you may be right about the caster issue (honestly couldn't say one way or the other), I'd say that it is very hard to get the front end of a Z to stick without a good deal of caster. So if you need the caster, the HLSD doesn't work well. Other methods of changing balance like stiffer rear bar would also cause problems.

[johnc]

the drag to the airborne side is 'multiplied' through the differential and TBR times the drag torque is applied to the other side.

 

I think that's why Mark said above that the ATB diff can be slower around a race track then a high lock percent CLSD. If the inside wheel contact patch can only handle (for example) 100 ft. lbs. of torque and the ATB bias ratio is 5:1, then the total torque at the contact patches is limited by the ATB internally (through heat) to 600 ft. lbs. - even though the outside tire might be able to support 750 ft. lbs. of torque at the contact patch with its greater grip.

 

With a high lockup percent CLSD you can get that 750 ft. lb. of contact patch grip but you'll be dragging the inside tire a bit and creating a push. On paper, you should be able to exit the corner faster. In reality, if you can drive through the push, you might be able to be faster for a couple laps until the rear tires get greasy.

[JMortensen]

I think that's why Mark said above that the ATB diff can be slower around a race track then a high lock percent CLSD. If the inside wheel contact patch can only handle (for example) 100 ft. lbs. of torque and the ATB bias ratio is 5:1, then the total torque at the contact patches is limited by the ATB internally (through heat) to 600 ft. lbs. - even though the outside tire might be able to support 750 ft. lbs. of torque at the contact patch with its greater grip.

 

With a high lockup percent CLSD you can get that 750 ft. lb. of contact patch grip but you'll be dragging the inside tire a bit and creating a push. On paper, you should be able to exit the corner faster. In reality, if you can drive through the push, you might be able to be faster for a couple laps until the rear tires get greasy.

That makes sense John, but if you can keep 1/5th of the traction on the inside wheel then the ATB has the advantage. If you can't, then I'll agree that he is right on this point. I obviously misunderstood what he was talking about and was incorrect when I thought he assumed the inside tire would spin.

 

EDIT, wait, no I'm not... If you put 750 ft lbs to a HLSD and the inside tire can only handle 50, then the inside tire will spin. The diff cannot reduce the amount of torque that comes out of the diff, it can only bias the torque. Sorry, brainfart there...

[Flexicoker]

I think we can all agree here, that the ideal solution is to run a spool, a ton of caster, and just lift the inside rear in the air around the corner =)

 

Hey, it works on karts.

 

In my car, if I had the money, I would run a Quaife. My personal opinion is that it is currently the best design out there. I may eat my words if I can't keep the inside wheel from spinning, but thats going to have to wait until I have moneys. I will probably put a CLSD first, because they're easier to get ahold of and cheaper.