The online racing simulator
(137 posts, started )
Quote from Bob Smith :Yes, isn't that the conclusion we came to?

Aparrently not...................

Why are you british people so snooty?
Quote from wheel4hummer :Wouldn't any clutch preload setting greater then the torque outputed by the transmission just make it a locked differential?

Quote from Bob Smith :Yes, isn't that the conclusion we came to?

No. But it is 5 am so I can't really prove anything by showing any "decent" calculations, but this. Although it is not about transmission torque it still shows that while turning the tires are turning at different speeds (or want to turn at different speeds) and this puts load on the differential. With open diff there is nothing to resist the tires from rotating at different speeds but with clutch pack there is the preload and the situation changes.

When the tires produce enough "grip" to create enough torque to overcome the preload torque -> the diff slips. In a way it is a clutch with certain value of torque that it can pass through without slipping. Once you have too much torque coming from the wheels the the diff slips. In a way the transmission torque has nothing to do with as long as the tires are able to take the forces coming from the differential or the other way around

Here's teh colorful picture (no pun intended):

Torque you get out from transmission doesn't make the diff slip (remember, 5am )
Attached images
So if the preload is set too high then the diff can't work as it should be? Is that right?
Quote from LRB_Aly :So if the preload is set too high then the diff can't work as it should be? Is that right?

Then it would act like a locked diff if I'm correct
Quote from mikey_G :Then it would act like a locked diff if I'm correct

Yes that's what i thought.
#56 - Vain
Let's put it straight:
The car with LSDifferential with preload drives down a straight. The driver leaves throttle and brakes alone and starts turning in left.
The front wheels start turning the car, which causes forces on the rear tyres. The front wheels try to make the left rear wheel slower than the right rear wheel.
These forces mean that there is a torque at the differential.
If this torque is smaller than what you set preload to the differential resists the torque and acts like a locked diff.
If this torque is bigger than what you set preload to the differential starts slipping. The torque it exerts is exactly what you set preload to. f.e. 100 Nm if you set preload to 100 Nm. Regardless of how much the driver turns the steering wheel, the diff won't exert more torque than that, 100Nm and no more.
If the driver starts accelerating now the differential is loaded and exerts additional torque from the power-lock setting, and pretty soon preload is neglectible.

That is my current position. No warranty though.

Vain
Sounds good to me, although in your first situation there would have to be a little throttle applied to negate the engine braking, else coast locking would be in effect.
I love how many people said pre load was needed and yet no one can decide what it is lol.
Between Hyperactives and Vains comment it makes sense, but is that right?
So pre load is a force, which under rolling conditions, will mean the diff will be locked until the wheels produce enough torque to overcome the pre load force and allow slip to occur.

So....?
Power lock is whent he engine is producing a torque (accelerating)
Coast lock is (a guess) when engine braking is taking place so the wheel rotating at a higher speed then the engine (obviously through drive ratios) so a low torque (or nrgative torque?) is being applied by the engine.
Pre load is under rolling condition and is minimum force needed to let the diff plates slip?
This is the way how I see a LSD diff
The preload thing are basically springs pushing 2 plates together, and you can adjust the force of the springs. If the difference of torque between the right and left wheel is smaller then the preload setting, it behaves like a locked diff. If there is a difference in torque of both wheels, and it is higher then the preload setting, the clutches start to slip.
The amount of slip allowed is limited by the power locking and coast locking. If the power lock is 80%, then there is only a 20% difference of torque is allowed between the wheels. I think you can figure out the coast story too.
Power lock and coast lock are only in working if the torque is higher then the preload.

Please correct me if I'm wrong, but this is how I kinda understood it from this topic.
Back to my first explanation (leaving out all my bogus calculations), the preload is in effect as long as the variable locking force generated by either power or coast lock is lower than it.

For the diff to lock by a percentage, the force that the clutch plates press together has to be variable. So the more input torque the is, the harder the clutch is pressed together - the force itself rises, but the percentage relative to the input torque is the same. The preload just imposes a minimum force of pressure on the clutch packs, as no input torque would also mean no pressure on the clutch which is equal to a open differential. Preload makes sure that this never happens.

If you set the preload very high and the locking factor low, then it could happen that the generated locking force is never higher than the preload, making the power and coast settings obsolete as only the preload will be in effect.
Quote from Greboth :Power lock is whent he engine is producing a torque (accelerating)
Coast lock is (a guess) when engine braking is taking place so the wheel rotating at a higher speed then the engine (obviously through drive ratios) so a low torque (or nrgative torque?) is being applied by the engine.
Pre load is under rolling condition and is minimum force needed to let the diff plates slip?

Preload is always there, it is the minimum torque vaklue that can and will be delivered from one tire to another through the differential. I'll make a definitive post later with fancy equation and all later if no one else won't. It is pretty simple what actually happens but you need A "few" factors in your equations to get the idea

Main thing with differentials is to control the longnitudal forces (caused by acceleration, decelaration and static) of the tires, it all starts and ends there
ok so first lets define the direction for torque traveling from the engine to the wheels as positive (essentially arbitratry)
also since no one challenged jbs forumlae ill simply assume theyre correct

then the diff with preload will act according to the following pseudo code:

if( Engine_Torque > 0 )
if( ( Max_Torque_transfered_through_Diff = Engine_Torque * Power_Lock ) < Preload )
else
if( ( Max_Torque_transfered_through_Diff = Engine_Torque * Coast_Lock ) < Preload )

and also a little graph (the locking factors are essentially the gradient
Attached images
#63 - J.B.
I pretty much agree with the graph, not sure about the pseudo code though. Shouldn't it be something like this?

`if( Engine_Torque > 0 ) if( ( Max_Torque_transfered_through_Diff = Engine_Torque * Power_Lock ) < Preload ) Max_Torque_transfered_through_Diff = Preload else Max_Torque_transfered_through_Diff = Engine_Torque * Power_Lockelse if( ( Max_Torque_transfered_through_Diff = Engine_Torque * Coast_Lock ) > Preload ) Max_Torque_transfered_through_Diff = Preload else Max_Torque_transfered_through_Diff = Engine_Torque * Coast_Lock`

Also the term "transfered through diff" can be confusing as it's not clear if the torque is being transfered from wheel to wheel or from gearbox to wheels. I would rename "Max_Torque_transfered_through_Diff " to "torque_fifference_between wheels".

Generally I think I can see this discussion converging to a common understanding so that's a good thing.

Quote from wheel4hummer :Wouldn't any clutch preload setting greater then the torque outputed by the transmission just make it a locked differential?

Too much preload could permanently lock the diff, yes, but I don't think the transmission torque is the relevant factor. Probably more to do with tyre slip ratios and longitudal forces etc.

Quote from Vain :Let's put it straight:
The car with LSDifferential with preload drives down a straight. The driver leaves throttle and brakes alone and starts turning in left.
The front wheels start turning the car, which causes forces on the rear tyres. The front wheels try to make the left rear wheel slower than the right rear wheel.
These forces mean that there is a torque at the differential.
If this torque is smaller than what you set preload to the differential resists the torque and acts like a locked diff.
If this torque is bigger than what you set preload to the differential starts slipping. The torque it exerts is exactly what you set preload to. f.e. 100 Nm if you set preload to 100 Nm. Regardless of how much the driver turns the steering wheel, the diff won't exert more torque than that, 100Nm and no more.
If the driver starts accelerating now the differential is loaded and exerts additional torque from the power-lock setting, and pretty soon preload is neglectible.

That is my current position. No warranty though.

Vain

I agree. Still some minor issues that would have to be worked out though. For example if the preload is the amount of tourque the clutch plates can take before slipping then once they start slipping the torque transfered should be a bit smaller than the preload value as dynamic friction coefficient is < static friction coefficient.

About the two formulas I used in this thread: I didn't come up with them myself, one was taken from here (page 10) and one from here.
Quote from J.B. :I pretty much agree with the graph, not sure about the pseudo code though. Shouldn't it be something like this?

Nope, you have to watch closely

This term:
(Max_Torque_transfered_through_Diff = Engine_Torque * Power_Lock)

Assigns the value of "Engine_Torque * Power_Lock" to the variable "Max_Torque_transfered_through_Diff", and at the same time uses the result for rest of the IF clause to compare with "< Preload".

\/\/\/ Haha, I was faster
Quote from J.B. :I pretty much agree with the graph, not sure about the pseudo code though. Shouldn't it be something like this?

`if( Engine_Torque > 0 ) if( ( Max_Torque_transfered_through_Diff = Engine_Torque * Power_Lock ) < Preload ) Max_Torque_transfered_through_Diff = Preload else Max_Torque_transfered_through_Diff = Engine_Torque * Power_Lockelse if( ( Max_Torque_transfered_through_Diff = Engine_Torque * Coast_Lock ) > Preload ) Max_Torque_transfered_through_Diff = Preload else Max_Torque_transfered_through_Diff = Engine_Torque * Coast_Lock`

you dont need the else path since the if argument already asigns the multiplication to max_torque

Quote :Also the term "transfered through diff" can be confusing as it's not clear if the torque is being transfered from wheel to wheel or from gearbox to wheels. I would rename "Max_Torque_transfered_through_Diff " to "torque_fifference_between wheels".

agreed although it should be max_torque_difference

Quote :About the two formulas I used in this thread: I didn't come up with them myself, one was taken from here (page 10) and one from here.

hehe i didnt want to imply that all stupidity falls back on you in case my graph is wrong it was just to make clear i didnt research the formulae at all
#66 - J.B.
I see.
*runs, ashamed by revealing coding n00bishness

Quote from Shotglass :hehe i didnt want to imply that all stupidity falls back on you in case my graph is wrong it was just to make clear i didnt research the formulae at all

Well now all stupidity falls back to Pat Symonds (and others).
Quote from AndroidXP :If you set the preload very high and the locking factor low, then it could happen that the generated locking force is never higher than the preload, making the power and coast settings obsolete as only the preload will be in effect.

I think I experienced this today in the XRT. Initially I had 35/35 and 250Nm preload. When in a coast situation slowing down into the 1st right hander on AS Nat, I was happy with the balance of the car. I then reduced preload to 100Nm and ended up with significantly more oversteer in the same situation (still at 35/35). So I guess the preload provided more torque than the locking on coast, which kept me more stable. Reducing the preload meant I ended up relying on the (lower) amount of torque provided in the coast situation.

If someone can please let me know whether I am interpreting this correctly, I would appreciate it!

If so, I assume the best thing to do would leave the preload low (100Nm or less perhaps) so that under a coast/power situation I am relying on my coast/power locking percentage, and then increase the coast locking to reduce my corner entry oversteer.
Quote from Michael Denham :If someone can please let me know whether I am interpreting this correctly, I would appreciate it!

Yes you do
#69 - Vain
Quote from J.B. :For example if the preload is the amount of tourque the clutch plates can take before slipping then once they start slipping the torque transfered should be a bit smaller than the preload value as dynamic friction coefficient is < static friction coefficient.

I can only judge by the technical drawings and texts linked here. Those say that the torque exerted by the differential due to preload is constant over the whole range of slipping.
From looking at the drawing I think that preload is also active while power is transferred through the diff. After all, all you're doing is pressing clutch plates together, they don't gt loose because power is transferred through the diff.
So when the diff is slipping the exerted torque should be 'preload + torque at input shaft * locking_factor', wether the torque at the input shaft is big or small, the clutch plates we press together with preload shouldn't mind. Or should they?

In that case the diagram above would be wrong.

Vain
Attached images
Quote from AndroidXP :Yes you do

Thanks! I guess the next thing is to figure out, for a particular power/coast percentage, what value preload needs to be at or below in order to have it not determine locking under power/coast. I wonder what the best way to go about this would be (rather than driving it and doing it by feel). Perhaps there's something in one of the replay analyzers that could help with that...
Hi guys,

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."

http://performancesimulations.com/files/diff2.jpg

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:

http://performancesimulations.com/files/diff4.jpg

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.

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.
Quote from jtw62074 :Hi guys

Thx Todd for dropping by very informative as always.

Just out of curiosity do you know what type of LSD is most commonly used in RL for FWD race cars?

Also what would be reasonable preload settings for FWD vs RWD cars for race in RL? i.e. What is considered a normal range and what is abnormal. I get the impression high preload diffs are mostly for drag (800nm) and 400nm would be considered pretty high for a track race car.
Something's bothering me. I hope that the "new" diff ain't gonna replace the closed diff just because you can make it behave almost the same. If very high preload settings showed to be faster then "normal" ,rl ones then it would be useless. Well I hope that this ain't the case but we probably have to wait for more laptimes/setup data.
Quote from LRB_Aly :Something's bothering me. I hope that the "new" diff ain't gonna replace the closed diff just because you can make it behave almost the same. If very high preload settings showed to be faster then "normal" ,rl ones then it would be useless. Well I hope that this ain't the case but we probably have to wait for more laptimes/setup data.

Yeah, this improvement to the diff won't solve the underlying problem that is thought to exist with the tires that make the locked diff so fast... But I would imagine it would lessen the difference in times between using a locked diff vs clutch pack. Although I don't know how much it will help those with godly car talents that can drive around any instability in a setup. Maybe more beneficial to guys like me who are only fairly quick and consistent with a stable car.