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Thread: For those who want to know a big more about the LSD.

  1. #1
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    For those who want to know a big more about the LSD.

    Here's a good discussion copied over from another forum:


    I basically wrote this post for another thread but thought it was good and people who didn't dive into the other thread might want to read it.
    The limited slip diff is one of those car parts that everyone assumes is a must have. Any car that doesn't have one is because the manufacture was too dumb or to cheap to install it. That just isn't true. It can decrease lap times but it can also upset the handling of a car. The Lotus Elise and Cayman very well might come without LSD's not because the companies were cheap but because the test drivers preferred the cars without.

    Just a few things starting with the open diff:
    1. Torque is like force, it's how hard you twist something.
    2. Power is force times velocity or in this case torque times rotational speed. If you push just as hard but move twice as fast you have twice the power.
    3. An open diff always sends equal TORQUE to each wheel. ALWAYS.
    4. Since an open diff sends equal torque to both wheels the wheel that spins faster gets more power. So that one wheel on ice gets the same torque as the wheel on dry ground but the ice wheel is the only one getting power since it's the only one spinning.
    5. The torque applied to the rear wheels (not the power) determines how hard the tires are pushing the car forward.

    So at this point we can figured out that with an open diff each rear wheel pushes just as hard. If one is one ice, neither can push that hard.

    Limited slip diffs come in a few basic types. You have the old spring loaded clutch pack type. Those have a fixed locking torque. Locking torque is what makes the output shafts try to spin at the same speed as the diff housing. For a clutch pack diff the locking torque is the torque needed say turn the wheel when the car is on jacks and the transmission is in gear. Next you have speed sensitive diffs. These are ones where the locking torque is related to the difference in speed between the axles and the diff housing. They act like an open diff if both wheels are spinning at about the same speed but act like a LSD when one wheel spins up. Finally we have ramp clutch, torque sensing clutch packs, Torsen, Quaifee (sp?) and other torque sensing diffs. In these diffs the locking torque is proportional to the torque into the diff. So when you are on the gas the diff has a lot of locking torque. When you are off the gas the diff is rather open. Even those all these torque sensing diffs have different guts, as a black box they all work about the same way. Since the clutch pack version is the easiest to see I used it in these pictures.


    Now on to the pictures...

    1. A basic clutch pack diff. This diff uses the separation force of the output gears from the spider gears to load up the clutch discs. That means this example is using a torque sensing diff. Note that because the clutches are between the housing and output any time the housing is spinning faster than the output the output will feel a torque in the forward direction. The opposite is true in reverse. There are two ways torque can be applied from the housing to the output; 1. via the spider gears, 2. via the clutch plates. The total torque to the output is ALWAYS the sum of those two torques.


    2. The open diff. Without the clutches the torque sent to each wheel is ALWAYS equal. The wheel on ice can't handle any torque so no torque gets sent to the wheel with grip. I stressed this because EVEN when we add clutches the SPIDER GEARS always send equal torque to each wheel. The clutches make up the difference.


    3.Now we turn to the right (imagine we are looking at the back of the car). The right wheel slows, the left wheel speeds up. We have relative motion in the clutches. Since this is a torque sensing, not speed sensing, diff it doesn't mater if the speed difference is 1/2 RPM or 100 RPM, the torque the clutches apply to the output shaft is still just a function of input torque.
    The right wheel is spinning slower than the diff. That means the torque on the right output shaft is forward (or trying to make the right wheel spin faster). The torque from the spider gears is also forward. So we have two forward torques added together. Call that T_spider + T_clutches.
    The left wheel is going faster so the torque the clutch applies to the output shaft is in the reverse direction. The equation looks like this: T_spider - T_clutches. So in one case we have addition and in the other subtractions. It's pretty clear that the addition case (ie the inside wheel) is going to get more torque. More torque at the wheel means more force on the ground.
    Since the inside wheel is pushing harder than the outside wheel the rear axle is creating an understeer moment. If the front wheels were on casters the car would try to straighten out! Of course the front wheels over power this with their own steering moment but this is why a LSD (and of course a spool which is like an LSD with REALLY REALLY high bias!) tend to make a car understeer. Its just most of the time the front wheels can compensate.



    5. The above is true until the inside tire slips. This is the case where everyone says, "See the LSD sends the power to the wheel with grip!" Well yes but that's because it sends more power to the slower wheel. When the inside tire slips it speeds up. Makes sense, it doesn't have the road to slow it down. Of course all the math above holds true. The inside tire is now the fast tire. That means the torque to the inside tire is T_spider - T_clutch. Since the outside tire is now the slow one it's torque equation is: T_spider+T_clutch. So the non-slipping tire gets more torque and everyone is happy.


    But there is a problem in that last bit. When you are cornering hard the outside tire is doing all it can to keep the rear end of the car from sliding out. When the inside tire loses grip it speeds up which means we get a lot of torque quickly transferring to the outside tire. The poor outside tire had just enough grip to handle pushing the car forward and keeping the tail in line. So now we spin thanks to the quick transfer of torque from the inside tire to the tire with grip! Fortunately this typically happens slowly and progressively enough that we can balance things and drive the car on the edge. Make no mistake, the LSD makes the edge sharper even though it doesn't always make it faster.

  2. #2
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    I wish my 335d w/ 425 ftlbs of torque at 1750 RPM had one. It could really use it.
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    Thanks mate, that's a good explaination of them.
    Life's too short to drive bad cars.

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    Quote Originally Posted by coolieman1220 View Post
    I wish my 335d w/ 425 ftlbs of torque at 1750 RPM had one. It could really use it.
    Even the 118d could do with one.
    Lack of charisma can be fatal.
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  5. #5
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    That's hilarious, we just finished 3 weeks of classes about gearboxes, diffs and AWD systems.

    Thanks Culver, nice explanation, and comprehensible to everyone, I could really use you at university instead of that selfish teacher.
    KFL Racing Enterprises - Kicking your ass since 2008

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  6. #6
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    Nice Culver, but you should go over Torsen to complete the course module

    I always find folks eyes glaze over when I try to explain to them how constantly meshed gears can direct torque. Clutch plates everyone grasps ususally first time

    "A woman without curves is like a road without bends, you might get to your destination quicker but the ride is boring as hell'

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    That’s useful information, that’s the best explanation have seen, thanks.
    Speed has never killed anyone. Suddenly becoming stationary, that's what gets you."
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  8. #8
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    Quote Originally Posted by Matra et Alpine View Post
    Nice Culver, but you should go over Torsen to complete the course module

    I always find folks eyes glaze over when I try to explain to them how constantly meshed gears can direct torque. Clutch plates everyone grasps ususally first time

    That scary picture is exactly why I decided to use the clutch system rather than the Torsen for my explanation

    I actually do know how that one works as well but I wouldn't want to try to put it in "simple" terms!

  9. #9
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    DAmn, coz I was hoping someone could as it takes me an eternity to try to explain it and usually have to give in before the listener tries to hang themself in desperation
    "A woman without curves is like a road without bends, you might get to your destination quicker but the ride is boring as hell'

  10. #10
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    thanx man. thats an amazing description. cleared up a lot of things for me.
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  11. #11
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    I just thought I would post an update to this. On another forum I have been having a debate with a person who simply does not buy into my claim that the slower wheel gets more torque. That would mean if your tires aren't slipping the inside tire gets more torque and if they are slipping depending on the amount of slip the outside tire is likely getting more torque. Since the other member couldn't buy this argument he also couldn't buy my claim that a LSD can cause understeer.

    Anyway, in an effort to add some substantive evidence to my claims I came up with two papers and a PPT presentation that Eaton corp was involved with looking at electronic control of AWD systems. The rear diff described in the papers was similar to the passive unit I described save for two things. The clutch was controlled electronically vs via input torque as would be the case with a Torsen, and the diff only had a single set of clutch plates that worked between only one of the two outputs and the diff housing. I intuitively felt you don't have to have symmetric clutches for these things to work but I didn't want to state that until I was sure. The math in the papers confirmed it.

    Enjoy... if you are nerdy enough to be interested... I was.
    http://ghost.engin.umich.edu/tcac/8_workshop06_lew.pdf
    http://www.me.umn.edu/~qhyuan/public...TorqueBias.pdf
    http://www.me.umn.edu/~qhyuan/public...06-01-1963.pdf

  12. #12
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    Culver I suspect it's because he is struggling with the concept of what no grip means to a shaft with torque applied to it. Viz it must spin faster. It all usually ties back to the confusion of torque and power and how they relate. Did the complex Eaton details alter his view ? I doubt it if I'm right in my conjecture that it's the basic modelling he is trying to cope with. Have used water-troughs analogy to explain some of why the torque goes to the open wheel by tilting. So level equal water goes to both sides tilt left ( ie less grip on one side ) and the water flows to that side. Not a perfect analogy of the real world but can help break-throgh the block some have on mechanical systems.
    Good luck, soudns liek you're doing a great job for mankind
    "A woman without curves is like a road without bends, you might get to your destination quicker but the ride is boring as hell'

  13. #13
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    To be honest I think he's stuck on two points. One, he can't feel the understeer so the understeer moment doesn't exist. I can understand this is hard for people to sometimes grasp. There was also a disconnect on the idea that a torque sensing diff would care about which wheel is spinning faster. Well since friction is always a retarding force/torque we need to know relative direction to know the direction of the clutch torque.

    Really I think the fundamental problem is an assumption that the Torsen marketing tag line is always true. The line about transferring from the wheel that slips to the wheel that grips is nice and all but not 100% true. It is true when both wheels spin at the same speed. It isn't true in a corner. With his firm knowledge that the diff somehow knows which wheel as more grip then it's easy to claim that the outside wheel in a turn has more grip due to the car leaning to that side thus it gets more torque.

    I don't think a break though in understanding is likely. When I presented the information on slide 9 in which Eaton corp engineers say that a LSD transfers torque to the slower wheel etc. he commented that those engineers, make the same mistake I was making (in his view) of not considering the reaction torques on the ground. He also suggested that his physics prof would have failed the engineers who released those papers.

    Having actually reviewed a few papers for publication in an IEEE journal I can't say I agree.

  14. #14
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    .......
    Quote Originally Posted by Peter Ustinov
    “If the world should blow itself up, the last audible voice would be that of an expert saying it can’t be done.”
    "A woman without curves is like a road without bends, you might get to your destination quicker but the ride is boring as hell'

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