The Torsen

[drivetrainUW-Platt]

Hey,
Here's a question that I have had since the first time i picked up the torsen, Is this the best differential for a fsae car? Basically i see it as a complex and heavy component. Rotating mass is always important to keep to a minium wherever possible. i have seen a few teams workin with atv differentials, curious how those have been going. I know ppl put up posts "building custom differential" and most mean just the housing for the torsen. we have already done this, reducing a lot of mass and mounting problems, but i still wonder if the torsen is just too much for our scale of car. I would love to actually make a custom limited slip, just using gears out of say a garden tractor diff...anyone else thought along the same lines???

[George]

I would say its not the best choice for an sae car.

Work out what happens to the toque division when the car goes around a corner, and what happens if the inside wheel becomes unloaded.

[drivetrainUW-Platt]

if the torsen isnt the ideal diff, why is it so popular then? i have been collecting my garden tractor diffs to see what i can come up with http://fsae.com/groupee_common/emoticons/icon_biggrin.gif

[BeaverGuy]

At the Detroit comp this year, when we were talking with one of the design judges he suggested that a limited slip on these cars wasn't neccesary. Has anyone recently ran with an open diff on one of these cars?

[MikeWaggoner at UW]

I see tires spinning slowly or wrong with a torsen on many of these cars. This may be something that should be reconciled with tuning and chassis, but with an open diff I think you'd get a backwards tire fire on corner exit.

[Denny Trimble]

If you have enough rear roll moment resistance (%), you can unload or lift the torsen to the point that acts like an open diff. On corner exit this will be "forwards" inside tire spinning, with the possibility of "backwards" inside tire spinning on corner-entry (if you have a single rear brake).

This year's Pontiac course was bumpy enough that our car was spinning one wheel on a certain corner exit, even though it didn't do that in all our testing before Detroit on a less-bumpy surface.

[Didier Beaudoin]

We actually ran an open diff. Not that we are a top-team or anything, much more of a bottom team in fact http://fsae.com/groupee_common/emoticons/icon_biggrin.gif. Anyway, we used this diff because it was cheap and easily obtainable and I must say it did work really great. We had absolutely no problem at corner exit. I can't say if it was better than a limited slip, because I've never driven a vehicle with a limited-slip, but it was working well.

[Ellipticelm]

Hi,
I wanted to know if there are any comparison made available bet the various diffs available for FSAE car and what their pros and cons are

[John Bucknell]

There's no simple answer for what kind of diff is best for any kind of road race car. There are non-active examples that approach the ideal sometimes, but aren't very adjustable for different circuits and can be very non-ideal. This is the reason why F1 and WRC use fully electronic limited slip via clutch packs.

If you are interested in the subject, it is relatively straightforward to determine why limited-slips are better than open diffs. Write a program that handles weight transfer in a corner and figure out how much torque you can plant. An open diff limits the axle thrust = 2 * the normal force on the unladen wheel * tire mu. In other words, you're coasting if you lift the inside tire (zero normal force on inside equals zero thrust). A torque-sensing diff with a bias ratio can generate axle thrust = (normal force on the unladen wheel * tire mu) * (bias ratio + 1). The Torsen (torque-sensing) can have up to a 3:1 bias ratio, so conceptually if your weight transfer puts 15% axle weight on the inside you could still get 60% of your straight-ahead torque down to the ground - assuming you haven't eaten up that traction for cornering. So why not solid axle? It forces the lesser laden wheel to spin at the same speed as the more laden wheel, generating a moment that usually understeers into and out of the corner (why go karts lift the inside). Effectively the Torsen does the same thing, only to a lesser degree if you use a single rear disc. Then there are speed sensing and simple preloaded clutch packs, and they have all sorts of properties I won't go into here. An optimal diff would distribute torque such that you get understeer or oversteer moments when the car needs it as well as optimally distributing torque to the tires that have grip. These optimal effectively combine some of the torque-sensing and some of the speed sensing properties.

The likely answer for most teams is pure economics. You either use an ATV (ie non-race) part, or a Torsen or you build your own. Specialized components aren't out there due to the lack of small light race cars used mostly at low speed besides FSAE.

[Kevin Hayward]

Guys,

As John said there are a few issues involved. The LSD will allow more drive but at the cost of an understeer moment. As the bias ratio increases it becomes more like a locked differential. As it lowers it becomes more open.

There will be a point at which the extra drive cannot be really used because of the resultant understeer. It makes perfect sense then that the ideal diff (ignoring complexity, cost and weight) would be a LSD with a certain bias ratio.

That ratio will be dependant on the available grip on both the front and the rear of the car as well as the type of corner the car is traversing.

This can all be simulated ... to give that nice value that doesn't mean as much as good testing. Based on what we found from our car simulated I would take a locked diff before an open ... but a LSD before a locked (although not by as much as it first appears)

As to what we found as a good starting bias ... well I might keep that between UWA and myself.

You should also be able to find the optimal TBR for any part of a track ... this of course could lead to the ultimate ... an active differential ... but then how much money, time and resources would you pump into it?

Kev

[Denny Trimble]

<BLOCKQUOTE class="ip-ubbcode-quote"><font size="-1">quote:</font><HR>The LSD will allow more drive but at the cost of an understeer moment. <HR></BLOCKQUOTE>
Kevin,
You don't mean to say a Torsen causes an understeer moment on corner exit, do you? I understand corner-exit understeer due to less normal load on the front tires, but the thrust is greater on the outside rear tire, which is an oversteer moment. Locked diffs generate understeer moment (until the inside wheel lifts), and open diffs are neutral in this sense.

Did anyone else read the diff section in Peter Wright's "under the skin of the Ferrari f1 2000"? He said they effectively lock their diffs in the braking zone for stability. They are more worried about stability than we are, and maybe they only do this in the straight-line phase of braking (not turn-in). But the effect of a single brake acting on a torsen is an understeer ("stabilizing") effect on corner entry as well. I'm not saying it's ideal for FSAE, but I also don't think it's horribly bad. Look at this year's top performers.

[Kevin Hayward]

Denny,

As far as my understanding goes when the more unevenly the torque between the two wheels the closer the speed of the wheels. At one extreme you have the open diff with theoretically equal torques but uneven speeds. At the other extreme you have the locked differential with unequal torques but the same speed. It is this same wheel speed that causes the understeer moment. Whether this is understeer or oversteer will depend on the side of the peak of the tyre curves (I think) ... I read a few papers on go-kart handling a while back and I think thats the general conclusion.

The LSD sits somewhere between the two ... uneven torques and uneven speeds. Hence somewhere between neutral and understeer (depending on vehicle attitude). The toque bias ratio is a way of showing "openness" or "lockedness" ... my supervisor would hate that use of english.

...

As for the rear brake issue ... I wont go over my views again but I do think that looking at the top finishers as it is a bad sample space. There are very few teams running twin rear brakes. However if you look at last year a car with twin rear brakes won the whole competition (and the endurance event) ... hence a twin beat all those singles. It is a crappy parametric analysis as there is not enough twin setups to rule out anomolies.

I think the answer has to come from either back-to-back testing or simulation. In the case of F1 I can understand wanting a understeer attitude (however I have read not all drivers drive cars setup this way) on corner entry. However I fail to see how that extends to FSAE. The conditions are very different given tight twisty tracks.

I would conted that the turn-in phase of a FSAE vehicle is the most difficult to get right ... in terms of being quick and not pushing. Generally high steer angles and considerable castor make it difficult to keep the tyre generating maximum grip. Conversely the rear end of the car (suspension-wise) is quite easy to get near ideal grip conditions. I doubt that a FSAE vehicle on the limit has enough front end grip (with a good setup) to account for the underteer moment generated through braking.

However this does depend on how the driver is braking. The guys at RMIT might be right about a good driver strategy of not trail braking. Hester does know how to drive faster than pretty much everyone in FSAE-A ... so I'm not prepared to argue too much on that point.

Reply if you disagree with the differential analysis.

Kev

[BryanH]

Kev, a very well thought out interesting arguement.

F1 values braking stability probably because the greatest potential for reducing lap times is in the last sector of each straight.I do think though that you can have stability under brakes AND sharp turn-in.

For what its worth Porsche have used torsens in their cars since about 1990 but the club sport or race versions of those cars all use plate style lsd's

[Kevin Hayward]

I agree that stability under braking and sharp turn-in is achievable. And if we assume that understeer = stability then I think the stabilising is best had from other areas than the differential. I think it is built into most FSAE cars to begin with ... probably too much of it built in. Which is why I suggest we do not need another additive source such as the diff.

Kev

[John Bucknell]

One last thought. Back to back testing of open versus limited slip versus locked cannot use identical suspension setups to get a true comparison. F1 designs their whole suspension and aero around what their diff can do, and therefore can overcome some of the non-idealness of their diff. Keep that in mind.

If you have understeer and you add a LSD, things will get worse. If you have sufficient adjustability to dial that corner-entry understeer out (unlikely I know, and scary to drive) - then the LSD won't be so much of a negative.

On the Porsche cup cars, the clutch packs they use allow adjustability that the Torsen does not. See my earlier comment on varying idealness of any one diff configuration from track to track.

[drivetrainUW-Platt]

A lot of good information has been given, I do have a few questions about what was stated. In the design of a LSD, how would one design a specific torque ratio? Would it be down by varying spring rates for the clutch plates, differnt plates, or differnt gears? i know the torsen has its own way of biasing, is there any way to change it's ratio? I would love to eventually design a lightweight LSD suited for our competitions starting with simply 4 normal differental angle cut(cant think of the technical term for them) gears. probably is far fetched, but i have 4 more years of this fun!!

[BryanH]

Primarily ramp angle on the vee part of the 2 end bits. the cross piece that holds the spider gears rides up these ramps and squashes the clutch packs. less ramp angle = more clamping force. More clutch plates = ditto. No bellvue spring = no preload, adding or heavier spring = more preload. Preload is measured by jacking one wheel off ground and using torque wrench to measure torque required to spin it.