One thing that had me puzzled about the Torsen diff is in trying to equate the parameter "% locking value" given by BMW to the Torque Bias Ratio parameter used by Torsen. I found a relationship between these that may apply.
The locking factor is S where S = 100% x (torque difference between the two wheels / total torque of both wheels)
You can define that one wheel is working on a surface with coefficient H while the other is on coefficient L and both wheels are receiving the most torque available from the diff and are at their limits of friction.
In this case
H = (S+1)/2 and L = (-S+1)/2
the torque bias ratio is H/L.
Now, with these we can plug in numbers and find that for most stock BMW limited slip diffs, which are rated at 25% lockup,
H = .625 and L = .375 so for BMW diffs, the TBR is 1.67
A 40% lockup diff would have a TBR of 2.33.
source:
http://www.unofficialbmw.com/all/drivetrain/all_differential_lockup.htmlI also emailed the manufacturer of the Torsen differential and received this reply to my question about TBR vs lockup in a 2000 Z3 coupe:
Yes, that unit was manufactured at our sister plant outside of Brussels, Belgium. Your 2000 Z3 would probably have a Torsen T-2 rather than a T-1 in its axle. We refer to the differential’s locking effect as its torque bias ratio or TBR. Torsen T-2 models typically have a TBR around 2.0:1. Think of the Torsen as a torque multiplier, so what it does is take the available torque that is being lost on the wheel that is spinning up or losing traction and through the differential multiplying it times 2.0 and sending it to the slower spinning tire which usually is the one with the better traction.
If you look on the products page of our website and click on the Torsen T-2 link it will take you to the actual copy of our technical information sheet. The one graphic where it shows 20% on one side of the differential and 80% on the other is not correct. The numbers should be more like 35% and 65%. It was a graphic design error we never caught.
We hope this better explains for you how the Torsen works. Thanks for the question and interest in Torsen!their website is:
http://www.torsen.com/This responder obviously was not certain of exactly what went into the Z3, but was interesting anyway.
Topic: small case vs medium case diffs (Read 20024 times)