[torsen] Re: [V8] differential/torque sensing

Keith Maddock Keith.Maddock at trw.com
Tue Mar 25 04:10:33 EST 2003

Sorry, apologize for not organizing my thoughts in one email, but forgot to address another point that bothers me.. 

Your claim 
" because friction is function of pressure force and material. Nothing else. 
Not speed, not contact area." 

I'm sorry to say that this *completely off-base* and untrue.   If your statement was true, I for certain wouldn't have a job!! 

Even in strictly textbook / classroom physics, a given Friction interface is said to have to different coefficients of friction: 
Static Mu (no speed difference between surfaces) and Sliding Mu (speed difference between surfaces). 

Now, enter the real world, and now especially the world of "tire vs road", and you have to consider the "Mu-Slip Curve".  This expresses the Coefficient of Friction as a function of the relative velocity of the tire vs. the road. 

To prove I'm not full of sh*t, here are two published papers... 

You can see this (shameful link to a competitor's technical paper, but was the easiest link I could find that I can share) in a Delphi technical paper 
Look at top of "PDF page" 4, Figure 1 "Lateral and Longitudinal Mu-Slip Curve " 

Also as backup, you can see a similar curve from our Airplane bretheren... 
"Document Page" 1, Figure 1 "Mu-SlipCurve" 

Further realize that the Mu-Slip curve is a different shape for different kinds of surfaces - on Dry Asphalt the mu doesnt fall as much with slip velocity, but on some wet concrete and jennite (parking lot sealer material) surfaces this curve is VERY "Peaky".  Meaning.. lots of friction at 10% slip, but a mere fraction of that at 20% and more slip.  (Read.. very challenging surfaces for ABS)  Even ice can vary from a relatively flat curve (basically extremely small friction no matter what the slip) for "wet" ice, but for dry (aka sticky) ice, it can also be a very peaky curve.  On some surfaces, especially deformable ones, like gravel or loose snow, the friction goes UP with increasing slip, due to the surface material accumulating in front of the tire and providing a "wedge" effect.  (the reason why some ABS systems increase stopping distance compared to "locked wheel" on these particular surfaces"

So to tie this back into the disucssion at hand and the basis of my claim - Torsen during braking - having different amounts of braking force causes different slip at front vs. rear axle. This will result in different coefficients of friction front vs. rear, coupled with different amounts of normal force front/rear, contributes to a TORQUE difference front to rear, which causes a locking effect in the Torsen.

So for certain, speed difference front/rear changes the friction/traction/torque inputs to the Torsen, which cause the change in bias ratio.

I'll easily give up the notion that the speed difference makes a change in the internal friction of the unit, I believe the Mu-Slip curve for a metal-oil-metal interface is quite quite flat.

Keith (who really needs to get back to work now)

Keith Maddock, TRW Automotive,  Koblenz, Germany
Slip Control Systems, Systems Design, Traction Control
+49 (0)261/ 895 2474    -   -   keith.maddock at trw.com

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