RE: Zexel Paper - My thoughts

[audidudi@mindspring.com (Jeffrey J. Goggin)]

Since I agree with Scott's assessment, there's not much point in offering a
separate one of my own.  However, I've taken the liberty of adding a few
comments of my own here and there...

* * * * * * * * * * *

>>1.1 INTER-AXLE DIFFERENTIAL: OPERATING MODES
>>An interaxle centre differential operates in the following 4 basic modes
>shown
>>in Figure 10.  In reverse, DRIVE becomes COAST and visa-versa.
>>MODE 1: Drive, Rear high axle torque
>>MODE 2: Drive, Front high axle torque
>>MODE 3: Coast, Rear high axle torque 
>>MODE 4: Coast, Front high axle torque
>>In DRIVE mode, a Torque Sensing differential will distribute the higher
>>driving torque to the axle that tends to turn slower than the other one.
>>In COAST mode the higher braking torque will be distributed to the axle which
>>tends to turn faster than the other one.
>
>A problem arises in "coast" mode scenario.  A car that oversteers on power,
>then gets throttle lifted has two unsettling characteristics in an audi awd
>car.  1)  Since the coast mode distributes braking torque to the axle turning
>faster you go back to 50/50 which is understeer, BUT 2) the lifting of the
>back of the car could cause  "resulting in a rapid drop off in lateral
>adhesion capability at the rear" (see below, another fancy definition of
>spin:).

Somehow, I don't think many of us are concerned about the Torsen's
performance in reverse (except perhaps for Joie Chitwood ... is he still
around?) and since the amount of engine torque being generated during the
Coast Mode is a mere fraction of that which is generated during the drive
mode (unless you're left-foot braking, in which case you're not really in
the Coast Mode), I don't believe the Torsen has as much influence here as
the paper's authors appear to be suggesting.

Also, note that the "braking torque" referred to above actually means
"engine compression braking" since it's NOT possible for the Torsen to
redistribute braking forces from the wheels to one end of the car or the
other ... unlike a locked center diff, of course, which can -- and does! --
do exactly that.  That's why some refer to it as the "poor man's ABS" and
braking distances tend to be shorter compared to an open center diff...
   
>>In case of too low a locking effect in mode 3 (DRIVE: reverse driving or
>COAST: rear high axle torque), the consequences are not relevant as far as
vehicle
>>stability is concerned.  Vehicle dynamics are not involved in reverse driving
>>and during a drop throttle manoeuvre, the front axle always tends to be the
>>faster one (therefore corresponding to mode 4).
>
>Not on power up oversteer, or if cf gets low enough.  The consequences of axle
>braking on lift are significant, the torque is all to the rear due to slip
>angle (O), then coasting creates a 50/50 trend, that's U to an audi awd car.
>"Tends to be" may exactly not be.  Let's try this at Steamboat cf's with a 90q
>10v, for example.

It's important to remember that the Torsen works with percentages and the
chassis responds to absolute values of input torque ... knowing just the
torque split doesn't necessarily allow you to calculate how this effects
handling since splitting zero 50/50, 78/22 or 22/78 all result in exactly
the same answer.

>>1.3 High Speed Cornering: Power Oversteering
>>During a cornering manoeuvre at low speed and low torque (Figure 11), the
>>higher driving torque will be to the rear axle (kinematic condition: front
>>axle turns faster than the rear axle).
>>
>>When more input torque is added, vehicle speed rises, the rear axle slip
>>ratio increases (elastic conditions catch up the kinematic conditions)
until the
>>rear axle reaches the speed of the front axle.  At that time there is no
>>differentiation at the centre differential, which operates as a rigid axle. 
>
>OK, defined audi awd above.  Start with U, then power up O, then the rear axle
>reaches the speed of the front now we have a "rigid axle" (50/50 dist) which
>is U.  Here comes the bite scenario...

Absolutely!

>>From this neutral "steady state" condition, there are two possible dynamic
>>behaviour evolutions:
>>a) The front axle slip ratio increases causing vehicle understeering.
>>The centre differential will react by biasing the surplus torque to the rear
>>axle thereby correcting the understeering.  Should this correction be
>>insufficient, the driver will naturally react by releasing the throttle which
>>will reduce the understeering.  This manoeuvre does not need driving skills
>and can be done by any driver.
>
>Thanks for the vote of confidence.  Care to comment as we lower cf?
>Ok, from the U-O-U we have above the possibility of a) which is U, OR
>
>>b) The rear axle slip ratio increases causing vehicle oversteering.
>>The centre differential will react by biasing the surplus torque to the front
>>axle, thereby correcting the oversteering (Figure 12).
>
>...  the possibility of b) which is O then U
>
>>In this situation the driver will require consistent assistance from the
>>centre differential because his instinctive reaction will be a throttle
release that
>>will worsen the initial oversteering instead of correcting it.  We know that
>>oversteering is extremely unstable.
>
>Mild understatement here.  What we have is U-O-U-O-U or U-O-U-U.  They say
>that the O is hard to control here, how bout 2 O's in the same turn.  Not sure
>the 3 U's in either scenario are any better, btdt.  Oversteering is extremely
>unstable, yup sure is, especially when you are Understeering the other times.
>And relative slip angle is also changing....

I agree with Scott.  I also find this very amusing ... the driver will
"require constant assistance from the centre differential" conveniently
overlooks the fact that more likely than not, it caused the problem in the
first place!  "I'm from the government and I'm here to help you," indeed...
  
This is also explains why the consensus seems to be that when faced with
this scenario, your best bet to get out alive (so to speak) is to put your
foot to the floor and drive over the inside apex ... lifting off will
encourage the car to rotate undesirably around its CG. (See?  I don't have
to use the "S" word, either!) 

>All in all, an interesting and very technical report.  Spin is a word that
>these authors did not want to use.  "Exceeding the load and slip limits" in
>the front of an audi, you go right off the outside of the turn.  "Exceeding
>the vertical load and increasing slip angles" at the rear, is a spin.  Both
>concepts kinda buried in verbiage.  But definitely addressed.  

Agreed ... if more technical papers were written this way, the makers of
Sominex (and other sleep aids) would quickly go out of business!

>This paper doesn't address how a Torsen can be fooled in a turn.  If it did,
>it might be more complete.  It might also directly conflict with the statement
>that the Torsen is:  "Anicipating loss of directional stability..." That's
>just not something the device can do consistently in a turn.

In a roundabout way, I think it does ... you just have to extrapolate it
from the information presented much the same way that you do with
Chocholek's paper.  There's enough talk about slip angles to make it clear
the paper's authors are aware of this (otherwise, why would they have
discussed how it behaves during understeer and oversteer conditions after
first claiming that it pro-actively prevents them from occurring?)

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   / |      _| o    | \       _| o  Jeffrey Goggin
  /__| | | / | | __ |  | | | / | |  audidudi@mindspring.com
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