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Zexel Paper - My thoughts

I had several opportunities to read the Zexel paper in depth over the past
couple days, and like Jeff, I don't see any 'new' ideas here, nor
'conflicting' information to Stan the torsen man's paper or his discussion of
the device with Jeff.  What I do see, is the funniest verbiage for simple
concepts.  I also think it to be somewhat incomplete, since it doesn't address
the main 'fooling' issue with the torsen, which is relative slip angle.  The
claim that the "driver will naturally react" to a torsen seems like somewhat
of an oxymoronic statement to me, but hey let's look at this in some detail:

>Today's vehicle designs optimise handling & dynamic stability in order to
>continuously improve active safety characteristics.
>As far as Torque Sensing differentials are concerned, the target is to
>efficiently control parameter "4", the Torque distribution to the wheels.
>fundamental idea is to take advantage of the vehicle's intrinsic dynamic
>behaviour parameters and their variations, which dictate its stability.  The
>Torque Sensing centre differential passively reacts to the wheel's
i>nstantaneous torque withstanding ability, thereby regulating the
>slip ratio characteristic.  

How 'bout:  "The basics is to allow maximum traction to all wheels for maximum

>This last parameter is fundamental for the wheel's
>lateral stability, as a wheel exceeding it's saturation level in terms of
>longitudinal forces (directly proportional to applied torque) will suddenly
>lose it's capability for lateral hold, with the subsequent loss of lateral
>stability leading to vehicle loss of control.

Above is one that I'll remember the next time I want to say SPIN

>This centre differential's passive basic characteristic actually turns out to
>be an active dynamic characteristic, as the parameters dictating its dynamic
>torque distribution are actually anticipating the vehicle's loss of
>stability.  This allows a particularly efficient and immediate corrective
>action during transitory situations at the limit of lateral acceleration.
>proactive operating mode does actually prevent an eventual loss of stability
>instead of correcting it after it's occurrence, as electronic systems with
>accelerometers and yaw rate sensors do.

BIG problem with the above, is that 'anticipating' relative slip angle is OUT
of the ability of the device, it can be fooled.  So I might take exception
with the "particularly efficient and immediate corrective action" part, since
the anticipated event, by definition really isn't happening.

>An interaxle centre differential operates in the following 4 basic modes
>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
>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

>Vehicle stability is not a prioritary argument for operating in modes 1 and 3
>however.  In case of too low a locking effect value in mode 1 (DRIVE, rear
>axle torque), the adverse consequence would be to let the front axle slip
>increase to high values.  This will cause increased understeering at the
>which is a situation that can be easily controlled.

...  Unless the fronts have reached their "saturation limit", in which case
you understeer right off the road...  Not so "easily controlled".
Not sure I'm with the boys on this, if an audi has power up oversteer, mode 1
is a big problem, cuz here we started the turn at o power U, power up O, now
they claim U.  "Easily controlled"????  Given a low powered audi on a high cf
surface, maybe....

>In case of too low a locking effect in mode 3 (DRIVE: reverse driving or
>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.

>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
>turns faster than the rear axle).
>When more input torque is added, vehicle speed rises, the rear axle slip
>increases (elastic conditions catch up the kinematic conditions) until the
>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...

>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
>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
>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....

>  Indeed, the rear axle's side slip angle
>rapidly increases (see Figure 13), reducing it's potential to withstand the
>driving torque and allowing increased longitudinal slip, resulting in a rapid
>drop off in lateral adhesion capability at the rear.

Hey let's just say SPIN next time boys.

>The front axle's side slip angle will normally not increase, as steering
>correction always tends to keep the front wheels in the correct trajectory. 
>Therefore the centre differential must ensure enough torque biasing
>to relieve the rear wheels from longitudinal driving forces, even for
>side slip angles causing a very high traction potential difference between
>front and rear axles.

Front slip angle "normally not increase"?  Steering correction at or near the
limit of adhesion sounds like an oxymoron to me.

>However, in a DRIVE (power ON) manoeuvre the dynamic weight shift to the rear
>helps the rear axle to keep it's traction potential, unlike in a COAST
>manoeuvre (power OFF) for which the dynamic weight shift to the front worsens
>the rear axle's traction potential by reducing the vertical load.

There's that SPIN word again

>  Therefore,
>the centre differential's locking effect value must be higher in coast than
>drive mode.

So keep your foot in it, is the suggestion.  The problem is that doing that
can cause torque to be sent to the front axle as soon as the rear axle speed
reaches the front on power up oversteer.  So you get U one way or the other.
Higher locking effect value in coast mode than in drive mode just makes
lifting a worse understeer problem.  

>The most critical situation for vehicle stability during cornering is the
>mode (power OFF), as this generally corresponds to a "panic" manoeuvre
>corner entry speed too high, or sudden decrease of curve radius).  In
>the dynamic weight shift further decreases the rear axle's vertical loads,
>reducing its potential adhesion capability.

Let's assign SPIN the F1 key, might make things easier.:)

>Furthermore, the sudden variation from positive torque (DRIVE) to negative
torque >(COAST) causes a critical transitory phase, as
>it generates a variation of several dynamic parameters.  I

Mild understatement again, btdt.  

>n this case, the
>centre differential has to bias the necessary amount of surplus braking
>to the front axle in order to relieve the rear axle in terms of torque.
>As vehicle oversteering starts, the rear axle's side-slip angle increases,
>reducing the longitudinal and subsequently the lateral grip capability (See
>Figure 14).  The centre differential has to further remove braking torque
>the rear axle and bias it to the front axle to ensure the rear axle's lateral
>stability.  The necessary TBR (Torque Bias Ratio) of the centre differential
>can reach high values, as the ratio between front and rear torque raises
>rapidly in this particular case where rear torque has to decrease while front
>torque has to increase.

The biggest problem here is that we are talking about going from maximum Trg
rear to minimum Trg rear.  According to this paper that is O going to U.  All
from just lifting the foot.  While at the limit of adhesion, that certainly
could give you an 'F1' as the unloading of the rear and the loading of the
front, combined with the torsen "braking of the faster axle" can easily exceed
the available traction at the front tires.  

>The ideal centre differential TBR layout in the 4 operating modes is a
>of vehicle dimensions (wheel base, track width, centre of gravity height,
>etc.), suspension elasto-kinematic design (stiffness front/rear, angular
>variations, etc) and engine torque characteristics for given road conditions.

So engine torque and center torsen could be good for dry cement pavement cf,
and not for anything less.  Given road conditions is a HUGE variable.

>Therefore the ideal design characteristics for a centre differential can be
>determined after a great deal of subjective vehicle tests.  The optimisation
>will be a compromise between different set-ups, depending on the surface
>conditions (dry asphalt, wet asphalt, snow, ice, etc).

And given that every chassis optimisation between the v8 and the 20vUrq are
different (but the torsen the same), audi sure did compromise some.  And we
haven't even addressed the surface conditions (cf).  When we do decrease cf,
we can see that ALL the 1-4 modes become more significant to chassis dynamics
while turning.

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.  

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.

Great F1 definitions tho :)

Scott Justusson