Torsens and slip angle ... final approach

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

Since this post seemed to get through to Dave -- presumably, if he can be
convinced, then everybody else will soon follow! -- I'm going back on my
word from yesterday and reposting it here...

* * * * * * * * * * * * * * * 

>i am saying that the torsen doesn't *care* about slip angles because, in the
>vast majority of cases, they make *no* difference to the coefficient of
>friction delivered by the tyre to the driveshaft.  reference carrrol smith.

Again, you are missing the point entirely, Dave ... Frankly, I don't know
how _I_ can make things any clearer or simpler for you.  Although trying has
left me exasperated, I'll give it one more shot, for old times sake.

The Torsen is a intended to be a compromise between an open diff and a
locked center diff ... for most people and under most circumstances, it
provides (most of) the benefits of both without the drawbacks of either.  It
works remarkably well for what it is and for most people, its theoretical
shortcomings remain theoretical.  I dare say you appear to fall into this
category...  ;^)

That said, how did an open diff differ from a locked center diff when you
drove your old Ur-Q around in tight circles?  With the locked diff, your car
protested mightly, didn't it?  But with open or unlocked diff, there was no
problem.  Why was that?  It was because the front and rear wheels were
tracing different paths and the tighter you made the circles, the bigger the
difference in path length there was between them.  Why does this have
anything to with a Torsen and slip angles?  Read on...     

An open center diff has no problem allowing the front and rear driveshafts
to rotate at different speeds and thus accomodates differences in path
length between the front and rear wheels without binding up or dragging any
tire(s) across the road surface.  It is also the least succesful in
maximizing grip.

On the other hand, a locked center diff forces both the front and rear
driveshafts to rotate together.  They have no way to speed up/slow down
relative to each other in order to accomodate the different path length of
the front and rear wheels, and one (or more) tires ends up being
scrubbed/dragged along the surface instead.  This is much worse (and much
more noticeable) than the Torsen's juddering because there is _no_
accomodation for a speed difference in the rotation of the two driveshafts.
It is also the most successful in maximizing grip but the tradeoff for this
is an increase in the amount of understeer.

Like the open diff, a Torsen does indeed differentiate but only up to a
point ... when torque is applied, it starts to bind up as its internal gears
jam.  Eventually, as it reaches its bias-ratio limit, the gears bind solid
(or very nearly so, depending upon the bias ratio) and it effectively ceases
to differentiate.  At the point this happens, it can no longer accomodate
any difference in speed between the two driveshafts and will begin to take
on the characteristics of a locked diff, which includes scrubbing the inside
rear wheel across the pavement surface.  Remove the torque input, however,
and the internal gears release and it behaves again very much like an open
diff.  Depending upon the circumstances, it can be either very good at
maximizing the amount of grip (acceleration in a straight line) or very poor
(braking in a curve); it also allows ABS to be used in most situations (but
not all: See what happens when you left-foot brake while your right foot's
flat against the floor) and because it acts very much like an open diff in
the absence of a torque input, it will allow the car to turn-in at least as
well as an open-diff (and sometimes better but I'm not going to go into that
here).

I assume you agree that in order for a car to turn, the front and rear
wheels must develop slip angles.  The front slip angle must also be larger
than the rear slip angle in order for the car to initiate a turn ... it
stands to reason then that the front wheels are also tracing a longer path
than rear wheels.  The slip angle difference between the front and rear
wheels causes a path-length difference between the wheels and this, in turn,
causes a difference in the rotational speed of the front and rear
driveshafts.  The Torsen doesn't know whether this difference in rotational
speed is caused by a difference in the amount of grip available at one end
of the car or the other or because the two ends of the car are driving along
different paths.  Being dumb, it can only determine that the two driveshafts
are rotating at different speeds and reallocates torque between them in an
effort to equalize this.

The net effect is that as the car begins to turn, the rear driveshaft starts
to rotate slower and the Torsen automatically starts to transfer torque
toward the rear wheels.  The tighter the turn, the larger percentage that
gets transferred ... in very tight turns, this can reach the bias-ratio
limit.  Granted, if there is no torque input of consequence (i.e., the car's
just coasting into the turn), the actual amount of torque might not be large
enough to change the handling balance of the car.  However, it IS usually
large enough to cause some mild "juddering" to be felt as the inside rear
tire is just lightly dragged across the road surface.

Note that none of the above has anything to do with grip/traction or the cf
of either the tires or the road.  It happens automatically, in every turn,
in either direction.  Once you understand this, you're well on your way to
understanding how a Torsen can be "fooled" into mis-allocating torque;
however, unless you're able to understand this, you'll never get it.

For now, don't complicate matters by assuming oversteering entrances to
corners, lifting of wheels, etc. ... once you've got a firm grasp of the
above concept, you'll quickly see how other pieces of the puzzle fall in
place and which ones are still missing.  There is definitely a place for
chassis dynamics but it can't alter the basic concept outlined above, only
ameloriate its effects.

As you know by now, I'm not the best writer in the world and if this still
doesn't make sense to you, take a model car with steerable front wheels,
coat them with powdered graphite, and "drive" it around in circles on some
white paper.  Then measure the path lengths of the front and rear wheels for
yourself...

Also, don't get too hung up on Carroll Smith's books ... wonderful as they
are (and they are!), they are not written with an AWD car in mind (or even
sedans, for that matter) and frequently you must extrapolate and/or
interpolate his comments to make them relevant for our purposes.  BTDT for
the past twenty years...

I'm cc'ing Scott J. a copy of this post so he is familiar with what I've
written and I'm sure he will answer any questions you may have about it ...
if you still don't understand, well, like I said, I've tried my best and
it's time for somebody else to take a crack at it.  No hard feelings
intended even if I was a bit snippy this morning...   :^)
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   / |      _| o    | \       _| o  Jeffrey Goggin
  /__| | | / | | __ |  | | | / | |  audidudi@mindspring.com
 /   | |_| \_| |    |_/  |_| \_| |  http://www.mindspring.com/~audidudi/
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