RE: Torsen defined

["Dave Eaton" <Dave.Eaton@clear.net.nz>]

i think we're getting mired in semantics here....

if we go back to the graph i described in torsen tech 103 "if it would help
to illustrate, draw a graph with the y-axis the "torque bias ratio" from 1
to 3, and the x-axis "speed difference" between the torsen output shafts in
rad/sec from 0 to 3.  draw a line from {0,1} straight up to {0.5,3} and then
straight from there to {3,3}.  the part of the curve with the gradient is
where the torsen is locked. when the speed difference of the output shafts
reaches 0.5 rad/sec, the bias ratio is reached and thereafter stays here
while the speed difference increases.  this graph is from a model of a
specific torsen ("4wd powertrain models for real-time simulation", freeman,
1991)"

...then this describes the operation of the torsen as a function, based on
the relative speed difference of the shafts.  however, the shaft speed
differences occur solely because of relative slip front & rear.  which is
entirely a function of tractive forces.  i am using the term to encompass
the net result of longitudinal forces, lateral forces and slip.  any
differential technology only sees tractive forces.  without electronic
control loops, they cannot do anything else.

there is a lot of confusion on this point.  in fact, with 4wd vehicles, side
slip angles will actually increase during acceleration.  this is because
lateral forces decrease when more of the tires traction potential is used up
by longitudinal forces.  it's the friction circle thing.  you have 2
contradictory things happening here.  1) the lateral forces are increased by
the dynamic axle load changes (i.e. acceleration or cornering or both) but
working against this increase is 2) the decrease in lateral traction
potential due to the greater requirement for longitudinal forces.  hence the
side slip angles increase.

these factors are very clear when seen graphically: mapping longitudinal
acceleration against lateral acceleration taking different side slip angles
and wheel steering angles into account.  i'm happy to provide some graphs
that porsche have derived for 4wd vehicle behaviour if anyone is interested.

btw, your equation of what the torsen "sees" at the output shafts is wrong,
because it does not take account of the way the torsen operates at low
torque inputs (where the shafts are free to differentiate), and pre-bias
ratio torque levels, where the differential's internal friction minimises
output shaft speed differences, and after the bias ratio where the diff
allows output shaft speed differentiation. for this reason, it is much more
usual to describe the torsen in both frictional terms (@ the bias ratio) and
stictional terms (pre bias ratio) as this encompasses it's operation over
the full range of operating parameters.

before the bias ratio there is little or no output shaft speed difference,
and so no shaft can "spin up".  a shaft will only spin up when torque input
exceeds traction available, and then only after the differential is at the
bias ratio.  once the bias ratio is reached output shaft speeds are only
then allowed to differentiate.

however, this is the same behaviour as the locked differential.  once
traction is lost on one output shaft, torque will be transferred to the
output shaft with traction.  however, while the torsen will minimise
transferred torque to the bias ratio, the locker can't and won't.

dave
'95 rs2
'90 ur-q
'88 mb 2.3-16

-----Original Message-----

Date: Mon, 1 Nov 1999 11:49:36 -0800 (PST)
From: Orin Eman <orin@wolfenet.com>
Subject: Re: Torsen defined

> >3) neither the locker or the torsen have any knwoledge of slip angles.
they
> >proportion torque based solely on tractive differences between the front
and
> >rear axles (front/rear slip).  both allocate torque to the axle with the
> >most traction.
> NO.  A torsen is fooled into allocating torque based on a turning radius.
> The conclusion is *not* that the torsen is allocating torque to the axle
with
> the most traction.  It's only allocating torque to the axle with the
highest
> resistance to torque.  That *can be* based on either a traction or a slip
> angle variable.

...agreeing with Scott here, but adding some more.

Firstly, the claim that torque is proportioned solely on tractive
differences is false.  What the torsen sees at the output shafts is:

traction at wheel + I * dw/dt

where I is the moment of inertia of that shaft and everything it's
connected to and dw/dt is the angular acceleration of that shaft.
That I BTW, isn't insignificant.  It's what you are reducing by
putting lighter wheels/tires on a car.

Secondly, another input to the torsen is the relative movement
of the output shafts.  Frictional forces inside the torsen are
always such as to oppose such relative motion, meaning torque
is always transferred to the slower turning output shaft,
_regardless_ of traction available at that shaft.

This means that if a slower moving shaft loses traction,
then the I * dw/dt term becomes significant.  Ie, that shaft
spins up - until the shaft speeds are matched, at which point,
torque is transferred to the shaft with traction..

What Scott presents as slip angle differences translates directly
to shaft speed differences.   The torsen doesn't know why
the shafts are turning at different speeds, it just tries to
make them turn at the same speed.

Orin.

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