tor$en in a centre application - zexel paper

[Dave Eaton <dave.eaton@minedu.govt.nz>]

following is the text from the paper i recently acquired from zexel about the
tor$en and traction control systems.  i have posted the chapter of the paper
which deals with the tor$en as a centre diff, and this makes interesting
reading.  especially when put alongside the lack of implementation information
in the chocholek paper which jeff has posted.

i have the paper scanned now, and all diagrams and figures re-produced, and
will post it to those interested shortly.

dave
'95 rs2
'90 ur-q
---------------------------------------
1 TORQUE SENSING IN A CENTREBOX

A Torque Sensing differential fitted as centre differential of an ALL WHEEL
DRIVE vehicle distributes the torque to the front and the rear axles. 
Generally the basic distribution ratio is 50/50 front/rear in "normal"
operating mode (straight road, low to medium wheel torques).

The necessity for different torque distribution appears at medium to high wheel
torques as soon as unstable driving situations occur such as cornering, sudden
lane changes, split-u road conditions or transitory DRIVE/COAST torque
variations, causing increased tyre slip ratios.  The aim of the Torque Sensing
differential is to instantaneously distribute the torque to avoid increased
longitudinal slip ratios of one of the driving axles in order to ensure the
maximum potential of each axle's lateral stability.

A vehicle's dynamic stability and handling characteristics are determined by a
list of parameters, which could be divided in 4 main groups.
1. Vehicle dimensions & weight distribution
2. Vehicle elasto-kinematic suspension & steering characteristics
3. Tyre design characteristics
4. Torque distribution to the wheels

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.  The
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
instantaneous torque withstanding ability, thereby regulating the longitudinal
slip ratio characteristic.  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.

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 directional
stability.  This allows a particularly efficient and immediate corrective
action during transitory situations at the limit of lateral acceleration.  This
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.

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.

1.2 Low-Speed Cornering

This shows that, in cornering at low speed, the centre differential operates
following mode 1 (forward driving) and mode 3 (reverse driving), as the front
wheels rotate faster than the rear ones because of the larger path radius.  For
these modes, the differential's locking effect value (TBR) should be low enough
to avoid windup torque within the driveline causing excessive loading, unsmooth
operation inducing tyre slip noise, stick-slip vibrations, etc.

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 high
axle torque), the adverse consequence would be to let the front axle slip ratio
increase to high values.  This will cause increased understeering at the limit,
which is a situation that can be easily controlled.

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).

The driving situations in which the vehicle's dynamic stability becomes a
serious matter of concern are mode 2 (power oversteering) and mode 4 (drop
throttle oversteering).

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. 
>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.

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).

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.  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.

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 capability
to relieve the rear wheels from longitudinal driving forces, even for increased
side slip angles causing a very high traction potential difference between
front and rear axles.

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

1.4 DROP THROTTLE OVERSTEER

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

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.  In this case, the
centre differential has to bias the necessary amount of surplus braking torque
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 from
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.

1.5 CONCLUSIONS

The ideal centre differential TBR layout in the 4 operating modes is a function
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. 
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).