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Link to a very good torsen description

This link is to what I think is a very good torsen description
Title: Differentials

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Hello all,

With the recent discussion on differential swaps, I tried to write a
description of how they work.

I wish I could include pictures for the following descriptions.  I'll
try my best to describe things with words.  It might help to find some
pictures to look at, or even better, some units to actually hold in your
hands and play around with.


A conventional differential consists of a housing that is directly
attached to the ring gear.  On the same axis as the differential housing
are two output shafts.  These pass through to the inside of the housing,
but are not directly connect to the housing.  Inside the housing
attached to each output shaft  is a 45 degree angle bevel gear (referred
to as output gears).  Placed between the two output gears are some more
45 degree bevel gears called spider gears.  The spider gears pivot on
rods that are attached to the housing (these rods are oriented radially
to the housing axis).

When the housing is stationary, rotation of one output gear causes the
other output gear to turn in the opposite direction.

When a car is driving in a straight line, and the wheels aren't
slipping, both output gears are turning at the same speed, because they
are coupled together through the ground.  The entire differential
assembly is spinning together as an assembly, but internally, there is
no movement of the gears with respect to each other.

When the car goes around a corner, the outer wheel has to spin faster.
The differential will be spinning at a speed that is halfway between the
speed of the inner wheel and the outer wheel.  Internally, the gears are
moving a speed that is the difference of the outer wheel speed minus the
inner wheel speed.  With respect to the housing, the inner wheel output
gear is actually spinning backwards, and the outer wheel output gear is
spinning forwards.

All of this works great as long as neither of the driven wheels exceeds
it's traction ability.  Force can be distributed to both wheels while
any difference in cornering speed is compensated for.  The main thing is
that this design is dependent on the two outputs being coupled together
through the ground.

When one wheel exceeds its traction, there is no reaction force to
enable power to be sent to the other wheel, so the system loses its
ability to function.

Note that if one wheel is stationary and the other spinning, the
spinning wheel will actually be turning at *twice* the speed that is
indicated by the speedometer.

Most limited slip differential designs work by attempting to detect
slippage and reacting (I'll refer to these as Reactive LSD's).  Some
other designs rely on directional force transmission characteristics, so
that power to the wheel with good traction isn't dependent on a reaction
force from the wheel with bad traction (I'll refer to these as
Directional LSD's).

All reactive mechanical designs face a fundamental issue:  they can't
tell the difference between one wheel going faster due to a corner, or
due to slippage.  This means that some type of compromise must be made
in how it is adjusted.  Setting the adjustment for very little slip
(lots of lock-up) helps maximize the amount of power that is transferred
to the ground, but will cause problems going around corners because it
won't allow enough of a difference between the inner and outer wheel.
Adjusting to allow more slip (less lock-up) helps cornering, but reduces
the LSD's effectiveness at increasing traction.

Typically, LSD's in production street cars are adjusted to have
somewhere between 25% to 40% lock-up.  70% lock-up is right on the edge
of where cornering issues start to become a problem.

Other considerations with Reactive LSD's are response time, and
smoothness of the reaction.

This is the type of LSD that BMW uses.  It falls under the reactive
category.  The general construction is the same as a conventional
differential with some added features.

The output gears are connected to the output shafts by splines so they
can slide.  Each output gear has a spring (coil type or spring washer)
that pushes it into engagement with the spider gears.  A characteristic
of bevel gears is that they try to push each other out of engagement.
This characteristic results in an axial thrust force that pushes the
output gear against its spring.  The amount of this thrust force is
proportional to the difference in the force being transmitted to the two
wheels.  When both wheels are spinning at the same speed, this thrust
force is zero.

Between the output gear and the differential housing are one or more
plate clutch disks. The thrust force of the output gear squeezes the
gear against the clutch disks and the housing.  This causes a coupling
between the output gear and the housing which overrides the spider

Because this design uses sliding friction as part of its operation, it
will wear with use.  It requires the use of a friction modifier in the
differential lubricant.  It can also generate a significant amount of
heat under heavy use (note that BMW adds a differential oil cooler to
the M roadster).

This design can be adjusted by changing the spring strength, number of
clutch disks, size of clutch disks, and to a small extent, the amount of
friction modifier in the gear oil.

Similar in concept to the plate clutch design.  The main difference is
that cones are used instead of disks.

Also called a Viscous LSD.  BMW used this design in the 325iX.  It also
can be classified as a reactive design based around a conventional

This design adds a viscous coupling between the two output gears.

The viscous coupling utilizes a characteristic of silicone fluid. When
silicone fluid is between two closely spaced moving surfaces, it acts as
a lubricant at slow speeds.  When the speed of the two surfaces
increases to a certain point, the fluid develops a shear force that
couples the two surfaces together.  The crossover between these two
conditions happens very rapidly.

The coupler has one side connected to a can and the other side connected
to a shaft that is inside the can.  There are a series of disk mounted
on the shaft. Between each of these disks are disks that are attached to
the can at their outer edge.  All of the disks have a bunch of holes
drilled in them.  The entire assembly is immersed in silicone fluid.

Under normal conditions, the can and the shaft are free to rotate
independently.  The silicone fluid allows the closely spaced disks to
slide next to each other.  When the speed difference between the can and
the shaft reaches a certain point, they are coupled together when the
shear action of the interleaved plates causes a transition in the fluid.

The Ferguson design is adjusted by the total surface area of the plates,
the spacing of the plates, and the formulation of the silicone fluid.

An important distinction between the way a Ferguson and clutch plate
unit behave is that the Ferguson reacts to differences in *speed*, while
the clutch plate unit reacts to differences in *torque* transmitted.

An advantage to the Ferguson is that it can be adjusted for up to 90%
lock-up without losing the ability to go around corners.

There are several disadvantages to the Ferguson:
A slipping wheel has to spin a bit before a reaction occurs.
When the reaction does occur, it's fairly abrupt.
Because it's speed reactive, it can cause problems with braking because
a locked up wheel's force will be transferred to the wheel that didn't
lock.  This is a non-issue with a torque reactive differential because
there is no torque being transmitted through the differential due to the
brakes.  For this reason, the Ferguson design is more popular to use for
the center differential in four wheel drive vehicles.


Unlike the Reactive LSD's, Directional LSD's aren't based on the
conventional differential.  They use various means to directly couple
the force applied to the differential to each output.  These designs
distinguish between the different directions that forces are applied.

When power is being transferred from the engine to the wheels, the
direction of the power transfer is from the differential housing to each
output shaft.  When going around a corner, the difference in wheel
speeds applies a force from one output shaft to the other output shaft.

No sane person would put one of these on a ti.  But it's useful to
briefly discuss it to illustrate a principle.

Loosely described, the differential housing is connected to each output
shaft by a ratchet.

When the vehicle is traveling in a straight line, applied power is
transferred from the differential housing to each output by locking both
ratchets.  If one wheel looses traction the other one doesn't care,
because it's still directly connected.  100% lock-up.

When the vehicle goes around a corner, the outer wheel needs to spin
faster.  The *direction* of the force that causes the outer wheel to
spin faster is from the ground, through the wheel, and *into* the output
shaft of the differential.  This causes the output shaft for the outer
wheel to spin faster than the housing, it's ratchet just starts clicking
away (these things are pretty noisy).  The inner wheel is then left with
the burden of handling all of the applied power (this makes for some
strange handling traits).

The actual design is a little more complicated.  (Simple ratchets like I
described wouldn't allow any power to be applied in reverse).  The main
use for this design is for drag cars that want to have maximum traction
in a straight line, with the ability to drive around corners just to
transport the car, or for off-road vehicles that often lift one wheel
off of the ground.


TORSEN is a concatenation of 'Torque Sensing'.

This design uses a characteristic of worm and ring gears.  A worm gear
is usually a long thin helical gear that mates with the edge of a large
diameter ring gear.  When the worm gear is turned, it causes the ring
gear to rotate.  Tried the other way: attempting to turn the ring gear
directly will just cause everything to lock solid.  Motion is allowed in
one direction only.  This is partly due to the typical high gear ratio
involved with a conventional worm and ring gear pair, but a major factor
is the interaction of the shape of the gear teeth.

The actual gears inside the torsen don't have the appearance of
conventional worm and ring gears, but they still are classified as worms
and rings.  In this case, the worm gears are significantly larger in
diameter than the ring gears.

Each output shaft passes into the differential housing, where it is
driven by an output gear.  This output gear is a worm.

The differential housing has several pairs (3-5) of ring gears (they
don't actually look like rings) that are mounted in cutouts in the
housing.  Each pair of ring gears are connected to each other by
conventional gears that act as synchronizers.  One ring gear of the pair
meshes with the right output worm gear.  The other ring gear of the pair
meshes with the left output worm gear.  The reason several pairs (3-5)
of ring gears are used is to increase load capacity.

When the differential housing rotates, the ring gears are rotated around
the output worm gears.  Thus, force is being applied from a ring gear to
a worm gear.  As described above, no relative motion can occur between
these two gears because they lock up solid.  This means that full force
is being applied from the differential housing to the output shaft.
This occurs regardless of whether or not the other output shaft has any
load (traction).

When the car goes around a corner and one wheel needs to go faster, the
force from the faster outer wheel goes *into* the differential through
the output gear.  Now we have a situation where a force is being applied
from a worm gear to a ring gear.  Relative motion between these two
gears is allowed when the force is in this direction.

To summarize the two main characteristics in a different way:
Forces between the housing and an output shaft (engine power to a wheel)
are directly coupled.
Forces between two output shafts (differences in speed between the two
wheels) allow the internal gears to rotate.

The real beauty of this design is that these two characteristics are
autonomous.  Both things can be happening at the same time.  Full power
can be applied while going around a corner.  The wheels are allowed to
turn at independent speeds.  Full torque can be applied to a wheel even
if the other has lost traction. (Up to the equivalent of about 80% lock
up).  Changes in the situation are automatically adjusted for instantly
by the inherent nature of the design.  Everything operates in a precise

There is no need to choose a trade off between maximum traction, and the
ability to go around corners.

It's also important to note that while this design relies on the
friction characteristics of the gear teeth to control its behavior, it
*doesn't* use friction to transfer power (like a Clutch Plate LSD).
This design doesn't have any more wear than a conventional differential.

The Torsen is probably one of the most elegant mechanical designs in
automotive history.

Unfortunately, I'm not aware of any source of Torsen's to fit BMW's.

Fortunately there is the...


The basic principle of the Quaife is similar to the Torsen.  The actual
implementation looks quite different.

There are pairs of helical gears riding in cutouts in the housing.  One
gear of the pair drives the right output gear, the other gear of the
pair drives the left output gear.  The output gears are also a type of
helical design.  While not technically classified as worm and ring
gears, the tooth faces are cut at angles that exhibit similar
behaviors.  One other difference from the Torsen design is that there
are springs that add supplimentary forces to adjust the frictional
loading of the gear teeth.

The description of the behavior of the Quaife is the same as the Torsen.

There is debate as to whether the Torsen or the Quaife is a better
design.  Supposedly the Torsen can achieve a higher ratio of torque
bias, while the Quaife has even smoother operation.  In my opinion, both
designs are ABSOLUTELY OUTSTANDING.  I haven't been able to compare the
two directly in the same type of car.

This is a moot issue anyway since it appears that the Quaife design is
the only one available for BMW's.


Up to this point, I've been discussing just the actual differential.  In
the ti, there is an entire differential assembly that contains not only
the differential, but also the ring and pinion gears, the input and
output flanges, and the assembly housing.

The ring and pinion gears perform a gearing reduction from the
driveshaft to the wheels.  Sometimes it is desirable to change the gear
ratio.  The general topic of gearing needs to be treated separately, but
I'll offer a brief summary of my opinions:

The stock ti with a five speed has a final drive ratio of 3.45:1.
A car modified with forced induction should keep this ratio.
A car modified with a six cylinder should keep this ratio (maybe,
depending on other factors).
A stock or slightly modified engine would have an acceleration benefit
from a ratio around 3.90:1.
A highly modified, higher RPM four cylinder would benefit from a ratio
around 4.10:1.

The point is, potential engine mods should be considered before deciding
to change the rear end ratio.

I'm still hopeful that the ASC + T can be reprogrammed to offer improved
performance.  It's possible that this could be good enough to make me
skip doing a differential transplant (maybe).

The factory type Clutch Plate LSD differential can be a real good choice
particularly because there's a bunch of good, relatively economical used
ones available.  For a little bit of money, the lock-up can be increased
(I like somewhere between 50% and 60% for spirited street driving).
This unit works well alone, or in conjunction with ASC + T.

The Quaife LSD is the most desirable choice (I really, really want one
for my ti).  I've had one before in a Scirocco, and it was simply
fantastic :).  There were many benefits, and no downsides at all.
Because it's reaction is so smooth and balanced, it should be
complimentary with the ASC +T.  Ok, there is one downside, it's quite
expensive :( .  I haven't priced it yet, but I'm sure it's well over a
thousand dollars, which doesn't include the cost of installing it into
the differential assembly.  (I still really, really want one).

One last thing to note, is that an LSD will increase throttle induced
oversteer.  Something else to be considered when thinking about
suspension tuning.

I hope this is helpful to understanding these things.  I realize that
the descriptions got really wordy at times.  I would again suggest
finding some units to look at while re-reading the descriptions to help
understand things.

Brian Brown.
BMWCCA #130878
'96 318tiS


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