Hi all,

Not sure if RAS is stilled filled with car sim creators as back in the
day. ;-)

I'm currently revising my differential code (in Racer) and trying to get
Salisbury diffs to work as a variation on LSD's (limited slip diffs).

For an LSD, I define:
- power_ratio; torque bias ratio for power-on
- coast_ratio; same for coasting (letting go off the throttle)
- preload; base spring-loaded torque

GPL defines diffs as 60/30/2 for example (power/coast/clutches).
From back in the day Niels Heusinkveld explained that:
- ratio=cos(angle)*(1+clutches).

So for example, cos(60)*(1+2) = 0.5*(1+2) = 1.5. So for the above diff
you get 1.5 torque bias ratio. Anything inbetween that keeps the diff
locked.

But for preload; how does GPL do that? Without some preload, the diff
would become a bit unstable, esp when one wheel is on the grass. Surely
all the clutches result in some preload torque. But how much friction
torque exactly?

Thanks for any ideas,
Ruud

A Salisbury is just an LSD that can have separate coast and power
locking, if I'm not mistaken. No difference in the math there.
You're probably already doing a Salisbury without knowing it.

As for the torque bias ratio with power/coast/clutches: I'd think
there'd be a friction coefficient in there too, but maybe in GPL Dave
just put it at 1. I don't know if there was any preload in the GPL
model. From what I can remember from driving it (it's been years and
years since the last time, mind you) there didn't seem to be any, or
at least very little. I'm not entirely sure quite frankly whether
changing the number of clutches changes the preload. From page 742 of
the great Milliken's "Race Car Vehicle Dynamics", the triangular
regions are controlled by number of clutches (and their friction
coefficient I'd think) and ramp angle, while the preload area is a
pretension torque that has to be overcome separately from this and is
controlled by the springs or a washer or whatever. Increasing the
number of clutches might increase the preload, but I'm not so sure
about that.

Here's a nice way out of that conundrum for you that I'd use: What
the engineer really wants in the end is to specify the preload
*torque* at the wheels rather than the preload spring force. That's
the important part for handling (anyone know what the spring rate of
the belleville washer or whatever is providing the preload is?). You
adjust the preload spring force to whatever gets you the desired
preload torque. So if you have preload torque as the input instead of
preload spring force, you bypass this problem entirely by keeping them
seperate. If you add a clutch and want 50NM preload torque before and
after the change, then you can just keep them separate. You might
assume somebody goes in and adjusts the preload spring a bit to
maintain that torque if indeed it changes. If I change the diff's
torque bias ratio, I want to make sure I'm not changing the preload
too without intending to.

Let me expand on this just a bit. To start out with, let's define
"preload torque" as the amount of torque required across an axle
(inputs from the wheels) to allow differential action to occur, which
is to allow the axle to go from locked to slipping. I.e., the old
adage about jacking up the car, grabbing hold of one wheel so it can't
rotate, then twisting the other wheel with a torque wrench to the
point where finally starts rotating. The torque that this occurs at
is the "preload torque" as used here.

"Preload spring force" or "preload force" or "spring force" here
refers to the force at the preload spring itself.

So references to "torque" refer to the torque across the axle, while
"force" references force at the actual "preload spring" which is just
a spring like any other. Ultimately in reality the preload spring's
force controls the torque. Ok, moving right along:

What folks have been doing (myself included) that have figured out non-
viscous diff modelling at all is to specify preload torque in the
setup screens directly, and understandably so. It makes sense from
the engineer's perspective because this is something that you want to
adjust separately from the torque bias ratio. Same goes in reality.
So if you go with this approach, don't model any change in preload
torque unless you change the preload torque directly. Not the number
of clutches, not ramp angle, nothing. You set preload torque directly
like described earlier. However, you could try something else:

Another way to go (you'd almost certainly be the first to do it in a
sim which might be appealing to you and win you even more points with
your Racer fans that go back almost as far as you and I do :-P )
would be to allow for the possibility that changing the number of
clutches does actually change the preload torque. However, if you do
this, then you need to specify preload differently. You aren't
setting the preload torque directly anymore.

Think suspension preload here for a minute as being analogous. On the
"far" side of the spring you have a fixed spot in space that comes
from how long the space between the spring stops at either end are.
On the other ("near") end you have the same thing, but it's adjustable
with a screw or something equivalent to a shock collar or what have
you. You have a spring rate that doesn't change. Whatever spring
compression you get out of that gives the preload spring force which
would change the preload spring torque.

Here's where the clutch pack number might (emphasis on "might," I'm
guessing here) have an effect on "preload" as you'd specify in this
new user input replacing the old "preload torque" could come in: That
distance between the 'shock collar' of the diff's preload setting and
the "far" side of the spring might get eaten up a little bit by that
extra clutch pack. This is what I suspect from looking at a cutaway
diagram of a Trac Loc LSD at least. I could be wrong, but if it
indeed does, then this would compress the preload spring a bit and
indeed change the preload force (and therefore preload torque).

So, with your whizbang new diff preload model that nobody's ever done
in a sim before, you could specify "preload" by letting people select
different length or rate springs, different washers of varying (but
not infinitely adjustable) "lengths" to eat up some of that space
between your "near" and "far" end points, while at the same time
displaying "preload torque" traditionally. Only in Racer now the
preload torque is not adjustable directly like it is everywhere else.
Now it's like showing the real downforce in Newtons or something
that's there for display so you know what you've got, but is really
controlled and adjusted in the setup screens by changing the wing
angle or ride height or whatever. This might be more realistic and
interesting for the die-hard gearheads that love to tinker with every
screw and bolt on the car you give them. If you change the number of
clutches you'll see the "preload torque" change in the display, but
are free to tune that back to how you had it before you changed the
number of clutches, which is sort of assumed to just happen by magic
in other sims if the number of clutches actually does any of this
stuff :-P

So for the not so mechanically interested player who is aware of
"preload torque" effects on handling, this doesn't complicate things
too much because they could still see the "preload torque" and adjust
things to get it close to how they want pretty easily just fiddling
with the adjustments, but adds some depth to the diff model which now
could let them choose from a slew of springs with various combinations
of rates and spring lengths, number and thickness of washers in some
diffs, and "preload length" in others. Perhaps the "preload length"
here might be adjusted on some diffs by turning a screw/collar. You
could specify the number of turns of the collar and multiply by the
pitch of the screw thread and use that.

I don't know if "put five more turns in the diff" is something you'd
ever hear at a track, but if it is, you could model it this way.

Anyway, just throwing an idea out there to help get you thinking if
you want to try something new in this area. If not, just set "preload
torque" directly and be done with it. Don't let changing the number
of clutches alter the preload torque at all.

Thanks for the elaborate reply (as always, most enlightening ).

....
That's how Racer (v0.8.6) does it now indeed for LSD's.

In Racer you can specify the type of diff; for an LSD, you directly
specify power_ratio, coast_ratio and preload (a torque in Nm).
For the Salisbury, internally I just use an LSD. I derive the ratios
from the ramp angles. I was just wondering how preload could be
calculated in a GPL kind of way. But atm, Racer can handle:

; Salisbury
diff
{
ratio=4.2
type=2
power_angle=60
coast_angle=30
clutches=2
clutch_factor=1.0
}

or

; LSD
diff
{
ratio=4.2
type=3
preload=500
power_ratio=1.5
coast_ratio=1.5
}

So the Salisbury diff is just turned into an LSD internally, but
tweaking it is just like in GPL.

I'll stick with adding an explicit preload in Racer v0.8.7 for the
Salisbury diff. That just seems a bit more flexible and still leaves
room for preload=0 (perhaps) GPL diffs.

Cheers,
Ruud