Developing a Proper Suspension Model

[Thorpedo]

Yeah... I would toss in a couple dollars for an accurate camber curve.

[Shankenstein]

Found a cool bit of code that might be useful for this crowd.

It's a MATLAB code that simulates shock dyno graphs.

Here's a cheat guide for our front suspension:
cwlbs = 618; srppi = 131; spmr = .92; shmr = .92; lsd = .65; knee = 3; hsd = .1;

And the rear suspension:
cwlbs = 539; srppi = 211; spmr = .83; shmr = .83; lsd = .65; knee = 3; hsd = .1;

TL;DR - calculate wheel rate, calculate the critical damping force, build a set of low speed damping forces, build a set of high speed damping forces, graph everything.

function y=critdamp(cwlbs,srppi,spmr,shmr,lsd,knee,hsd)
%cwlbs=corner weight, lbs minus unsprung for more accuracy
%srppi=spring rate, lbs per inch
%spmr=spring motion ratio
%shmr=shock motion ratio
%lsd=low speed damping, percentage of critical
%hsd=high speed damping, percentage of critical
%knee=location of knee, in inch per second

lbf2n=4.448; % 1 lbf = 4.448 newtons
m2i=39.37; % 1 meter = 39.37 inch
p2kg=0.4536; % 1 lb=0.453 kg
if (spmr>1)+(shmr>1)
disp('Motion ratios must be less than 1, but I''ll convert it for you')
spmr=1/spmr;shmr=1/shmr;
end
wheelratestandard=srppi*spmr^2
wheelratemetric=wheelratestandard*lbf2n*m2i
cd=2*sqrt(wheelratemetric*cwlbs*p2kg)/lbf2n/m2i/shmr^2
vel=(0:0.1:20);

damp=lsd*cd*(0:0.1:knee);
hispeed=damp(end)+(0:0.1:20-knee)*cd*hsd;
damp=[damp hispeed(2:end)];
plot(vel,damp,'r','linewidth',2,'displayname',['LS:' num2str(lsd*100) '% Knee:' num2str(knee) ' ips HS:' num2str(hsd*100) '%'])
legend('off');legend('show','location','east')

[redlined600]

Originally Posted by Shankenstein

If anyone has those curves, it would be a huge service to the community for choosing the "optimal ride height." I use quotes because you can always set the static values of camber and toe... but if it changes quickly under the normal weight transfers of racing, we might have to tweak the geometry.

If no one does it by the time I pull my car out of storage in spring I will likely do it. I did it on my Miata, it's not hard, just takes time.

[Shankenstein]

Just as a quick exercise, I wanted to see what spring rates would yield different natural frequencies.

Ks = 4*pi^2*f_natural^2*m_sprung*motion_ratio^2
note: OptimumG uses motion ratio of wheel/spring (>1)

Here's what I found (fronts and rears in kg/mm).
1.5 Hz = 3.000 / 3.213
1.6 Hz = 3.413 / 3.656
1.7 Hz = 3.853 / 4.127
1.8 Hz = 4.319 / 4.627
1.9 Hz = 4.813 / 5.156
2.0 Hz = 5.332 / 5.713
2.1 Hz = 5.879 / 6.298
2.2 Hz = 6.452 / 6.912
2.3 Hz = 7.052 / 7.555
2.4 Hz = 7.679 / 8.226
2.5 Hz = 8.332 / 8.926
2.6 Hz = 9.012 / 9.655
2.7 Hz = 9.718 / 10.412
2.8 Hz = 10.452 / 11.197
2.9 Hz = 11.211 / 12.011
3.0 Hz = 11.998 / 12.854

That covers most of the coilover rates out there.

Far North Racing suggests:
Street car: 0.8 Hz
Occasional autocrosser: 1.0 - 1.5 Hz
Full-bore autocrosser: 2.2 - 2.5 Hz

Most people don't recommend a completely flat ride. For a street car, you might use 1.5 Hz front and 1.7 Hz rear. That puts us at 3K/4K. Most of the lowering spring kits are in that ballpark or slightly stiffer.

For a track car, 2.3 Hz in the front and 2.5 Hz. That puts us at 7K/9K. KW, Ground Control, and RSR coilovers have similar ratios, but slightly softer. Interesting to see how many coilovers are super-stiff in the front. That probably leads to a better feel and less actual grip.

[RBbugBITme]

Cool thread. I'll see what I can contribute after this weekend.

[ZDan]

Originally Posted by Shankenstein

Ks = 4*pi^2*f_natural^2*m_sprung*motion_ratio^2
note: OptimumG uses motion ratio of wheel/spring (>1)

This is the inverse of what is usually used for motion ratio.
For the FR-S/BRZ, motion ratios are ~0.95 front and ~0.75 rear, from what I've gathered... So in the equation above you would use (1/0.95) and (1/0.75) for "motion ratio".

Important to use the right units of course, kg for mass and N/m for spring rate is easiest. N/m is kg/mm * 9.81 * 1000

Here's what I found (fronts and rears in kg/mm).
1.5 Hz = 3.000 / 3.213
1.6 Hz = 3.413 / 3.656
1.7 Hz = 3.853 / 4.127
1.8 Hz = 4.319 / 4.627
1.9 Hz = 4.813 / 5.156
2.0 Hz = 5.332 / 5.713

Your spring rates look too low and too close together to get those natural frequencies. What did you use for mass and motion ratio?
Assuming 2950 lb. car (with driver), 54/46 weight distribution and subtracting 50 lb. from total weight at a corner to get sprung weight, I came up with 338kg sprung mass for a front corner and 286kg sprung mass for a rear corner.
Looking at 2Hz for an FR-S/BRZ, I get:

front Ks = 4pi^2 * 2Hz^2 * 338kg * (1/.95)^2 = 59,141 N/m = 6.0 kg/mm

rear Ks = 4pi^2 * 2Hz^2 * 286kg * (1/.75)^2 = 80,290 N/m = 8.2 kg/mm

Running your 5.332 and 5.713 kg/mm spring rate numbers, or 52,307 N/m and 56,045 N/m, I get
f = (1/2pi) * sqrt(k*motionratio^2/m)
f front = (1/2pi) * sqrt (52,307*0.95^2 / 338kg) = 1.88 Hz
f rear = (1/2pi) * sqrt(56,045*0.75^2 / 286kg) = 1.67 Hz

2 Hz is generally a pretty good street/track compromise. That is, too stiff for the street and too soft for the track!

The rule *used* to be to have a slightly higher rear natural frequency than front, but that has reversed over the past ~15 years or so.

For feel, my impression is that biasing stiffness to the rear improves feel and biasing to the front reduces it, but "feel" is often subjective...

[RBbugBITme]

So here is the front info I can gather. I admittedly have never analyzed a strut suspension in this software before so maybe I input something wrong but the data points are exact.

Front suspension @ stock ride height
Roll center height: 3.140" (Drops below the ground plane at only 1" bump)
Caster: -5.937 deg
Motion ratio: .95 and rising rate with bump. -1.5" bump (or lowered ride height) =.997MR. -2.5" bump = 1.050MR
Camber gain: -0.262 deg at 1" bump travel. Parabolic curve bottoms out at only 1.6" of bump travel, camber gain switches to positive



Pure roll scenario from -3 deg (right turn) to +3 deg (left turn) @ stock ride height
The black vertical line indicates -1 deg of roll and the data points at -1 deg are in the colored boxes on the right.



This one is particularly nasty. This is a plot of -3 to 3 deg of roll at a ride height of -3 on the far left to +2 on the far right in 0.10" steps. The vertical black line is at -1" ride height which is right around where the roll center goes crazy shooting off to infinity and switching back and forth above and below the ground plane. I wouldn't personally ever set a BRZ to a 1" drop after looking at this without roll center correction.


Unfortunately, I think there is very little I could say about this layout that's positive. I've heard the OEMs have used the rubber bushing deflection to their advantage which I can't do, perhaps that was done with this suspension but installing sphericals, delrin, or polyurethane would eliminate that anyway.

If anyone thinks this was worth a little donation for my time, donate something to alz.org. On to the rear...

[Captain Snooze]

Originally Posted by RBbugBITme

I wouldn't personally ever set a BRZ to a 1" drop after looking at this without roll center correction.

Could you please explain (in simple language ) what the consequence of dropping more than 1" inch is?

[RBbugBITme]

I can't believe I'm condoning this but if this is all correct, you're going to want to drop your car at least 1.5" and probably increase caster a degree. At that point you still have pretty bad but controllable camber gain (about +1deg per deg of roll), you keep your roll center from shooting off to infinity but it is still passing back and forth through the ground plane (not good) and the moment arm to the CG is seriously non-linear. So with that drop I'd get some kind of roll center correction but I haven't analyzed that yet.

-3 to +3 pure roll, no steering, at -1.5" drop

[Thorpedo]

These graphs are REALLY helping me understand what is going on with our suspension and I'm starting to understand the problems you are outlining.

Thank you for your time, a donation will be made later today.

Originally Posted by RBbugBITme

I can't believe I'm condoning this but if this is all correct, you're going to want to drop your car at least 1.5" and probably increase caster a degree. At that point you still have pretty bad but controllable camber gain (about +1deg per deg of roll), you keep your roll center from shooting off to infinity but it is still passing back and forth through the ground plane (not good) and the moment arm to the CG is seriously non-linear. So with that drop I'd get some kind of roll center correction but I haven't analyzed that yet.

-3 to +3 pure roll, no steering, at -1.5" drop

[Racecomp Engineering]

Awesome stuff, thanks Ryan!

What software is that?

- Andy

[RBbugBITme]

WinGeo

[Calum]

@RBbugBITme

What ride height, relative to stock, would you say is best? Or is it just a matter of also preforming the roll center correction when lowering?

[7thgear]

Originally Posted by RBbugBITme

do you have a higher rez version?