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Old 01-25-2013, 02:51 AM   #15
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@Dave-ROR

Is it possible to sticky this? I think it's a great project that could end up helping to educate a lot of people here and would hate to see it lost under a bunch of 'Need help picking coilovers!' threads.
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Old 01-25-2013, 09:12 AM   #16
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I'll be bumping it soon enough.

The rear suspension is not a normal type... so I've been testing alot of variants. It looks like "Double Wishbone + upper toe link + S link" should get the job done (although it's not really true here). The last few setups I've modeled have been "trailing arm + 2 links" or "H arm + upper link". I'm really a fan of H arms, since they kill toe movement, but otherwise allow for a smooth camber curve. Alas, Subaru didn't ask for my help.

In other news, my Hot Lava Auto FR-S has been ordered and will arrive somewhere between 2 weeks to 2 months from now. Getting plenty of access to a car for measuring the geometry coordinates will be much easier. Looks like I'll be spending alot of time with the calipers in the next few months (between this and the aero thread).
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Old 01-25-2013, 12:13 PM   #17
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I'd say the most accurate suspension model for the rear would be the upper a-arm with three links. For those who have RCVD it's in section 17.6.

I've only used WinGeo (which I loathe) of the programs mentioned, but the suspension type is not an "option" when building the model.
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Old 01-25-2013, 01:26 PM   #18
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Originally Posted by EarlQHan View Post
I'd say the most accurate suspension model for the rear would be the upper a-arm with three links. For those who have RCVD it's in section 17.6.

I've only used WinGeo (which I loathe) of the programs mentioned, but the suspension type is not an "option" when building the model.
WinGeo isn't that bad....
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Old 01-25-2013, 01:41 PM   #19
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I agree. The lower links are just that... unaffiliated links.

Lotus is significantly easier to use than WinGeo (IMHO), but this is one of it's shortcomings. It prefers to shoehorn things into one of their included suspension styles (like 20 types), which greatly simplifies the process... you just have to get creative with your interpretation of the style.

Ex: double wishbone really means 4 body points, 2 suspension points, 2 shock/spring attachment points (all with 3 rotational degrees of freedom). Then, 2 body points + 1 suspension point = 1 rigid member (LOL). Lower shock/spring mount moves with the wishbone, upper moves with the body. All body points are rigidly connected. All suspension points are rigidly connected to the knuckle which is in series with a spring (tire) and ground.

Once the "fudged" version is up and running, you can build a "proper" version from scratch. If the results are close, you'll know that your assumptions are probably OK. Typically, the results are so close it's not worth your time to make the custom setup at all though. Take your time and get the fudged version perfect.
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Old 01-25-2013, 08:54 PM   #20
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@Dave-ROR

Is it possible to sticky this? I think it's a great project that could end up helping to educate a lot of people here and would hate to see it lost under a bunch of 'Need help picking coilovers!' threads.
BTW that mention never got flagged in my notifications so I never saw it.

Stuck now
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Old 01-26-2013, 12:54 AM   #21
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Quote:
Originally Posted by Shankenstein View Post
I'll be bumping it soon enough.

The rear suspension is not a normal type... so I've been testing alot of variants. It looks like "Double Wishbone + upper toe link + S link" should get the job done (although it's not really true here). The last few setups I've modeled have been "trailing arm + 2 links" or "H arm + upper link". I'm really a fan of H arms, since they kill toe movement, but otherwise allow for a smooth camber curve. Alas, Subaru didn't ask for my help.

In other news, my Hot Lava Auto FR-S has been ordered and will arrive somewhere between 2 weeks to 2 months from now. Getting plenty of access to a car for measuring the geometry coordinates will be much easier. Looks like I'll be spending alot of time with the calipers in the next few months (between this and the aero thread).
The measuring bit looks like a headache. This link was from a site Dave linked to for shocks.

http://farnorthracing.com/modeling.html

Do you have any of your own tips you can share?

Where he talks about telescoping rods attached to height gauges, I was thinking of a laser pointer instead (make sure it's parallel to the base and record the height above the surface, the set and zero your gauge accordingly).

Thoughts?
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Old 01-26-2013, 02:16 AM   #22
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That guy is rather smart. Getting coordinates in Cartesian coordinates is difficult, but using plumbs and telescoping magnets is a brilliantly ghetto solution. It sounds perfect for items that can be +/- a couple millimeters, then bust out the calipers for small measurements.

I usually work in spherical, which sounds nuts, but it's easy to implement. Distances + angles. Rulers and string will give you point-to-point distances quite accurately. Up your precision by knotting 1 end of the string around a nail, and having a friend hold it. Redneck engineering! Magnetic angle finders will turn distances into positions. Of course you'd need a few quality reference parameters and some common sense "eyeballin' it" to ensure that the results mean anything.

What have you guys done to better understand your previous vehicles? For SAE Baja and Formula cars, we built from a model... this is reverse engineering an existing product, which I've only done a couple times. I stand to learn alot from you guys (and have high expectations!)
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Old 01-26-2013, 02:58 AM   #23
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my cars on the rack...looks like we do some measuring tomorrow..

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Old 01-28-2013, 12:12 PM   #24
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While we look forward to RobiSpec's analysis, I'll provide some brain food.

There are multiple systems interacting in a car suspension, with different natural frequencies and damping characteristics. The lowest decade (1-10Hz) is responsible for almost all system dynamics, but all of them should be mentioned. The system looka like dis:


1) Upper system (fix x_2 and w):
Sprung weight + suspension spring. This motion is damped by the suspension damper. These are very low frequencies (0.5-5 Hz).

f_nat1 = constant * sqrt(spring rate / sprung mass)
b_1 = damper constant / sqrt(spring rate / sprung mass)

2) Middle system (fix x_1 and w):
Unsprung weight + suspension + tires. This motion is damped by both the suspension damper and tire damping. These are generally much higher frequencies.

f_nat2 = constant * sqrt([spring rate + tire rate] / unsprung mass)
b_2 = damper constant / sqrt([spring rate + tire rate] / unsprung mass)

3) Lower system (fix x_1 and x_2)
If we assume that all of the car's weight is sent to the ground, the parts involved are the sprung weight + unsprung weight + tires. This motion is damped by the tire, which is generally a very low damping factor (tires bounce).

f_nat3 = constant * sqrt(tire rate / [sprung mass + unsprung mass])
b_3 = tire damping constant / sqrt(tire rate / [sprung mass + unsprung mass])

Due to the low damping capabilities of tires, it's best to let the dampers handle vibration control. For tire dynamics to minimally affect suspension dynamics, a decade of frequency separation should be sufficient.

F_tire > 10 * F_susp
sqrt(tire rate / unsprung mass) > 10 * sqrt(spring rate / sprung mass)
If both values are more than one,
tire rate / unsprung mass > 100 * spring rate / sprung mass
tire rate / spring rate > 100 * unsprung mass / sprung mass

for our example:
6500 / 131 > 100 * 83 / 618
49.6 > 13.43 --> sufficiently separated

I guess I should amend the above statement. Thanks for pointing it out!

Continuing this thought:
If we calculate the max spring rate that can be used without being affected by tire dynamics (at stock pressures):
max front wheel rate = 484 lbs/in
max front spring rate = 526 lbs/in
max rear wheel rate = 422 lbs/in
max rear spring rate is = 548 lbs/in

At autox pressures, max spring rates would be 809 (front) and 843 (rear). In metric, that's 14.2k and 14.8k. Interesting, not that anyone would want to run them that stiff anyways.

Last edited by Shankenstein; 01-30-2013 at 02:55 PM.
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Old 01-28-2013, 04:52 PM   #25
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After updating the original post to include Newtons, I re-verified the natural frequencies and added the new ones using the racing aspirations calculator (LINK

f_nat1 = 1.3 Hz front, 1.5 Hz rear
f_nat2 = 31.3 Hz front, 22.1 Hz rear (stock pressures)
f_nat3 = 9.03 Hz front, 8.08 Hz rear (stock pressures)

From this, we can infer that there is some small interaction caused by the tires at stock pressures. Bumping up the pressures to autocross level (10000 lbs/in rate):
f_nat2 = 30+ Hz (autox pressures)
f_nat3 = 11.1 Hz front, 9.9 Hz rear (autox pressures)

Now we see that the tire's natural frequency jumps up ~23%, which decreases it's involvement in the bounce dynamics of the car. The added pressure also decreases sidewall flex, which maintains a more even contact patch.

Last edited by Shankenstein; 01-30-2013 at 02:58 PM.
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Old 01-30-2013, 11:25 AM   #26
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New discussion point: Sway bars!

Roll center (according to SAE) - The point in the transverse vertical plane through any pair of wheel centers at which lateral forces may be applied to the sprung mass without producing suspension roll.

Layman's definition - This is a neutral point for your suspension. Applying lateral force at this height will generate no roll (vertical movement at either corner).

Let's consider a 1.0 g turn in a 2645 lbs car. That means ~2645 lbs force will be applied to the center of mass/gravity. Here's an illustration:


4 possible options:

1) Roll center height = center of gravity
There is no roll. If there is sufficient grip in the tires, your car will turn like a go-kart or a door-hinge (flat). This does sent alot of force through the control arms, and the spring/damper are not used at all.

2) 0 < roll center height < center of gravity
There will be a moment (torque) generated, since the lateral force is applied at a different height than the reaction force.

Torque = Force * distance
Roll Torque = 2645 * abs(center of gravity height - roll center height)

Since there is a torque, there will be reaction forces. Typically this duty falls on the springs and sway bars. Most race cars try to keep the roll center height at 15-30% of the center of gravity height.

3) roll center height = ground height
The control arms won't be loaded, and all forces will be sent through the spring/damper. Not horrible, just sub-optimal.

4) roll center height < ground height
The spring/damper will see an amplified force, and can cause the control arms to see the wrong type of force (compression vs tension). This isn't necessarily bad, but I can't recommend ever having an underground roll center, unless you overbuild the spring/damper to compensate for it.

TL;DR - Try to keep the roll center between the center of gravity and the ground. Lower is better, but don't go underground.

Load Transfer
Let's assume that we stay between #2 and #3 (because that's how a properly designed suspension should be). In a cornering maneuver, the reaction forces are generated when the outside spring is compressed and the inside spring is extended. For simplicity, let the roll center height be 10 in. Let's initially assume that there is no sway bar and the reaction force at both ends is half of the total reaction force:

Reaction force = 1/2 * roll torque / half track
Reaction force = 1/2 * [2645 lbs * 0.53] * abs(18.1-10 in) / 29.9 in
Reaction force = 189.3 lbs

Deflection = reaction force / spring rate
Deflection = 189.3 lbs / 131 lbs/in
Deflection = 1.445 in

Roll angle = arctan(deflection / half track)
Roll angle = 2.767 deg

Sway Bars
Sway bars add coupling between the wheels. Any difference in height will create a torque that will "lift" the outside wheel in an attempt to equalize the wheel heights again.

Situations:
1) In a single wheel bump, the full length of the bar is used to control one end, so the bump stiffness is halved from the numbers calculated.

2) In a two wheel bump, the whole bar has no effect.

3) In a turning maneuver, it should follow the formula:

K = pi*G*d^4*(MR) / (16*R*L)
where
pi = 3.141592653
G = elastic modulus
d = bar diameter
MR = motion ratio of control arm swaybar link
R = radius arm of sway bar
L = length of sway bar

basic data:
G = 8.14 x 10^10 Pa for spring steel
d = 0.018 m (front) 0.014 m (rear)
MR = not sure... but it's 0.6 on a Miata
R = not sure... but it's 0.225 m (front) and 0.121 m (rear) on a Miata
L = not sure... but it's 0.830 m (front) and 0.850 m (rear) on a Miata

Therefore:
K (front) = 14375 N/m
K (rear) = 17761 N/m

From this, we see that the FR-S is a sports car built with soft springs and stiff roll bars. This means that it will feel silky smooth on the highway, but any difference in wheel height will be heavily resisted. Strictly speaking, this is not good race car dynamics... but it works great on street cars.
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Old 01-30-2013, 11:39 AM   #27
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wow! This thread should be called Suspension 201. I am learning a lot of good and interesting stuff. Thanks Shank for sharing.
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Old 01-30-2013, 12:05 PM   #28
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It's good outlet for creative thought. The 86 community has alot of smart people (including a few manufacturers). I get to throw down the theory in my own words, and it only helps the community.

Experienced people will peer review it (and hopefully correct me), and newer people will learn from it. Once my FR-S comes in, I'm sure things will get less theoretical and more hands-on.

Thanks for reading, and know that questions/comments are always welcome.
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