Developing a Proper Suspension Model

[Shankenstein]

Originally Posted by jonnyozero3

Shankenstein - this is great. Thank you for starting it.

What products are you aiming to model first to work on your own personal suspension goals? Just curious.

First order of business is to analyze the stock setup. Find its strengths and weaknesses from a geometry point of view.

Second order of business is to analyze the effects of lowering springs, coilovers, sway bars, spacers, wheel offsets, camber plates, etc. Each one changes the geometry and system dynamics. I want to know the effect.

Third order of business is to connect the model results with the track. Start with the model's optimal setup, see how it performs on track/autocross. We'll watch tire temperatures, wear rates, and lap times. If you tweak the camber, and tire temperatures are more evenly distributed, you should probably stick with it (unless lap time dropped significantly).

The tough part here is keeping things objective. Getting feedback about 0 vs 1/8" toe, with the same driver on the same track, on the same day... which one feels more stable and yields better lap times. That's subjective, but still has value.

Fourth order of business is to identify where the model was wrong. Identify where a computer can be helpful and where it leads you astray. I guarantee that some stuff will look great on a computer but will perform poorly.

Examples:
Currently, some people will say that front springs should be stiffer than rear springs. Some people will say 10k springs are a great idea. Some recommend wide tires + offset + camber (because grip!). Hopefully we can see what effect 255 vs 215 tires make.

The FT86 forums are hoppin'. Theory nerds, track Stigs, and some people with too much $$ to spend. Let's put all 3 types to work. I think we can develop a set of recommendations for new guys and old guys... for each budget and purpose.

*steps off the soapbox*
I'm still waiting on my FR-S to arrive. I did get one of those extendable magnets and some huge paper, for doing the coordinates in XYZ this time.

[Dimman]

A geometry thought:

There was talk about use of asymmetrically deforming bushings in the car. Do the geometry programs take bushing deformation into account, or would you have to manually offset the pivot points? Which would also vary by the amount of force, right?

Anyone out there want to code up an open source force-based suspension-geometry/FEA hybrid program? There are OS CAD and FEA programs that could be used as a starting point.

[EarlQHan]

Originally Posted by Shankenstein

Ran across the CAD drawing for the AST 4150 (front right) strut. For the sake of building our database of dimensions, some reverse engineering was done. This data is provided for non-commercial use. If you try to rip off AST (one of the premier suspension manufacturers), expect their lawyers to sue you, the 86 community to shun your products, and numerous internet photographs of your product being teabagged in public places. Save us (and our giblets) the trouble, and just don't do it.

Distance between strut bolts is 60.5 mm --> 2.4"
Thickness of lower flange is 25.4 mm --> 1"
Distance from strut center to lower bolt is 60.7 mm --> 2.4"
Length from lower bolt to upper mount top is 392 mm --> 15.4"
Upper thread is a M12x1.25-25, with 5 mm of thread relief
Diameter of damper rod is 22 mm
Diameter of spring perch is 60 mm
Length of spring available is 181 mm --> 7.1"
Distance from lower bolt to sway bar mount is 115 mm --> 4.5"
Distance from strut center to sway bar mount is 50 mm --> 2"
Diameter of sway bar mount is 10.2 mm --> 0.4"



Edit: Main post updated with only the relevant parameters!

I wouldn't worry about getting sued. The magic happens on the inside. Anyone with a ruler can figure out what's in that diagram.

Originally Posted by Dimman

A geometry thought:

There was talk about use of asymmetrically deforming bushings in the car. Do the geometry programs take bushing deformation into account, or would you have to manually offset the pivot points? Which would also vary by the amount of force, right?

Anyone out there want to code up an open source force-based suspension-geometry/FEA hybrid program? There are OS CAD and FEA programs that could be used as a starting point.

There are advanced programs out there that do suspension models with K&C data so they take bushing deflection, installation stiffness, component stiffness, etc. into account.

[Shankenstein]

With the STI strut brace being introduced, I thought it would be good to bring them up in the discussion... since it's theory and all. Much of it is copy-pasta from that thread, so if you've read it there, disregard.

I'll use this discussion as a source: http://www.e30m3project.com/e30m3per...bar_theory.htm

Strut bars have 2 purposes:
1) Stiffen the tower to tower lateral movement (tower to tower bar)
2) Couple strut flex to a neutral chassis position (tower to firewall bars)

Many people discuss the chassis surrounding your suspension as being a parallelogram. While it's not completely true, it provides a useful illustration.



Point 1 makes the top line in the parallelogram more rigid. In most cars, the other 3 lines are already very stiff. This turns your trapezoid into a parallelogram (a good thing).

Point 2 makes the angles at each corner of the parallelogram more rigid.

During compression, the strut towers want to bend inward. A strut bar is put into compression and resists this quite well.

During cornering, one strut tower wants to move inward, while the other moves outward. A strut bar ties these deflections together, stiffening the one that deflects more (like a sway bar does for vertical motion). Since the inside tire's camber is less relevant to maximum grip, you sacrifice some deflection to improve the situation on the outside tire.

All this is dependent on the struts flexing. Modern chassis design is rather rigid, so it's not as important as in an 80s Civic or my RAV4 (an SUV version of the Corolla).

When I installed my strut brace (1.5" square tubing w 1/4" plate on each tower), the handling limits did not really improve... but the consistency of when the tire broke loose was much better. Strut flex begets more camber and grip, and in many cases is not a bad thing. I value the stability and consistency more than ultimate grip. Go kart vs. muscle car, if you will.

Point 2 is irrelevant if you consider the front and rear suspension as independent parallelograms. They aren't... so preventing either from differing too much from the unstressed geometry is important. Also, triangles are stronger than parallelograms, so tying into the firewall (however flimsy it may be) is still good for structural rigidity of all components in the party.

Modern cars indeed make strut braces pretty irrelevant, since the structures are inherently more rigid. That said, if the M3 guys estimate 0.5 degrees camber change due to tower flex, I'm willing to add some reinforcement to prevent it. Some brave soul can install a strain gage on their cusco bar and see that there are indeed forces through it... but the magnitude of the deflection just isn't what it was 30 years ago. Bushings are another story for another day though.

[MrH]

Wow, awesome work everyone! I don't know how I missed this thread before. I was hoping to create a crude version of this to simulate various spring rates.

I think I've still got my Matlab model I made when I had my miata. I'll see if I can find it on an external hard drive somewhere and plug some of these numbers in.

I bookmarked this thread and will take some time to read it over the next few days. If there's anything I can do to help contribute, let me know!

[u/Josh]

Originally Posted by MrH

Wow, awesome work everyone! I don't know how I missed this thread before. I was hoping to create a crude version of this to simulate various spring rates.

I think I've still got my Matlab model I made when I had my miata. I'll see if I can find it on an external hard drive somewhere and plug some of these numbers in.

I bookmarked this thread and will take some time to read it over the next few days. If there's anything I can do to help contribute, let me know!

I have been wanting to do the same, but school has kept me too busy. I want to create a simulation of the 1/4 car model posted a few posts back to see how different spring constants and damping curves change vehicle response to bumps. I also wanted to use it to try to quantify the effects of reducing unsprung weight.

Shankenstein, not too important but I noticed a small mistake in the first post. I think the tire radius should be ~12.3" or .31 meters, not 9".

[MrH]

Originally Posted by u/Josh

I have been wanting to do the same, but school has kept me too busy. I want to create a simulation of the 1/4 car model posted a few posts back to see how different spring constants and damping curves change vehicle response to bumps. I also wanted to use it to try to quantify the effects of reducing unsprung weight.

Shankenstein, not too important but I noticed a small mistake in the first post. I think the tire radius should be ~12.3" or .31 meters, not 9".

That's basically what I did in college. Made a model in matlab with the spring rate, damping rate, motion ratio, unsprung weight, etc. Then simulated hitting expansion joints and potholes at different speeds to see how it would react. I did this all this my NC miata back then.

I made it all in Matlab at the time, but it's been years since I've played with it. If you have any questions or just want someone to bounce ideas off of, feel free to shoot me a PM!

[AlexTheGreek]

I definitely applaud this tread because it looks like a great ressource for the gt86 engineering types to get information about their vehicle's geometry and available methods for modelling vehicle kinematics.

Whether or not it's actually necesary is a whole other story. But who cares, nerds rule! Let's keep it going. +1 for Shankenstein and his/her efforts to start this thread.

[Lonely Sushi]

Well.... I was just on my way to the shop with my plumb bobs to measure all the pickup points and model the suspension when I found this. This is going to save me hours of measuring! Thanks guys

Now.. next is to find strain gauges to see some forces around the bars and chassis and go from there

[Lonely Sushi]

Originally Posted by Shankenstein

New discussion point: Sway bars!


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.

sorry for the double post. But would you care to explain why you think this is not good race car dynamics?

Unless the camber gain in roll is so high to gain some benefit, controlling roll to keep the desired camber and manage weight tansfer is a good thing . Softer springs (with the correct frequency / rate) can help tires stay on the road longer instead of jumping about like the local tracks we have here in Taiwan and some of our public roads in US. I've always try to design my cars with springs on the soft side and use the bars as the major tuning tool.

Another point to add to this fantastic post is that it is also a good idea to maintain the relative distance between roll center and the center of mass for both front and rear when you start messing with the ride heights and such. It can help maintain the car's characteristic that many of us like so far in stock form

[plucas]

By the way, if you have had experience with Matlab, look into Octave. Octave is an open source program that does numerical computations. The language is very similar to Matlab. The only issue is that it runs on linux (not an issue if you are like me and already run linux ).

So basically all this suspension modeling could be done in octave by many people who share the coding. The code could be combined into one awesome suspension model. Just my 2 cents though

[u/Josh]

Originally Posted by Lonely Sushi

sorry for the double post. But would you care to explain why you think this is not good race car dynamics?

I believe the typical explanation for this is that with a sway bar your spring rate is different if the car is rolling than if the car is hitting a bump so you have to compromise between these two situations when choosing damping curves.

[andrew20195]

Originally Posted by u/Josh

I believe the typical explanation for this is that with a sway bar your spring rate is different if the car is rolling than if the car is hitting a bump so you have to compromise between these two situations when choosing damping curves.

I may be way off here, but I would think that even on a race car you would run digressive or regressive damping curves to soak up high speed bumps while allowing stiffer damping for low speed suspension movement, so it doesn't seem like you would really be compromising.

Of course, with soft springs and stiff sway bars, you might end up with more dive and possibly more squat than you want for ideal handling on a track, especially with sticky tires.

[neurokinetik]

Originally Posted by Shankenstein

New discussion point: Sway bars!

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)² / (16*R²*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

If I am thinking correctly here, I think the R variable is supposed to be the axial distance from the center of the swaybar to the center of whichever mounting hole you are using (in case of an adjustable bar). Think of it like attaching a lever to the end of a pipe, and the measurement would be as if you are looking straight down that pipe and taking the measurement of the length of the lever that way. So that means that using the Miata figures will not be accurate.

The motion ratio should be calculated by measuring the distance from the inner control arm pivot point to the swaybar endlink mounting point, and comparing that to the length of the entire control arm. It probably also won't be 0.6, as it is on a Miata.