@Shankenstein @EarlQHan @plucas

I have a copy of Matlab and I'm a relatively decent (if rusty) coder. If we want to collaboratively use it as a tool to model our suspension mathematically I'd be more than happy to help.

Cheers
Nathan

I am literally the worst at controls. It doesn't help my controls prof got canned the semester after I had him since he didn't pass his reviews. I passed that class by the skin of my teeth. As for matrix math, I blame dyslexia... which I don't have...

I've been accepted to Cranfield University's Advanced Motorsports Engineering program in England. I was also accepted to Oxford-Brookes Masters in Motorsports Engineering, also in England, but I turned down their offer in favor of Cranfield. I may defer though...

I'd be game. Nathan, I'm also going to shoot you a PM about composites...

I would be up for this :D

I did some of my elective work in controls, it would take a bit of work for me to recall everything but I'm sure I could get back into it.

@EarlQHan-PM replied, we should setup a skype session or something on the suspension modelling front.

Cheers
Nathan

Of these, I think comparing different damping curves, along with testing the effects of changing unsprung weight are most interesting. Also, the frequency response would be interesting just to show why it is smoother when you drive faster over bumps. I'll plug this in to MATLAB when I get a minute free at school.

I have thought about trying to convert this to a 4 wheel model and I can't quite get my head around how y1, y2, etc should be constrained to represent an actual chassis. What I have come up with so far is that if you consider the chassis to be the x-z plane then the points (x1,y1,z1) and (x2,y2,z2) etc, would have to all lie on the same plane; Where xi and zi are the coordinates where the i'th wheel is. It's late, I hope this makes sense.

Wait. First, let's all get on the same reference frame. Are we all thinking X is the longitudinal direction of the car, Y is the lateral direction of the car, and Z the vertical?

Also, where are we going to place the origin? Center of the wheels on the ground plane?

I just went with the notation of y being vertical (in the direction of bump travel) like Earl used to derive the transfer function. Then I guess X can be longitudinal and Z is lateral. The origin should probably be in the center of the car so for example the coordinates for the front passenger mass would be (I am guessing at the numbers here):

(50",y,30")

I know the X and Z coordinates would actually be a function of Y but for small angles I think this is negligible?

The Hancha user is me (or plucas) ;] I used the vars x, y, and u for the transfer function rather than x1, x2, etc. since it makes it easier to keep track of the variables. In terms of the car as a global coordinate system, I use the X, Y, Z variables as stated above.

If we can create a sophisticated enough model, the suspension would see movement in all three coordinates along their respective arcs.

I just plugged the quarter car transfer function you derived into MATLAB. The constants are mostly guesses, so let me know what needs to be changed. One thing that seems weird to me is that the step response has a final value of zero when I think it should be one.

edit - 'unsprung weight' should be 'unsprung mass' and 'tire spring weight' should be 'tire spring rate'

http://i.imgur.com/osZSMGs.png

The impulse response is correct and you want the function to eventually get to zero. This is representing the wheel oscillation, which will oscillate when excited by a bump and eventually settle.

Side note: from a subjective standpoint, from what I've been told, typically around four oscillations for the settling time said to "feel good," rather than shooting for a critically damped model. A critically damped suspension will be back breaking and the vertical accelerations happen too quickly for a driver to really respond to them.

Yeah, the impulse looks good, but the step reponse should have a final value of 1, not zero. I'm not sure where the error is coming from though.

Edit - just found the error. I made a mistake entering your transfer function. I'll upload new plots in a second.

Is there a way to get the picture a bit clearer? I'm struggling to read the key XP

http://i.imgur.com/pOFCffi.png
http://i.imgur.com/yfl1M0G.png

The only odd thing left is the natural frequency seems to be around 5 Hz, which I think is way to high to be true. I guess one (or more) of my assumed values is off by quite a bit.

The rates are off. Shankenstein has already done the base estimates:

http://www.ft86club.com/forums/showp...38&postcount=1

I think there may be a mistake in his post because I am getting the front rate to be 131 lb/in = 22,000 N/m. I'll plug that number in tomorrow and check the results.

And it seems my damping coefficient was way off as well. I don't remember where I got this plot from but it is probably useful to some of you. This is a front stock BRZ damper. I'll try 6700 N*s/m.

http://i.imgur.com/ceBSHT1.png

To contribute:
m_1 (unsprung mass) = 37.6 kg
m_2 (sprung mass) = 280.4 kg (front) 244.5 kg (rear)
k_1 (stiffness of tire) = 350 N/mm (at 30 psi)
k_2 (stiffness of suspension) = motion ratio * spring rate = 2.11 N/mm (front) 2.8453 N/mm (rear)

We can construct a piece-wise interpolation that's easily mapped using a "spline" fit. How to Spline Like a Boss

note: Sign convention usually has compression as positive displacement/velocity and rebound as negative displacement/velocity.

damping coeffficient = Force/velocity

damping ratio = actual damping coefficient / critical damping coefficient

We want a damping ratio of nearly critical (1.0) for roll and pitch modes, but ride can be 0.5 - 0.8 for some driveability.

If anyone has not read these, please do! OptimumG Technical Papers

WRT ride frequencies:
spring rate = 4 * pi^2 * ride frequency^2 * sprung mass * motion ratio^2
2294.2 = 4 * pi^2 * f_r^2 * 280.4 * (1/0.92)^2
f_r = 0.42 Hz

That's a very soft ride. Sway bars stiffen it up in roll though. That's another calculation for another day.

I'm still getting 21.11 N/mm. Perhaps your are still in units of Kg/mm?

The good news is this works out to be 1.6 hz ride frequency. Anyone know why we see the highest gain in the bode plot at around 5 hz not 1.6 hz?

Mistake was exactly what you said. Used an online calculator, and I shouldn't have trusted it.

The original post is updated.

spring rate = 4 * pi^2 * ride frequency^2 * sprung mass * motion ratio^2
22970 = 4 * pi^2 * f_r^2 * 280.4 * (1/0.92)^2
f_r = 1.325 Hz (front)

Notice that the motion ratio is inverted. If you leave it as 0.92, you will get 1.5 Hz as you got.

The rear comes out to be 3.8154 Hz. It is definitely stiffer in the rear, but it doesn't quite feel THAT stiff. Once we can confirm the rear motion ratios, we can state it with confidence.

I've updated the numbers but I noticed as I decrease the dampening the system seems to become more damped. Check out the difference in the step response when I change damping constant 'b' from 6000 to 25000. That can't be right?

http://i.imgur.com/Gcy40xR.png
http://i.imgur.com/EmQAMX4.png
http://i.imgur.com/f8kATc1.png

Are you using the standard definition of MR or the "racing" definition. Racing definition is WMD or Wheel = MR*Damper

Damn, I was hoping to not have to review controls, but I will do so now... :[

I've seen it represented both ways.

The way I've always heard is from the suspension design perspective:
motion ratio = (distance from pivot to shock mount) / (distance from pivot to knuckle)

OptimumG and others explain it from a vehicle dynamics perspective as:
motion ratio = tire travel / shock travel

Both versions make sense, but just a matter of convention. Which version do you plan to use?

I prefer tire/shock since that's just the way I've learned it. Plus WMD is easy to remember, weapons of mass displacement ;]

That only has a minor effect on the spring rate, and is done before the rate is even put into the program (for now). The problem with the damping is larger than that, although this does remind me that I need to consider the motion ratio of the damper as well.

Quick question, and I apologize if I missed it in the thread...also looked on the google doc spread sheet...

Does anyone know what the OEM scrub radius is? I'm looking at wheels, and want to discuss the possible offsets vs. scrub changes with my boss.

The rear ride frequency is wrong, that's why it seems so high. Using that formula you get 1.51 Hz for the rear, not 3.8.
I used K=36998 N/m, sprung weight=244.5 kg, motion ratio=1.299.

since you asked, the Tire Radius should be 12.3" for 215/45r17, but I guess it squishes down a little with the weight of the car if that matters.
sorry, I'm a little late in the game here, but this is a really interesting thread:thumbsup:

Springs, Swaybars, Wheel Rates and Frequency
 

I put together some calculations to give some context to spring rates, swaybar rates, wheel rates, and undamped frequencies.

Here are some assumptions I used for to calculate wheel rates due to springs and bars:

Front Spring Motion Ratio
1.0
Front Spring Angle (based on nominal SAI)
15.5 degrees
Front Bar Motion Ratio (same as Front Spring combined MR due to attachment to the strut):
0.964
Rear Spring Motion Ratio (measured)
0.78
Rear Bar Motion Ratio (measured)
0.59
Rear Spring Angle (still needs to be verified – I know it’s not perfectly vertical but it doesn’t look that large either; as long as it remains smallish it shouldn’t affect calcs much)
4 degrees

BRZ Spring Rates (measured by Vorshlag http://www.vorshlag.com/forums/showp...16&postcount=5)
160 Front / 200 Rear lb/in
FRS Spring Rates (measured by Vorshlag http://www.vorshlag.com/forums/showp...16&postcount=5)
125 Front / 220 Rear lb/in

Front Swaybar Diameter
18 mm
Rear Swaybar Diameter
14 mm

Front Swaybar Spring rate (measured by Eibach http://www.phastekperformance.com/20...-sway-bars.htm)
141 lb/in
Rear Swaybar Spring Rate (measured by Eibach http://www.phastekperformance.com/20...-sway-bars.htm)
113 lb/in

To get wheel rates, I multiplied the rated spring rate by the square of the product of the Motion Ratio and Cosine of the Spring Angle. The calcs:
The wheel rate for the bars is the wheel rate in roll. For one-wheel bump, those bar wheel rates would be halved. The reason they're doubled in the roll calculation is because in roll, as the loaded side (outside) travels in bump, the unloaded side (inside) droops the same amount, so it's actually double the "twist".

The "Front Dist" and "Rear Dist" columns indicate how biased the total wheel rates (front + rear) are front to rear. This isn't that relevant without weights (and hence frequencies which I'll touch on below), but it's interesting to compare it to the 55/45 weight distribution of the car. I've seen with other cars how wheel rate front/rear bias closely matches the weight distribution of the car, which makes sense.

Notice how much work the front bar is doing – it provides a lot more wheel rate than the springs do. So looking at the springs and bars combined in roll:
WRf = Wheel Rate Front
WRr = Wheel Rate Rear
WRtot = WRf + WRr

The BRZ is overall about 4% stiffer than the FRS, but it is also more front biased. What the “Roll Share” columns are calculating is how much of the wheel rates in roll are due to the springs and bars (i.e. for the BRZ, in the front, the springs are providing 36% of the roll resistance, while the bar is providing the remaining 64% of the roll resistance – so ~2/3 of the roll resistance is coming from the bar). For the rears the springs are doing more work than the bar. If you run the calculations for front and rear combined, the bars are providing 56% of the total roll resistance for the BRZ and 58% for the FRS.

Adding a little more context, it's useful to calculate the undamped natural frequency of the suspension as a normalization to determine "how stiff" a car actually is. Calculating the NF takes into account spring rates and weights and results in a metric that can be compared across different cars. And in general, there are ranges of frequencies that are desirable based on what you want to do with the car (smooth ride, sporty street, low speed track, high speed track, etc).

Assumptions: I started with the published curb weight of the BRZ Limited (2776 lbs), assumed a 55/45 weight distribution, 90 lbs front unsprung mass, 83 lbs rear unsprung mass, 60 lbs less over the rear axle due to lower fuel, and added 145 lbs to both axles for driver weight. Also assumed symmetrical left/right weights. This comes to corner weights of 707 lbs per front and 548 lbs per rear. Obviously more accurate numbers could be attained from corner weighting. The equation to calculate NF is 3.13*sqrt(kw/m), where kw is the corner wheel rate in lb/in, and m is the corner weight in lbs. Using these corner weights and the wheel rates above:
The “Ride” NFs (Hz) are based on the spring only, the “Roll” NFs are for the springs and bars in roll. I actually have never seen that “Roll Frequency” metric anywhere before, but thought it would be useful to see the overall roll stiffness normalized.

The information isn’t that surprising – Ride NFs are right in line with sporty cars (similar to a stock 2008 STI), Roll NFs are also similar, although for the twins there is a lot less rear roll stiffness (mainly due to the disproportionately small bar).

So knowing all the equations and motion ratios, it should be straightforward to calculate individual setups. E.g., adding only a Strano front bar to the mix (advertised as 85% stiffer than the stock front and common for stock class autocrossers) increases overall roll stiffness by 36% and biases the overall roll rate to 76% front (up from 67%). Another setup – the RCE T2s that come in 400/400 result in NFs of 2.27 Hz Front and 2.16 Hz rear.

Check my numbers?

Much appreciated guys!

I have updated the original post to reflect the corrected numbers and included Wepeel in my "Thanks" line. Excellent work, and it's obvious that you know ALOT about suspension design.

Much appreciated Grodenglaive! The tire diameter in my wheel section does line up with your number. The natural frequency calculation was definitely off. Thanks!

So the Strano sway bar may only add 36% stiffness and RCE definitely makes for a more harsh ride... but the suspension is no longer dominated by sway bar dynamics.

Just wanted to say, this was a pretty good post!

- Andy

Great looking thread, guys. Kudos to @Shankenstein for starting this and adding a lot of useful information.


I stumbled upon this while looking for a computational model of the BRZ suspension. I am a mathematician with a slight theoretical physics background and strong computer science skills. So not much engineering experience.

Does anyone have suggestions on a resource for rapidly learning the ME side of a good suspension setup? Specifically what the ultimate, theoretical goals of an ideal setup are, and the fundamental theory that drives suspension design. Books, technical papers, online articles, forum posts, etc would all be appreciated.


I would be happy to help out with this project once I get up to speed, looks like it's off to a great start!

Quick update. Added the stock shock manufacturer and shock dyno data from RaceComp Engineering. It's old news, but I didn't read the "official" suspension/brake thread from here: LINK

typo in the ride frequencies (FR-S rear is listed twice).

i'm annoying...sorry! :lol:

is this the only source of an OEM damper dyno?

@Racecomp Engineering
@Shankenstein

Can you guys confirm that the information in the 1st post has been peer reviewed and can be taken as absolute fact, particularly the OEM weight distributions and motion ratios and damper travels.

We posted one very early on, not in this thread but somewhere. It looks similar.

EDIT: it's in post one here. :)

I looked through everything on page 1 the other day (see when I caught a typo) and everything looks pretty good.

- Andy

thank you

if possible, can it be posted in its original medium (so that it could easily be overlayed over another graph)

I'll see what I can do later today.

- Andy

You can read Tune to Win by Carroll Smith. There's a section for suspension geometry.


Sent from my iPhone using Tapatalk

The usual legal mumbo jumbo.

Shankenstein shall not be held liable for any personal or business decisions made using information supplied to this or any other website. Although Shankenstein may be a licensed engineer, Shankenstein has never been contracted by FT86Club or any other entity (private or public) to disseminate accurate information in this thread or others on this site. Any confidence in Shankenstein's posts should be tempered by the fact that Shankenstein is probably tired, daydreaming, at work, and/or drooling over build logs while posting.

That being said, the vast majority of the information has been read over numerous times by people smarter than me. It should be more accurate than most forum posts, if that counts for diddly squat. :iono:

Well, i was simply hoping for more peer-editing

particularly when it comes to motion ratios. I've yet to find anyone diagraming the suspension piecemetal.


Two weeks ago i took apart the rear coilover and attached the damper back to the car without the spring.

I then took measurements of how much the wheel travelled vs how much the damper shaft travelled and got some wild results.

even accounting for measurement error, i could not get close to the 0.75 figure ( was averaging around 0.85 ish).

Furthermore i would get different results depending on where along the path i measured. Full droop to oem height i averaged around 0.9.. from OEM height along about 1.5" of compression i averaged 0.80ish (need to check my notes, its been two weeks)

now i'm curious...