The 2nd Official Shock Dyno Thread
 

Shoutout to @GTM_Challenge for starting this discussion (Link to Thread), @RaceComp_Engineering and @Dave-ROR for the contributions in their monster thread.

There's alot of great information scattered throughout the Interballz about dampers and shock dyno data. I'm hoping to consolidate things for the 86 community.

First off... the terms: damper, dashpot, shock absorber, shock, dampeners, etc are all the same thing. They are transducers that convert one form of energy to another. Movement (velocity) is turned into heat. They can be compared to an electrical resistor, friction, or a nozzle (fluid flow through a small orifice).

Good reference material:
Link to OptimumG's Technical Papers (highly recommended)
Link to Westfield Guide
Link to Roehrig Dynos
Link to Penske troubleshooting
Link to Penske Double Adjustable Manual
Link to Tein's guide
*insert more stuff here*

Things we care about:
Natural frequency
This is the frequency at which a spring-mass system will vibrate/resonate at from a step input. Looks like this:
http://upload.wikimedia.org/wikipedi...oscillator.gif

You can calculate it using this:
http://upload.wikimedia.org/math/e/d...83f7abcd95.png
where

k = spring rate (in kg/s^2)
m = sprung mass (in kg)
pi = tasty

Generally,

• 0.5 - 1.2 Hz for passenger cars
• 1.2 - 1.8 Hz for sportscars
• 1.8 - 3.0 Hz for modified sportscars
• 3.0 - 5.0+ Hz for aero-dominated cars

Our OEM natural frequencies are:

Front = 1.37 Hz
Rear = 1.33 Hz

Damped Natural Frequency
When you introduce a damper, it affects the system. You move from this governing equation of motion:
http://upload.wikimedia.org/math/f/2...37d26bb7cf.png

to this:
http://upload.wikimedia.org/math/7/6...e3b37a84bd.png

The first term describes the acceleration and forces. The second term describes the damping and loss terms. The third term describes the spring and restorative terms.

The terms can be connected back to real parameters:
http://upload.wikimedia.org/math/6/d...aa1d7bbb3c.png
where

w_o = natural frequency (in radians)
k = spring rate (in kg/s^2)
m = sprung mass (in kg)

and
http://upload.wikimedia.org/math/b/2...12b64103e8.png
where

zeta = damping ratio (unitless)
c = damping coefficient (in kg/s)
k = spring rate (in kg/s^2)
m = sprung mass (in kg)

Damping Ratio
Many theory guys will tell you that zeta = 0.707 is the best, and I tend to agree. Many tuners will tell you zeta = 0.65, which is just fine too. You want to choose a value that has the right mix of rise time, settling time, overshoot, and steady-state bias. Unless your suspension is ridiculously overdamped, you probably won't have steady-state bias. Rise time is important, but not the most relevant to the discussion right now. Let's focus on settling time and overshoot (which are related).

Settling time is the amount of time it takes for a system to recover from a step change. Generally, we talk about 95% settling time which means you won't see any more deviations beyond (0.95, 1.05). Overshoot is relatively simple topic.

Here's what a few different values look like:
http://upload.wikimedia.org/wikipedi...ping_1.svg.png

For zeta = 0.5, you can estimate the 95% settling time to be ~5, and the overshoot to be 15%.

General suggestions:

low speed (< 2 [Front] or 1.56 [Rear] in/sec) compression = 0.66
high speed (> 2 [Front] or 1.56 [Rear] in/sec) compression = 0.33
low speed (< 2 [Front] or 1.56 [Rear] in/sec) rebound = 0.75
high speed (> 2 [Front] or 1.56 [Rear] in/sec) rebound = 1.50

As you can guess, this means we'll be soft during speed bumps, well-controlled during normal humps in the road, and sluggish when going over potholes.

Google Doc that I'm attempting to fill with shock data: LINK to Google Doc


List of Shock Dyno Data:
OEM SHOWA:
http://philbedard.com/pics/shockdyno.jpg

RaceComp Engineering Tarmac T2:
Front
http://www.ft86club.com/forums/pictu...pictureid=8136
Rear
http://www.ft86club.com/forums/pictu...pictureid=8137

KW Clubsport:
Front
http://farm8.staticflickr.com/7289/8...21212bed_b.jpg
Rear
http://farm8.staticflickr.com/7282/8...1ac013df_b.jpg

Fortune Auto 500 series:
http://www.fortune-auto.com/BRZ%20SH...EP%20GRAPH.jpg

Ohlins DFV:
Front
http://farm8.staticflickr.com/7285/8...92e35ee7_b.jpg
Rear
http://farm8.staticflickr.com/7286/8...c01cfa9e_b.jpg

ISC N1:
http://i167.photobucket.com/albums/u...results001.jpg
http://i167.photobucket.com/albums/u...noresults2.jpg

OEM Springs:
http://philbedard.com/pics/brzvsfrs.jpg

I'm getting much lower natural frequencies for BRZ.

Front spring rate is 156 lb/in = 27328 N/m
Front motion ratio is ~0.95
Front wheel rate is 27328 N/m * 0.95^2 = 24663 N/m

Front weight is ~2915 lb *.54 = 1574 lb.
Weight on one front wheel = 787 lb. = 357 kg
Unsprung mass ~55 lb. = 25 kg
Sprung mass at one front corner ~357 kg - 25 kg = 332 kg

f = 1/2pi * sqrt(k/m) = 1/2pi * sqrt(24663 N/m / 332kg) = 1.37 Hz

Going through the rear using 198 lb/in spring rate, 0.75 motion ratio, and 280kg sprung mass at one rear corner, I get 1.33 Hz for the rear.

2 Hz is pretty unheard of for "normal" stock street cars. Very stiff for a production car. My FD on 13kg front 11kg rear springs is at 2 Hz (1.96F/2.03R), and it's *way* stiffer than a BRZ!

so Zeta is critical damping im assuming. Upon quick search on google, it seems that the frequency list for road cars vs sports cars and race cars varies between both @ZDan's findings and @Shankenstein's findings.

Fairly good reference article: http://www.rqriley.com/suspensn.htm

Off the top of my head, I think those natural frequencies are quite high. I've had a few beers but they're not that high stock. More like 1.3 to 1.5 ish.

I'll try to contribute some...umm...later.

- Andy

c is not "ideal damper piston speed". c is damping in units of force per velocity. In SI units, Newtons over meter-per-second, or N/(m/s), often shown as N-s/m. For shocks c is not constant, as shown in the plots c is ideally higher for low shock speeds and lower for higher speeds, continuing to decline with velocity. A shock with a constant c would just be a straight line starting at zero and increasing linearly with velocity.

Ahem... dampeners...



subed.:D

Ahem, they are most certainly NOT "dampeners"!

As usual, my posts are full of errors... just to keep everyone on their toes. Those values were borrowed from another thread, and the guidelines were from the Westfield guide.

Guilty as charged. No excuse, Drill Sargent!

From the suspension modeling thread, I've copy-pasta'd this:

Front (FR-S) = 1.24 Hz
Front (BRZ) = 1.43 Hz
Rear (FR-S) = 1.54 Hz
Rear (BRZ) = 1.47 Hz

It's not exactly your 1.37 & 1.33 Hz values, but we're atleast away from the 2.1 Hz value before (Doet!).

Those numbers are also too high. Looks like they incorrectly multiplied the spring rates by the motion ratios to get the wheel rates. You have to multiply spring rate by the SQUARE of the motion ratio to get the wheel rate.

Get out.

jk. ;)

- Andy

http://grammarist.com/usage/dampen-damper-dampener/

They mean essentially the same thing in this instance.

@Racecomp Engineering : Do you have the T2 charts available to add to this thread?

Yes, I will add those and the T0 charts later today.

- Andy

Main post updated. Some errors fixed, and hopefully it flows better.

Forgive me as I continue to nit-pick!

Confusing way to do the units.
Spring rate is more logically done in units of force per distance rather than kg/s^2. Pounds per inch (lb/in) or Newtons per meter (N/m). Coilover springs are often rated in "kilograms per millimeter", but it's important to note that that is kilograms-FORCE per millimeter (kgf/mm). 1kgf = 9.81N.
So you take spring rate in kgf/mm and multiply by 9810 to get the rate in N/m, which works in the equations.

Ditto for the damping. Newtons per meter-per-second, N/(m/s) or N-s/m makes more sense to use than kg/s.

In both cases, the units are actually the same if you swap N for kg-m/s^2, it's just a question of presenting them in a context that makes sense or not.