Reading milliken it appears that desireable damping ratios for chassis are between .7 and 1 while unsprung ratios are greater than 1 for overdamping.

Upon analysis of the or current vechile, i can only get a damping ratio for unsprung mass that is much lower than that of the chassis.

From analysis of the car weight, is it fair to say this is likely to be due to the small mass ratio between unsprung and sprung mass and the low spring rates used when compared with a standard heavier race car.

Is this a standard problem within Formula SAE design constraints or can someone give me ideas for solving this problem.

Can you post some of your numbers/calculations? Approximately what your masses are, spring rates, estimated tyre rates, etc. Only need your rough numbers to see if you're doing it right - you don't have to give any secrets away.

Remember, sprung mass bounces on springs and tyres in series, while "unsprung" mass bounces between spring and tyre in parallel (which, to me, makes the name "unsprung" pretty silly).

Damping ratio of 1 or more is much too stiff. For racing maybe 0.5-0.7. For comfort more like 0.25. With conventional dampers you will have different ratios for body bounce, pitch, and roll, and for wheel hop - you can't "optimise" them all at the same time.

But, in practice, for FSAE I don't see too many problems with damping.

Z

unsprung weight: 15kg
sprung weight each front wheel: 43kg
spring rate: 1010lb/in approx.
tyre spring rate: 760 lb/in (Goodyear 13x6.5's)

What's your installation ratio (shock motion / wheel motion)? You'll need that to calculate your wheel rate (Kw = Ks * IR^2)

What are your damper forces at the speed you care about (perhaps 1 to 5 in/s)?

motion ratio of 1:1 wheel to shock.

we haven't decided on a final damping co-ef yet. we are doing prelim calcs for this purpose. The current shocks (Penske units) are hopefully going on a dyno next week. Last years team didn't have enough time to evaluate any damping stuff, they are just stock off the self configuration.

OK, do you have an extra zero in there somewhere?

1010 lb/in wheel rates are a little high for FSAE, unless you have some sort of downforce device I haven't heard of.

Does the fact that the tire is softer than your spring raise a red flag?

just slightly.

110 lb/in springs sorry.

my shot in the dark for damping ratio was .65. how does that sound? anybody want to explain how to find this value without just guessing?

here is some info:
motion ratio: 1:1
front spring rate: 130 lbs/in
rear spring rate: 160 lbs/in
chassis Hz: 3.2
critical damping constant (chassis): 39.657 lbs/in/sec
front wheel Hz: 24.43
rear wheel Hz: 23.5
front corner critical damping constant: 15.893
rear c.c.d.c.: 19.103
front damping coeff: 10.33
rear damping coeff: 12.417

does anyone want to check if i have a mistake in my spread sheet??

i also have a spot to plug in damper velocities, and it gives me the force on the damper, what is a good damper velocity in in/sec to use for this?

It seems like the damper velocites would vary depending on the situation. you need some sort of disturbance profile to estimate the effect it will have on your wheel load ie a pothole velocity curve will be different than say the shaft speeds from the car rolling in a corner. I am aware that most dampers incorperate shims for blow off which serves to reduce the damping rate at higher speeds but where should this "nose" be? I would suspect that LVDTs on your current suspension should give you a good idea on the speeds.

yes, of course the dampers are going to move with all sorts of velocities, i would like to know a "top speed" so i can calculate the maximum force that the dampers put into the chassis.

...yeah i guess i could figure a speed out, but that would be a little tedious.

Paterson,

Here is how I figure it. I have converted your units to metric, and added a bit to body mass in case you didn't include the driver (or do you have a very light car?).

Car details:
=============
Wheel Assembly = 15kg
1/4 Body = 50kg
Kspring = 20 kN/m (~20 kg/cm)
Ktyre = 130 kN/m

So;
Kbody-bounce = (Ks x Kt)/(Ks + Kt) = 17 kN/m (springs in series)
Kwheel-hop = Ks + Kt = 150 kN/m (springs in parallel)

Resonant Frequencies (assuming no damping):
===========================================
Given by;

N = 1/2pi x sqrt(K/mass)

So;
Nbody-bounce = 0.16 x sqrt(17,000/50) = 2.9 Hz

This is only for symmetric body "bouncing" (or "heaving"). In practice bounce and pitch are coupled and somewhat more complex (I'll leave for another time...). Real "bounce mode" will be similar frequency to above while pitch and roll will be higher.

Nwheel-hop = 0.16 x sqrt(150,000/15) = 16 Hz

This should be reasonably accurate, but only while tyre on ground. Once tyre starts to leave ground (ie. severe wheel-hop) frequency and required damping go down, but grip disappears!

Critical Damping Coefficients for above:
========================================
Note that these are only "critical" in the mathematical sense of lowest damping for no overshoot. Given by;

Cc = 2 x sqrt(K x mass)

So;
Ccb-b = 2 x sqrt(17,000 x 50) = 1.8 kN/(m/s)
Assumes damper between body and ground! (See notes below)

Ccw-h = 2 x sqrt(150,000 x 15) = 3 kN/(m/s)

So what dampers do you need?
============================
If you use dampers with C = 2 kN/(m/s) then Damping Ratio for wheel-hop is 0.67. This is more than enough, possibly too much. Same dampers will give DR > 1 for control of the body in bounce, so VERY stiff control of body bounce, and even stiffer in pitch and roll. Too stiff dampers on a bumpy track feel as if you are driving through thick mud - lots of drag and not a good thing. Much too stiff dampers take the springs out of action, so the car ends up bouncing on its tyres, which is as bad, maybe even worse than, too soft dampers. TOO STIFF IS NOT GOOD!

Bottom line is that C = 2 kN/(m/s) is the stiffest you will need with the above set-up. This is about the softest range for normal racecar dampers.

So really there is no justification for using push/pullrods-&-rockers to get the motion ratio up so that you can get "good control from the dampers". The extra motion ratio just increases the effective shaft stiction forces which is also bad (plus all the other disadvantages of rockers that I mentioned elsewhere).

Z

Jack,

Maximum damper force depends on the maximum bump size! Denny suggested damper velocities of 1 - 5 in/sec., which is about maximum range for body motions. Any velocities above this come from bumps, hence your damper stiffness should be reduced (ie. blow-off) above this range. Maximum bump velocity in FSAE?? Say, 20 in/sec would be a VERY severe pothole. Typically, the "knee" can start at 2 - 4 in/sec.

Your figures? Hmmmm. Compare them and your calcs to my above post...

Z

PS. (Edit) I've had another look at your figures, and converting units and using masses ~same as Paterson's, your damping coefficients come out about the same as mine.

Your guess at DR = 0.65 is ok, based on what seems to work in practice. IE., if you experiment with different dampers until the car "feels good", then do the calcs later, you find that DR is from 0.2 (for comfort, but a bit "floaty") to 0.7 (for very stable platform, but a bit "draggy").

This message has been edited. Last edited by: Z,

Interesting topic and something i wish i'd had more time to investigate this year.

Obviously, a damping ratio is given by c/cc where c is the coeficient of damping and cc the critical damping for a mode of vibration. Now, perhaps in my youth and inexperience i'm making a mistake, but i could swear that non of the equations in this thread correctly express terms for the natural frequencies of the various suspension modes (In the side view alone there area 4 modes of vibration, sprung mass pitch and translation, front unsprung mass and rear unsprung mass!). If these are not correctly expressed, then neither will the critical damping and damping ratios etc. I can apreciate the need for simplifying the situation, but i have neither the ability nor patience to solve for more than two modes. Instead, i found the best way to select damper rates is as follows:

Equations of motion -> simulink model -> input damping rates and iterate until your satisfied.

This allows you to model non-linear dampers (i.e. different compression and rebound rates) and different road disturbances at different speeds. For example, here's a pic of the response in the side view to a single road disturbance at around 30mph. The dashed lines are the unsprung mass displacements and the dotted the lines the suspension travel.



I found that the best damping ratio in pure translation was not the best for combined pitch and translation (the front had an adverse affect on the rear). Decreasing the damping ratio resulted in a faster net recovery of the front and rear (i.e. faster return to normal load on tyre before disturbance, and therefore lateral force etc). Something to think about.

If anyone would like a copy of the simulink model i used, just PM me. It's far from perfect so i don't mind sharing.

BTW, what mode of vibration is recomeded as 3Hz. Is it an actual mode, or a simplified mode (i.e sqrt[corner mass(kg)/wheel spring rate(n/m)/(2*pi)])? Might be worth a seperate thread altogether.

thanks Z,

that is what my spreadsheet has been indicating. I an unsure as to the advantages of a overdamped chassis. I though a slightly underdamped chassis would be better to drive.

Only just started reading this post. Lots of really good stuff.

Jack, the speeds we have seen in data acquisition seem to peak at about 100mm/s for "smooth" tracks. In this sort of setup the damper spends most of its time under 25mm/s. However on rougher conditions (ie Detroit) we see peaks of 150-175mm's with much more spread out velocities. We end up working on a damper shape based on the rougher conditions mainly because the "knee" location really does not matter as much for smooth surfaces. The upper end Z's suggestions of around 50-100 mm/s is around what we aim for.

One of the things that should be noted looking at these speeds is that they are quite low. These are for 1:1 motion ratios. This is one of the reasons mountain bike shocks suck. In order to get an unmodified MBD working well you need motion ratios less than 1 (wheel moving more than the shaft), around 0.6 works with the Fox shocks. This further reduces the shaft speed of the damper. Hysteresis ends up being a big problem for them and the lower the speeds the more noticeable the effect. Unfortunately it is the lower speeds that you want accurate control as they deal with the handling issues. Basically the MBD's do not shift enough fluid for control at these speeds. Just thought I'd mention that as the damping coefficients that are calculated etc do not end up being what the car sees under real conditions. Possibly one of the reasons to look into the whole digressive vs. progressive damper curves.

We also end up designing for very similar force-velocity curves for both rebound and compression. The valves we use allow us an adjustment range of damping ratios between around 0.4 and 1. We can change this range by changing some of the internals ... but it hasn't been necessary. Once again Z's suggestion of around 0.6 is pretty much how it pans out after track tuning.

David's pitch analysis is definitely on the right track. The dampers become incredible tuning tools for the transitional pitch effects such as throttle off oversteer. Also has to make you wonder whether there should be different settings for different events ...

Cheers,

Kev

Kev,

Seriously. Stop procrastinating and get back to working on your PhD.

A friendly reminder from a NY airport,
Nick & Jase

Good information,

we have just been working out our roll gradients for the system and are geeting results in the order of .2 deg/g. Seems very low to me! Anyone got any advice as to what is the standard for the SAE competition, i would guess around 1-1.5 deg/g? Thoughts?

that does seem very low (stiff). >1 deg/g would be more suitable for low speed. are you running very close to the ground? the parking lot is pretty bad in some spots.

ihave been working on our shocks spring rate , and have calculated , like 260 lb/inch in front and 430 lb/inch rear . with installation ratio of arnd 1.23:1 , pretty much same for rear and front and car weight arnd 320-330kg with driver , so wanna know , that is this too stiff for this much weighing car. our car was having a traction problem at the rear previous year,, if its too stiff , hw can we play with our adjustable MBD's , to lower our spring rate ..
the dyno is not available with us , to chk for differnet combinatiions,, thats a big prob for us too and roll gradient from the springs comin out to be 1.125 .....
and wats the general spring rate value with fsae teams.,, and at this spring rate in front, we can observe that our nose can touch durin brakin g(its lukin too losse to our likin)

vivek bithar
Team defianz racing team
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