Damping ratio and coefficient question

[adambrouillard]

I'm trying to find out my damping ratio. From the OptimumG stuff I put this together, but I'm not sure it's right.

Sprung weight per corner is 270 lbs. The wheel rate is 190lbs/in.

Ccr = 2 sqrt ( mass * wheelrate)

so my Ccr is 453.

I also have a shock trace that shows 200 lbs of rebound force at 2.5 inches per second. That would be 80 lbs per inch per second.
Is the damping coefficent
80 lbs per second?

and therefore is my damping ratio 80/453 = .18?

this is with the damper on full hard

[phoenix]

Originally Posted by adambrouillard

I'm trying to find out my damping ratio. From the OptimumG stuff I put this together, but I'm not sure it's right.

Sprung weight per corner is 270 lbs. The wheel rate is 190lbs/in.

Ccr = 2 sqrt ( mass * wheelrate)

so my Ccr is 453.

I also have a shock trace that shows 200 lbs of rebound force at 2.5 inches per second. That would be 80 lbs per inch per second.
Is the damping coefficent
80 lbs per second?

and therefore is my damping ratio 80/453 = .18?

this is with the damper on full hard

I think you may have some units mixed up in your calculations.

The 200lbs of rebound force on the trace is probably 200 lbs/ft, not 200lbs/in

Therefore your wheel rate in the first calculation needs to be in lbs/ft too - i.e. 2280 lbs/ft

Critical damping with the mass given, and no other input (i.e. hitting a bump) would then be about 185.82lbs/ft at some piston speed.

This is the point where I get stuck also!

The piston/damper shaft speed on rebound depends on the magnitude of the bump the suspension is recovering from, so is a variable. With no bump encountered - e.g. the wheel passes over a dip in the road and the wheel is rebounding from the static deflection only - with the mass and wheelrates given rebound speed would be 7.452 inches/second by my calculations.

So, from the above, critical rebound damping from a 1.42" deflection (i.e. static deflection) would be 185.82 lbs/ft of rebound damping force at 7.462 inches per second.

You obviously have a lot more damping force than that - 200lbs/ft at 2.5 inches per second.

[phoenix]

Originally Posted by adambrouillard

I'm trying to find out my damping ratio.

........and therefore is my damping ratio 80/453 = .18?

this is with the damper on full hard

Damping ratio is the ratio between rebound stiffness and bump stiffness and is commonly in the range 3:1 to 1:1

i.e. rebound stiffness can be upto 3 x bump stiffness, sometimes more on very soft sprung cars or cars with very long suspension travel such as rally/offroad cars (Bilsteins for Escort Mk1 & 2 fronts are available as 260/60 or 300/70 Nm for example) ; equal bump and rebound stiffness (ratio 1:1) is more likely to be found on very stiffly sprung cars used on very smooth surfaces.

[phoenix]

OK - a bit of confusion here. There are two uses of the term 'damping ratio': the one I mentioned above is the common one that racers and (at least some) damper manufacturers use to describe their damping and the mathematical use of the term.

Having dug out a text book from my university days, in dynamics the term damping ratio is the ratio of actual damping (C) to critical damping (Ccr) - correctly expressed by you above as C/Ccr.

Sorry for the confusion.