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Suspension modeling question

 
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deathfrombelow



Joined: 17 Nov 2007
Posts: 4

PostPosted: Sat Nov 17, 2007 4:15 pm    Post subject: Suspension modeling question Reply with quote

I came across this great site while researching how to model my cars suspension so that I can investigate specs for different brands of coilovers. So far everything I have been doing is pretty simple. I've been using very basic equations for a damped harmonic oscillator. I know that this is far from the most accurate method, but I think it should get me in the ballpark.

Does anyone have any suggestions on how I can add the gas pressure of the damper to this model? At first I thought I could just estimate how much force it takes me to compress a damper and then subtract that force from the spurng weight. Example, if it takes about 50 lbs of weight to get the damper to compress then just take that off of the sprung weight. I thought this would be an acceptalbe approximation until I came across a damper that takes about 150 lbs and I can barely compress it at all. If I just subtract the 150 lbs from the unsprung weight, it has a very large effect on what I come up with for damper curves. Please advise.
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Wiisass
Head suspension nerd


Joined: 09 Nov 2005
Posts: 131
Location: Philly

PostPosted: Thu Nov 22, 2007 3:42 pm    Post subject: Reply with quote

What equations are you using and is it a 2 degree of freedom system? If it's not, it won't be very accurate at all considering that the rebound (extension) side is going to have different values than the compression side. I use a simple 2 DOF spring mass damper system for a lot of my base calculations, and then exapnd into a 4-corner model or one of my spreadsheets that I have setup to take pretty much everything into account.

As for gas pressure, you need to consider it a spring if at all. But in most cases, it's negligable. The spring rate from the gas pressure is in parallel with the main spring, so it would be added to the main spring rate and then modified by the installation ratio.

Also, how are you measuring gas pressure? If it's not measured right, you are going to have bad values. Some dampers will have a lot of preload on the shim stacks on the compression side making them hard to compress by hand. So if you compress the damper 1" and it takes x lbs of force to do that, you need to let the inside of the damper settle and then measure the amount of force it takes for that damper to remain at 1" of travel.

Tim
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deathfrombelow



Joined: 17 Nov 2007
Posts: 4

PostPosted: Thu Nov 22, 2007 7:57 pm    Post subject: Reply with quote

Thanks for your reply. I am using a very simple 1 degree of freedom system. The variables are sprug mass, spring rate and damper rate and motion ratio. I'm not really sure how to figure out what is critically damped for the 2 degree of freedom system. I also don't know the spring rate of the my tire, so I thought that the 1 DOF system would be good enough for a starting point. I will try and post up the equations that I am using tomorrow.

Wiisass wrote:
What equations are you using and is it a 2 degree of freedom system? If it's not, it won't be very accurate at all considering that the rebound (extension) side is going to have different values than the compression side. I use a simple 2 DOF spring mass damper system for a lot of my base calculations, and then exapnd into a 4-corner model or one of my spreadsheets that I have setup to take pretty much everything into account.

As for gas pressure, you need to consider it a spring if at all. But in most cases, it's negligable. The spring rate from the gas pressure is in parallel with the main spring, so it would be added to the main spring rate and then modified by the installation ratio.

Also, how are you measuring gas pressure? If it's not measured right, you are going to have bad values. Some dampers will have a lot of preload on the shim stacks on the compression side making them hard to compress by hand. So if you compress the damper 1" and it takes x lbs of force to do that, you need to let the inside of the damper settle and then measure the amount of force it takes for that damper to remain at 1" of travel.

Tim
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Wiisass
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Joined: 09 Nov 2005
Posts: 131
Location: Philly

PostPosted: Sat Nov 24, 2007 12:18 pm    Post subject: Reply with quote

That model won't get you very far. You only have part of half of the system, you need the tire in there and the unsprung mass to come up with more of it. Modeling the gas pressure at this point for you is pretty pointless.
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deathfrombelow



Joined: 17 Nov 2007
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PostPosted: Sat Nov 24, 2007 9:00 pm    Post subject: Reply with quote

Tim,

I know that you just said that the model that I was using would give very poor results, but here is the equation that I was using:

%Critically Damped = Lambda / ( 2 * sqrt ( K * M ) )

Where
Lambda (taken from shock dynos) = force / damper speed
K = spring rate
M = sprung mass

For a dyno plot a particular coilover, I would pick off half a dozen or so points off of both the rebound and compression plots. I then would calculate lambda for those points and then the % critical damping for each point in both rebound and compression. From the research that I had done, I expected the idea coilover to be about 65% critically damped at slow speeds and taper down to maybe 30-40% at higher speeds.

I thought that producing graphs of % critically damped vs damper speed would give me a good comparison of the coilovers out there for my WRX.

I have tried searching the internet for a detailed explanation of how to determine % critically damped for a 2 degree of freedom system with out much luck. Perhaps it is because there is not an easy equation like the one that I listed above and I need to calculate it using log decrement from a graph of the displacement over time.

I have also found several references to an equation for Road holding.

Rh = sqrt(pi*As*w1^4*(4*B*u^2 *d^2+B^2*u^3-2*B*u-1)/(4*g^2*u(u-1)*d*w2)

Where
As = 8
w1=sqrt(k1/m1)
w2=sqrt(k2/m2)
u=(m1+m2)/m1
B=w1^2/w2^2
g=9.8
d=damping coefficient (% critically damped)

One minimized Rh by varying d to find the optimal damping coefficient. This takes into account the tire spring rate and the unsprung mass. I have read that the damping ratio of a tire is around 7%, so I am assuming that the calculated damping coefficient would just be for the strut.

I have attempted to measure the spring constant of the tires on my car by measuring the compression of the tire where it meets the ground and by calculating the weight on that tire.

Would the Road holding equation be a better approximation than the 1 degree of freedom model? Am I still barking up the wrong tree? I appreciante any help or advice that you could give that would get me going in the right direction.
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Wiisass
Head suspension nerd


Joined: 09 Nov 2005
Posts: 131
Location: Philly

PostPosted: Tue Dec 04, 2007 2:01 am    Post subject: Reply with quote

You're vibrations equations are correct, but they won't give you what you think they are. Also, depending on how you look at it, you will only be getting one side of the damper curve. You really need to look at it as a 2DOF system and figure out how each spring contributes to either side of the damper. The damping coefficients won't be the same in both directions, so applying the numbers you're calculating to both rebound and compression is giving you nothing of use.

I mean you're on the right track, you just need to put more thought into the basic model and then you will have a much better approximation to what you need.

As for the road holding equation, where did you find it? From everything I could find and the equation, it looks like it's calculating transmissibility of the suspension. It also only considers a damper with a single damping coefficient, meaning the same during compression or rebound, so it's missing part of the system. Unless it's just a measure of transmission of the road to the chassis, then it would be using the compression damping coefficient. So it may be of some use, but seems like it's not going to help too much for what you want it to.

You're best bet would be to start with a Vibrations textbook or even Racecar Vehicle Dynamics by the Millikens. This will at least give you a better starting point for the analysis you want to do.

Or you could gather the data and pay me to analyze it for you, that's always an option.

Tim
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deathfrombelow



Joined: 17 Nov 2007
Posts: 4

PostPosted: Fri Dec 07, 2007 5:26 pm    Post subject: Reply with quote

Here is where I found the info on Road Holding http://www.fsae.uvic.ca/Car/car2005-Damping.htm

According to this webpage, the Road Holding is suppose to help you determine the ideal % critically damped at high speed damper velocities. The goal is to minimize Road holding by choosing the critical damping ratio. I don't see why you couldn't solve it for either rebound or bump, but without the real source document for the background on this equation who knows if that is valid. For what it is worth, this equation tells m that around 35% critical damping is right for my car.

I've been accounting for the difference in rebound and bump damping rates. If I just add the tire's spring rate and the coil's spring in series for a spring, that should be better that what I was doing. I wish I had the money to pay for a more detailed analysis, but I need to save my pennies for the new dampers that I want to buy.
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