I am currently a senior doing a research project on the damping effects with stance coilovers throughout a turn. I had a few technical questions about mapping these oscillations with theoretical equations and was wondering if you guys knew anyone who works with car suspension engineering.

Any help or further questions would be nice!

This program would help assist drivers in tuning their suspension for tracks at a much faster rate by mapping the oscillations and reducing them as fast as possible by adjusting the damping settings. Any input on the goods/bads of this for your tracking days is appreciated.

Thanks
Joe

If thats correct then you will run into mixing of data since an improper damper on one corner is going to yield pitch and yaw results giving you a dynamic curve in relation to the dynamic shift of the chassis. You would have to have some sort of baseline for a natural curve to isolate the damper effect.

The easiest method would be to install sensors on the bottom and top of the spring to measure distance. That would you independent results regardless of tire spring oscillation, chassis flexure, and allow you to focus on steady state and recovery situations. This is the method that has been used in the past.

The program would have to record positions rapidly and install into a database for each corner. You'd then utilize a plot function to show movement of the shock over time. I'd set time to be scaled with an input.

I think you will find that Stance is crap.

The sensor method does seem very practical but I feel if the accelerometer can just record vertical displacement we would be fine as well. Labview coupled with the accelerometers will record the data in real time and store it on a graph which would display the displacement changes over time.

I am currently trying to model this system using MATLAB but haven't been able to find much information on non harmonic driven oscillations.

thx for your opinion nismo_freak

You'd need to measure hub displacement relative to the body in a vertical axis like I said before. Otherwise you will be missing the midrange to high speed valving picture.

what are your questions. i have no idea what exactly you're trying to find out, other than modeling your coilovers. do you want to find the damping ratio or something?

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As for modeling I will be using the Runge Kutta method with a sprung and unsprung damping and spring model.

We found that we need to find the forces being placed on each of the tires as the weight of the car shifts. This is all a function of gforce and turning radius. So using this forcing function and placing it into the runge kutta we can chart the different displacements that the suspension will face over the course of braking, turning, and accelerating.

The only unknown I have left is the c in mx'' + cx' + kx = F(t)

We are making good progress with this project. Some of the key things I have learned thus far about racing is that light rim weight and camber angle does matter. Wider tires provide more traction. This might be obvious to some of you guys but I truly didn't understand this until I saw some equations and actually thought about it hahaha. Weight transfer is crucial since it distributes the grip on your tires.

If you guys want any links or further information about this stuff just let me know!

get the plot in force vs velocity like this one:

after you get the plot, you need to get an equation for the high and low speed damping for both jounce and rebound. if it's linear like the above shock, then it should be pretty easy(the damping coefficient will be a constant). if it's more logarithmic, then you will need a regression (from excel, matlab, etc), and the cx' will be a c*ln(x') or c*sqrt(x') or whatever fits best.

then you verify your model with testing using lvdt's and appropriate daq stuff.

alright now I just have to look further into this to see if rebound etc will have any impact on my c factor.

Are you saying to use these values in an Mx'' + cx' + kx = F equation to solve for c?

upon further inspection if its a linear graph y=mx +b should suffice...

Modified by bootscut at 7:44 PM 4/18/2008

So with this dyno there seems to be 4 sections:
Low speed rebound
High speed rebound
Low speed compression
High speed compression

thats 4 different c values!

So when the sprung mass and unsprung mass model collide (or compress) depending on the velocity of the shock @ this time the damping coefficient will either be a low speed compression c or high speed compression c.
When the sprung mass and unsprung mass retract from each other (rebound) my damping coefficient will be a low speed rebound or high speed rebound.

This is a lot of variables to enter into my MATLAB program! But this is the only way to get the most accurate model.

Now I am unsure how the sprung mass and unsprung mass move relative to eachother... I guess I can look @ the plots I have made so far to see if there is some sort of correlation. I really hope to show you guys what I have made so far. I am learning a lot about the intricacies of suspension tuning!

If you guys have any questions or general comments please let me know!

:D

that's exactly how i would approach the problem. i'm very interested to see your results.

also, just an fyi for the low and high speed sections: the low speed section is the damping coefficient used while the car's body is rolling(eg: slaloms), the high speed damping is the number you should use for driving over bumps. you might have already known that though.

Quote, originally posted by bootscut »

Now I am unsure how the sprung mass and unsprung mass move relative to eachother... I guess I can look @ the plots I have made so far to see if there is some sort of correlation. I really hope to show you guys what I have made so far. I am learning a lot about the intricacies of suspension tuning!

Remember that the response depends on the force input frequency, and the natural frequency of the system.

When Input Freq. << N.F of Sys., the Amplification response is 1 (So the sprung mass will match the amplitude of the input frequency)

When Input Freq. = N.F, Amplification factor is very large. So the sprung mass will have very high amplification.

And Finally, when Input Freq. >> N.F, the Amplification factor approaches zero, and you get a silky smooth ride.

I think the velocity on the graph represents the shock movement. Basically how fast its moving up or down; so initially at low speeds we will have a c_rebound_low and c_compression_low. My program will use a bunch of if else statements which will apply these different c values if the velocity is increasing (rebound) and if its a certain range (low vs high speed damping).

Quote, originally posted by crzycav86 »

Remember that the response depends on the force input frequency, and the natural frequency of the system. When Input Freq. << N.F of Sys., the Amplification response is 1 (So the sprung mass will match the amplitude of the input frequency) When Input Freq. = N.F, Amplification factor is very large. So the sprung mass will have very high amplification. And Finally, when Input Freq. >> N.F, the Amplification factor approaches zero, and you get a silky smooth ride.

I will look further into this but our forcing function is not a simple harmonic oscillator therefore it does not have a frequency i.e Fsinwt. Our equation is F(t) which is a weight transfer force that depends purely on the change of g-force on the car. So I am inputting different forcing functions that may look like a triangle, zig zag, or squiggly blob lol. Basically my forcing function is dependent on the weight transfer of the car from braking to turning and exiting the turn. So I can't just match frequencies since we don't exactly have one in the first place [=

The method I am using is a finite difference method or runge kutta which allows an infinite amount of inputs into the system

Right. Well if your forcing function is a step function instead of harmonic, you should notice that the velocities stay in the "low speed" range. Because the shock speeds due to body roll are much slower than in bumps. Thats why the slopes in these sections are different as well - you want different equations of motion depending on whether you're going over a bump or if the body is rolling.

Also, you can find a lot of useful information in vehicle dynamics textbooks such as gillespie and milliken & milliken. you probably have a copy somewhere in your school.

It basically says the car is moving in the range of + .5 inches which seems reasonable given the impulse forcing function.

The bottom graph is of the system as a whole w/o the additional tire model, this seems to be less accurate and is easily overdamped by the current damping settings

We have a presentation tomorrow so I will be able to upload the entire slideshow etc. I have learned a lot so far and we haven't even begun testing, I just hope that our theoretical model is somewhat close to the actual readings we will get when we test since a lot of minor things have been assumed.

There are definitely a lot of other parameters that should be considered, however given the time and funding for the project a lot of it was simplified in order to fit into the class description.

I ended up getting an A on the project but it didn't work. Our data acquisition was horrible, so LVDTs really seem necessary in order to further minimize error that can be encountered.