21 replies to this topic

[Greg Locock]

Has anybody got a matlab script that correctly turns a normal set of pacejka coefficients (ie in units of kN for Fz, SI elsewhere, and degrees as angular measure), into a usable matlab model?

[cheapracer]

Greg if I knew what you were talking about - well then I would know what you were talking about

Anyway, the only thing I have that touches that subject is some Excel sheets to visualise 3 tyre curve's plots. Don't bag me out too much if it's totally useless to you!

http://uploading.com...ecurve.zip.html

Password; greg

[Greg Locock]

Thanks for trying.

Pacejka models are used to codify that sort of data into a small number of coefficients. It includes things like the tire load sensitivity, camber gains, saturation and so on.

Here's an explanation that drops out just as it gets to the important bit.

http://www.racer.nl/...nce/pacejka.htm

You might have some luck if you look on the sae store for his papers www.sae.org and the google for the paper number

Luckily Brian B has already written about this

http://phors.locost7.info/phors22.htm

Crazy people are welcome to decipher the second page, the first page is what I'm interested in.

[kangaloosh]

Yes,

Sending PM.

Chris

[exFSAE]

Keep in mind, Pacejka coefficients are NOT non-dimensional.

It's super easy to come up with a matlab script that spits out force and moment based on input parameters, but you'll need to know ahead of time if it will expect Newtons, KN, lbs, degrees, radians..

[Greg Locock]

Yes, we'd worked that out, but I've tried four different models, some of them with defined units, and none of them worked properly, hence my frustration, and the thread title. To make it even more fun the tool I am supposed to use at work for this is currently broken, that's why I was writing my own.

[exFSAE]

It should be real easy to do. Just a function with a couple lines of equations. The sign and unit conventions are killer though!

[Paolo]

Hi Greg

I have worked a lot with Pacejka models in Matlab; I have also written a software able to find optimum Pacejka coefficients starting from test data using genetic algorithms.

If I can be of any help I''ll be happy to; I only have one problem: I did not understand what your problem is...

my fault, of course, but if you'll care to elaborate I'ìll see what I can do.

What do you mean by "usable Matlab model"?
An array of results or actual code lines giving forces as an output when provided with coefficients and loads as input?
Or something else?

[Greg Locock]

Hi Paolo

Chris sorted me out for now. The problems were the usual embarrassing finger trouble type stuff, I am very rusty on Matlab.

However having got the programming settled down now I find a new problem - if you divide the aligning torque by Fy you get the trail.

Now, physically, the trail can't move outside the contact patch. (Well OK, perhaps it can, but not by much)

But for our (proprietary) curve fits I get trails all over the place, partly because near 0 slip angle the curve fitted curves don't quite go through the origin together. That's because we curve fit for Fy, and AT, and so trail is an outcome.

For me this is crazy bad news because the trail directly affects the SWT, and most of my work is related to steering efforts etc.

I also get very bad results when I include camber.

Incidentally for anyone who is interested but can't afford to buy Matlab (ie non-millionaires), I am now using www.octave.org at home which is an open source (ie communist) equivalent of Matlab. The bulk of the syntax is identical and they have improved their graphics and editing a lot with v3. Highly recommended. I still prefer Scilab but it is subtly different from Matlab throughout, trying to work in both makes my head spin, whereas Octave to Matlab and vice versa is pretty easy.

[Paolo]

Well, I don't know how much you can fiddle with your proprietary curve fitting; I usually write the stuff from scratch and it helps solve these problems.
One thing I would do, in this case, is setting limits to the search space; i.e. do not accept solutions that bring too high a trail or accept them but giving them a fitness penalty.
Another thing that can be done is to give higher fitness to solutions that provide a better fit around zero slip angle.

What happens around zero slip angle is anyway heavily affected by the particular Pacejka model you are employing; I experimented with "basic" early model and with Pacejka 96, and the latter is a lot more sophisticated, mainly to give a better fit in the zone of your interest, yet is a lot more prone to give "impossible" results with minimal coefficient variations.
I personally prefer to employ non-binary evolutionary algorithms there, since they allow extremely fine parameter adjustment at the price of slighty longer calculation times, and are not restricted by the initial choice of search space boundaries, that is, if I made a wrong assumption on where a coefficient value lies they can "correct" my mistake.

[Gecko]

Originally posted by Greg Locock
But for our (proprietary) curve fits I get trails all over the place, partly because near 0 slip angle the curve fitted curves don't quite go through the origin together. That's because we curve fit for Fy, and AT, and so trail is an outcome.

For me this is crazy bad news because the trail directly affects the SWT, and most of my work is related to steering efforts etc.

I also get very bad results when I include camber.

It sounds like a very similar problem to the center of pressure for airfoils in aerodynamics, where you divide the moment with the lift to get its location. Of course, an airfoil can have a moment (and most all cambered ones do) even when there is no lift present, so the center of pressure is ill defined in that situation.

What aerodynamicists like to do is define a location that is not the ratio between moment and force, but rather a location around which the moment curve is flat with respect to the changesin angle of attack. This decomposes the moment into a constant component that is there regardless of lift, and a separate component that is due to lift.

Trail for a tyre is likewise ill defined when lateral forces approach zero. Essentially what you can do is to decompose the torque into a constant component that is there regardless of any lateral force generated, plus the torque due to the actual lateral force. For the Pacejka curves, take the aligning torque at the point where the lateral force is 0, and subtract it from the total curve for the aligning torque. Now the division between the shifted torque curve and the lateral force will behave well and give you the tyre analogue of the aerodynamic center, but you have to keep in mind that the tyre has an additional torque (the one you subtracted) that does not originate from the net side force (as you say, this occurs especially in cambered situations, much like for an airfoil).

[Ben]

Originally posted by Greg Locock

Incidentally for anyone who is interested but can't afford to buy Matlab (ie non-millionaires), I am now using www.octave.org at home which is an open source (ie communist) equivalent of Matlab. The bulk of the syntax is identical and they have improved their graphics and editing a lot with v3. Highly recommended. I still prefer Scilab but it is subtly different from Matlab throughout, trying to work in both makes my head spin, whereas Octave to Matlab and vice versa is pretty easy.

Good to know - I'd always wondered how those two compared, but never had the time - plus full Matlab license at work means I've never needed to.

We give fitted Pacejka coeffs for DTM, Sportscar and F3, but personally if it were me doing the simulation at a team I'd want the raw F&M data. Particularly if you're using something like RaceSim that has it's own model that want Cornering Stiffness vs. Load and "mu" vs. load.

Having run a slip angle sensor on an LMP all year I can say with some certainty that Flat-tracs over estimate friction. In addition most Pacejka fitting is done on a sparse set of data - i.e. most of the data is generated by fixing one parameter and sweeping another - this gives you clusters of points with relatively little in between.

We've come across people using SurGE (google "SurGE surfacing") to fit a smooth surface through the test data and then fit Pacejka to that surface rather than the raw data.

I haven't had to fit recently because we're using RaceSim rather than Pacejka. From a race tyre perspective I don't find Pacejka very useful. If I were simulating I'd be developing a model using the techniques in Pacejka's book - i.e. TreadSim using a combination of stretched string and brush models and measuring the stiffness of the real tyre to generate inputs and using friction data derived from track testing. Thermal effects could then be added on top.

I have a big problem obsessing over Pacejka coefficients when the tread surface temp ramps up over the course of a test run. It strikes me as wasted effort for a model that doesn't consider this thermal effect on grip.

Ben

[Greg Locock]

All good points (the aero analogy is dead on in my opinion). I'm actually just giving these models to some students who are building a quarter car model, so linear range is fine, and anything that is in the ballpark will do.

I agree that Flattrac data is of limited use, we routinely apply corrections of 20% to the forces they generate. Now that we have wheel force transducers that are reasonably small we could in theory go and measure our own tire data at the same time as the dynamics of the car (dream on).

[Ben]

Old thread alert!!

I mentioned TreadSim before and must confess I've never bothered to type the thing out of the appendix to Pacejka's book. Fortunately they've published a pdf of the appendix on a website:

http://books.elsevie...s/appendix2.pdf

Pasted the code into Matlab and it appears to run with one line commented out - matlab should tell you which one depending on how you copy it. Haven't worked out the implication of the line yet though :-)

Ben

[Greg Locock]

Line 129? looks like it was some idle musings in a comment. Not wishing to look a gifthorse in the mouth, but sheesh guys, ever heard of structured programming?

Anyway thanks for that, I suppose I'm going to have to buy that book.

[Ben]

Originally posted by Greg Locock
Line 129? looks like it was some idle musings in a comment. Not wishing to look a gifthorse in the mouth, but sheesh guys, ever heard of structured programming?

Anyway thanks for that, I suppose I'm going to have to buy that book.

Pretty it ain't, agreed. Some other good tyre stuff here:

http://www.ipg.de/up.../15_Fevrier.pdf

http://www.ipg.de/up...c_200611_03.pdf

It looks like Dufornier's thermo-mechanical model has three zones of tread - much like TreadSim can have but with thermal effects added on top. Seeing as Dufornier's ex-Michelin, I'm guessing the Michelin model's similar.

Ben

[exFSAE]

Pac at least gets you somewhat settled for linear range effects, which do help set up limit conditions. Particularly if your tread rubber is ridiculously thin and is a temperature-insensitive brick. Ahem.

But yea, there are much better items out there.

[munks]

Old thread alert!!

I mentioned TreadSim before and must confess I've never bothered to type the thing out of the appendix to Pacejka's book. Fortunately they've published a pdf of the appendix on a website:

http://books.elsevie...s/appendix2.pdf

Pasted the code into Matlab and it appears to run with one line commented out - matlab should tell you which one depending on how you copy it. Haven't worked out the implication of the line yet though :-)

Ben

Any chance you have that file lying around somewhere? It's no longer available.

I'd like to try it out, but I don't really plan on typing in 16 pages of Matlab code and praying that I didn't make a typo or seven.

[Greg Locock]

Any chance you have that file lying around somewhere? It's no longer available.

I'd like to try it out, but I don't really plan on typing in 16 pages of Matlab code and praying that I didn't make a typo or seven.

I've got the pdf or the matlab somewhere, pm me for it.

[louisgag]

I've got the pdf or the matlab somewhere, pm me for it.

I too would be interested in the matlab file I anyone has it handy.

-Louis

[Greg Locock]

I too would be interested in the matlab file I anyone has it handy.

-Louis

I have it but not handy, give me a few days

[mansour]

Hi Greg

I have worked a lot with Pacejka models in Matlab; I have also written a software able to find optimum Pacejka coefficients starting from test data using genetic algorithms.

If I can be of any help I''ll be happy to; I only have one problem: I did not understand what your problem is...

my fault, of course, but if you'll care to elaborate I'ìll see what I can do.

What do you mean by "usable Matlab model"?
An array of results or actual code lines giving forces as an output when provided with coefficients and loads as input?
Or something else?

I dear Paolo
right now I am working Hard!! on finding pacejka coefficients by Simulate Annealing algorithm ... but my solution is extreamly depend on primary value of coefficient... it is really tormenter for me because I have read some articles claim that they have found the coefficient without being sensitive to the start point of coefficients but I CANT ... please if it is possible help me in this... and also I am wondring if I could have your Matlab code of GA to get some ideas of that...
that is my Email Address if it is needed: smtoraabi@ymail.com
thank you
with regards
bye for now