Tire Analysis Best Approach?

Hello Everyone,

My name is Nils and I am a current member of the chassis group on Michigan Tech's FSAE Team; I'm new to tire analysis, and not incredibly proficient with Matlab, so pardon the rookie questions.

I have been trying to effectively generate Fy vs. SA curves to analyze tire characteristics, both to make an informed decision on tire compound (R25B vs. LC0), and to optimize camber gain, and have tried the following approaches.

- I have gotten the mrandim matlab code provided by the TTC to run for rounds 1-3, but since not many 10in tires (the tire size our team uses) were tested in this range, it is of limited use for us as I am most interested in round 5 data. I have downloaded the code provided by Bill Cobb but have not made significant progress getting it to run.

- I imported the TTC raw data into excel, and plotted SA vs. Fy manually for different Fz loads. However this process is very tedious, and somewhat inaccurate since the data is not a smooth line. In theory I could put a higher degree polynomial best fit line on this plot, and subsequently compare a plot of these best fit lines for different tires/different Fz's?

- In searching for additional resources online, I found an MFeval matlab code (https://www.mathworks.com/matlabcent...e/63618-mfeval) which evaluates magic formula 6.1.2 with provided coefficients in a .TIR file. In going through older TTC threads, I was able to locate the .TIR files for rounds 4 and 5 on that forum (round 5: http://www.fsaettc.org/viewtopic.php...hilit=tir#p717), however the file does not seem to have all the coefficients which this program needs to run. I copied in the following coefficients over from a .TIR example file provided with the code, and got the code to run, but the plots are not right, which makes sense since the coefficients are not correct for the given tire.

Sorry for the long post; does anyone have advice on how I might better evaluate this data and get the results I'm looking for (SA vs. Fy plot at different Fz loads/camber angles)? Unfortunately our school does not have access to OptimumTire.

Thanks for any and all advice!


Below are the additional coefficients which I needed to copy into the TTC TIR file to get the MFeval program to accept it:

$-------------------------------------------------OPERATING_CONDITIONS
[OPERATING_CONDITIONS]
INFLPRES = 68947.6 $Tyre inflation pressure
NOMPRES = 68947.6 $Nominal tyre inflation pressure
$---------------------------------------------inflation_pressure_range
[INFLATION_PRESSURE_RANGE]
PRESMIN = 65000 $Minimum valid tyre inflation pressure
PRESMAX = 75000 $Maximum valid tyre inflation pressure
PFZ1 = 0.8260162 $Pressure effect on vertical stiffness
Q_RE0 = 1.00093 $Ratio of free tyre radius with nominal tyre
Q_V1 = 0.0007860039 $Tyre radius increase with speed
Q_RA1 = 0.4998311 $Square root term in contact length equation
Q_RA2 = 1.426644 $Linear term in contact length equation
Q_RB1 = 1.297038 $Root term in contact width equation
Q_RB2 = -1.500634 $Linear term in contact width equation
PPX1 = -0.9782748 $linear influence of inflation pressure on
PPX2 = 0.5317977 $quadratic influence of inflation pressure on
PPX3 = 0.002880684 $linear influence of inflation pressure on peak
PPX4 = -0.2125442 $quadratic influence of inflation pressure on peak
LKYC = 1 $Scale factor of camber force stiffness
PEY5 = -3.982573 $Variation of curvature Efy with camber squared
PKY4 = 3.193074 $Curvature of stiffness Kfy
PKY5 = -15.40705 $Peak stiffness variation with camber squared
PKY6 = -1.110033 $Fy camber stiffness factor
PKY7 = 0.3001414 $Vertical load dependency of camber
PPY1 = 0.4216594 $influence of inflation pressure on cornering
PPY2 = 1.095625 $influence of inflation pressure on dependency of nominal tyre load on cornering stiffness
PPY3 = 0.07316054 $linear influence of inflation pressure on lateral peak friction
PPY4 = -0.197418 $quadratic influence of inflation pressure on lateral peak friction
PPY5 = -0.7908439 $Influence of inflation pressure on camber
LKZC = 1 $Scale factor of camber torque stiffness
QDZ10 = 2.05206 $Variation of peak factor Dmr with camber squared
QDZ11 = 5.083876 $Variation of Dmr with camber squared and load
PPZ1 = 0.8313204 $effect of inflation pressure on length of pneumatic trail
PPZ2 = -0.1946372 $Influence of inflation pressure on residual aligning torque
RBX3 = 19.90875 $Influence of camber on stiffness for Fx combined
RBY4 = 89.98708 $Influence of camber on stiffness of Fy combined
QSX4 = 0.1527435 $Mixed load lateral force and camber on Mx
QSX5 = 14.81053 $Load effect on Mx with lateral force and camber
QSX6 = 10.68144 $B-factor of load with Mx
QSX7 = 7.215284 $Camber with load on Mx
QSX8 = -4.145403 $Lateral force with load on Mx
QSX9 = -0.3814996 $B-factor of lateral force with load on Mx
QSX10 = -2.530221 $Vertical force with camber on Mx
QSX11 = 36947.57 $B-factor of vertical force with camber on Mx
QSX12 = 0 $Camber squared induced overturning moment
QSX13 = 0 $Lateral force induced overturning moment
QSX14 = 0 $Lateral force induced overturning moment with camber
PPMX1 = -0.05338798 $Influence of inflation pressure on overturning moment
QSY4 = 4.0E-5 $Rolling resistance torque depending on speed ^4
QSY5 = 0 $Rolling resistance torque depending on camber squared
QSY6 = 0 $Rolling resistance torque depending on load and camber squared
QSY7 = 0.85 $Rolling resistance torque coefficient load dependency
QSY8 = -0.4 $Rolling resistance torque coefficient pressure dependency
Q_V2 = 0.01985276 $Vertical stiffness increase with speed
Q_FZ2 = 14.85126 $Quadratic term in load vs. deflection
Q_FCX = 0 $Longitudinal force influence on vertical stiffness
Q_FCY = 0 $Lateral force influence on vertical stiffness

Time to drop the Plug 'N Play methodology and instead, roll up your sleeves and work out a strategy to get your team the information and recommendation(s) on what tire to use and what conditions that tire will work best with.

BTW: I've never seen or heard of a tire used on a cornering vehicle that ran in slip sweep conditions at a constant load. So, why would you bother to study the data in those conditions? In most cases, tires hunt in pairs, so utimately you need a way to study your car's tire usage by means of paired operations.

That's just a hint, more will follow once the Peanut Gallery has chimed in ...

Not fluent in Matlab? Time to get started because your next employer will probably expect it, even to service the robots working the cheesburgher line.

Thank you for your input. That was actually the purpose of this thread: to get additional information/recommendations on how we might best go about comparing different tires. In the past our team has mostly used certain tires because it's what we've used in the past, or because most other teams were using them. While this approach is not entirely invalid, in the spirit of FSAE I would like to move our team towards making more informed decisions on which tires to run, which would subsequently enable us to better design future suspensions around the tire.

I apologize for the confusion; I should have clarified: it was never my intention to evaluate tires at constant loads, since this is obviously not a realistic scenario. Rather I was looking to establish behavioral trends between the different compounds over a range of Fz's.

Nils,

Start small.


In reality, the Pacejka model you are trying to wield is a sophisticated, expansive, and sensitive set of equations.
If you don't understand the factor of influence of the modifying parameter you are using or missing, you gain no advantage to using it.

I will echo Bill Cobb's long time sentiment of starting with a 4-term Pacejka mode. This can easily be done in Excel for your learning and transferred to Matlab, where large scale processing can be done more efficiently.
I have a 4 term PAC model and a PAC94 model I built in Excel that I use to quickly and easily illustrate to people how the term sensitivities work.
This also gives them an interface that non-software savvy people are familiar with to play around with.
a well fit 4 term model will get you 90% of the understanding you need to be successful. 94 will get you 94% of the way there. 2002 will get you 96%, 2006 will get you lost. ;)


F = Fz · D · sin(C · arctan(B·slip – E · (B·slip – arctan(B·slip))))

slip Slip angle/Slip Ratio
B Stiffness factor
C Shape factor
D Peak factor
E Curvature factor
BCD Stiffness

Fz (N) Normal tire load

F Force output (lat force with slip angle or longitudinal force with slip ratio)



You are also probably missing a lot on the data processing side as well. The tire loads are very small for the machine, so there are a lot of oscillations present.
I suggest some sort of collapsing and filtering of the data before you touch any of it for design decision making. Once it is cleaned up you can start to see things clearer, even in Excel.
From there just look for trends, trends, trends. Explore the tire sensitivities. Figure out what makes her happy. Roses? Hot 240 grit asphalt? Long walks on the beach? Warm 120 grit concrete? Cold, damp red clay under the lights on a Friday night?

Examples:
Hold Fz constant, plot F vs camber.
Hold Fz constant, plot F vs tread temperature.
Hold Fz constant, plot F vs pressure.
Hold slip angle constant, plot F vs FZ.
Hold Fz constant, plot Mz vs slip angle (useful for designing steering system and driving driver feedback)
Hold Fz constant, plot Mz vs slip ratio (not as necessary with low kingpin offsets, but can play a dominating role in steering feedback pending your suspension geometry)
Hold Fz constant, plot Mx vs slip angle
Hold slip constant, plot Mx vs Fz
Plot Fy/Fz vs Fz against a few parameters.
Try to flip all your constant Fz assumptions and plot against changing load.

etc, etc, etc

Remember that testing is required to scale the tire data to a mu and response that you expect from your track surface. Seeing 2.4 G capable tire on TIRF belt? Well, it's probably only about 1.5 G capable once you put it on the track. Correlate what you can.

Can you identify the trends that most efficiently (highest mu) operate the tire?
Can you find ways to design and set up your car to maximize the effectiveness of these trends in being the baddest, fastest guy out there?

A) You need to get into the simplified tire model. It will take out 90% of the trash.

B) You need a simple (Capture the Essence) vehicle model to evaluate how 4 tires work together in pairs. This model must have a load transferring mechanism (side to side and /or front to rear).

C) You need a database of calculated tire properties and tire model coefficients. This database needs to be hooked into your vehicle sim so you can ask the sim to evaluate any tire(s) you wish in Think Time. T.T = the time it takes to ask the next question).

D) You need a way (procedure) to evaluate any of the tire constructions your team would consider. ISO procedures describe common yet effective tests to run not only in simulation, but also out on the track, airport, parking lot or in the school gym. So, METRICS (steering gain, steering effort, max lateral acceleration, lap time, braking decel, whatever).

E) You need a database to store the conditions, input parameters, and metrics determined from your sim runs AS WELL AS present and future road tests that will be run to validate your sim. So plan ahead. This system can result in eye-poppin' results, presentations and FSAE point scores. From this you will be able to abandone the notion that you want to and be able to "optimize all 4 tires to operate at their individual peak mus", because you will know 'WHY' your sim gens 1.6 g's max lat even though the TTC mu is higher. All this will help you with steering control by the driver, steering effort estimation, Ackermann setting, and whether to bother with an "optimized' camber curve. Yes. I did say bother. Get the data, run the play, document your findings and validate with a test.

F) All this can be done in Matlab and Excel. I've posted a Sample System on the TTC forum for a Tire database with tires from all or most of the TTC test rounds AND a NONLIN procedural deal that allows you to select a processed TTC tire and fly it through an ISO4138 Constant Radius test. The sim is pure Matlab and the tire database is an Excel workbook. This workbook has 2 sheets having a 4 term Pacejka-Lite coefficient set and another with MF-5.2 fitted terms.
It's all done with Matlab's Guide process which takes all the pain out of quickly generating GUI processes and makes it extremely easy to debug your callbacks.

Then, when all is said and done, you can expect a nicely written complementary article in "The Daily Bull".

Like so...

No, the tire coefficients shown are not for an Avon tire, the selector is just starting off at the first tire in the list.

Attachment 1268

Some serious rear weight distribution you've got there, Bill.

Yeah, but them there tars has gots really high load sensitivity. So weze all happy. Note the atrocious steering compliance, too. Fortunately, there also ain't no big deal from Mz.
Notice my Tilted Kilts number ? We are 5% over the weight distribution, just like that there book says on some page higher than 747, Appendix F.
Here, let me hold your beer and take her for a spin. Wait until I toss some anti-Ackermann at it. You'll be sittin' up on the wheel !

Now do you see why starting with a decent Sim is a good idea ? Some poor student driver's family could probably sue you for the appearance of gross filth in the seat of their (formerly) colorful driving pajamas.

BTW: My admittedly scant search of Round 1 thru 7 tire files seems to indicate that there is really just one good tire and more rim doesn't help it.

The approach proposed by MCoach and BillCobb will probably save you a whole bunch of time and frustration. I sure wish I had the same advice when I was looked at the tire data back then.

Starting small will save you the grief of debugging an implementation of MF, trying to find where you swapped that coefficient that wasn't supposed to be there. Sure you came to compare two tire compounds but why not make an informed tire choice against all the options you've got?
And if that's still too mathematically/computationally strenuous, I am certain you have the ability to fit a line through the middle of an FY/SA curve at some nominal condition and build your first database with just one metric. No one said anything about how sophisticated your first time simplified tire model had to be (and then go join the Dynamic Event testing threads with your findings). Then again a 4-term Pacejka shouldn't be difficult.

The Pacejka model isn't the end all, be all either. GM and older Pratt and Miller fits use piece-wise functions to fit the tire characteristics.
Those work really well too as the tire steady state response is generally able to be categorize as linear, transitional, or frictional for where it is on the curve.


Bill your steering compliance fit might be representative of some of the FSAE cars I had seen in my day, possibly even polite at that.
You are just missing the +/- 8 degrees of on-center steering lash. ;)

Quote:

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Originally Posted by MCoach

Bill your steering compliance fit might be representative of some of the FSAE cars I had seen in my day, possibly even polite at that.
You are just missing the +/- 8 degrees of on-center steering lash. ;)

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I've got data from a Cup car that was pretty loose, too. These were cases of engine power enhancement by using a dummy pump and also a drive belt that mysteriously would break just before the hood pins were secured.

But a Corvette R&P valve fitted into a 600 RB gear: Priceless !

Quote:

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Originally Posted by BillCobb

I've got data from a Cup car that was pretty loose, too. These were cases of engine power enhancement by using a dummy pump and also a drive belt that mysteriously would break just before the hood pins were secured.

But a Corvette R&P valve fitted into a 600 RB gear: Priceless !

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Off topic, but I'm still surprised at how much "wind up" is considered acceptable in the steering system with these cars under load.
If you clamp the wheels or hubs in place and try to steer the car you can get a good +/- 25 degrees of elastic steering wheel angle from center.

Quote:

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Originally Posted by MCoach

Off topic, but I'm still surprised at how much "wind up" is considered acceptable in the steering system with these cars under load.
If you clamp the wheels or hubs in place and try to steer the car you can get a good +/- 25 degrees of elastic steering wheel angle from center.

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Is that with the pump motored or with an auxillary hydraulic supply plumbed in ? Otherwise, that's normal for the range of T-bar windup in the valve body. You would be twisting the T-bar up against the stops.

To edumacate yourself, take a valve body and clamp it in a vise. Then put a Vice-Grips on the pinion shaft and twist away. Under flowrate/pressure conditions and with an input torque, the valve body opens and the pressure pushes the power piston to try to close the valve.

Think of it as a high capacity power transistor: A little bit of input is amplified to produce a very large output. And you should know what that means: It's an unstable system in the absence of damping (friction) or flow limiting. People complain about the lack of road feel with power steering, but with an "optimized" (get that Z ?) damping setup and very low friction, and nimble fingers, the feel can be totally haptic.

Quote:

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Originally Posted by BillCobb

BTW: My admittedly scant search of Round 1 thru 7 tire files seems to indicate that there is really just one good tire and more rim doesn't help it.

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Are you referring to the data itself (I saw on a recent ttc post you we're mentioning some irregularities with data) or are you suggesting there really is one tire to rule them all (by this testing metric).

My challenge is to have you easily answer your own question. I've put together pics of the tools needed to produce a certifiable, high confidence decision. Now its time to discover this for yourself. No need to "optimize" your tire selection. TIRF already has done the hard work.

Stay tuned to the TTC Forum. I'll show you how to best paddle thru the swamp.

Quote:

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Originally Posted by MCoach

Off topic, but I'm still surprised at how much "wind up" is considered acceptable in the steering system with these cars under load.
If you clamp the wheels or hubs in place and try to steer the car you can get a good +/- 25 degrees of elastic steering wheel angle from center.

---

Like Bill touched on already, these steering systems are just inherently prone to lots of compliance. Not sure what team you are working for, but take a look inside your pumps and see how "stock" they really are. Lots of R&D work has been done on them already just to get them to the level they are at currently. Ultimately I think it's why so many open wheel drivers struggle in stock cars, you really can't trust what your hands are feeling most of the time. Which in a good open wheel or prototype car is not the case.

Quote:

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Originally Posted by theTTshark

Like Bill touched on already, these steering systems are just inherently prone to lots of compliance. Not sure what team you are working for, but take a look inside your pumps and see how "stock" they really are. Lots of R&D work has been done on them already just to get them to the level they are at currently. Ultimately I think it's why so many open wheel drivers struggle in stock cars, you really can't trust what your hands are feeling most of the time. Which in a good open wheel or prototype car is not the case.

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I certainly have seen the internals, and I understand, it's just not the same as a rack. There really isn't a lot of reverse efficiency inherent to the design either. Almost every single part of those pumps been modified from a back yard bottle rocket and made it into a NASA shuttle.

Quote:

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Originally Posted by BillCobb

My challenge is to have you easily answer your own question. I've put together pics of the tools needed to produce a certifiable, high confidence decision. Now its time to discover this for yourself. No need to "optimize" your tire selection. TIRF already has done the hard work.

Stay tuned to the TTC Forum. I'll show you how to best paddle thru the swamp.

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Ready to row my boat for sure.

Worth noting, we have done our own analysis on tires and at least using our methods there are some pretty clear trade offs between compounds and sizes that can make the answer less clearcut.

OK, so you have preliminary results for tire model functions. Analyze them with a vehicle dynamics simulation and evaluate their capability and suitability. FSAE car's are not that complicated mechanisms and the tires are essentially mono-ported, so warm up the weapons.

Now lets get back to that quintessential problem of locking your nuts.

Fit a neural network

Quote:

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Originally Posted by Steve Krug

Fit a neural network

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Please tell us how this worked out for you.

What little I've seen along these lines (including a project by an intern we had one summer) was hopeless for understanding vehicle dynamics, but I'm willing to look at new results.

Quote:

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Originally Posted by Steve Krug

Fit a neural network

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Fine. But what does an ANN or an RNN bring to the table (read that STUDENT'S table) other than a model of the data ? Really, you want a model of the TIRE which was tested and have obtained a bag of data for it from a test facility.

May I point out that some of the TTC data has some questionable events and traits (Especially Round 5) that will be perfectly represented by an error minimizing NN. But is that what you want ? Or would you like a tire model that is easy to produce results for, fits PFG, ignores the blemishes and pimples from the testing process, can be factored into a vehicle model and used to predict it's stability, steering gain, max lat and that so wonderfully overstated 'yaw damping' metric ? All of this while looking hopelessly into a design judges blank stare resulting from a complete lack of understanding of the AI subject ? Extra points if your data model is common with the tire manufacturers. Otherwise there is an obvious translation cost. That won't sit well in closing arguments in an employment interview.

Or was this suggestion accompanied by a Flux Capacitor hack ?

I've found that using the cousin of a neural network, the genetic algorithm (followed by some gradient based cost minimisation), is a great method for determining the coefficient values for MF 5 onwards, provide the raw data is treated properly as per Mr Cobb. If you pay reasonable attention to the advice given in Pacejka's text, you can get get very reliable fits within the testing regime in relatively small computational time.

A big benefit of GA is that very large populations can be efficiently computed in parallel compared to gradient based methods (e.g. lsqcurvefit), as the algorithm doesn't need to dip out of the cost function solving to determine the slope. I'm no comp sci expert, but from my experience, gradient based methods are really good minimising the cost function within a particular n-dimensional well, while GA is quite good at identifying where all the wells are in that n-dimensional space.

Quote:

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Originally Posted by BillCobb

Fine. But what does an ANN or an RNN bring to the table (read that STUDENT'S table) other than a model of the data ? Really, you want a model of the TIRE which was tested and have obtained a bag of data for it from a test facility.

May I point out that some of the TTC data has some questionable events and traits (Especially Round 5) that will be perfectly represented by an error minimizing NN. But is that what you want ? Or would you like a tire model that is easy to produce results for, fits PFG, ignores the blemishes and pimples from the testing process, can be factored into a vehicle model and used to predict it's stability, steering gain, max lat and that so wonderfully overstated 'yaw damping' metric ? All of this while looking hopelessly into a design judges blank stare resulting from a complete lack of understanding of the AI subject ? Extra points if your data model is common with the tire manufacturers. Otherwise there is an obvious translation cost. That won't sit well in closing arguments in an employment interview.

Or was this suggestion accompanied by a Flux Capacitor hack ?

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Agreed.

Just throwing down a challenge :).

Quote:

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Originally Posted by Steve Krug

Agreed.

Just throwing down a challenge :).

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OK, so what does Tesla use for setting tire and vehicle parameter specifications and submissions ? Is there actually a 'Tire & Wheel Release Group' empowered to analyze/synthesize, specify, integrate, validate and audit tire performance ? Or is this done by your tire suppliers ?

What models, Math products and testing methods are in place? This would be a good time to frame potential new Industry vehicle dynamics employees on how things get done as a template for FSAE project teams (IMHO).

Quote:

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Originally Posted by BillCobb

OK, so what does Tesla use for setting tire and vehicle parameter specifications and submissions ? Is there actually a 'Tire & Wheel Release Group' empowered to analyze/synthesize, specify, integrate, validate and audit tire performance ? Or is this done by your tire suppliers ?

What models, Math products and testing methods are in place? This would be a good time to frame potential new Industry vehicle dynamics employees on how things get done as a template for FSAE project teams (IMHO).

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Speaking on behalf of only myself and Wisconsin Racing:

Investing time into vehicle dynamics controls, sensor technology, and computer science seems like a good background for being involved in projects like FSAE-Electric, FSAE-Combustion, FS-Driverless, and dynamics analysis in industry.

Dug out this thread from last year, I'll guess that some of you are working with Round 8 TTC data.
For those that don't follow XKCD, today's comic summarizes many of the problems in data analysis:
http://www.explainxkcd.com/wiki/inde..._Curve-Fitting
or the original at: https://xkcd.com/2048/