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Thread: Tire Analysis Best Approach?

  1. #1

    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:

    INFLPRES = 68947.6 $Tyre inflation pressure
    NOMPRES = 68947.6 $Nominal tyre inflation pressure
    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

  2. #2
    Senior Member
    Join Date
    Mar 2008
    Brighton, MI

    Tire Modeling

    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.

  3. #3
    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.

  4. #4

    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 Ě D Ě sin(C Ě arctan(BĚslip – E Ě (BĚslip – arctan(BĚslip))))

    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?

    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?
    Kettering University Vehicle Dynamics
    Formula SAE 2010 - 2015
    Clean Snowmobile Powertrain 2012 - 2015

    Boogityland 2015 - Present

  5. #5
    Senior Member
    Join Date
    Mar 2008
    Brighton, MI

    Now 4 the fun part(s)

    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".

  6. #6
    Senior Member
    Join Date
    Mar 2008
    Brighton, MI

    Straw Man

    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.

    Nonlin with TTC Hack.jpg

  7. #7
    Some serious rear weight distribution you've got there, Bill.
    Kettering University Vehicle Dynamics
    Formula SAE 2010 - 2015
    Clean Snowmobile Powertrain 2012 - 2015

    Boogityland 2015 - Present

  8. #8
    Senior Member
    Join Date
    Mar 2008
    Brighton, MI

    Koons fan

    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.

  9. #9
    Senior Member
    Join Date
    Mar 2008
    Brighton, MI
    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.

  10. #10
    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.

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