MRA non-dimensional tyre model questions (scaling facotr? valid range?)

[Yunlong Xu]

Hi guys. I have some questions with the MRA non-dimensional tyre model that I think many teams are using. I hope you can share your experience and ideas of working with this model with me.

The tyres that we are using are the Avon 7.2/20-13. The friction coefficients given by the model are extremely high (something like 2.8 for maximum longitudinal coefficient) and therefore I decided to adopt a scaling factor last year.

The scaling factor I used last year was 0.7 (hence, assume real performance is 70% of the predicted performance in the model). It was purely just an educated guess so I planned to get the car tested and use the test data to calibrate the scaling factor but that just didn’t work out as we didn’t have enough test runs last year.

I’m wondering what your teams are using as a tyre scaling factor? Did you get that by testing or any other way? Did you use different scaling factors for longitudinal and lateral performance?

What is the valid range that we can use for this tyre model? As said in the documentation that comes with it, of course running the model at an inclination angle of 20 degrees clearly wouldn’t give anything close to the actual result. But what about slip ratios, what is the range of slip ratios that the model is comfortable with ?(the model shows approximately constant coefficient of friction of about -2.2 from slip ratio of -0.3 to full lock-up at -1, I’m not convinced) What about slip angles? Is it still good up to 30 degrees?

cheers

[Yunlong Xu]

Hi guys. I have some questions with the MRA non-dimensional tyre model that I think many teams are using. I hope you can share your experience and ideas of working with this model with me.

The tyres that we are using are the Avon 7.2/20-13. The friction coefficients given by the model are extremely high (something like 2.8 for maximum longitudinal coefficient) and therefore I decided to adopt a scaling factor last year.

The scaling factor I used last year was 0.7 (hence, assume real performance is 70% of the predicted performance in the model). It was purely just an educated guess so I planned to get the car tested and use the test data to calibrate the scaling factor but that just didn’t work out as we didn’t have enough test runs last year.

I’m wondering what your teams are using as a tyre scaling factor? Did you get that by testing or any other way? Did you use different scaling factors for longitudinal and lateral performance?

What is the valid range that we can use for this tyre model? As said in the documentation that comes with it, of course running the model at an inclination angle of 20 degrees clearly wouldn’t give anything close to the actual result. But what about slip ratios, what is the range of slip ratios that the model is comfortable with ?(the model shows approximately constant coefficient of friction of about -2.2 from slip ratio of -0.3 to full lock-up at -1, I’m not convinced) What about slip angles? Is it still good up to 30 degrees?

cheers

[exFSAE]

This is a question better asked in the TTC forums.

As for what range the models are valid in... first thing to do is compare the models to the raw data in the range they were tested in. Make sure the fit is good at all and not junk.

Beyond that I wouldn't use it much past the range the tire was tested... certainly not 30 degrees slip, nor will your car be anywhere near that range.

[Yunlong Xu]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by exFSAE:
Beyond that I wouldn't use it much past the range the tire was tested... certainly not 30 degrees slip, nor will your car be anywhere near that range. </div></BLOCKQUOTE>

Thanks exFSAE. Yes I can see what you mean as the data of lateral forces only goes to up about 15 degrees.
So how does your team simulate the vehicle perfromance for slip angles outside of the confidence zone of the test data? Or maybe you just don't ever go up to 15degrees of slip angle?

But I've seen many teams saying that their maximum steering angle is about 30degrees either way. And therefore you will definately have a slip angle larger than 30degrees on one of the wheels on steering full lock. Do really use the whole range of that steering angles on the track or do they just use the large steering angles for pushing the car around the paddock?

[STRETCH]

Yunlong,

I think you need to revise the definition of slip angle. Just because the wheel is steered to 30degrees, does not mean the slip angle is at least this. There is a kinematic steering angle that you need on the front tyres just to roll round a corner, before you add any slip angle at all. Hence the slip angle is always less than the steering angle of the tyre. From memory, the Avons peak at about 6 degrees slip angle, anything above this and your car is understeering.

[Yunlong Xu]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by STRETCH:
Yunlong,

I think you need to revise the definition of slip angle. Just because the wheel is steered to 30degrees, does not mean the slip angle is at least this. There is a kinematic steering angle that you need on the front tyres just to roll round a corner, before you add any slip angle at all. Hence the slip angle is always less than the steering angle of the tyre. From memory, the Avons peak at about 6 degrees slip angle, anything above this and your car is understeering. </div></BLOCKQUOTE>

Hi Lee,

I'm not sure what you mean by the 'kinematic steering angle'. The way I define slip angle is (and I'm pretty confident it is correct): the angle between the velocity at the wheel centre and the tyre orientation(the axis in the tyre cooridnate).

The velocity at the wheel centre is just a function of the vehicle velocity,vehicle goemetry and the yaw rate(v' = v + w x r)

I admit I was wrong to say that the slip angle is 'definately' greater than the steering angle, but I believe I can give many scenarios where you can get slip angles greater than your maximum wheel steering angle

1) The car is initially going straight, then a step input of steering angle of 30 degrees to the left will immediately result in a slip angle of 30 degrees

2) The car is initially turning left in steady state. (so v is towards front left, steering angle and yaw rate are both anti-clockwise). Then imagine a step input that changes the steering angle to 30 degrees to the right. In this scenario, you will definatley get a slip angle greater than 30 degrees!

[exFSAE]

I'd be surprised if teams were truly using 30 degrees of steer angle, much less slip angle.

If I remember right (it's been a while), the Ackermann angle for the tightest possible corner at competition is only around ~23 degrees. When you put the numbers together for the yaw rate influence, etc, you'd probably see the required slip angle is quite a bit less than that.

Plus, on FSAE cars you have the very significant addition of wheel and suspension compliance that will steer the wheel back out of the corner. Even if a team's DAQ was anticipating 30 degrees of road wheel angle, with compliance it's probably a good bit less.

Another BIG thing to bear in mind is force from tire test data are generally presented in the WHEEL co-ordinate system. To get "true" lateral force thats perpendicular to the motion of travel, you have to use some trig. You can then also get cornering drag.

At 15 degrees slip for example, only 96.6% of the "Fy" channel is perpendicular to the forward velocity vector. 25.9% (!!) is parallel to the velocity vector and slowing the car down. Something to keep in mind.

Finally, yes, it is possible to have very high slip angles briefly on these cars. But if your driver is going around the course using step steer inputs, or hanging the rear end out around every corner.. you have more basic problems to sort out than in depth vehicle dynamics http://fsae.com/groupee_common/emoticons/icon_smile.gif

[Yunlong Xu]

Thanks exFSAE,

Your reply explains a lot to me. But my real trouble is how to simulate the vehicle dynmacis when the slip angle is outside of the TTC test validated range. It's always tempting to increase the slip angle even more as the TTC data doesn't acctually peak at it's maximum tested slip angle...

I am aware of the difference/relation between tyre lateral force and vehicle lateral force and have implmented into my model. But your advice on this has definately takenme to a new way of thinking of maximising the lateral acceleration/force.

What I am thinking about doing now is to imagine a step input steering on a car going straight(i know step input is not good, but it's here just for simplification as in this scenario the steer angle = slip angle). And then plot the tyre data as Fy*cos(Alpha) against Alpha(slip angle). And this plot should in fact show a peak within the range of TTC validated data! And that peak gives a hint on the maximum slip angle in the range of operation.

Any comment? Also it would be great if you could share with me what is the maximum slip angle that your car ran in the past years.

[exFSAE]

Don't know off hand what the old cars I worked on ran in terms of slip angles. Not many folks have optical slip angle sensors in this series, though I do know at least one team had them in 2008 and I believe another one has some this year. In any event I think it's DAQ overkill.

Another thing to keep in mind with regard to where that peak is... is what happens when the grip level comes down and you start applying scaling factors. I see you've done this... though I'm not sure specifically how. You have to be really careful in how you do it... multiplying the whole curve by a scalar is not the way to do it, as that will affect linear range parameters like cornering stiffness, plysteer, camber thrust, etc. I think Doug or Edward mention this point a number of times as a benefit of their tire model.

When you scale the peak grip level down by itself, the peak location should change. Sometimes it goes down, sometimes it goes up http://fsae.com/groupee_common/emoticons/icon_smile.gif The scaling factors just kinda guess at it.

In any event I guess it comes down to what kind of simulation you're trying to do, and what you're trying to get out of it. Personally, I would use the raw TTC data to sort out general tire behavior, target hot inflation, find suitable rim width, and to see if there are any tires that at a glance are obviously poor choices.

From there maybe use scaled fit data in some fairly simple steady state simulation to sort out camber gains and spring/bar rates. Since you know the limit behavior in the fit model probably isn't going to be an exact match of reality anyway, you might as well stick to tuning the linear range. This will probably get you the first 90% of the tuning you need.

Then when you actually build the car you can do the other 90% of the tuning, on a weld-distorted compliant frame, springs that don't have the same rate, and floppy 3-piece wheels.

As tempting as it is, I think any analysis past simple steady state stuff is often a waste of time in this series. A lot of teams still have trouble sorting static alignment out, much less measuring TRUE K&C rates, as-built installation ratios, real spring rates, etc.

That's just my opinion though.

[Yunlong Xu]

Thanks for the advices. I think I'm really learning a lot today!

For our tyre choice, the TTC data actually agrees with the MRA model quite well. The scaling factor that I implemented was due to the suspicion that the the tyres will have less grip on the track than on the test rig where they did the TTC since the TTC results(and the MRA model as well) showed really high friction coefficient, high enough to be unconvincing.

So my logic is simply that while the surface the tyres are running on changes from the test rig to the track, the entire performance curve should be effected.(ie,lower cornering stiffness, camberthrust, etc in the linear region as well) And that's the reason why I applied the scaling factor(0.7 being my own guess by looking at the maximum lateral and longitudinal acceleration that other teams can get)to the whole curve. I too believe that this can't be the most scientific way of doing it. Are you also saying that the scaling factor should be implemented in a different way? If so could you please point to me some reference on that? (I don't think I've seen that in RCVD, if that's the Doug and Edward book that you are talking about)

I agree with you that there's just so much that you can do by simple steady state analysis. The model I'm currently building/developing is a full transient performance one in Matlab/Simulink. I know that this is not the most efficient way to improve the car's performance but it can be a highly efficient way of learning about vehicle dynamics and control of the car!. I have really learned a lot just by solving questions while working on it!

[Zac]

Cornering Stiffness is largely surface independent. I would not recommend using a simple scaling factor. I'm not overly familiar with the MRA model, but I believe it will let you scale down grip level without influencing the linear range portion of the curve too much.

[Yunlong Xu]

Hi guys, thanks for all the tips you gave.
I just found a good thread on this while doing some more reading and searching in the forum
http://fsae.com/eve/forums/a/t...48/m/15510029041/p/2 (http://fsae.com/eve/forums/a/tpc/f/125607348/m/15510029041/p/2)

I think these will probably conclude this thread and give whoever has the same question and finds this thread a good source of learning

[Silente]

Hi,

i'm working on simple steady state model to figure something out about our car.

I am finding the same problems than Yunlong, but i am working with a Pac 96 model instead of the MRA.

I am trying to figure out how to work on tire curves and on pac equation to apply a scaling factor in the right way, keeping into account not only the lower maximum force but also the different Slip Angle at which it is going to be reached.

On which parameters of Pac 96 model we should work to have the right effetc on tire curves?

[BillCobb]

I posted a scaling function demo on the TTC forum. Its an open code Matlab function.