Extrapolating Load sensitivity characteristics

[J-rob68]

Hello again.

To follow up with a previous post it seems like there is a decent grey area that these tires are leaving us in. By these tires I'm referring to the 10" Hoosiers and by grey area I'm referring to the Normal loads well within formula range that haven't been tested at the TTC facility.

The TTC data being the great resource that it is has provided us with data from normal loads of 222N-1112N. However as stated in a previous post its not unreasonable for some teams to reach as high as 1800 N of FZ on these tires. With such loading being highly dependent on cornering and aerodynamic characteristics of that maneuver it would seem that the Load sensitivity of the tires would be quite significant in these regions.

So I bring this topic to all those far more knowledgeable than I, as I would be interested in seeing what typical behavior for these tires are at higher loads. Is the load sensitivity linear? constant? Progressive? Digressive?

With this decent pool of data at relatively low normal loads is there a reasonable or semi accurate way any of you have gone through to extrapolate our data out to fit these loading conditions? This seems like a pretty universal challenge that most teams should be facing no?

Signed,
- A curious engineer.

[MCoach]

If load sensitivity may be so significant, would that be a reason for you to consider designing around a 13" tire which may not have such significant load sensitivity characteristics relative to the loads you see in FS? How would you imagine going about extrapolating such data and trusting it?

Hm...tire at a,b,c conditions such as skidpad produces z aligning torque. Extrapolate your model to an expectation and go testing. At a' , b', c', did we get the expected response? No? Where is our model in/correct? This is ideally where you end up, a model that is extended beyond the provided TTC data and "correct". I put correct in quotes because it will depend on the time of day and whether your best friend's little brother picked his nose that day.


How about doing something simple like trying to test vertical tire stiffness using a hydraulic press and a scale or whatever configuration you can (for the love of all that is racing, keep it clean, and safe) come up with to be able to load a tire and wheel and measure it consistently and accurately. See how your calculations and model line up with testing that feature, then extrapolate from there, re-measure, check against your model.

You'll have a simple comparison of one of the easiest characteristics we have to measure to compare against what you have now to look for correlation. You can try different pressures and temperatures if you're feeling adventurous.

You can extend this method of guess and check to other whatever you feel that you can accurately measure.

[Pennyman]

Have you used tire modelling software?

[J-rob68]

Pennyman,

No I havent used any particular tire modeling such as optimum K or the like. Most of everything I've worked with has been based off of the TTC data and the Pacjeka equations. Data analyzed and conditioned we than completed an MMM matlab code. However these are all utilizing Pac 2002.


Mcoach,

There are many "attractive" features of the 13" tires. Cornering stiffness and cornering stiffness variation being one of them. However after all the factors are weighed they dont align with our team goals and overall we are better suited with the 10's. I suppose a torque sensor in the steering column and a set of skidpad tests could do you well. testing procedure being adding whatever weight at prescribed locations to the car and going out and running the skidpad. Than you know your weight transfer, your new fz on the tire and your new steering weight which you can back calculate to Fy. For obvious reasons vehicle lateral accel cannot be used to validate the new FY but this wouldnt be a terribly unreasonable method for getting a curve to work with.

[Claude Rouelle]

Jason speaks about steering torque... What a good topic on its own...

A steering wheel (steering column) toque sensor is surely one sensor which could be VERY useful. I only have seen 2 FSAE teams, a Canadian and Brazilian using it (Maybe there are more but I have not seen them) and these 2 teams were using its data at, at best, maybe 20 %

I encourage teams that test extensively and with good organization and data analysis to install and properly use one

Here are some examples

A. Steering Angle (Ya xis) Vs Steering Torque (X axis) graph at different speed.
1. Looking at the hysteresis "height" will give you a good idea of the steering system friction; what is the window of steering angle change with the steering torque still at zero
2. Looking at the hysteresis "width"; the steering torque "dead band" will show you how big the window of steering torque can be despite no steering angle.
3. The gradient (slope) of Steering Angle (deg) Vs Steering Torque (Nm) and the linearity (or non linearity) and how much this changes with the speed will tell you how much the driver do react or not to the steering torque.
Which lead me to ask an important question (I need to be humble here; I learnt so much from Bill Cobb on this topic): is you driver position (steering angle) of force/torque (steering torque) sensitive? A big debate here

Similarly:

B. Steering angle Vs Lat G at different speed Look at the gradient and hysteresis width and height at steering angle = 0 and Lat G = 0. What does it tell you?

C. Steering torque Vs steering angle at different speed. Look at the gradient and hysteresis width and height at steering torque = 0 and steering angle = 0. What does it tell you?

D. Yaw rate (gyro) Vs steering angle.. IF the signal is not linear and has a lot of hysteresis good luck for the driver to exploit the car and tires

E. Yaw acceleration (multiply it by the yaw inertia and you have the Yaw Moment) Vs the steering Torque. Do that at different speed. Basically that is the version Force of the D (D being movement and position) Basically you compare 2 torque: one input (steering torque ) and one output (yaw moment) will tell you about the car "reactivity"

Use a slalom to do this test.

These new topics (and many others) are developed in the fall version of the 4 day OptimumG seminar. The next two seminars in September are in Montreal, Canada and In Graz, Austria

[BillCobb]

(For use with CCF as well as CCR) (That's THREE puns, folks !!!)

Obvious way to study tire overload is with Mx. If the tire carcass is buckling, then Houston, you have a problem and it will reveal itself here. While I would never recommend extrapolating slip data more than 1/2 degree, going for extra load with analysis can be done if some simple observations are made:

A tire under severe load never shows second partial derivative anomalies. It should be smooth and make sense considering the parts involved.

If you perform multi-segment nonlinear transient analysis (step test procedure), then the understeer and sideslip derivatives wrt lateral acceleration ought to be smooth and indicative of 'expected' behavior. Response times vs. lateral acceleration also ought to show systematic changes: no secondary derivative shape changes. Transient response characteristics are more revealing of load issues because overloads tend to be momentary and not a steady state phenom. There can be some higher order effects showing up in the near center response times because the nonlinearities (softness) of the steering system can show their ugly head as a large amount of understeer in this region.

Use of this type of test procedure and the corresponding data analysis summary is also revealing because it will show knowledgeable readers how overstated the need to 'operate at peak slip angle' is. Vehicles with a pair of tires on an axle just can't be operated 'at peak slip angle(s)' because the other axle just won't co-operate. Plus the inside tire won't cooperate in the deal.

Plotting the load and slip angle trails during a severe maneuver on a carpet plot of tire data is shown on the a forum thread. The car is at max lat but obviously none of the tires are at their peak slip angle. You have to be in moment balance, not just force balance.

Once you have the simulation cooking, you can judge whether the tested tires are the ones you will use on your team car. If you really need 'more tire', make them duallys. (Is that allowed ??)

[Fra881]

(For use with CCF as well as CCR) (That's THREE puns, folks !!!)

Obvious way to study tire overload is with Mx. If the tire carcass is buckling, then Houston, you have a problem and it will reveal itself here. While I would never recommend extrapolating slip data more than 1/2 degree, going for extra load with analysis can be done if some simple observations are made:

A tire under severe load never shows second partial derivative anomalies. It should be smooth and make sense considering the parts involved.

If you perform multi-segment nonlinear transient analysis (step test procedure), then the understeer and sideslip derivatives wrt lateral acceleration ought to be smooth and indicative of 'expected' behavior. Response times vs. lateral acceleration also ought to show systematic changes: no secondary derivative shape changes. Transient response characteristics are more revealing of load issues because overloads tend to be momentary and not a steady state phenom. There can be some higher order effects showing up in the near center response times because the nonlinearities (softness) of the steering system can show their ugly head as a large amount of understeer in this region.

Use of this type of test procedure and the corresponding data analysis summary is also revealing because it will show knowledgeable readers how overstated the need to 'operate at peak slip angle' is. Vehicles with a pair of tires on an axle just can't be operated 'at peak slip angle(s)' because the other axle just won't co-operate. Plus the inside tire won't cooperate in the deal.

Plotting the load and slip angle trails during a severe maneuver on a carpet plot of tire data is shown on the a forum thread. The car is at max lat but obviously none of the tires are at their peak slip angle. You have to be in moment balance, not just force balance.

Once you have the simulation cooking, you can judge whether the tested tires are the ones you will use on your team car. If you really need 'more tire', make them duallys. (Is that allowed ??)

Can you please elaborate more on the tyre overload study with Mx, and on the physical reasons of load sensitivity?

[Zac C]

Can you please elaborate more on the tyre overload study with Mx, and on the physical reasons of load sensitivity?

MX data can pretty easily be processed into a pneumatic scrub value, which represents the lateral location of the normal force vector. If you plot pneumatic scrub vs. slip angle for a pretty big range of loads you'll see some rather dramatic effects once the load ratchets up. It's been a while since I looked at any of the TTC data so I can't recall if the behavior is witnessed there or not, but you'll see it in most passenger car data sets.

There's a stupid easy way for you to learn about what's going on first hand. Go get yourself a mountain bike, take the front pressure down to about 5 psi, and throw it into a corner (helmet and mouth guard are recommended for this experiment). You'll get a nice physical sensation and view of the tire rolling over under cornering force, before (probably) hitting the deck.

[DougMilliken]

There's a stupid easy way for you to learn about what's going on first hand. ...
Old age (and treachery<grin>?) suggest starting this experiment at a higher pressure. Run successive trials, with each trial at a bit lower pressure.

More to the point, if anyone calculates "pneumatic scrub" and plots (per Zac's post above) from TTC data, consider posting it on the TTC forum -- this could make a nice contribution.

[BillCobb]

Take the partial derivative of MX/FZ wrt FY and compute the lateral stiffness of the tire. If you look at the effect of camber and pressure, you'll be inclined to figure out where the tire is happiest to operate. Running this play on a tire test machine is 'amazing' (to use a well worn out Hollywood phrase). You can hear when a race tire runs best. (Frying bacon sound).

Buy the FLIR iPhone add on [~ $260 on eBay] and LOOK at the tire tread heat distribution). The video from this would be a 'cool' way to augment the next TTC session).

[BillCobb]

Engineering, not wrenching.

New School.

[Fra881]

There's a stupid easy way for you to learn about what's going on first hand. Go get yourself a mountain bike, take the front pressure down to about 5 psi, and throw it into a corner (helmet and mouth guard are recommended for this experiment). You'll get a nice physical sensation and view of the tire rolling over under cornering force, before (probably) hitting the deck.

I have clear this problem, but it is related, as you say, to pressure.
With more load it is possible to increase the tyre pressure (and perhaps camber) in order to keep it solid and in a correct position relatively to the ground.

However, after correcting any stability and contact patch difference with this kind of settings, the more loaded tyre will still have a lower friction coefficient than the lighter loaded tyre. Why is this?

[mech5496]

Ehm, load sensitivity? Or you mean the physics behind load sensitivity?

[Fra881]

Ehm, load sensitivity? Or you mean the physics behind load sensitivity?

load sensitivity is just a name, it's not a reason:


Can you please elaborate more on the tyre overload study with Mx, and on the physical reasons of load sensitivity?

[BillCobb]

The Chemistry and Physics of micro and macro adhesion between two surfaces.

[BillCobb]

If you don't care for that explanation, think of it as 'ROUNDOFF ERROR".

[Zac C]

I have clear this problem, but it is related, as you say, to pressure.
With more load it is possible to increase the tyre pressure (and perhaps camber) in order to keep it solid and in a correct position relatively to the ground.

However, after correcting any stability and contact patch difference with this kind of settings, the more loaded tyre will still have a lower friction coefficient than the lighter loaded tyre. Why is this?

As a good insulator, rubber doesn't have any coulombs.

[BillCobb]

That's why you have two tires: One from coulomb A and one from coulomb B.

[Z]

Jason, Fra881,

Here is my dumbed-down, big-picture, explanation of Tyre-Load-Sensitivity.

Firstly, let's define:
Coefficient-of-Friction = Force-Tangential/Force-Normal,
or Mu = Ft/Fn, with (Ft = Fx,y, Fn = Fz) in the usual car terminology.

This Mu = Ft/Fn equation is so beloved by Physicists that many of them consider it to be a fundamental, unbreakable, Law of Nature. Truth is, it is only a rough and ready "Rule of Thumb". It applies reasonably well to contact between HARD and SMOOTH surfaces, but only over a VERY SMALL RANGE OF FORCES.

At very low levels of Fn and Ft the equation fails. This is typically because of the "Van der Waal's forces" (ie. the weak electrostatic forces between molecules of the two surfaces) that allow flies and geckos to walk on walls and ceilings. Similarly, a small piece of sticky tyre rubber will easily cling to a vertical wall (ie. Fn = 0, so Mu = Ft/0 = INFINITY!), or even to a ceiling (ie. Fn = -ve, so Mu = -ve!).

At the opposite extreme of forces the problem becomes one of "Strength of Materials". For a given cross-sectional contact-area, say, the area of your tyreprint, as the Fn and Ft forces increase the various compressive and shear stresses also increase, and eventually something breaks. In the case of your tyre rubber it is its shear strength that gives up first, so Ft necessarily has a maximum level. (Technically, shear is compression + tension, both at 45 degrees to the Ft loads, and ultimately the rubber fails in tension, though after much stretching.)

Anyway, consider the typical FSAE tyreprint area, about as big as your hand. In the miniscule range of shear forces from about Ft = 10 N to say 1,000 N (1 -100 kg) the "Friction Equation" holds reasonably well. But down around 0.001 N (tiny), or up around 10 MN (1,000 tons!) you should not put any trust in "Mu".

Looking at it a slightly different way, for a given tyreprint area you can do multiple "Mu tests" and then plot Ft on a vertical axis against Fn on horizontal axis. The slope of the line from origin to a point on the curve is Mu. But from the above "Strength of Materials" considerations it should be obvious that Ft has a definite upper limit, or ceiling, above which the curve cannot go. This limit is the "ultimate shear strength" of the whole tyreprint. In practice, this limit is approached gradually as little bits of the tyreprint fail one after the other.

Interestingly, it is not always the "tyre" that does the failing. Off-road tyres, such as on farm tractors, have hard "knobs" that embed themselves into the softer soil. Bulldozers have steel "cleats" that do the same thing. As the Ft loads increase, it is the soil that first starts to fail in shear. As all farmers know, more Fn (ie. Fz) helps a little, but NOT much. The best way to get more Ft (ie. drawbar pull) is to fit wider tyres, because these provide more tyre/soil AREA to carry the shear loads.

Similar applies in FS/FSAE. :)

Z

[BillCobb]

From some older (Round 3? Data). This is at a constant, moderate vertical load, which is not the way a tire sees a cornering scenario. The offset at zero slip angle is typical of some classes of tires (as in 'race' tires). What happens under traction and braking is another thing to contemplate over a few pints.
So, if you are using scrub radius values in any of your hand-waving design reviews, this result changes everything. I suppose I should have reversed the X axis direction. Rights turns are to the left. Oops...