Friction as a function of area

[VanWEric]

There are three basic types of friction: kinetic static and rolling. When you slid the mass blocks around in physics, you were learning about kinetic and static friction, and all that F=µN stuff is true.

What rob is talking about is rolling friction. All forms of friction ARE dependent of surface area, but in kinetic and static, only very slightly. The force dependent on area is several orders of magnitude weaker than the µN force, so the formula is Ff = µN + really really small number. Rolling friction is almost entirely dependent on the weak forces. This is because the tire is technically not moving against the road. If it was, it would be skidding. Watch a wheel go for a bit -- the point in contact with the road stays on the same bit of road until it get lifted off of it. So when your tires start spinning, you lose the effect of having the extra area.

I will go look in my new physics C text tonight. Maybe i can clear it up. And if i am dead wrong, which i probably am, i apologize. But i do hold that you need to consider the difference between kinetic and rolling friction.

Take a look at these sites.


http://www.school-for-champions.com/...onrolling2.htm

http://hyperphysics.phy-astr.gsu.edu/hbase/frict2.html

[Gary Dillard]

Originally posted by M. Krass

If the material on your wheel is not a smooth surface, in that it interacts with the carpet fibers, your traction will increase. There is no set factor that determines how effective this is.

Whereas the smooth surface of a wheelchair wheel propels the robot due to friction, an irregular surface that meshes with the carpet fibers propels the robot due to both friction (the sliding force between the smooth portions of the wheel and the carpet) and torque (the contact between two surfaces perpendicular to the direction of movement)

OK - Tomorrow night when my daughter (IBApril180 on this board) is over we will post the results of her science experiment here, which I must admit surprised me. Using Brecoflex belts and FIRST spec carpet, the traction increased by DECREASING the amount of contact area! This appeared to be because the impact of additional deformation of the carpet due to higher local pressure was a higher order effect than the additional quantity of "nubs" interacting with the carpet. It threw our F = mu*N + nu*A hypothesis out the window. Stay tuned.

[Adam Y.]

OK - Tomorrow night when my daughter (IBApril180 on this board) is over we will post the results of her science experiment here, which I must admit surprised me. Using Brecoflex belts and FIRST spec carpet, the traction increased by DECREASING the amount of contact area! This appeared to be because the impact of additional deformation of the carpet due to higher local pressure was a higher order effect than the additional quantity of "nubs" interacting with the carpet. It threw our F = mu*N + nu*A hypothesis out the window. Stay tuned.

That can't be right. The formula isn't right but there some correlation between surface area and traction. Ahhh I see if you have two objects with the same pressures the one with more surface area will have greater traction than the one that doesn't. Which is why tank treads work and you need the bogies in the treads so that there is pressure on the track all the way through.

[Madison]

Originally posted by Gary Dillard
OK - Tomorrow night when my daughter (IBApril180 on this board) is over we will post the results of her science experiment here, which I must admit surprised me. Using Brecoflex belts and FIRST spec carpet, the traction increased by DECREASING the amount of contact area! This appeared to be because the impact of additional deformation of the carpet due to higher local pressure was a higher order effect than the additional quantity of "nubs" interacting with the carpet. It threw our F = mu*N + nu*A hypothesis out the window. Stay tuned.

Oooh. Bring it on

Your daughter can have a white paper on her hands. I'm looking forward to reading that, and it's just in time, too.

Are you sure that there aren't characteristics of the belting that may be contributing to that discovery in ways other materials might not? Do the results hold true for the wheelchair wheels, for example?

[Jim Meyer]

Last year we did a similar test with neoprene pad material (available from spi). Our test was slightly different in that we had two wheels surfaced with this material and also a large plate surfaced with the same stuff. We were using about 70 lb. of dead weight and some FIRST carpet. Our test indicated that the double wheel (still at 70 lb. of normal force) slightly outperformed the single wheel and the sheet underperformed both. We also tested all three of these at different weights, but I won't bore you with the details.

My conclusion was that there is an optimum amount of surface area for a corresponding weight for these two materials. Too much surface area and the tread floats on top of the carpet fiber. Too little and you don't have as much fiber engagement. It also seemed to me that the coefficient of friction verses contact area (at a fixed normal force) curve has a pretty flat top. Here's my ASCII drawing of what I think it looks like based on my somewhat limited experiments where mu is the coefficient of friction and SA is surface area (again for a constand normal force):

mu
|   ________
|  /        \_____
| /
|/_____________ SA

[Lloyd Burns]

On an experiential plane, the Frictional Force being independent of area in contact is bothersome. Perhaps the problem has to do with the transition from static friction to kinetic friction (the point at which the surfaces start to slip, which does affect the "traction" the robot has.

Up to the transition, Ff = u Fn, with a large mu, and after the transition, in sliding, the mu becomes lower. In Physics they demonstrate that the total force is independent of area by putting a rectangular block on s table and using a spring balance to measure the force. But no mention was made of the force per unit area, ever.

I'm guessing, but I think the transition is related to the shear force, which has a limit in force/area units (p.s.i., eg).

Perhaps someone in the tire industry could hop in, but when I drove on snow-covered ice, with my rwd Rambler 440 station wagon, I spun the rear wheels on the hill, until I softened the tires by temporarily letting some air out. Perhaps the snow-ice interface reached limiting shear force, and the greater area allowed greater total force, and greater traction resulted. (?)

[IBApril180]

Originally posted by Gary Dillard
OK - Tomorrow night when my daughter (IBApril180 on this board) is over we will post the results of her science experiment here, which I must admit surprised me. Using Brecoflex belts and FIRST spec carpet, the traction increased by DECREASING the amount of contact area! This appeared to be because the impact of additional deformation of the carpet due to higher local pressure was a higher order effect than the additional quantity of "nubs" interacting with the carpet. It threw our F = mu*N + nu*A hypothesis out the window. Stay tuned.

Results are in the technical discussion forum

http://www.chiefdelphi.com/forums/sh...threadid=15719

[patrickrd]

Everybody has really good points. Unfortunately, as many have said, F=mu*N is only a model of friction, and often not very good.

I did a lot of experimentation on this a few months ago and can offer some vague yet useful advice. It's vague because models for any two given surface can be extremely different in behavior than other surfaces.
- Friction increases with normal force
- Friction increases when you dig into the carpet
- Disqualification probability increases when you have sharp edges that dig into the carpet. However this is also a good way to get better traction.
- Sharp, hard material that has very small grooves (or cleats) that dig into the carpet gets better traction. Think soccer cleats. Flexible material (such as rubber) gives into the carpet and does worse. Idea is to maximize pressure by the carpets on the cleats so the cleats can dig as far into the ground as possible.
- Surface area generally has negligable effect on traction... but in general more surface area causes more traction, up to a point before it starts getting worse.
- Effective coefficient of friction decreases as normal force increases... mu goes downwards to some constant as normal force goes to infinity. The more the two dig into each other, the less mu is a "constant".
- EXPERIMENT. The best way to maximize your traction is to make a simple apparatus where you can apply a constant normal force, and measure the amount of tangential force to make a wheel slip. Test different ideas. Use a normal force that your robot will typically provide (e.g. 30-35 lbs).

[Skip 2 my Bartz]

Our team wondered about this, too, so we performed an experiment. Our conclusion was that Mu is unaffected by area.

[JVN]

Originally posted by Skip 2 my Bartz
Our team wondered about this, too, so we performed an experiment. Our conclusion was that Mu is unaffected by area.

That's not true.
For many materials the amount of grip you get IS dependant on the surface area. As patrick mentioned earlier, you simply need to experiment to find what is best.

The way I do it, is instead of calculating mu for a material. I solve for mu for an entire robot. This way I can tweak surface area, material types, wheel configuration, and other variables to solve for the best mu.

In the FIRST world - Experimentation is the key to good traction. Especially this year with the 3 different surfaces.



I recommend before anyone else posts in this thread they go back and READ the kabillion other discussions on this same topic!!!

[Adam Y.]

Yup and it is possible to get coefficents of friction higher than 1. I think rubber is one material where this is possible. It has something to with the chemistry of rubber and the way it deforms.

[Jnadke]

Surface area does come into play with the materials we use because the surfaces can deform. When surfaces deform the meshing (and coefficient of friction) can change when the weight distribution is changed.

Simply put, more weight in a small area can cause the carpet to "flatten" which is why only 4 wheels with 30lbs of pressure each will not perform as well as, say, 6 wheels with 20lbs of pressure each.

I am not sure at what pressure the carpet fibers begin to "flatten". This will need to be experimented with.



Technically, surface area does not directly affect the F = "mu" * "weight" equation. It does, however, change how the weight is distributed (pressure acting on the carpet... as long as the weight remains the same) and can change how the surfaces mesh, which is one factor in calculating the coefficient of friction (mu). It will only change how the surfaces mesh, however, if one or more of the surfaces can deform (and if the pressure exceeds tolerance).

[Alex1072]

Regarding Rolling static, and Kinetic friction:

Here's what I got from our discussion of it in physics. Rolling friction is caused by the cohesion of the two surfaces; as the wheel rolls forwards, the back edge has to lift up off of the floor. This takes a force. This effect is also present in static and kinetic friction, but it is drowned out by the mu*N component. An important factor in cohesion is the temperature of the surfaces; the hotter the surfaces, the better they stick. This means that as you increase the velocity of the object, friction causes it to heat up, and the cohesion increases. Also friction is extremely complicated and from what I understand there are no good models for it to date in physics. All the f=mu*N and f=b*v^2 stuff are just empirical approximations.

[Lloyd Burns]

many laws are approximations : Hooke's law, "ut tenso sic vis" (as the length, so the force) talks about deformation of a beam or the extension of a coil spring caused by a force.

Hooke developed it on a coil spring, but it appleis to almost any elastic change caused by an appliction of force - except for coil springs, deformation of which involves a combination torsion, bending, and witchcraft. :-)