Friction 4

[harrytos23]

Hi everyone,

I tried searching more about this question but I'm getting different answers from different websites/forum. I might as well ask it here.
This piece of rubber is 4"x2.15", it's not much of surface area but better than nothing at all.

My question now is, is it really true that the contact patch/area will not have a different friction force than a single point of contact? Because many sources and people saying that the friction is not affected of the surface area of the contact point and just wanted to confirm that. And side question is, what formula should I use to calculate the friction force of it using the area as well? Thank you guys!!

 

[3DDave]

There are huge books written to describe friction.

The main friction theory is for relatively rigid items where the applied forced do not affect the way the surfaces interact.

Rubber is not a material that obeys that theory when the mating surface is not smooth; it conforms and interlocks, moving from a pure friction to mechanical interaction. This is how rubber tires gain more grip on rough surfaces than on smooth ones and why narrower tires can sometimes have more grip for the same applied load. There isn't a particular formula to predict that though there are studies and rough results from testing.

On some surfaces there is chemical adhesion which moves beyond mechanical interaction; for example when rubber is vulcanized onto metal. This is why sometimes very low pressure tires, as on dragsters, have more grip than narrow tires - they have a larger adhesive area under the conditions they are operated. Put a dragster on loose snow and it won't be moving.

In many materials reducing the contact to a point load will result in mechanical interlock as one surface fails and yields, forming a dent; the resulting restraint is the amount of force required to gouge a path into that material. This is how higher contact pressures from smaller tires are unable to operate on loose sand, where the force required to tear the sand grains from each other is very low.

The main theory is reduced to applying to those cases where neither side gouges into the other nor mechanically conforms to the other and doesn't have loads that exceed material yield strength. For gross cases changing from some largish area to a larger area doesn't increase or decrease the shear capacity from the friction. It is a theory that is more than good enough against the backdrop of variability.

Take 2 squares of steel and measure the force to drag each on a smooth surface and add the measured forces and the sum will be little different than putting one on top of the other and the force required for dragging them both.

Look for volumes written on tribology for more detail.

 

[IRstuff]

Don't have a whole lot to add, but I'm on ski vacation, and I note that longer skis on snow go faster than shorter skis

 

[waross]

longer skis on snow go faster than shorter skis

Possibly the longer skis don't pack the snow as much as the shorter skis?

 

[3DDave]

Same with ships for some reason.

 

[GregLocock]

For displacement hulls? Wave resistance. https://en.wikipedia.org/wiki/Wave-making_resistance

But as the first graph in the article shows, the effect isn't especially strong for typical hull forms, and for a slender hull with a constant semicircular cross section is practically irrelevant, skin friction dominates.

 

[Snickster]

Here is very good discussion on friction from book: Engineering Materials 1 (an introduction to their properties and applications), MIchael Ashby/David Jones, 2nd edition. It also has a discussion of friction with rubber surfaces. It is a very good book on basics of materials, you might want to get a copy.

 

[rb1957]

Friction is "just" the inplane force developed by an out-of-plane force. The factors that affect are many and various ... probably the twothree most important would be surface finish/roughness, and the two interacting materials, and lubrication.

 

[GregLocock]

DRH Jones was my materials lecturer, that book was originally published as a collection of prints from the overhead projector slides he used. Funny guy, very entertaining.

 

[freturetechno]

The relationship between friction force and contact area can be counterintuitive. According to classical friction theory, particularly Amontons’ laws of friction, the friction force (FfF_fFf) is given by:

Ff=μNF_f = \mu NFf=μN
where:

• μ\muμ is the coefficient of friction (static or kinetic),
• NNN is the normal force (perpendicular force pressing the surfaces together).

This equation implies that friction force is independent of the apparent contact area. Instead, friction is determined by the normal force and the material properties (via μ\muμ). The reason behind this is that while increasing the contact area distributes the normal force over a larger surface, it does not change the total normal force itself.

However, in cases involving soft materials like rubber, real-world effects such as adhesion, deformation, and surface texture may cause deviations from the classical model. In such cases, friction may exhibit some dependence on the actual contact area.

If you are looking for a formula that includes area, you would need to consider a more detailed model, such as those incorporating real contact mechanics, like the Greenwood-Williamson model for rough surfaces or adhesive friction models used in rubber friction analysis.

 

[LittleInch]

That's a great paper by Snickster there.

So for me the answer to the question "My question now is, is it really true that the contact patch/area will not have a different friction force than a single point of contact?"

Is that it all depends on the relationship between pressure and friction factor of the material. If the FF remains exactly the same then yes, the effect of area is not relevant to the force. Real life though is not an ideal situation and this is why it varies if you try to prove it.

Friction factors are in any event variable from a static friction and then a variable kinetic friction.

I'm guessing you're not of an age where you have driven cars without anti lock brakes and hence don't fully appreciate the difference between a tyre / rubber just at the point of locking up and actually locking up / skidding when the friction force actually goes down. The highest friction factor is from memory, about 15% slip then drops as the tyre locks up. that's one good reason (apart from steering still working) why anti lock brakes are so effective and became mandatory about 20 years ago as they keep the tyre in the highest friction factor zone.

One of my favourite phrases on this site is that friction is like an unreliable friend. Never there when you need it, but appears and hangs around when you don't. It's also highly variable.

So many things affect the friction factor as noted above in terms of "stickiness" / hardness of the rubber, the effect of wear / heat of friction, other variables in roughness of the surface, any sort of lubricant - even a micro film of condensation say - that it is actually very difficult to get the same friction factor for each variation of area.

SO if you have say 50% of the area on exactly the same surface, rubber typ etc, then I would expect you would get the same force +/- 10%.

If though you reduce your big flat area to say four dots in each corner and say 1% of you current area, then I would expect the force could vary by +/- 25% or more.

Does that make sense?