[ODE] friction and restitution

[Dimitris Papavasiliou]

On Sunday 03 October 2004 11:23, Geoff Carlton wrote:
> I believe the original post suggested multiplying the roughness, and
> averaging the solidness and bounciness.  This would give a proper result
> in the cases you stated.
>
> Geoff
>
> Gary R. Van Sickle wrote:
> >This seems both physically right and wrong to me.  The "right" is the
> >"roughness" parameter, seeing as that's a major contributor to the
> > resulting friction.  The "wrong" is simply averaging the two to get a
> > "physically plausible" result:
> >
> >Roughness1    Roughness2    Avg
> >0  (smooth)   0             0 (no friction, seems reasonable).
> >0             1 (rough)     0.5  (if #1 is 100% smooth, shouldn't this
> > still be zero friction?)
> >1             1             1 (if we say 1==infinte friction, maybe this
> >makes sense)
> >
> >I wonder if simply multiplying the two roughness numbers together wouldn't
> >be more accuracte, to the infamous first-order.  Then anything on a
> >completely smooth surface (==0) has no friction (==0), two surfaces with
> >infinite roughness (==1) have infinite friction (==1), and any in-between
> >combinations are in-between.

Friction is not that simple I'm afraid. It depends on a whole lot of 
parameters, not only on roughness. And even if you only consider roughness 
the the smoother the surface the bigger the friction. Think about it: disc 
brakes and clutch plates in cars for example have to be pretty shiny to 
generate enough friction to stop or move the car.

At a microscopic level, the smoother the surfaces, the closer the atoms of  
each surface come to each other and the stronger the bonds between them. 
That's why other parameters like elasticity (think of rubber) come into play. 
More elastic surfaces can be squeezed together so that the actual contact 
surface gets larger and friction too.

That all being said, I suppose if you only want to have some control over 
friction then this approach is ok but if you need a little more accuracy 
(like a pool simulation for example) then you might run into trouble. For 
example suppose wood-wood friction coefficient is u11 and wood-steel is u12 
and u1 and u2 are these roughness parameters. Then:

u11 = u1 * u1 and
u12 = u1 * u2

So if the actual friction coefficient of steel to steel is u22 then how close 
does u2 * u2 come to u22? Would it be a relatively good approximation for all 
such pairs (at least for "normal" everyday materials)?

[And even more important: is it even physically logical to assign such a 
friction parameter to a single surface? That is wouldn't it be possible for 
two materials that generally give high friction coefficients with other 
materials (and thus should have high friction parameters) to give a low 
coefficient when in contact with each other because of some weird phenomenon 
at the microscopic level? (Although I suppose that shouldn't be the case with 
most "every-day" materials).]

I guess defining these measures on pairs is the only sure way to go but I was 
hoping to avoid it because it makes things (in my case) quite complex.

Dimitris