Re: Model for sliding friction

From: Edward Green (spamspamspam3_at_netzero.com)
Date: 08/20/04 

Date: 20 Aug 2004 15:06:02 -0700

iantaylor2uk@yahoo.co.uk (Ian Taylor) wrote in message news:<2eefbf19.0408200651.3e67cd84@posting.google.com>...

> spamspamspam3@netzero.com (Edward Green) wrote in message news:<eca320d0.0408191405.1d967c73@posting.google.com>...

> > ... interference points
> > are ecountered with area density N as we slide. Assuming that in
> > bending out the way and springing back each interference diverts
> > energy U into lattice vibrations, we get a sliding shear stress N<U>.

<...>

> > Now, if we assume that as we slide Austria over Switzerland that the
> > mountains get out of the way by deflecting into the ground, and that
> > the ground itself is pre-loaded by the compressive stress by which we
> > are clamping the nations together (which does not change appreciably
> > over the displacement of the mountains since we are clamping thick
> > sections of the mantle together :-), <U> scales with the compressive
> > stress. So we get the entire law back.
 
> The approach taken by Greenwood is to model the surface as consisting
> of N asperities, each with a radius of curvature R. The load carried
> by each asperity is W/N (where W = total load).

If the heights are all the same, anyway.

> If the asperity
> heights are all the same, then if Hertzian theory is applied to the
> asperities, you find that the area of contact is proportional to load
> raised to the power 2/3

...<emphasis added>...

> (whereas in practice we know that contact area
> is directly proportional to the load).

Now, I'm just curious why you say that. Is that because some
experiments have shown this, or by reasoning backwards from the simple
behavior of the coefficient of sliding friction? If the latter, I'd
claim it doesn't follow. If the former, I'd want to know just how the
contact area was operationally defined. Are we talking about
something macroscopic, like some kind of blue check (is that the term
of art?) for mechanical interference on machine parts?

> However, if we assume the
> heights of the asperities are distributed normally (ie by a Gaussian
> distribution) then a more detailed calculation, taking into account
> the height distribution, does indeed find that contact area is
> proportional to load.

Ok. Well, that makes me feel happy ... since I was able to get on the
back of an envelope the chief features of the law with no calculation
at all.

> Details of this calculation may be found in the following reference:
> "Fundamentals of Friction: Macroscopic & Microscopic Processes",
> edited by I.L. Singer & H.M. Pollack (NATO ASI Series, Series E:
> Applied Sciences - Vol 220, Kluwer Academic Publishers, 1991)
>
> Hope this helps

Thanks.

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