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Is Tribology Approaching Its Golden Age? Grand Challenges in Engineering Education and Tribological Research

Mike Ciavarella's picture

An interesting paper by VL Popov which suggests many problems of tribology are still very far from being remotely solved.  Despite the very detailed theories for example on rough contact using fractal surfaces on which we have debated mainly academically , there is not a single theory for any quantitative prediction of friction coefficient which can vary by 1 order of magnitude and its dependence on many variables, let alone wear coefficient which can vary up to 7 orders of magnitude.  What is left to do, other than measure?   Is tribology bound to be in practice just an experimental area?  We need some game changing idea.

The paper is here.   Incidentally, it is very similar to a recent presentation I gave about "Fractals in Tribology" as a seminar both in Bari and in Paris, which I attach.   As I discuss in the presentation, the introduction of fractals in tribology has not yet provided any new quantitative insight in tribology (including my own contributions!), and easily has ended up with ill-posed problems of paradoxical predictions of zero or infinite --- see the example of adhesion, where Fuller and Tabor or Pastewka and Robbins suggest no object can stick to any other object, or viceversa everything should stick like in Kendall's sticky Universe, respectively.  I discuss the reason for these paradoxical results in the presentation.


PDF icon fractals-tribology_5.pdf2.51 MB


Dr. Michael Nosonovsky's picture

Thank you for interesting and educational papers... I agree with most of these concepts, in particular, with the importance of the thermodynamic approach... I personally think (for many years) that given friction is a dissipative process, it is desirable to deduce frictional properties from the Second Law of Thermodynamics and from non-equlibrium thermodynamics principles... Several years ago, we had a book where we tried to address some of these matters, but

M. Nosonovsky & V. Mortazavi. Friction-Induced Vibrations and Self-Organization: Mechanics and Non-Equilibrium Thermodynamics of Sliding Contact (CRC Press/Taylor & Francis, 2013) 


Mike Ciavarella's picture

dear Michael, an interesting book full of ideas. I have downloaded a copy for free at

I am not in a position to judge much of it, except the many parts where you collect more standard results in friction dynamics like TEI or Adams instability with Coulomb friction.

When you move to review Soviet-time ideas on entropy, I generally loose you, as probably I don't know much of these attempts. Have they led anywhere?

But I would need also to check carefully all your results, before I can use them.  For example, just after (3.45)

"In other words, if the coefficient of friction increases with the sliding velocity, the system is unstable."


This is generally the opposite of what you find normally true. There is a huge literature against this.  Are you sure of this result?


Dr. Michael Nosonovsky's picture

Dear Mike,

Thank you for your interest in our book!... It looks like you discovered a mistake (thank you), when the stability criterion is satisfied, the system is STABLE, not unstable. When d mu / d V > 0 (friction increases with velocity), it is stable!

I don't think we reviewed Soviet-time ideas on entropy. As far as non-equilibrium thermodynamics, some are from Nobel prize winning Lars Onsager and Ilya Prigogine (who lived far away from the USSR!) :) , others may be from the last two decades. I hope they will lead somewhere.





Mike Ciavarella's picture

In your equality, there is d(mu)/dV, and the rest is certainly positive.  So where is the error coming from? It sounds you should rewrite the entire paragraph (if not more....)


thanks, m

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