# coupling between rolling resistance and axial adhesion of particles on surfaces

In my blog "Rolling Moment Resistance of Particles on Surfaces," I've talked about this topic/problem a little bit. We are looking for understanding/characterizing of coupling between rolling resistance moment and axial adhesion of particles on surfaces. It appears that rolling resistance is much softer and axial adhesion bond stiffness. Possibly, these two modes of motion are weakly coupled. I am interested in finding out if there is any (ongoing) work on this problem. Rolling moment resistance is important for various practical adhesion problems since it controls the stability of particle networks such blood clogs and removal of particles, etc.

### Is the issue that you're

Is the issue that you're referring to that, for identical materials, a tangential force acting on a particle does not induce any relative normal displacement, the contact normal stresses are symmetric and therefore the moment due to the tangential force and interfacial shear stresses does not get balanced? We encountered that issue with the rolling cylinder problem (JAM, 2005, p. 633-) and somewhat artificially put in a higher adhesion energy at the trailing edge than at the leading edge. This was "rationalized" by claiming that bonds have more time to form, the contact gets "cleaned" by the rolling (which includes local sliding) motion.
Northeastern University

### particle motion

I have seen your results. Now I need to convert your formulation into the way I look at the problem as a two-degree-of-freedom system (out-of-plane and rolling/rocking angle).

The axial motion is well established - in short, the JKR formula becomes a highly nonlinear spring (Peri&Cetinkaya, Phil. Mag. 85(13), 2005).

In (Dominik and Tielens, Phil. Mag. A 72(3), 1995), an expression for rolling/rocking moment (without the onset of rolling - rocking) has been derived.

I am hoping to find a way to see the coupling between these two modes of motion to make sense some of my experimental observations. I believe your formulation can shed some light on this.

### Hello!  since these ideas

Hello!

since these ideas are a little artificial anyway (there is also a paper by Carbone and Mangialardi on JMPS using different adhesion energies), whereas there is a huge literature on viscoelastic rolling, starting from Tabor 1952, Greenwood and Tabor 1958, and many russian papers, why do not take that approach?

Regards, Mike

### specific papers addressing rolling resistance

Yes, the literature is immense, yet we have a specific problem (artificial or not).

Do you know any specific paper(s) on rolling resistance and its nonlinearity?

### Take the papers I mentioned

Take the papers I mentioned by Greenwood and see the citations.

### specific results

As I had written earlier, we need specific papers/results at this point.

### lazyness

cetin

do not be lazy, I mentioned Greenwood and Tabor 1958, it is very easy to find the full reference

Hysteresis Losses in Rolling and Sliding Friction
J. A. Greenwood, H. Minshall, D. Tabor
Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 259, No. 1299 (Jan. 24, 1961), pp. 480-507

Abstract

Previous work on the mechanism of rolling friction has shown that it is mainly due to elastic hysteresis losses in the rolling elements. Under conditions of uniform tension or torsion it is generally assumed that the energy dissipated by hysteresis is a constant fraction (the hysteresis loss factor) of the elastic energy introduced during the cycle. This elastic input energy has been calculated for a hard cylinder or sphere rolling on rubber, and with the above assumption expressions have been obtained for the rolling friction. These expressions predict correctly the dependence of rolling friction on load, ball or cylinder diameter and elastic constants of the rubber. However, the absolute values of the frictional force are too small. The experimental values are two to three times the theoretical estimates. This suggests that it is invalid to use the hysteresis loss factor, as measured in a simple deformation cycle, for more complex cycles such as those involved in rolling. For a thin-walled rubber tube to which tensional and torsional stresses could be applied, the hysteresis energy losses for complex stress cycles were measured. In such a system there are two relevant shear stresses which contribute to hysteresis losses; if these are plotted graphically, a deformation cycle can be expressed by a stress diagram which, in general, will form a closed loop. A hypothesis is put forward which suggests that the losses in the cycle are proportional to the square of the length of this loop. An investigation of different types of stress cycle show that this hypothesis may be used fairly reliably to estimate energy losses in complex stress cycles. In particular it may be shown that if the rubber is deformed in such a way that its elastic strain energy is constant throughout the cycle, marked hysteresis losses occur. The earlier concept would predict no energy loss. This result is of general importance and explains the earlier discrepancies between theoretical and experimental values for the friction of rolling cylinders and spheres. Although this hypothesis has limitations (these and alternative hypotheses are discussed) it is applicable to the deformation of material by a hard roller and an analysis is given for a long cylinder rolling on rubber. It is shown that the losses are over three times as great as those deduced from the earlier concept and for a spherical roller the loss is about twice as great as earlier estimates. This is in good agreement with experiment. The analysis is extended to the case of rolling over short distances and it is shown that the resistance increases linearly from zero as a cylinder, starting from rest, commences to roll. An experimental study indicates that this is approximately true. Only when each element has passed under the roller and out of the contact region does the hysteresis loss reach its maximum steady-state value. For minute displacements of a roller, there is evidence that adhesion may not be entirely destroyed, and though, in general, rolling friction is dominated by hysteresis losses, it is suggested that under these limiting conditions the effect of adhesion may not be negligible.

and some citations

Rolling friction of a viscous sphere on a hard plane - gruppo di 12 »
NV Brilliantov, T Poeschel - Europhysics Letters, 1998 - publish.edpsciences.org
Page 1. EUROPHYSICS LETTERS 1 June 1998 Europhys. Lett., 42 (5), pp. 511-516
(1998) Rolling friction of a viscous sphere on a hard plane ...
Citato da 26 - Pubblicazioni correlate - Ricerca Web - ACNP Posseduto Biblioteche

Rubber rolling on rough surfaces - gruppo di 4 »
KNG Fuller, AD Roberts - Journal of Physics D: Applied Physics, 1981 - iop.org
Page 1. J. Phys. D: Appl. Phys., 14 (1981) 221-39. Printed in Great Britain
Rubber rolling on rough surfaces KNG Fuller and AD Roberts ...
Citato da 14 - Pubblicazioni correlate - Ricerca Web - ACNP Posseduto Biblioteche

The effects of wall and rolling resistance on the couple stress of granular materials in vertical … - gruppo di 3 »
HP Zhu, AB Yu - Physica A: Statistical Mechanics and its Applications, 2003 - Elsevier
Quick Search: within All Full-text Sources Quick Search searches abstracts, titles,
Citato da 13 - Pubblicazioni correlate - Ricerca Web

Rolling friction of a hard cylinder on a viscous plane - gruppo di 13 »
T Pöschel, T Schwager, NV Brilliantov - The European Physical Journal B-Condensed Matter, 1999 - Springer
Page 1. Eur. Phys. J. B 10, 169–174 (1999) T HE E UROPEAN P HYSICAL J OURNAL B
c EDP Sciences Societ`a Italiana di Fisica Springer-Verlag 1999 ...
Citato da 13 - Pubblicazioni correlate - Ricerca Web - ACNP Posseduto Biblioteche

Rolling as a" continuing collision" - gruppo di 13 »
NV Brilliantov, T Pöschel - The European Physical Journal B-Condensed Matter, 1999 - Springer
Page 1. Eur. Phys. J. B 12, 299–301 (1999) T HE E UROPEAN P HYSICAL J OURNAL B
c EDP Sciences Societ`a Italiana di Fisica Springer-Verlag 1999 ...
Citato da 7 - Pubblicazioni correlate - Ricerca Web - ACNP Posseduto Biblioteche

Friction, lubrication and wear: a survey of work during the last decade - gruppo di 3 »
FP Bowden, D Tabor - British Journal of Applied Physics, 1966 - iop.org
British Journal of Applied Physics, Journals sitemap: ...
Citato da 6 - Pubblicazioni correlate - Ricerca Web - ACNP Posseduto Biblioteche

Microdynamic analysis of the particle flow in a cylindrical bladed mixer. - gruppo di 3 »
YC Zhou - Chemical Engineering Science, 2004 - cheric.org
■ Home > 연구정보 > 문헌DB > 학술지 검색. Chemical Engineering Science,
Vol.59, No.6, 1343-1364, 2004 [Full Text via CrossRef]. ...
Citato da 6 - Pubblicazioni correlate - Copia cache - Ricerca Web - ACNP Posseduto Biblioteche

Rolling as a frictional equilibration of translation and rotation - gruppo di 6 »
NL Sharma, DD Reid - Eur. J. Physics, 1999 - iop.org
Page 1. Eur. J. Phys. 20 (1999) 129–136. Printed in the UK PII: S0143-0807(99)95155-
3 Rolling as a frictional equilibration of translation and rotation ...
Citato da 3 - Pubblicazioni correlate - Ricerca Web

Impact of reinforcing filler on the dynamic moduli of elastomer compounds under shear deformation in … - gruppo di 3 »
XD Pan - Rheologica Acta, 2005 - Springer
Page 1. Introduction The wet sliding friction of reinforced rubber compounds
affects the safety of the driving public. Before the ...
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Rolling and sliding friction in compliant, lubricated contact - gruppo di 3 »
J de Vicente, JR Stokes, HA Spikes - Proceedings of the Institution of Mechanical Engineers, Part …, 2006 - journals.pepublishing.com
Page 1. Rolling and sliding friction in compliant, lubricated contact J
de Vicente 1 , JR Stokes 2 , and HA Spikes 3Ã 1 Department ...
Citato da 1 - Pubblicazioni correlate - Ricerca Web - ACNP Posseduto Biblioteche

cetin,

I think the following sources will shed light on what you are looking for (basically, a discussion of JKR or other type adhesion and rolling friction). This is a very interesting problem which is not trivially derived from simple non-adheisve contact, as others have suggested. Many researchers in discrete element methods have investigated this by expanding on Hertzian and Hertz-Mindlin formulations of local elasto-plastic behavior of spherical interacting asperities (though the formulation is equally correct for perfectly spherical bodies interacting). If you can characterize the surface of your particles reasonably well, the following sources provide models for the coupling between adhesion and rolling resistence:

1. Derjaguin, B.V., Muller, V.M., and Toporov, Y.P., Effect of contact deformations on the adhesion of particles. Journal of colloid and interface science, 53(2), 1975,  314-326.
2. Kadau, D., Bartels, G., Brendel, L., and Wolf, D.E., Contact dynamics simulations of compacting cohesive granular systems. Computational Physics Communications, 147(1-2), 2002,  190-193.
3. Luding, S. (2006a). "About contact force-laws for cohesive frictional materials in 2D and 3D." Behavior of Granular Media.
4. Luding, S., Contact models for very loose granular materials. 2006b.
5. Tomas, J., Micromechanics of particle adhesion. 2006.
6. Walton, O.R., Numerical simulation of inelastic frictional particle-particle interactions. In Particulate Two-Phase Flow, M. C. Roco, ed., Butterworth-Heinemann, Boston, 1993, 887-911.
7. Walton, O.R., Potential discrete element simulation applications ranging from airborne fines to pellet beds. SAE 2004 Transactions J. Aerospace, 2004.
8. Walton, O.R. (2007). "Adhesion of Lunar Dust." 2007-214685, NASA, Hanover, MD.
9. Walton, O.R., De Moor, C.P., and Gill, K.S., Effects of gravity on cohesive behavior of fine powders: implications for processing lunar regolith. Granular Matter, 2006.