The dynamics of rolling on rough surfaces is of great interest from the viewpoint of functionality, noise production, and for the diagnostics of many technical systems, such as gears, ball bearings, wheel–rail, tire–road systems, and many others. The main difficulty in analyzing the rolling noise is solving the problem of contact between two elastic rough bodies. In this work the method of dimensionality reduction was used for solving this problem.
The method of dimensionality reduction has been proposed for contact problems in  and was extended to contact of rough surfaces in [2,3].
The work can be found in the book chapter
M. Popov, J. Benad, V. Popov, M. Heß - Acoustic Emission in Rolling Contacts, (Method of Dimensionality Reduction in Contact Mechanics and Friction, Springer, 2015, pp 207-214)
of the book
V. Popov, M. Heß - Method of Dimensionality Reduction in Contact Mechanics and Friction, Springer, 2015.
The following video shows - in principle - a simulation of a rough wheel rolling on an elastic surface. Such a simulation was a part of this work.
Further publications of this work:
M. Popov, J. Benad, V. Popov, M. Heß - Akustische Emission beim Rollen, (Methode der Dimensionsreduktion in Kontaktmechanik und Reibung, Springer, 2013, pp 207-214).
M. Popov, J. Benad - Numerische Untersuchung von Emission in einem Rollkontakt mit rauen Oberflächen, (Proceeding of Tribologie-Fachtagung, Göttingen, 2013, pp. 1/1-1/6).
 - V.L. Popov, S.G. Psakhie. Numerical simulation methods in tribology - Tribology International, v. 40, 916-923. (2007)
 - T. Geike, V.L. Popov, Mapping of three-dimensional contact problems into one dimension. - Phys. Rev. E., v. 76, 036710, 5 pp. (2007)
 - T. Geike, V.L. Popov. Reduction of three-dimensional contact problems to one-dimensional ones. - Tribology International, v. 40, 924-929. (2007)