Emanuel Willert, Markus Hess, Valentin L. Popov

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Recently the method of dimensionality reduction (MDR) has been introduced to solve axisymmetric contact problems easily and exactly. The list of tasks that this method can deal with comprises normal, tangential, adhesive and rolling contacts with simply connected contact areas between elastic or viscoelastic bodies. Due to its simplicity and easy applicability the MDR provides the possibility of fast and comprehensive studies of contact problems in technological or biological systems, for example bearings, artificial hip joints, wheel-rail systems or others. Within the complicated three-dimensional contact theory those studies, in most cases, cannot be done without a tremendous mathematical or numerical effort.
In view of all this, the torsional contact problems have been disregarded until now, although it is known that torsion is a major reason of wear and possible failure of system components. Therefore, in the present paper, we extend the MDR to contacts of axisymmetric profiles under superimposed normal and torsional loading.

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Lubkin J.L., 1951, The torsion of elastic spheres in contact, Journal of Applied Mechanics, 18, pp. 183-187.

Hetényi M., McDonald Jr. P.H., 1958, Contact Stresses Under Combined Pressure and Twist, Journal of Applied Mechanics, 25, pp. 396-401.

Kartal M.E., Hills D.A., Nowell D., Barber J.R., 2010, Torsional contact between elastically similar flat-ended cylinders, International Journal of Solids and Structures, 47, pp. 1375-1380.

Jaeger J., 1995, Axi-symmetric bodies of equal material in contact under torsion or shift, Archive of Applied Mechanics, 65, pp. 478-487.

Trejo M., Fretigny C., Chateauminois A., 2013, Friction of viscoelastic elastomers with rough surfaces under torsional contact conditions, Physical Review, E88, 052401.

Popov V.L., Psakhie S.G., 2007, Numerical simulation methods in tribology, Tribology International, 40, pp. 916–923.

Hess M., 2011, Über die exakte Abbildung ausgewählter dreidimensionaler Kontakte auf Systeme mit niedrigerer räumlicher Dimension, Cullier Verlag, Berlin.

Popov V.L., Hess M., 2015, Method of dimensionality reduction in contact mechanics and friction, Springer.

Popov V.L., 2015, Kontaktmechanik und Reibung, 3. überarbeitete Auflage, Springer.

Popov V.L., Hess M., 2014, Method of dimensionality reduction in contact mechanics and friction: A users handbook. I. Axially symmetric contacts, Facta Universitatis, Mechanical Engineering, 12(1), pp. 1-14.

Jaeger J., 2005, New Solutions in Contact Mechanics, WIT Press.

Bracewell R., 1965, The Fourier Transform and Its Applications, McGraw-Hill Book Company.

Johnson K.L., 2001, Contact mechanics, Cambridge University Press.


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