Contact engineering

Contact engineering

Contact engineering is a 2nd semester course held at University of Ljubljana, Slovenia.


2. semester - University of Ljubljana, Slovenia


Prof. Dr. Mitjan Kalin, Assist. Prof. Marko Polajnar

Course Points (ECTS)


Contact Information

University of Ljubljana, SLO

Course Overview

Module objectives

The course goal is to acquaint the students with the fundamentals of the study of the contact between two elastic or plastic bodies in relative motion, the distribution of force, temperature and contact stresses both on and under the surface; for the case of one-way and reciprocal sliding, and for rolling. Furthermore, the students learn about the effects of friction and thermoelastic study of contacts, including the determination of critical points for the formation of damages, as well as about the process of improvement of tribological properties of contact surfaces using suitable contact surface finishing techniques, focused on the preparation of substrate for the deposition of surface layers, the properties of surface layers, the layered surface mechanics, the selection of contact surface finishing process, as well as some practical applications of contact mechanics in mechanical engineering.

Knowledge outcome

The student will master the fundamentals of contact analysis in one-way and reciprocal sliding and rolling. They will learn to determine the critical points for the formation of damages on and under the contact surface. They will master the planning process for the improvement of resistance and tribological properties of contact surfaces, as well as the procedure for the selection of contact surface finishing process and parameters with regard to the stress-strain state. They will understand the importance of proper surface preparation, treatment and modification in ensuring the optimal contact properties.


Outline syllabus

  • Contact between two surfaces; Elastic contact between two curved surfaces: geometry, forces, velocities and stress-strain field; The influence of load on the contact stresses: line, semi-elliptical, inverse semi-elliptical and arbitrary continuous contact pressure distribution, normal and tangential load; Hertzian contact theory: contact between single- and multi-layer surfaces; Stress analysis of contact in motion: one-way sliding, reciprocal sliding, micro and macro slip, rolling; Elastic-plastic contact: elastic deformation, plastic deformation, the influence of tangential load, surface load-carrying capacity; Contact between rough surfaces: the influence of micro- and macro-roughness on the distribution of stress-strain field; Thermoelastic contact, thermal instability of contact; Interactions between surface and surroundings, surface energy.
  • Contact surface characterization; Microscopy; Surface film analysis techniques EDS, X-Ray, IR, XPS, Auger,...; profilometry and topography, surface load-carrying capacity; Contact surface hardness and elasticity; Residual stresses in surface layers, surface layer adhesion.
  • Improving the tribological properties of contact surfaces; contact surface texturing: the methods of texturing and the effects thereof on the tribological properties; Overview of contact surface finishing processes: tribological properties, advantages, disadvantages and limitations; Protective surface layers: types and tribological properties, diamond and diamond-like coatings, multicomponent and multilayer coatings; preparing contact surfaces for finishing; the influence of hardness, roughness, residual stresses, surface finishing method and contact conditions; Stress-strain analysis and the tribological response of finished contact surfaces; The criteria and procedure for selecting the contact surface texturing and/or finishing, examples of applications in mechanical engineering.

Monitoring of student progress:

  • Written and oral examination
  • Report on accomplished exercises
  • Accomplished project work


  • K.L. Johnson: Contact mechanics, Cambridge University Press, Cambridge, 1985
  • I. Iliuc: Tribology of thin layers, Elsevier, Amsterdam, 1980
  • T.A. Stolarski: Tribology in Machine Design, Butterworth Heinemann, Oxford, 1990
  • F.W. Bach, A. Laarmann, T. Wenz: Modern Surface Technology, Wiley-vch, Weinheim, 2006
  • B. Bhushan, B.K. Gupta: Handbook of tribology – Materials, Coatings and Surface Treatments, McGraw-Hill, New York, 1991
  • K. Holmberg: Coatings Tribology, Elsevier, Amsterdam, 2009
  • K.N. Strafford, P.K. Datta, J.S. Gray: Surface engineering practice, Ellis Horwood, New York, 1990
  • C. Donnet, A. Erdemir: Tribology of diamond-like carbon films: fundamentals and applications, Springer, New York, 2008