Numerical Methods for Lubricated Contact Problems

  Cranktrain Copyright: Birgit Reinartz

Lecture “Numerical Methods for Lubricated Contact Problems” is an elective course suitable for students in the Master programs “Computational Engineering Science”, “Simulation Sciences”, “General Mechanical Engineering”, and others.



Violeta Karyofylli

Research Associate


+49 241 80 99931




Winter semester 2019/20: The course is not offered.

Preliminary meeting: -

Start: -

Lecture: -

Exercise: -



Lecture: Dr.-Ing. Birgit Reinartz

Exercise: Julian Angerhausen, M.Sc., Violeta Karyofylli, M.Sc.


Lubrication is the process of reducing friction or wear between two moving bodies by applying a lubricant. However, even a lubricant cannot avoid contact between the solid surfaces at all times, then elastic or plastic deformation takes place. Applications are to be found everywhere in our daily life: a piston moving inside a cylinder, a gear-wheel propelled by a wind turbine, a chain moving heavy loads, or a vehicle bearing.

The lecture focuses on how one can tackle lubricated contact problems by numerically solving a fluid-structure interaction problem with contact. We will start with the numerical solution of the Reynolds equations and the similarity theory of the lubricated Hertzian contact, and move on to rough surface computations and elasto-plasto contact mechanics and finally look at today's most advance methods for lubricated contact based on finite element methods and computational fluid dynamics. In the practical sessions, we use either Python or MATLAB to program our own LCP solver and apply the commercial solver FIRST to gain some first hand experiences with numerically solving applied lubricated contact problems. A visit to the ifas lab and its experimental facilities emphasizes how experiment and computation work hand in hand to tackle today’s engineering problems.

The module consists of a lecture with 2 SWS and an exercise with 1 SWS, and carries 5 ECTS points. During the first half of the semester, there will also be a practical session to help you prepare the homework project.


  • Introduction to coupled systems and respective numerical solution procedures, monolithic and partitioned solution strategy, system elimination, co-simulation
  • Fluid system: differential equations and numerical schemes, acceleration and stabilization techniques
  • Structural system: differential equations and numerical schemes, contact models
  • Mesh generation and mesh deformation algorithms, mesh vanishing techniques
  • Coupling conditions and enforcement, spatial and temporal coupling, finite interpolation, dual mortar method, acceleration techniques, stabilization methods, predictor-corrector schemes
  • Solution strategies for thermoelastic deformations, realization of different time scales
  • Multidisciplinary design optimization for lubricated contact problems


  1. Khonsari, Michael M., and E. Richard Booser. Applied tribology: bearing design and lubrication . John Wiley & Sons, 2017.

  2. Huang, Ping. Numerical calculation of lubrication: methods and programs . John Wiley & Sons, 2013.

  3. Yang, Bin, and Tod A. Laursen. A mortar-finite element approach to lubricated contact problems . Computer Methods in Applied Mechanics and Engineering 198.47-48 (2009): 3656-3669.


The final grade will be based on both the 20 min. oral exam (either in English or German) (50%) and the written report of the homework problem (either in English or German) (50%).

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