Computational Methods for Rolling Contact Phenomena



Instructor Information: Prof. Dr.-Ing. Udo Nackenhorst, Institut fur Baumechanik und Numerische Mechanik, Department of Civil Engineering, University of Hannover

Descrizione introduttiva

Rolling contact is of interest in many technical applications. Examples are car tires, railways, roller bearings etc. Questions arise from wear, fatigue and deterioration of wheels and rails, safety, comfort and durability of tires until to the high frequency dynamic behaviour of rolling wheels related to rolling noise generation. The physical mechanisms on these questions often are not well understood yet. One reason is that detailed phenomena taking place in the contact region are not observable by measurements in general. For example it is impossible to measure the contact-stress and slip distribution in wheel-rail contact under high speed conditions. Analytical methods are limited to linear elastic cases and rather simple contact geometries. Therefore, reliable and efficient numerical methods are needed for improving the performance of rolling systems.
This course gives an introduction into computational approaches based on the finite element method for the numerical analysis of rolling contact problems. The state of the art of computational rolling contact analysis will be demonstrated illustratively by industrial applications ranging from 3D wheel-rail contact over large deformation, tire-road contact including inelastic material properties, up to high frequency noise radiation of rolling tires. The participants will be introduced into the theoretical foundations and key-features will be investigated interactively on simple examples.


Topic of this course is the finite element modelling of rolling contact problems. The state of the art of computational methods with emphasis to industrial problems such like tires or railway systems will be taught.
A first step for the general understanding will be the discussion of the physical phenomena observed on deformable bodies in rolling contact by use of analytical solutions available for simple geometries. With this basic knowledge computational approaches based on the finite element method shall be learned. In contrast to quasi-static as well as impact problems, rolling is occupied by large rigid body motions, which is treated numerically efficient by use of a special relative kinematics, the so called Arbitrary-Lagrangian-Eulerian (ALE) description. The participants will be introduced into the continuum mechanics of the ALE-approach and its finite element approximation. Special emphasis will be laid onto the 'non-classical'contributions within this approach, like inertia-effects, the treatment of inelastic material properties as well as local frictional contact and the transient dynamic behaviour of rolling bodies.
The capabilities, as well as advantages and disadvantages of alternative numerical approaches like boundary element methods, pure Lagrangian finite element methods (explicit vs. implicit) will be discussed. Hints on limitations of commercial finite element codes with respect to rolling contact analysis will be given.
Goal of this course is to familiarize the participants with the physical, mathematical and numerical specialities for the treatment of industrial rolling contact problems. They will be introduced to judge the problems nature for choosing suitable computational approaches and the details behind.


Problemi inerenti lo scambio di massa e di energia: richiami sui meccanismi di scambio termico di base; equazione generale della conduzione; convezione esterna ed interna; strato limite termico e fluidodinamico; equazioni di conservazione della massa, della quantità di moto e dell’energia; equazioni di Navier-Stokes e relative condizioni ai limiti; meccanismi di scambio termico combinati, stazionari e non stazionari. Metodi numerici per la risoluzione delle equazioni differenziali alle derivate parziali: classificazione delle equazioni differenziali alle derivate parziali e relativo significato fisico; direzioni caratteristiche e loro significato fisico; volumi finiti ed elementi finiti; formulazione debole delle equazioni di Navier-Stokes; trattamento delle condizioni ai limiti; problematiche di stabilizzazione e algoritmi per la risoluzione delle equazioni di Navier-Stokes. Programmazione agli elementi finiti: formulazione debole di problemi ellittici con costruzione e assemblaggio delle matrici locali, trattamento delle condizioni al contorno, analisi e rappresentazione dei risultati; problemi bi e tri-dimensionali; esercitazioni numeriche al calcolatore. Modellazione numerica di problemi complessi di scambio termico: simulazione al calcolatore di problemi complessi di scambio di massa e di energia, in condizioni stazionarie e non stazionarie; tecniche per il post-processamento dei risultati; esercitazioni al calcolatore circa l’utilizzo di codici di calcolo commerciali, finalizzate allo studio di processi termici di interesse pratico.


Engineers (and other scientists, see prerequisites) seeking on solutions for optimizing rolling contact behaviour of industrial products by use of computational methods.
PhD and post-graduate students for a basic introduction and evaluating their own research project in this field.


The participants should be familiar with:

  • basics of continuum mechanics: balance laws, large deformation theory.
  • basics of constitutive theory: plasticity, visco-elasticity, friction.
  • finite element methods for implicit non-linear static solutions (Newton-methods)
  • basics of computational contact mechanics (TCN-COURSE MMCBTA03-07)
  • numerical (FE) treatment of transient dynamic problems (explicit vs. implicit)

Materiale didattico

The course will be taught by use of Power-Point presentations. Photocopies of the slides will be supplied to the participants.



Da definire


Da definire

Livello / tipologia

Corso Teorico/Applicativo

Costo di partecipazione

400€ + IVA

È richiesta la preiscrizione, non è impegnativa e non comporta l'obbligo di partecipazione.