Paviath Integrated Solution Paviath


UM Rolling Contact Fatigue

UM Rolling Contact Fatigue module is intended for simulation of the accumulation of contact fatigue damages in railway wheels.

The module may be used for implementing of multivariant comparative calculations, for example, for solution of the problem of the wheel tread profile optimization according to a contact fatigue criterion.


UM Rolling Contact Fatigue allows the user

• To define the velocity of accumulation of contact fatigue damages in wheels with the different tread surfaces by using the data which are obtained by simulation of railway vehicle dynamics by means of the UM Loco;

• To consider wheel profile wear-out effect on the rate of accumulation of contact fatigue damages (using module UM Wheel\Rail Wear);
• To represent processes of the stress modeling and the damage accumulation in the wheel with the help of graphic user interface including isolines and coloring.

Rolling Contact Fatigue

Fatigue strength criterion

The equivalent stress based on the Dang Van’s criterion [1], including amplitude values of the maximum shear stresses and influence of the hydrostatic stress, is used in the module for calculation of contact fatigue strength.The calculated equivalent stresses are compared against to damaging stresses which are defined by means of a wheel steel contact fatigue diagram obtained by using experimental data. The fatigue diagram determines dependency between the number of cycles up to crack/destruction of the wheel material and the equivalent stress level [2, 3].The cumulative damage in a wheel point is defined using the contact fatigue diagram by summation of the calculated damages.

Fatigue strength criterion

Wheel model

The finite element model of a wheel fragment with the elastic constraints on its surfaces is used [4]. Such a model allows defining the stresses in the subcontact layers of the wheel with the minimum computing time and with the sufficient accuracy. It is convenient to accumulate the contact fatigue damages in the nodes of the finite element scheme also.

Wheel model

Solution of the contact problem

The accumulated fatigue damages correspond to one radial section of the wheel which is contacted with a rail once during one revolution of the wheel. So, number of the contact problem solutions is equal to number of the wheel revolutions on the considered running distance.

The following results of simulation of railway vehicle dynamics in UM Loco are used for definition of contact forces on every step: the normal force; position of contact points on the wheel and rail profiles; angle of rotation of a wheel relatively a rail around the longitudinal axis; longitudinal and lateral creep and spin values.

The normal and tangential force distributions in the contact patch are determined by using the fast algorithms.

Solution of the contact problem I

The algorithm used for the solution of the normal contact problem does not suppose numerical integration that significantly reduces CPU efforts and time consuming. The algorithm treats well both multipoint and conformal contacts. The tangential contact forces are defined by using FASTSIM algorithm.

The obtained forces are applied to the nodes located on the contact surface of the finite element mesh of the wheel and by solving FEM problem the equivalent stresses in the nodes of the scheme are obtained and compared against the damaging stresses [5].

Solution of the contact problem II


The following assumptions are used.

• The materials of the contacting bodies are uniform, isotropic and elastic.
• The temperature level arising in a wheel does not influence on a stress state and mechanical properties of wheel material considerably.


Example of comparative calculation

The example of calculation of the rate of accumulation of contact fatigue damages in the wheels with the different tread profiles is presented below. Representation by isolines and coloring are used for animated image of the calculation results.


1. Ekberg A. Rolling contact fatigue of railway wheels – computer modeling and in-field data / Proceedings of 2nd mini conf. Contact mechanics and wear of rail/wheel systems. Hungary, Budapest. 1996. P. 154…163.

2. Increasing resistance of the railway wheels in operation by using carbonitride hardening of steel / L.M. Shkolnik, D.P. Markov, U.S. Proydak etc. // Herald of the Railway Research Institute (JSC VNIIZhT). 1994. No 6. P. 40…44. (in Russian)

3. Sakalo A.V. Contact fatigue strength of railway wheel steel // Herald of the BSTU. 2011. №2. P. 35…41. (in Russian)
4. Sakalo A.V. Method of simulation of contact stresses by using finite element fragments on elastic foundation // Herald of the VSTU. 2009. №9. P. 71…76. (in Russian)
5. Sakalo A.V. Improvement of the railway wheel tread profile according to a contact fatigue criterion. PhD thesis, Moscow, 2011. (in Russian)

comparative calculation