2. Industrial context#

The purpose of this document is to describe the implementation of a structure calculation in vibration fatigue. We are more particularly interested in studies on rotating machines (turbine blades for example). These components are stressed by static loading (centrifugal force linked to the rotation of the machine) and by dynamic loading (vibrations induced by the flow of the fluid). The lifespan of the structure depends both on the dynamic part (amplitude of stress variations) and on the static part (average stress).

Static loading is generally well known; the dynamic part is difficult both to measure and to calculate. It is therefore not possible to directly implement the classical tools for calculating lifespan, based on the evolution of constraints over time (see note below).

Conversely, it may be interesting to estimate the maximum amplitude of variation admissible by the structure, for one or more natural modes of vibration. This amplitude can then be compared with the vibrations measured on site (measurements BVM for example).

The approach of such a study is as follows:

  • calculation of the stress associated with static loading;

  • calculation of the stress associated with the specific mode in question;

  • application of fatigue criteria to calculate, at each node of the mesh, the maximum admissible vibration to have unlimited endurance of the structure.

The last step can be done with the CALC_FATIGUE operator (TYPE_CALCUL = “FATIGUE_VIBR”). The principle of the calculation, its implementation in Code_Aster, and an industrial example are described in the following chapters.

Remarks:

A number of hypotheses are introduced for the calculation, see next paragraph. The aim here is to estimate, conservatively, an acceptable vibration level. If the temporal evolution of the constraints in the structure is known, it is necessary to use the conventional functionalities of the operators CALC_FATIGUE or POST_FATIGUE (with uniaxial or multiaxial criteria, cycle counting methods,…) .

Apart from turbines, the methodology presented here could also be applied to the vibration analysis of pipe lines (the average stress then corresponding to the internal pressure), or for wind turbines.

The calculation requires prior knowledge of the breaking stress and the endurance limit of the material.