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                <term xml:lang="en">Time-stepping method</term>
                <term xml:lang="en">Bladed-disk assembly</term>
                <term xml:lang="en">Trubomachines</term>
                <term xml:lang="en">Modal Synthesis</term>
                <term xml:lang="en">Unilateral Contact</term>
                <term xml:lang="fr">roue aubagée</term>
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                <term xml:lang="fr">Lagrangien</term>
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              <p>The optimization of modern turbomachines through the diminution of aerodynamic losses leads to more frequent contacts between the fixed and rotating components. Modal interaction is one of the phenomena that may arise from these contacts with potential dangerous consequences for the integrity of the turbomachine. This paper presents the validation of a 3Dcontact algorithm – within the context of the finite element method – allowing to efficiently study the phenomenon of interaction. It is based on the forward increment Lagrange multiplier method which allows the combination of explicit time integration with the respect of non penetration conditions. This contact algorithm is validated with respect to another algorithm based on an implicit time integration procedure and the commercial software Ansys. It is highlighted in this paper that results obtained with the proposed algorithms match reference results. Also, results emphasize that the presented algorithm allows for energy conservation. This contact algorithm is then used in combination with reduction techniques to simulate a blade-tip/casing contact case with 3D industrial finite element models.</p>
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              <p>Afin d'optimiser le rendement des turbomachines aéronautiques, les concepteurs cherchent à réduire les pertes aérodynamiques entre les différents étages de la structure. Ces pertes sont directement liées aux jeux entre les parties tournantes et fixes qui sont donc réduits au minimum. La contre-partie de cette optimisation réside dans le fait que les contacts entre parties tournantes (rotor) et statiques (stator) deviennent plus fréquents. Parmi les phénomènes d'interaction rotor/stator pouvant être créés par ces contact, citons le problème d'interaction modale dont les conséquences peuvent être critiques pour l'intégrité de la turbomachine. Ce papier présente la validation d'un algorithme de contact 3D utilisé pour la simulation de telles interactions rotor/stator dans une configuration non-accidentelle. Cet algorithme de contact repose sur un schéma temporel explicite (différences finies centrées) et l'utilisation de la méthode des multiplicateurs de Lagrange pour le traitement du contact, qui permet notamment de respecter les conditions de non-pénétrabilité. Cet algorithme de contact est validé par comparaison à deux autres codes de contact: (1) un algorithme avec schéma d'intégration temporelle implicite et traitant le contact à l'aide de la méthode du bi-potentiel; (2) un code industriel, ANSYS. Les résultats obtenus mettent en évidence la qualité de l'algorithme proposé dont il est également montré qu'il permet la conservation de l'énergie totale du système. À la fin de l'étude, un cas d'application est détaillé: l'algorithme de contact est utilisé pour simuler un cas de contact aube/carter avec des modèles éléments finis 3D.</p>
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