Reduced order modeling of blades with geometric nonlinearities and contact interactions

This article presents a methodology dedicated to the vibration analysis of turbomachine blades accounting for both geometric nonlinearities and nonlinear blade-tip/casing contacts in a numerically efficient way through the use of reduced order models. Contact is numerically handled with Lagrange multipliers and the equation of motion is integrated forward in time using an explicit central difference time integration scheme. Nonlinear internal forces caused by large displacements are evaluated using the stiffness evaluation procedure. Three reduction techniques are compared in this article, namely a nonlinear extension of the Craig-Bampton method, the proper orthogonal decomposition and a modal derivatives-based approach. These numerical methods are applied on an open industrial compressor blade model, the NASA rotor 37 blade, in order to promote reproducibility of results. The reduction methods are first applied to the blade subjected to a harmonic excitation, without contact interactions. An indicator accounting for both local and global comparison criteria is defined to more easily compare the performance of each method. When also accounting for blade-tip/casing contacts, the presented results underline that the modal derivatives-based approach is particularly well-suited for an accurate description of the blade's dynamics. This method is then employed for an in-depth analysis of the NASA rotor 37 vibration response over a wide angular speed range considering a typical contact scenario. Obtained results feature time and frequency domain signals along with stress fields. They suggest that accounting for geometric nonlinearities has a strong impact on the prediction of contact initiated interactions.