Reduced-order modeling of mistuned bladed disks with geometric and contact nonlinearities

This thesis introduces a new methodology to study the dynamics of mistuned bladed disks with geometric and contact nonlinearities in a numerically efficient way. The methodology is based on a reduction procedure. This allows to overcome the difficulties related to the high computational costs of nonlinear dynamic simulations performed on industrial finite element models.

First, a methodology is developed to study the contact interactions of a single rotating blade with geometric nonlinearities. The reduction method is based on the modal derivative approach, which is adapted to retain physical degrees-of-freedom in the reduced space for the implementation of contact. In order to limit the size of the reduced system, a modal derivative selection criterion is proposed. The nonlinear internal forces due to large displacements are evaluated in the reduced space using the stiffness evaluation procedure. Contact is numerically handled using Lagrange multipliers. The methodology is then generalized to full bladed disk structures using component mode synthesis techniques with fixed interfaces. Mistuning can also be included in the reduced space.

Through this work, the numerical strategy is applied to an open industrial compressor bladed disk model based on the NASA rotor 37 in order to promote the reproducibility of results. The obtained results and, when applicable, their comparison with full-order model results give confidence in the methodology. In-depth analyses, including clearance consumption computations and frequency analyses with a continuation procedure, allow to understand and characterize the combined influence of contact and geometric nonlinearities on the structure’s dynamics.

Besides providing an accurate description of the time dynamics of the structure, the new methodology also allows to extract quantities of interest that are relevant for both researchers and industrial designers such as contact interaction maps, contact wear maps, critical angular speeds or stress fields in the structure. This non-intrusive strategy can be used in combination with any commercial finite element software.