Reduced Order Modeling of Bladed Disks with Geometric and Contact Nonlinearities

Because of the new environmental regulations in aeronautics, engine manufacturers have to drastically reduce their environmental footprint. To achieve this, new engine architectures are being considered to improve the performance of turbojet engines and reduce their fuel consumption. First, aerodynamic losses are decreased by reducing the clearance between the blades and the surrounding casing. This can lead to contact events between the blades and the casing even in nominal operating conditions. Moreover, the engine weight can be reduced by designing lighter and slender blades. As a consequence, the blades can undergo large displacements and deformations.

Because of the high costs associated to full-scale experimental setups, it is particularly important for manufacturers to have at their disposal accurate predictive numerical strategies allowing to account for these nonlinear structural considerations from the beginning of the design process. As the direct use of industrial 3D finite element models in dynamic analyses requires high computational capabilities, many recent works are devoted to the construction of nonlinear reduced order models.

A methodology based on reduced order modeling techniques has been recently derived to study the contact interactions of single blades undergoing large displacements. The methodology is here extended to full bladed disks with cyclic symmetry. Each sector of the high fidelity model is projected onto a basis composed of Craig-Bampton modes and a selection of their modal derivatives. A second reduction allows to reduce the cyclic boundary degrees-of-freedom. The internal nonlinear forces due to large displacements are evaluated in the reduced basis with the stiffness evaluation procedure. Contact is numerically handled with Lagrange multipliers.

The numerical strategy is here applied on an open industrial compressor model, the NASA rotor 37, in order to promote reproducibility of results. This work demonstrates that reduced order models provide a computationally efficient alternative to full order finite element models for the accurate prediction of the time response of structures with both distributed and localized nonlinearities.