Assessment of Geometric Nonlinearities Influence On NASA Rotor 37 Response to Blade Tip/Casing Rubbing Events

This paper uses a recently derived reduction procedure to study the contact interactions of an industrial blade undergoing large displacements. The reduction technique consists in projecting the dynamical problem onto a reduction basis composed of Craig-Bampton modes and a selection of their modal derivatives. The internal nonlinear forces due to large displacements are evaluated with the stiffness evaluation procedure and contact is numerically handled using Lagrange multipliers. The numerical strategy is applied on an open industrial compressor blade model based on the NASA rotor 37 blade in order to promote reproducibility of results. Two contact scenarios are investigated: one with direct contact between the blade and the casing and one with an abradable material deposited on the casing. The influence of geometric nonlinearities is assessed in both cases. In particular, contact interaction maps and abradable coating wear pattern maps are used to identify the main interactions that can be detrimental for the engine integrity.

Assessment of Geometric Nonlinearities Influence on NASA Rotor 37 Response to Blade Tip/Casing Rubbing Events

This paper uses a recently derived reduction procedure to study the contact interactions of an industrial blade undergoing large displacements. The reduction technique consists in projecting the dynamical problem onto a reduction basis composed of Craig-Bampton modes and a selection of their modal derivatives. The internal nonlinear forces due to large displacements are evaluated with the stiffness evaluation procedure and contact is numerically handled using Lagrange multipliers. The numerical strategy is applied on an open industrial compressor blade model based on the NASA rotor 37 blade in order to promote re-producibility of results. Two contact scenarios are investigated: one with direct contact between the blade and the casing and one with an abradable material deposited on the casing. The influence of geometric nonlinearities is assessed in both cases. In particular, contact interaction maps and abradable coating wear pattern maps are used to identify the main interactions that can be detrimental for the engine integrity.

Comparison of Reduction Methods for Finite Element Geometrically Nonlinear Beam Structures

The aim of this contribution is to present numerical comparisons of model-order reduction methods for geometrically nonlinear structures in the general framework of finite element (FE) procedures. Three different methods are compared: the implicit condensation and expansion (ICE), the quadratic manifold computed from modal derivatives (MD), and the direct normal form (DNF) procedure, the latter expressing the reduced dynamics in an invariant-based span of the phase space. The methods are first presented in order to underline their common points and differences, highlighting in particular that ICE and MD use reduction subspaces that are not invariant. A simple analytical example is then used in order to analyze how the different treatments of quadratic nonlinearities by the three methods can affect the predictions. Finally, three beam examples are used to emphasize the ability of the methods to handle curvature (on a curved beam), 1:1 internal resonance (on a clamped-clamped beam with two polarizations), and inertia nonlinearity (on a cantilever beam).

Dynamic Analysis and Reduction of a Cyclic Symmetric System Subjected to Geometric Nonlinearities

The search for ever lighter weight has become a major goal in the aeronautical industry as it has a direct impact on fuel consumption. It also implies the design of increasingly thin structures made of sophisticated and flexible materials. This may result in nonlinear behaviors due to large structural displacements. Stator vanes can be affected by such phenomena, and as they are a critical part of turbojets, it is crucial to predict these behaviors during the design process in order to eliminate them. This paper presents a reduced order modeling process suited for the study of geometric nonlinearities. The method is derived from a classical component mode synthesis (CMS) with fixed interfaces, in which the reduced nonlinear terms are obtained through a stiffness evaluation procedure (STEP) procedure using an adapted basis composed of linear modes completed by modal derivatives (MD). The whole system is solved using a harmonic balance procedure and a classic iterative nonlinear solver. The application is implemented on a schematic stator vane model composed of nonlinear Euler–Bernoulli beams under von Kàrmàn assumptions.