Stability analysis of periodic solutions computed for blade-tip/casing contact problems

Abstract

This article focuses on the stability assessment of mechanical systems featuring a nonlinear interface on which are applied unilateral contact constraints. The regularized-Lanczos harmonic balance method is used to compute periodic solutions for each system. For each considered mechanical system, the implementation of distinct stability assessment numerical algorithms (including the Newmark 2 n -pass method and Hill’s method using eigenvalue sorting) relying on Floquet theory allows for an in-depth investigation of their convergence and accuracy. From a single-degree of freedom impactor impacting a fixed obstacle to the industrial finite element model of a transonic compressor blade impacting a deformed casing, the gradually increasing complexity of the considered mechanical systems provides new insight on which stability assessment numerical algorithm may be the best suited when dealing with contact nonlinearities. From a numerical standpoint, attention is paid to specific developments that were identified as key for enhancing the numerical efficiency of the stability assessment process including the iterative solver, the computation of analytical derivatives, the scaling of the problem and the use of fast Fourier transforms. Particular attention is also paid to the influence of the Lanczos filtering procedure and its implications in terms of stability assessment. While it is found that both the Newmark 2 n -pass method and Hill’s method with eigenvalue sorting can be successfully applied on large industrial systems featuring a nonlinear interface, the faster convergence of Hill’s method is underlined and suggests it may be a better option for an accurate and efficient stability assessment on which Lanczos filtering has a negligible influence. • Local stability analysis of periodic solutions computed using a Harmonic Balance Method. (HBM) based numerical strategy for contact problems of increasing severity. • Analytical expression of blade-tip/casing contact forces related Jacobian matrices. • Numerical considerations for efficient HBM computations and in-depth comparison of time and frequency domain-based stability assessment algorithms. • Detailed application on both academical impactors and an industrial blade: NASA rotor 37. • Influence of Lanczos filtering over stability assessment.