Rotational Speed-Dependent Contact Formulation for Nonlinear Blade Dynamics Prediction

Considering rotational speed-dependent stiffness for vibrational analysis of friction-damped bladed disk models has proven to lead to significant improvements in nonlinear frequency response curve computations. The accuracy of the result is driven by a suitable choice of reduction bases. Multimodel reduction combines various bases, which are valid for different parameter values. This composition reduces the solution error drastically. The resulting set of equations is typically solved by means of the harmonic balance method. Nonlinear forces are regularized by a Lagrangian approach embedded in an alternating frequency/time domain method providing the Fourier coefficients for the frequency domain solution. The aim of this paper is to expand the multimodel approach to address rotational speed-dependent contact situations. Various reduction bases derived from composing Craig–Bampton, Rubin–Martinez, and hybrid interface methods will be investigated with respect to their applicability to capture the changing contact situation correctly. The methods validity is examined based on small academic examples as well as large-scale industrial blade models. Coherent results show that the multimodel composition works successfully, even if multiple different reduction bases are used per sample point of variable rotational speed. This is an important issue in case that a contact situation for a specific value of the speed is uncertain forcing the algorithm to automatically choose a suitable basis. Additionally, the randomized singular value decomposition is applied to rapidly extract an appropriate multimodel basis. This approach improves the computational performance by orders of magnitude compared to the standard singular value decomposition, while preserving the ability to provide a best rank approximation.