Nodal Diameter-Dependent Modal Damping Method for Nonlinear Blade Dynamics Prediction Considering Variable Rotational Speed

Abstract

Since industrial large-scale models of friction-damped bladed disks for vibration analysis usually comprise numerous degrees of freedom, reduction techniques are required to facilitate the application of frequency and time domain solution methods. Common approaches utilize modal representations of the vibrational behavior considering either fixed, free, or hybrid interface conditions as well as elastic response to either unitary displacements or unitary forces acting on interface degrees of freedom to ensure static completeness. These modes serve as a basis for reduced description of the equation of motion. Often global damping concepts such as Rayleigh damping or hysteretic damping are applied afterwards. If mode-wise damping ratios are known, these can be introduced using modal damping formulation. Provided that variable rotational speed-dependence of the structure is of interest, an expanded speed-independent multi-model reduction basis is needed. The aim of this paper is to provide a nodal diameter-dependent modal damping approach to account for such damping information in case of variable rotational speed. Therefore, basis transformations between surrogate and multi-model basis are required. Attention will be paid to dealing with linearly dependent bases. Periodic solutions induced by multi-harmonic excitation are sought using a harmonic balance approach. The influence of multi-harmonic excitation onto the vibrational behavior is analyzed, serving as a starting point for nodal diameter-dependent modal damping investigations. Accuracy and scope of the method are finally discussed.

Rotational Speed-Dependent Contact Formulation for Nonlinear Blade Dynamics Prediction

“…Throughout this study, the vibrational frequency dependence of the stiffness matrix is neglected, which is a commonly applied assumtion in this setting and appealing due to the simplification of the numerical treatment [3]. For further details on the assumptions for deriving the stiffness and damping matrices, the interested reader is referred to the literature [4,12]. The structure is excited by the harmonic forces f e and is subject to nonlinear contact interactions captured by f nl .…”

“…The multi-model reduction is now applied to a large-scale, cyclically symmetric blisk model depicted in Fig. 5, which was already used by the authors in related work [4,12] As mentioned above, using many fixed or free interface modes for reduction, allows the model to reproduce the dynamics under contrary interface condition sufficiently well. To observe the models capability of automatically choosing the correct representation, e.g.…”