Reduced Order Modeling Based on Complex Nonlinear Modal Analysis and Its Application to Bladed Disks With Shroud Contact

Abstract

The design of bladed disks with contact interfaces typically requires analyses of the resonant forced response and flutter-induced limit cycle oscillations. The steady-state vibration behavior can efficiently be calculated using the multiharmonic balance method. The dimension of the arising algebraic systems of equations is essentially proportional to the number of harmonics and the number of degrees of freedom (DOFs) retained in the model. Extensive parametric studies necessary, e.g., for robust design optimization are often not possible in practice due to the resulting computational effort. In this paper, a two-step nonlinear reduced order modeling approach is proposed. First, the autonomous nonlinear system is analyzed using the generalized Fourier-Galerkin method. In order to efficiently study localized nonlinearities in large-scale systems, an exact condensation approach as well as analytically calculated gradients are employed. Moreover, a continuation method is employed in order to predict nonlinear modal interactions. Modal properties such as eigenfrequency and modal damping are directly calculated with respect to the kinetic energy in the system. In a second step, a reduced order model is built based on the single nonlinear resonant mode theory. It is shown that linear damping and harmonic forcing can be superimposed. Moreover, similarity properties can be exploited to vary normal preload or gap values in contact interfaces. Thus, a large parameter space can be covered without the need for recomputation of nonlinear modal properties. The computational effort for evaluating the reduced order model is almost negligible since it contains a single DOF only, independent of the original system. The methodology is applied to both a simplified and a large-scale model of a bladed disk with shroud contact interfaces. Forced response functions, backbone curves for varying normal preload, and excitation level as well as flutter-induced limit cycle oscillations are analyzed and compared to conventional methods. The limits of the proposed methodology are indicated and discussed.

Dynamic Modeling and Projection-Based Reduction Methods for Bladed Disks With Nonlinear Frictional and Intermittent Contact Interfaces

“…Figure 13 shows different types of contact interfaces in a blisk, which may lead to nonlinear behavior. While fir-tree joints (which join the blades to the disk) with improper fits or cracked blades [119,120,124,159,164] result in intermittent contacts, frictional damping mechanisms such as shrouds [11,50,74,80,143,146,165,166], under-platform [96,141,154,[167][168][169][170], or ring dampers [5,62,68,79,145] operate in the microslip regime (spatially and temporally varying stick and slip conditions in a contact region).…”

“…In the past, such methods have been applied to simple models with relatively few DoFs [70]. Reduction of the dynamics of large models such as blisks with complex friction nonlinearities using NNMs is quite challenging due to high computational costs and remains a field of active research [74,75].…”

Conjectural bifurcation analysis of the contact-induced vibratory response of an aircraft engine blade

“…This contribution brings further developments to previous numerical and experimental investigations limited to the framework of a single blade [10,6]. Possible contacts between neighbouring blades [11,12] are not accounted for. Even though it now seems possible to conduct simulations able to accurately predict critical angular velocities as well as the corresponding abradable coating wear patterns, experimental data sets show unexpected and sudden variations in the blade vibratory responses [6] that remain unelucidated.…”

Sensitivity and Forced Response Analysis of Anisotropy-Mistuned Bladed Disks With Nonlinear Contact Interfaces

“…In order to be able to calculate the nonlinear forced response of realistic bladed disk models with keeping the computation costs low, a model reduction method needs to be applied, e.g. [19,20].…”