Vibration Modeling of Bladed Disks Subject to Geometric Mistuning and Design Changes

Abstract

In this paper, a new reduced-order modeling technique is presented for bladed disks that feature large, geometric deviations from a nominal design. Various finite-element-based reduced-order models (ROMs) have been proposed in the literature for bladed disks with small blade-to-blade differences, called mistuning. Many of these techniques rely on the fact that mistuned-system normal modes can be effectively represented using a linear combination of the normal modes of the nominal (tuned) system. However, when the mistuning or geometric deviation is large, the number of tuned-system normal modes required to describe the mistuned-system normal modes increases dramatically. In this work, a method for large mistuning is formulated by employing a mode-acceleration method with static mode compensation. By accounting for the effects of mistuning as though they were produced by external forces, a set of basis vectors is established using a combination of tuned-system normal modes compensated by static modes. The obtained basis vectors approximately span the space of the mistuned-system modes without requiring a much more expensive modal analysis of the mistuned system, and they provide much better convergence than tuned-system normal modes. Furthermore, in order to extend the method to higher frequency ranges, quasi-static modes, in which inertia effects are included, are employed in place of static modes in the modeacceleration formulation. It is seen that ROMs based on the new technique are extremely compact, yet they accurately capture the vibration response of bladed disks subject to geometric mistuning or design changes.

Next-Generation Modeling, Analysis, and Testing of the Vibration of Mistuned Bladed Disks

“…To address this, a new reduced-order modeling approach for bladed disks subject to damage or geometric design changes was developed in this research program [1,17]. This new technique employs a mode-acceleration formulation with static mode compensation (SMC) to account for the effects of the geometric changes on the mode shapes.…”

“…New methods were developed for identifying blade mistuning parameters from test data and for running experimental Monte Carlo assessments of the effects of mistuning on the system forced response. To date, this work has been published in 13 conference papers [1][2][3][4][5][6][7][8][9][10][11][12][13], 3 journal papers [14][15][16], and parts or all of 5 doctoral dissertations [17][18][19][20][21]. …”

Robust Analysis of Design in Vibration of Turbomachines

“…It should be noted that, if convergence is slow, then the reduced-order model is not sufficiently small and so would not be efficient and effective to implement the probabilistic model of uncertainties and above all, to perform a robust design optimization. In another hand, it is well recognized today that, if the use of the tuned modes for constructing the reduced-order model is efficient for blade material properties modifications, it is not always the case for blade geometric modifications (see for instance [14,17]). In addition, the blade geometric modifications induce a problem related to incompatibility representations between the tuned modes calculated with the mesh of the tuned bladed disk and the structural matrices of the geometrically modified bladed disk calculated with another mesh.…”

“…This is no longer the case for mistuned and/or detuned structures which need a full structure formulation. To reduce numerical computational costs while solving the mistuning problem on finite element meshes of realistic bladed disks, many reduced-order methods have been introduced (see [6,[9][10][11][12][13][14][15][16]). In general, reduced-order models are obtained by substructuring a bladed disk into disk and blades components (see e.g.…”

“…Consequently, large geometric detuning can be difficult to take into account with such a method. To solve the problem of geometric detuning, without using substructuring, a method named Static Mode Compensation (SMC) has been proposed in [14], and used in [18], in which the mistuned system is represented by the full tuned system and by virtual mistuning components. But this method needs a convergence acceleration to be performed, which requires a large amount of computation.…”