Optimization of Intentional Mistuning Patterns for the Mitigation of the Effects of Random Mistuning

Abstract

This paper focuses on the optimization of intentional mistuning patterns for the reduction of the sensitivity of the forced response ofbladed disks to random mistuning. Intentional mistuning is achieved here by using two different blade types (denoted as A and B) around the disk. It is thus desired to find the arrangement of these A and B blades (AIB pattern) that leads to the smallest 99th percentile of the amplitude of blade response in the presence of random mistuning. It is first demonstrated that there usually is a large number of local minima and further that the cost of a function evaluation is high. Accordingly, two novel, dedicated optimization algorithms are formulated and validated to address this specific problem. Both algorithms proceed in a two-step fashion. The first step, which consists of an optimization in a reduced space, leads to a series of good initial guesses. A local search from these initial guesses forms the second step of the methods. A detailed validation effort of this new procedure was next achieved on a single-degree-of-freedomper-blade model, a reduced order model of a blisk, and that of an impeller considered in an earlier study. In all validation cases, the two novel algorithms were found to converge to the global optimum or vei-y close to it at a small computational cost. Finally, the results of these optimization efforts further demonstrate the value of intentional mistuning to increase the robustness of bladed disks to random mistuning.

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

“…Mistuning occurs when there is a variability across the sectors of the blisk in a parameter, which affects its dynamics. Variations in different material properties such as mass, stiffness, and damping as well as in geometry across sectors have been studied in literature [4,5,[8][9][10][11][12][13][14]27,[105][106][107]. The consequence is that the sector-level system matrices are nonidentical across sectors.…”

“…Different blade stiffness patterns with the same variance may exhibit drastically different AFs. In fact, sometimes, intentional mistuning patterns are introduced into design to ensure small AFs [3,14,106,108,109]. Several studies have been conducted to calculate the theoretical upper bounds for AF when mistuning is introduced in a linear blisk [9,28,110].…”

“…Hence, the use of ROMs becomes essential. Mistuned ROMs may also be useful in other scenarios where repeated simulations of blisks are necessary, such as mistuning identification from blisk response measurements [27,[113][114][115][116], optimizing intentional mistuning patterns in blades [3,14,109], deciding mistuned damper arrangements [117,118], or detecting abnormalities in the structure such as cracks [119,120].…”

“…(16) and sector level mistuning components shown in Eq. (14). FMM further uses the approximation that the tuned modes in flat blade-dominant regions may be generated from cantilevered blade modes.…”

“…If any sector of the blisk is considered to be geometrically and materially identical to any another, the DoFs of the blisk dynamic may be reduced by a factor of the number of blades by the application of suitable constraints. However, it is well known that even small differences, which exist between different sectors in practice due to manufacturing tolerances, collectively called mistuning, can have significant effects on blisk response amplitudes [4][5][6][7][8][9][10][11][12][13][14]. Mistuning may be small when the variability in parameters between the sectors does not significantly affect the modes of the structure, or large when the response of the mistuned blisk in a certain frequency range cannot be captured by a set of nominally cyclic symmetric or tuned modes whose natural frequencies lie in the corresponding range.…”