Ronnie Bladh

Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks—Part I: Theoretical Models

Component mode synthesis (CMS) techniques are widely used for dynamic analyses of complex structures. Significant computational savings can be achieved by using CMS since a modal analysis is performed on each component structure (substructure). Mistuned bladed disks are a class of structures for which CMS is well suited. In the context of blade mistuning, it is convenient to view the blades as individual components, while the entire disk may be treated as a single component. Individual blade mistuning may then be incorporated into the CMS model in a straightforward manner. In this paper, the Craig-Bampton (CB) method of CMS is formulated specifically for mistuned bladed disks, using a cyclic disk description. Then a novel secondary modal analysis reduction technique (SMART) is presented: a secondary modal analysis is performed on a CB model, yielding significant further reduction in model size. In addition, a straightforward non-CMS method is developed in which the blade mistuning is projected onto the tuned system modes. Though similar approaches have been reported previously, here it is generalized to a form that is more useful in practical applications. The theoretical models are discussed and compared from both computational and practical perspectives. It is concluded that using SMART, based on a CB model, has tremendous potential for highly efficient, accurate modeling of the vibration of mistuned bladed disks.

Compact, Generalized Component Mode Mistuning Representation for Modeling Bladed Disk Vibration

New techniques are presented for generating reduced-order models of the vibration of mistuned bladed disks from parent finite element models. A novel component-based modeling framework is developed by partitioning the system into a tuned bladed disk component and virtual blade mistuning components. The mistuning components are defined by the differences between the mistuned and tuned blade mass and stiffness matrices. The mistuned-system model is assembled with a component mode synthesis technique, using a basis of tuned-system normal modes and attachment modes. The formulation developed is general and can be applied to any mistuned bladed disk, including those with large geometric mistuning (e.g., severe blade damage). In the case of small (i.e., blade frequency) mistuning, a compact reduced-order model is derived by neglecting the attachment modes. For this component mode mistuning model, the blade mistuning is projected first onto the component modes of a tuned, cantilevered blade, and then projected again onto the tuned-system normal modes via modal participation factors. In this manner, several natural frequencies of each mistuned blade can be used to capture systematically the effects of the complex physical sources of mistuning. A numerical validation of the developed methods is performed for both large and small mistuning cases using a finite element model of an industrial rotor.

Reduced Order Modeling and Vibration Analysis of Mistuned Bladed Disk Assemblies With Shrouds

This paper presents important improvements and extensions to a computationally efficient reduced order modeling technique for the vibration analysis of mistuned bladed disks. In particular, this work shows how the existing modeling technique is readily extended to turbomachinery rotors with shrouded blades. The modeling technique employs a component mode synthesis approach to systematically generate a reduced order model (ROM) using component modes calculated from a finite element model (FEM) of the rotor. Based on the total number of degrees of freedom, the ROM is typically two or three orders of magnitude smaller than the FEM. This makes it feasible to predict the forced response statistics ofmistuned bladed disks using Monte Carlo simulations. In this work, particular attention is devoted to the introduction of mistuning into the ROM of a shrouded assembly. Mistuning is modeled by projecting the mistuned natural frequencies of a single, cantilever blade with free shrouds onto the harmonic modes of the shrouded blade assembly. Thus, the necessary mistuning information may be measured by testing individual blades.

Dynamic Response Predictions for a Mistuned Industrial Turbomachinery Rotor Using Reduced-Order Modeling

This paper explores the effects of random blade mistuning on the dynamics of an advanced industrial compressor rotor, using a component-mode-based reduced-order model formulation for tuned and mistuned bladed disks. The technique uses modal data obtained from finite element models to create computationally inexpensive models of mistuned bladed disks in a systematic manner. Both free and forced responses of the rotor are considered, and the obtained results are compared with benchmark finite element solutions. A brief statistical study is presented, in which Weibull distributions are shown to yield reliable estimates of forced response statistics. Moreover, a simple method is presented for computing natural frequencies of noninteger harmonics, using conventional cyclic symmetry finite element analysis. This procedure enables quantification of frequency veering data relevant to the assessment of mistuning sensitivity (e.g., veering curvatures), and it may provide a tool for quantifying structural interblade coupling in finite element rotor models of arbitrary complexity and size. The mistuned forced response amplitudes and stresses are found to vary considerably with mistuning strength and the degree of structural coupling between the blades. In general, this work demonstrates how reduced order modeling and Weibull estimates of the forced response statistics combine to facilitate thorough investigations of the mistuning sensitivity of industrial turbomachinery rotors.

Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks—Part II: Application

In this paper the component-mode-based methods formulated in the companion paper (Part I: Theoretical Models) are applied to the dynamic analysis of two example finite element models of bladed disks. Free and forced responses for both tuned and mistuned rotors are considered. Comprehensive comparisons are made among the techniques using full system finite element solutions as a benchmark. The accurate capture of eigenfrequency veering regions is of critical importance for obtaining high-fidelity predictions of the rotors sensitivity to mistuning. Therefore, particular attention is devoted to this subject. It is shown that the Craig-Bampton component mode synthesis (CMS) technique is robust and yields highly reliable results. However, this is achieved at considerable computational cost due to the retained component interface degrees of freedom. It is demonstrated that this problem is alleviated by a secondary modal analysis reduction technique (SMART). In addition, a non-CMS mistuning projection method is considered. Although this method is elegant and accurate, it is seen that it lacks the versatility and efficiency of the CMS-based SMART. Overall, this work shows that significant improvements on the accuracy and efficiency of current reduced order modeling methods are possible.

Effects of Multistage Coupling and Disk Flexibility on Mistuned Bladed Disk Dynamics

The effects ofdisk flexibility and multistage coupling on the dynamics of bladed disks with and without blade mistuning are investigated. Both free and forced responses are examined using finite element representations of example single and two-stage rotor models. The reported work demonstrates the importance of proper treatment of interstage (stage-to-stage) boundaries in order to yield adequate capture of disk-blade modal interaction in eigenfrequency veering regions. The modified disk-blade modal interactions resulting from interstage-coupling-induced changes in disk flexibility are found to have a significant impact on (a) tuned responses due to excitations passing through eigenfrequency veering regions, and (b) a designs sensitivity to blade mistuning. Hence, the findings in this paper suggest that multistage analyses may be required when excitations are expected to fall in or near eigenfrequency veering regions or when the sensitivity to blade mistuning is to be accounted for Conversely, the observed sensitivity to disk flexibility also indicates that the severity of unfavorable structural interblade coupling may be reduced significantly by redesigning the disk(s) and stage-to-stage connectivity. The relatively drastic effects of such modifications illustrated in this work indicate that the design modifications required to alleviate veering-related response problems may be less comprehensive than what might have been expected.

Forced Response Analysis of a Mistuned Compressor Blisk Comparing Three Different Reduced Order Model Approaches

Accurate structural modeling of blisk mistuning is critical for the analysis of forced response in turbomachinery. Apart from intentional mistuning, mistuning can be due to the manufacturing tolera ...

Using Tiptiming and Strain Gauge Data for the Estimation of Consumed Life in a Compressor Blisk Subjected to Stall-Induced Loading

Using tip timing technology to record blade vibratory behavior has grown to become an industry standard over the past decade. Typically, the technology gets used during engine prototype testing to verify safe operation of the blades and thus the engine through synchronous and non-synchronous excitation events. Another common application is blade health monitoring, where the technique is used to detect deviations in natural frequencies and/or amplitudes compared to the virgin state. In both cases, acquired response data are used to establish that blade stresses remain below the high cycle fatigue limit. More rarely is tip timing data used as basis for remaining life estimation.As an example of how tip timing technology can be used beyond traditional resonance clearance for new blade designs, this paper presents an assessment of the fatigue damage incurred to a transonic compressor rotor subjected to stall-induced dynamic loading. The compressor rotor in question is equipped with tip timing, as well as strain gauges for a limited set of airfoils. The dynamic loads at stall are non-synchronous and highly erratic in nature, leading to quasi-static response of multiple modes. To facilitate a conceptually straightforward time domain finite life fatigue analysis, different strategies are employed to reconstruct the stress-time signal from tip timing data. This in turn allows for quantification of accumulated damage cycles, which is here done through simplified and traditional rainflow counting techniques.Additionally, a non-standard way of processing of tip timing data was employed to overcome one of tip timing method drawbacks — frequency aliasing. As an approach the nonuniform Fourier transform was applied to the same data sets. The results obtained are thoroughly evaluated and compared with strain gauges results highlighting the benefits and limitations of the respective approaches for highly complex stress-time histories such as stall events.Copyright

Leakage-Induced Compressor Blade Excitation due to Inter-Segment Gaps

A comprehensive investigation is presented related to leakage-induced blade excitation from shrouded vane segments found in industrial gas turbine compressors. The focus of the investigation is to explore the excitation mechanism acting on downstream rotor blades that stem from the particularly complex leakage flows around the hub inter-segment gaps.The aerodynamic forces are here determined using 3D nonlinear time-marching CFD simulations. The employed computational model encompasses the two rear-most stages in an existing industrial gas turbine compressor. The inter-segment gap is implemented in the next-to-last stator, varying from no gap to twice the nominal gap size.Obtained results indicate that the excitation induced by the inter-segment gap leakage flows is distinctly multi-harmonic and unexpectedly strong. As much as five times the excitation strength of upstream wakes was observed already for the nominal gap. The induced unsteady forces were found to derive from two different sources: (i) a large separation producing local forcing in the hub region; and (ii) circumferentially varying flow speed resulting in distributed forcing over the entire blade.The findings imply that the excitation induced by inter-segment gap leakage flows can be a significant contributor to blade vibratory responses in the intermediate engine order range, and thereby add to the knowledge base related to blade dynamic integrity.Copyright

Forced Response Analysis of a Mistuned Blisk Using Noncyclic Reduced-Order Models

The importance of mistuning analysis lies on understanding the distribution of the vibrational energy around the blisk. The large vibration amplitudes of individual blades inherent in mistuned blisks reduces the high cycle fatigue margin significantly. It is therefore important to perform mistuning analyses at a high accuracy while keeping the computational cost at an acceptable level. Because numerous analyses with large amount of degrees of freedom models are commonly performed, it is frequent to employ reduced-order models such as to reduce the computational effort. In this paper, a unique way to address the reduced-order model is presented, where each blisk sector is attached as individual substructures with the free-interface approach known as Craig–Chang. This implementation is compared against a fixed-interface approach known as Craig–Bampton in terms of accuracy for disk- and blade-dominated modes. Neither of these approaches applies cyclic symmetry, making them more accurate in the presence of mi...