Component Mode Mistuning Research Articles

Modelling and analysis of a bladed drum subject to the Coriolis and mistuning effects

The interaction between the Coriolis and mistuning effects on a finite-element model (FEM) of a simplified bladed drum compressor has been investigated in this paper. The Subset of Nominal Modes (SNM), the Component Mode Mistuning (CMM) and the Integral Mode Mistuning (IMM) techniques have been chosen and adapted to consider the reduction of the Coriolis matrix. Both free and forced responses of the ROMs have been validated using the FEM solutions as the benchmark. A new analysis using Monte Carlo simulations has been performed to consider disc and blade mistuning independently, and to study the domination of one over the other. The impact of the Coriolis effect has been highlighted through observation of the model with and without the Coriolis matrix. The evolution of the global dynamic behaviour with rotational speed has been investigated for the first time for different excitation frequencies and engine orders (EO). This in-depth investigation of a blisk allowed a better understanding of the interaction between the Coriolis and mistuning effects. The blade-dominated responses and the modes which remain close to the veering regions have strong mistuning effects, with significant localisation and amplitude magnification. The results mainly highlight that the disc-dominated and the blade–disc responses tend towards a tuned behaviour with the appearance of travelling waves.

Experimental Investigation of Bladed Disk Dynamics at Design Speed Under Synchronous Vibration

This work presents an experimental and computational investigation of a rotating bladed disk excited with air jets. The bladed disk is accelerated through critical speeds corresponding to specific engine orders of interest while air jets apply a constant forcing. These conditions induce synchronous vibrations in the blades. The experimental results were used to compute mistuning and damping values of the system, which were used in the computational analyses. This work uses a parametric reduced order model (PROM) that can adjust the system stiffness based on the rotational speed within the reduced space. Component mode mistuning was coupled with the PROM to create a mistuned model capable of capturing the mistuned system dynamics. Computational values for the blade frequency, amplitude, and damping were compared with experimental results to show how the computational model presented in this work can be used to characterize a rotating bladed disk.

Control of mistuning level using hard coating for blisks based on mistuning identification technique

Mistuning will lead to vibration localization of blisk, which seriously affects the service life of blisks. To control the mistuning level of blisks, a novel control method using hard coating is proposed. In this method, the thickness of hard coating is designed according to mistuning state of blisk substrate, so that, the mistuning level can be controlled and the vibration localization can be reduced in the designed coated blisk. Herein, the identification technique based on component mode mistuning (CMM) reduced-order model is improved to calculate the mistuning of blisk substrate and mistuning adjustment of coatings with different thicknesses. Based on the premise that the influences of the mass, stiffness and damping mistuning on the coated blisk response are all considered, a reduced-order model of the coated blisk is established, which includes the blisk substrate mistuning and the coating mistuning adjustment. It is rare to consider so many kinds of mistuning in previous studies. Based on this model, the function of coating thickness and coated blade response is obtained by the polynomial function fitting technique. Then, coating thicknesses can be determined with the target that the responses of each coated blade are equal. The first and second bending responses of the numerical and actual cases before and after coating are compared to verify the effectiveness of this method. It is found that the localization response amplitude is reduced significantly, and the mistuning level is effectively controlled.

Vibration response prediction of coated blisks under multi-point non-contact excitations using mistuning identification data

The mistuning and excitations of the real engineering coated blisk are very complex and it is difficult to predict the vibration response. In this study, a numerical method of response prediction for coated blisks under multi-point non-contact excitations is proposed. The purpose of applying multi-point non-contact excitations to the blades is to get closer to the actual excitations condition of coated blisks. A non-rotating coated academic blisk is used as the research object, the component mode mistuning (CMM) reduced-order technique focusing on blade mistuning is improved to establish the response prediction model of the coated blisk, which includes quantized parameters of the blade substrate mistuning and the mistuning caused by coating. Meanwhile, the effects of the mass, stiffness and damping mistuning of the blisk substrate and the coating on the response are comprehensively considered in the model. In order to preserve the simulation accuracy of the response prediction model, the blade substrate mistuning and the mistuning caused by coating are identified, and the reduced-order model (ROM) is updated by the identification results of mass and stiffness mistuning. The response predictions of the numerical case and actual case of the non-rotating simplified coated academic blisk are carried out respectively. For the numerical case, the results of response prediction are in good agreement with the response calculation results of the high fidelity finite element model (FEM). Compared with the numerical case, the error between the predicted response and the tested response is larger, but this error level is sufficient to meet the requirements of engineering applications. All the results show that the proposed method is effective for predicting the response of the non-rotating coated academic blisks under multi-point excitations.

Mistuning identification for coated blisks using small amount of experimental data

Because the coatings are likely to produce new mistuning which aggravates the vibration failure of coated blades, it is particularly important to study the mistuning identification for coated blades. In this study, the degrees of freedom of the whole disk of the coated blisk is completely constrained, and the orders of the dynamic model of the coated blisk based on component mode mistuning (CMM) method is further reduced. Based on this model, a novel mistuning identification method for the coated blade of the coated blisk by small amount of experimental data is proposed, which can identify the mass, stiffness and damping mistuning of the blade substrates and coatings. The input parameters with high amount of data, such as modal shape matrix, are removed from identification formulas, thus, both the amount of data for identification calculation and the workload of vibration testing are reduced. The mistuning identifications of the numerical case and actual case are carried out respectively, and the identification process of the mistuning identification method in this paper is compared with the one based on the classical CMM model. It is shown that the mistuning identification method is effective and feasible, and the identification efficiency is higher than the classical CMM identification method.

A structural damping identification technique for coatings on blisks based on improved component mode mistuning model

Abstract Since the structural damping characteristics of damping coatings are much higher than that of the blisk substrate, the structural damping differences of coatings in each sector directly affect structural damping of the coated blisk. Therefore, for the coated blisk, it is very important to identify the structural damping differences caused by coating. A novel method for structural damping identification of coatings on the coated blisk is proposed. The component mode mistuning (CMM) model is improved for establishing reduced order model (ROM) of coated blisks. In the model, based on the consideration of blisk substrate, the coatings on each sector are decomposed into the mistuned substructures which are independent of each other. Based on this model, the identification formula for structural damping coefficients of coatings on each sector is deduced. A numerical case is given to illustrate the identification procedure. The vibration test methods for obtaining input parameters of damping identification are demonstrated by an actual case. The damping identifications of numerical case and actual case are carried out. The identification results shown that the identification method had high identification accuracy and can be well applied for the damping identification of the hard coating and viscoelastic coating.

Damping mistuning identification of coated blisks by means of vibrational test

In order to accurately capture the damping mistuning of each sector of coated blisks, a novel identification method was proposed. Based on component mode mistuning (CMM) method, a dynamic model for damping mistuning identification of coated blisks is established. The novelty of this model is that it can predict and quantify the damping mistuning of blisk substrate and coating through the frequency deviations between coated blades and nominal cantilever blades. Based on this dynamic model, the identification algorithm of damping mistuning was obtained. The mass and stiffness mistuning of the blisk substrate and coating are considered in this algorithm, and the damping mistuning of blisk substrate and coating can be identified independently. A six-step identification procedure of damping mistuning for coated blisks is then proposed, where the operation sequence of theoretical simulations and vibration tests is introduced, as well as the method of using input parameters in each step. In addition, the damping mistuning identifications of a numerical case and an actual case are carried out to verify the feasibility of the developed algorithm and the identification procedure.

Hybrid reduction of mistuned bladed disks for nonlinear forced response analysis with dry friction

An efficient model order reduction technique for forced vibration analysis of a mistuned bladed disk with friction contact is presented. The present method applicable for small blade-to-blade mistuning, provides significant reduction in time without loss of accuracy for the nonlinear statistical analysis of mistuned bladed disks. This is achieved by obtaining a reduced order model of the mistuned bladed disks without generating its stiffness and mass matrices and considering the effect of mistuning on the static modes used in the reduction. This new approach can be interpreted as a hybrid of two existing techniques: Component mode mistuning (CMM) and a Dual model order reduction technique. The Dual method is a free interface based Component Mode Synthesis (CMS) method whose unique formulation makes it appropriate for mistuning analysis. The reduction basis in Dual approach includes free interface normal modes and residual flexibility attachment modes of mistuned bladed disk. These modes are computed using CMM and a proposed approximate approach, respectively. The resulting governing equation are solved in the frequency domain using Harmonic Balance method while contact forces are computed by an Alternating Frequency–Time method and a node-to-node 3D coupled contact model. The method is applied to a simplified shrouded turbine bladed disk, the results demonstrate the accuracy of the proposed method and the importance of tackling friction nonlinearity and mistuning simultaneously.

Parametric Reduced Order Models for Bladed Disks With Mistuning and Varying Operational Speed

A considerable amount of research has been conducted to develop reduced order models (ROMs) of bladed disks that can be constructed using single sector calculations when there is mistuning present. A variety of methods have been developed to efficiently handle different types of mistuning ranging from small frequency mistuning, which can be modeled using a variety of methods including component mode mistuning (CMM), to large geometric mistuning, which can be modeled using multiple techniques including pristine rogue interface modal expansion (PRIME). Research has also been conducted on developing ROMs that can accommodate the variation of specific parameters in the reduced space; these models are referred to as parametric reduced order models (PROMs). This work introduces a PROM for bladed disks that allows for the variation of rotational speed in the reduced space. These PROMs are created by extracting information from sector models at three rotational speeds, and then the appropriate ROM is efficiently constructed in the reduced space at any other desired speed. This work integrates these new PROMs for bladed disks with two existing mistuning methods, CMM and PRIME, to illustrate how the method can be readily applied for a variety of mistuning methods. Frequencies and forced response calculations using these new PROMs are compared to the full order finite element calculations to demonstrate the effectiveness of the method.

Vibration Characteristics of Rotating Mistuned Bladed Disks considering the Coriolis Force, Spin Softening, and Stress Stiffening Effects

Bladed disks of engine rotors usually operate at harsh conditions of high rotating speeds, which may lead to nonnegligible rotordynamic effects, including Coriolis force, spin softening, and stress stiffening effects. These effects on the vibration of mistuned bladed disks are seldom discussed in available investigations. In this paper, the vibration characteristics of rotating mistuned bladed disks are addressed by considering these rotordynamic effects. First, finite element (FE) models of bladed disks are used to obtain the governing equations of motion, and an efficient method for getting the stress stiffening matrix of sector model is developed. Then, the effective component‐mode mistuning method (CMM) is employed to create compact, yet accurate, reduced‐order models (ROMs). Finally, the models are validated and used to study the influences of Coriolis force, spin softening, and stress stiffening effects on the vibration of bladed disks with frequency mistuning factors. Numerical results show that these rotordynamic effects could significantly affect the vibrations of mistuning bladed disks, especially in the ranges of high speed, and should be carefully considered during analysis.

Mistuning identification and model updating of coating blisk based on modal test

Abstract Compared with a single material structure, the coating blisk contains at least two kinds of materials, thus the mistuning modeling and identification are more challenging than the usual bladed disk structure. In this study, on the basis of the component mode mistuning (CMM) and modal test, a method of mistuning identification was proposed for the coating blisk. The CMM model of the coating blisk was described firstly. Considering the mass and stiffness mistuning of the blisk substrate and coating materials simultaneously, the mistuning identification formula of the coating blisk was derived. Then, a novel method for the mistuning identification of coating blisk by measuring only two point modal coordinates of the blades was proposed. For the simplified numerical model and the relevant actual structure of coating blisk, the mistuning identifications were performed respectively, it was shown that the identification results are basically consistent with the predefined mistuning, which proved the rationality of the proposed mistuning identification method. Finally, based on the identification result of actual coating blisk, the original finite element model (FEM) of coating blisk was updated, and the simulation precision of FEM was improved.

Multistage Blisk and Large Mistuning Modeling Using Fourier Constraint Modes and PRIME

Current efforts to model multistage turbomachinery systems rely on calculating independent constraint modes for each degree-of-freedom (DOF) on the boundary between stages. While this approach works, it is computationally expensive to calculate all the required constraint modes. This paper presents a new way to calculate a reduced set of constraint modes referred to as Fourier constraint modes (FCMs). These FCMs greatly reduce the number of computations required to construct a multistage reduced order model (ROM). The FCM method can also be integrated readily with the component mode mistuning (CMM) method to handle small mistuning and the pristine rogue interface modal expansion (PRIME) method to handle large and/or geometric mistuning. These methods all use sector-level models and calculations, which make them very efficient. This paper demonstrates the efficiency of the FCM method on a multistage system that is tuned and, for the first time, creates a multistage ROM with large mistuning using only sector-level quantities and calculations. The results of the multistage ROM for the tuned and large mistuning cases are compared with full finite element results and are found in good agreement.

Mistuned Higher-Order Mode Forced Response of an Embedded Compressor Rotor—Part II: Mistuned Forced Response Prediction

This paper is the second part of a two-part paper that presents a comprehensive study of the higher-order mode (HOM) mistuned forced response of an embedded rotor blisk in a multistage axial research compressor. The resonant response of the second-stage rotor (R2) in its first chordwise bending (1CWB) mode due to the second harmonic of the periodic passing of its neighboring stators (S1 and S2) is investigated computationally and experimentally at three steady loading conditions in the Purdue three-stage compressor research facility. A nonintrusive stress measurement system (NSMS, or blade tip-timing) is used to measure the blade vibration. Two reduced-order mistuning models of different levels of fidelity are used, namely, the fundamental mistuning model (FMM) and the component mode mistuning (CMM), to predict the response. Although several modes in the 1CWB modal family appear in frequency veering and high modal density regions, they do not heavily participate in the response such that very similar results are produced by the FMM and the CMM models of different sizes. A significant response amplification factor of 1.5–2.0 is both measured and predicted, which is on the same order of magnitude of what was commonly reported for low-frequency modes. In this study, a good agreement between predictions and measurements is achieved for the deterministic analysis. This is complemented by a sensitivity analysis which shows that the mistuned system is highly sensitive to the discrepancies in the experimentally determined blade frequency mistuning.

Nonlinear dynamics of mistuned bladed disks with ring dampers

In turbomachinery applications, rotating bladed disks (blisks) are often subject to high levels of dynamic loading, such as traveling wave excitations, which result in large response amplitudes at resonance. To prevent premature high cycle fatigue, various dry friction dampers are designed for blisk systems to reduce the forced responses. Ring dampers are located in the disk, underneath the blades, and are held in contact with the blisk by centrifugal loading. Energy is dissipated by nonlinear friction forces when relative motions between the ring damper and the blisk take place. To investigate the dynamic responses of blisk–damper systems in the presence of the nonlinear frictional contacts, conventional methods based on numerical time integration are not suitable since they are computationally expensive. This paper presents a reduced-order modeling technique to efficiently capture the nonlinear dynamic responses of the blisk–damper systems. Craig–Bampton component mode synthesis (CB-CMS) serves as the first model reduction step. A novel mode basis that mimics the contact behavior under sliding and sticking conditions is developed to further reduce the CB-CMS model while maintaining its accuracy. The resulting reduced nonlinear equations of motion are solved by a hybrid frequency/time domain (HFT) method. In the HFT method, the contact status and friction forces are determined in the time domain by a three-dimensional contact model at each contact point, whereas the reduced equations of motion are solved in the frequency domain according to a harmonic balance formulation. Moreover, to investigate the effects of blade mistuning, which can lead to drastic increase of forced responses, an extension of the reduced-order models (ROMs) is developed based on component mode mistuning. Forced responses computed by the proposed ROMs are validated for both tuned and mistuned systems. A statistical analysis is performed to study the effectiveness of ring dampers under random blade mistuning patterns.

Reduced-Order Models of Blisks With Small Geometric Mistuning

A technique for generating reduced-order models (ROMs) of bladed disks with small geometric mistuning is proposed. Discrepancies in structural properties (mistuning) from blade to blade can cause a significant increase in the maximum vibratory stress. The effects of mistuning have been studied over the past few decades. Many researchers have studied the dynamic behavior of mistuned bladed disks by using ROMs. Many of these techniques rely on the fact that the modes of a mistuned system can be approximated by a linear combination of modes of the corresponding tuned system. In addition, the tuned system modes have been modeled in component mode mistuning by using modal participation factors of cantilevered blade modes. Such techniques assume that mistuning can be well modeled as variations in blade-alone frequencies. However, since geometric deformations contain stiffness and mass variations, mistuning can no longer be captured by cantilevered blade modes alone. To address this, several studies have focused on large and small geometric mistuning. These studies exploited the difference between tuned (with perturbed geometry) and nominal tuned mode shapes. In this work, we extend on that approach and devote particular attention to the development of ROMs of bladed disks with small geometric mistuning. The methodology requires only sector-level calculations and therefore can be applied to highly refined, realistic models of industrial size.

Nodal energy weighted transformation: A mistuning projection and its application to FLADE™ turbines

In recent years, several researchers have developed reduced-order models (ROMs) to efficiently and accurately calculate the forced response of blisks with known small mistuning. Small mistuning consists of the small blade-to-blade structural differences which destroy the inherent cyclic symmetry of the structure. This paper presents a nodal energy weighted transformation (NEWT) which can be used to construct ROMs of mistuned blisks and dual flow path systems, such as FLADE™ turbines. The NEWT approach can be interpreted as a hybrid of two existing techniques: component mode mistuning (CMM) and the subset of nominal modes (SNM). Similar to the previous methods, NEWT assumes that the mistuned modes of the system are a linear combination of tuned modes. However, NEWT differs from its predecessors in the blisk substructuring and in the mistuning projection. Numerical results obtained using full order models, CMM, and NEWT are presented and compared over multiple frequency ranges for a finite element model of a blisk and that of a FLADE™ turbine. These results show that ROMs based on NEWT have several attractive features: (a) the accuracy of the ROMs is comparable to ROMs based on CMM, and can be improved by increasing the size of the projection mode subset; (b) no necessary modifications are needed to analyze FLADE™ turbines; and (c) the response of all modes can be predicted well even if they are not blade dominated.

Analyzing mistuned multi-stage turbomachinery rotors with aerodynamic effects

A great deal of research has been conducted on accurately modeling large cyclic structures such as turbomachinery rotors. Accurate modeling of realistic industrial turbomachinery requires overcoming several challenges. The first is the excessively large size of the finite element models (FEMs) needed, which can contain millions of degrees of freedom per stage of the rotor. The second challenge is the presence of small random variations in the structural properties known as mistuning, which arise from operational wear and/or manufacturing tolerances, and destroy the cyclic symmetry of the FEMs. The third is the complexity of turbomachinery models, which often include multiple stages that often have a mismatched computational grid at the interface between stages. The fourth challenge is associated with modeling the aerodynamic loads on the turbomachinery rotor. Much research has been conducted to overcome the first two challenges. By combining cyclic symmetry analysis and component mode mistuning (CMM), compact single-stage reduced order models (ROMs) can be created to accurately capture the free and forced response of these systems. These highly efficient ROMs can be developed from single sector calculations and can be of the order of the number of sectors in the stage. Recently, the third challenge associated with the complexity of modeling multiple stages has been addressed by the authors. Their method uses cyclic symmetry and CMM to form single-stage ROMs (using only single sector models and single sector calculations), and then combines these single-stage ROMs by projecting the motion along the interface between stages along a set of harmonic shape functions. This method allows for the creation of compact ROMs of multi-stage systems with mistuning using sector only calculations. The fourth challenge has been addressed only for single-stage systems by computing a complex aerodynamic matrix (which contains stiffness and damping terms) using an iterative approach. In this work, some of the effects of the aerodynamics on multi-stage systems are explored. The methodology consists of first creating efficient structural ROMs of a multi-stage rotor using the method previously developed, and then iteratively calculating the complex aerodynamic matrices for each stage. A new way to account for the effects of a shift in frequency due to mistuning on the complex aerodynamic matrix is also proposed. Additionally, a new classification of complex multi-stage aeroelastic modes is introduced. The presented results focus on exploring the influences of the aerodynamics and mistuning on the multi-stage response. A variety of numerical results are analyzed for two stages of an industrial rotor.

Detection of Cracks in Mistuned Bladed Disks Using Reduced-Order Models and Vibration Data

A novel methodology to detect the presence of a crack and to predict the nonlinear forced response of mistuned turbine engine rotors with a cracked blade and mistuning is developed. The combined effects of the crack and mistuning are modeled. First, a hybrid-interface method based on component mode synthesis is employed to develop reduced-order models (ROMs) of the tuned system with a cracked blade. Constraint modes are added to model the displacements due to the intermittent contact between the crack surfaces. The degrees of freedom (DOFs) on the crack surfaces are retained as active DOFs so that the physical forces due to the contact/interaction (in the three-dimensional space) can be accurately modeled. Next, the presence of mistuning in the tuned system with a cracked blade is modeled. Component mode mistuning is used to account for mistuning present in the uncracked blades while the cracked blade is considered as a reference (with no mistuning). Next, the resulting (reduced-order) nonlinear equations of motion are solved by applying an alternating frequency/time-domain method. Using these efficient ROMs in a forced response analysis, it is found that the new modeling approach provides significant computational cost savings, while ensuring good accuracy relative to full-order finite element analyses. Furthermore, the effects of the cracked blade on the mistuned system are investigated and used to detect statistically the presence of a crack and to identify which blade of a full bladed disk is cracked. In particular, it is shown that cracks can be distinguished from mistuning.

Reduced Order Models for Blade-To-Blade Damping Variability in Mistuned Blisks

A novel reduced order modeling methodology to capture blade-to-blade variability in damping in blisks is presented. This new approach generalizes the concept of component mode mistuning (CMM), which was developed to capture stiffness and mass mistuning (and did not include variability in damping among the blades). This work focuses on modeling large variability in damping. Such variability is significant in many applications and particularly important for modeling damping coatings. Similar to the CMM based studies, structural damping is used to capture the damping effects due to the mechanical energy dissipation caused by internal friction within the blade material. The steady state harmonic responses of the blades are obtained using the novel reduced order modeling methodology and are validated by comparison with simulation results obtained using a full order model in ANSYS with a maximum amplitude error of 0.3%. It is observed that there is no strong correlation between the engine order of excitation and both the variation in the response from blade to blade and the blade amplification factors. The effects of damping mistuning are studied statistically through Monte Carlo simulations. For this purpose, the blisk model is subjected to multiple traveling wave excitations. The uncertainty in the various mechanisms responsible for dissipation of energy and the uncontrollability of these dissipation mechanisms makes it difficult to assign a reliable value for the loss factor of each blade. Hence, large variations (up to ±80%) in the structural damping coefficients of the blades are simulated.

A Statistical Characterization of the Effects of Mistuning in Multistage Bladed Disks

A great deal of research has been conducted on the effects of small random variations in structural properties, known as mistuning, in single stage bladed disks. Due to the inherent randomness of mistuning and the large dimensionality of the models of industrial bladed disks, a reduced order modeling approach is required to understand the effects of mistuning on a particular bladed disk design. Component mode mistuning (CMM) is an efficient compact reduced order modeling method that was developed to handle this challenge in single stage bladed disks. In general, there are multiple stages in bladed disk assemblies, and it has been demonstrated that for certain frequency ranges accurate modeling of the entire bladed disk assembly is required because multistage modes exist. In this work, a statistical characterization of structural mistuning in multistage bladed disks is carried out. The results were obtained using CMM combined with a multistage modeling approach previously developed. In addition to the statistical characterization, a new efficient classification method is detailed for characterizing the properties of a mode. Also, the effects of structural mistuning on the characterization of the mode is explored.