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

1998 ◽  
Author(s):  
Ronnie Bladh ◽  
Matthew P. Castanier ◽  
Christophe Pierre
Keyword(s):  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Reduced Order Modeling ◽  
Forced Response ◽  
Modeling Technique ◽  
Computationally Efficient ◽  
Bladed Disks ◽  
Reduced Order ◽  
Synthesis Approach

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 of mistuned 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.

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

1999 ◽  
Vol 121 (3) ◽  
pp. 515-522 ◽  
Author(s):  
R. Bladh ◽  
M. P. Castanier ◽  
C. Pierre
Keyword(s):  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Reduced Order Modeling ◽  
Forced Response ◽  
Modeling Technique ◽  
Computationally Efficient ◽  
Bladed Disks ◽  
Reduced Order ◽  
Synthesis Approach

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 of mistuned 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.

scholarly journals A Reduced Order Modeling Technique for Mistuned Bladed Disks

1997 ◽  
Vol 119 (3) ◽  
pp. 439-447 ◽  
Author(s):  
M. P. Castanier ◽  
G. O´ttarsson ◽  
C. Pierre
Keyword(s):  
Monte Carlo ◽  
Degrees Of Freedom ◽  
Order Reduction ◽  
Reduced Order Modeling ◽  
Modeling Technique ◽  
Mode Analysis ◽  
Bladed Disks ◽  
Engineering Structures ◽  
Element Analysis ◽  
Reduced Order

The analysis of the response statistics of mistuned turbomachinery rotors requires an expensive Monte Carlo simulation approach. Simple lumped parameter models capture basic localization effects but do not represent well actual engineering structures without a difficult parameter identification. Current component mode analysis techniques generally require a minimum number of degrees of freedom which is too large for running Monte Carlo simulations at a reasonable cost. In the present work, an order reduction method is introduced which is capable of generating reasonably accurate, very low order models of tuned or mistuned bladed disks. This technique is based on component modes of vibration found from a finite element analysis of a single disk-blade sector. It is shown that the phenomenon of mode localization is well captured by the reduced order modeling technique.

Application of a Reduced Order Modeling Technique for Mistuned Bladed Disk-Shaft Assemblies

2007 ◽  
Author(s):  
Bartolome´ Segui´ ◽  
Euro Casanova
Keyword(s):  
Finite Element ◽  
Synthesis Method ◽  
Element Model ◽  
Reduced Order Modeling ◽  
Forced Response ◽  
Modeling Technique ◽  
Disk Model ◽  
Reduced Order ◽  
Bladed Disk ◽  
Global Dynamic

This paper presents a reduced-order modeling technique, based on a component mode synthesis method specifically tailored for bladed disks, that allows the resulting low-order model to be attached to a shaft. Mistuning is included in the bladed disk model and the shaft is modeled using uniaxial finite elements according to the rotordynamic approach. The proposed formulation is applied to an example finite element model of a bladed disk, for both tuned and mistuned blades. Comparisons are made between the reduced model and the full finite element solution for free and forced responses in order to assess the methodology. The forced response amplitudes of the blades are found to vary significantly with the inclusion of a flexible shaft. This work suggest that stage independent analyses might not be adequate for predicting the global dynamic response of rotating assemblies of turbomachines.

Geometric Mistuning Reduced-Order Models for Integrally Bladed Rotors With Mistuned Disk–Blade Boundaries

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Joseph A. Beck ◽  
Jeffrey M. Brown ◽  
Alex A. Kaszynski ◽  
Charles J. Cross ◽  
Joseph C. Slater
Keyword(s):  
Degrees Of Freedom ◽  
Principal Component ◽  
Element Model ◽  
Forced Response ◽  
Solid Model ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Small Areas ◽  
Eigen Analysis ◽  
Connection Type

New geometric mistuning modeling approaches for integrally bladed rotors (IBRs) are developed for incorporating geometric perturbations to a fundamental disk–blade sector, particularly the disk–blade boundary or connection. Reduced-order models (ROMs) are developed from a Craig–Bampton component mode synthesis (C–B CMS) framework that is further reduced by a truncated set of interface modes that are obtained from an Eigen-analysis of the C–B CMS constraint degrees of freedom (DOFs). An investigation into using a set of tuned interface modes and tuned constraint modes for model reduction is then performed, which offers significant computational savings for subsequent analyses. Two configurations of disk–blade connection mistuning are investigated: as-measured principal component (PC) deviations and random perturbations to the interblade spacing. Furthermore, the perturbation sizes are amplified to investigate the significance of incorporating mistuned disk–blade connections during solid model generation from optically scanned geometries. Free and forced response results are obtained for each ROM and each disk–blade connection type and compared to full finite element model (FEM) solutions. It is shown that the developed methods provide accurate results with a reduction in solution time compared to the full FEM. In addition, results indicate that the inclusion of a mistuned disk–blade connection deviations are small or conditions where large perturbations are localized to a small areas of the disk–blade connection.

scholarly journals Comparative Study of Blades Reduced Order Models With Geometrical Nonlinearities and Contact Interfaces

2020 ◽  
Author(s):  
Elise Delhez ◽  
Florence Nyssen ◽  
Jean-Claude Golinval ◽  
Alain Batailly
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Performance Indicator ◽  
Element Model ◽  
Reduced Order Models ◽  
Computationally Efficient ◽  
Reduced Order ◽  
Reduction Methods ◽  
Blade Tip ◽  
Reduced Space

Abstract This paper investigates the use of different model reduction methods accounting for geometric nonlinearities. These methods are adapted to retain physical degrees-of-freedom in the reduced space in order to ease contact treatment. These reduction methods are applied to a 3D finite element model of an industrial compressor blade (NASA rotor 37). In order to compare the different reduction methods, a scalar indicator is defined. This performance indicator allows to quantify the accuracy of the predicted displacement both locally (at the blade tip) and globally. The robustness of each method with respect to variations of the external excitation is also assessed. The performances of the reduction methods are then compared in the case of frictional contact between the blade tip and the surrounding casing. This work brings evidence that reduced order models provide a computationally efficient alternative to full order finite element models for the accurate prediction of the time response of structures with both distributed and localized nonlinearities.

Effects of a Cracked Blade on Mistuned Turbine Engine Rotor Vibration

2007 ◽  
Author(s):  
Akira Saito ◽  
Matthew P. Castanier ◽  
Christophe Pierre
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Time Integration ◽  
Element Model ◽  
Forced Response ◽  
System Response ◽  
Turbine Engine ◽  
Reduced Order ◽  
Hybrid Interface ◽  
Engine Rotor

An efficient methodology for predicting the nonlinear forced vibration response of a turbine engine rotor with a cracked blade is presented and used to investigate the effects of the damage on the forced response. The effects of small, random blade-to-blade differences (mistuning) and rotation on the forced response are also considered. Starting with a finite element model, a hybrid-interface method of Component Mode Synthesis (CMS) is employed to generate a reduced-order model (ROM). The crack surfaces are retained as physical degrees of freedom in the ROM so that the forces due to contact interaction in three-dimensional space can be properly calculated. The resulting nonlinear equations of steady-state motion are solved by applying an alternating frequency/time-domain method, which is much more computationally efficient than traditional time integration. Using this reduced-order modeling and analysis framework, the effects of the cracked blade on the system response are investigated for various mistuning levels and rotation speeds. First, the advantages of the selected hybrid-interface CMS method are discussed and demonstrated. Then, the resonant frequency shift associated with the stiffness loss due to the crack, as well as vibration localization about the cracked blade are thoroughly investigated. In addition, the results of the nonlinear ROMs are compared to those obtained with linear ROMs as well as blade-alone ROMs. It is shown that several key system vibration characteristics are not captured by the simpler models, but that some insight into the system response can be gained from the blade-alone response predictions. Furthermore, it is demonstrated that while the effects of the crack often appear similar those of mistuning, differences between the effects of mistuning and damage can be discerned by observing and comparing the response across different families of system modes.

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

2000 ◽  
Vol 123 (1) ◽  
pp. 100-108 ◽  
Author(s):  
R. Bladh ◽  
M. P. Castanier ◽  
C. Pierre
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Theoretical Models ◽  
Companion Paper ◽  
Reduced Order Modeling ◽  
Bladed Disks ◽  
Reduced Order ◽  
Component Interface ◽  
Forced Responses

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 rotor’s 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 a Cracked Blade on Mistuned Turbine Engine Rotor Vibration

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Akira Saito ◽  
Matthew P. Castanier ◽  
Christophe Pierre
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Time Integration ◽  
Element Model ◽  
Forced Response ◽  
System Response ◽  
Turbine Engine ◽  
Reduced Order ◽  
Hybrid Interface ◽  
Engine Rotor

An efficient methodology for predicting the nonlinear forced vibration response of a turbine engine rotor with a cracked blade is presented and used to investigate the effects of the damage on the forced response. The influence of small random blade-to-blade differences (mistuning) and rotation on the forced response are also considered. Starting with a finite element model, a hybrid-interface method of component mode synthesis (CMS) is employed to generate a reduced-order model (ROM). The crack surfaces are retained as physical degrees of freedom in the ROM so that the forces due to contact in three-dimensional space can be properly calculated. The resulting nonlinear equations of steady-state motion are solved by applying an alternating frequency/time-domain method, which is much more computationally efficient than traditional time integration. Using this reduced-order modeling and analysis framework, the effects of the cracked blade on the system response of an example rotor are investigated for various mistuning levels and rotation speeds. First, the advantages of the selected hybrid-interface CMS method are discussed and demonstrated. Then, the resonant frequency shift associated with the stiffness loss due to the crack and the vibration localization about the cracked blade are thoroughly investigated. In addition, the results of the nonlinear ROMs are compared with those obtained with linear ROMs, as well as blade-alone ROMs. It is shown that several key system vibration characteristics are not captured by the simpler models, but that some insight into the system response can be gained from the blade-alone response predictions. Furthermore, it is demonstrated that while the effects of the crack often appear similar to those of mistuning, the effects of mistuning and damage can be distinguished by observing and comparing the response across multiple families of system modes.

Reduced Order Models of Mistuned Cracked Bladed Disks

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Olguta Marinescu ◽  
Bogdan I. Epureanu ◽  
Mihaela Banu
Keyword(s):  
Finite Element ◽  
Effective Means ◽  
Structural Response ◽  
Element Model ◽  
Reduced Order Modeling ◽  
Reduced Order Models ◽  
Bladed Disks ◽  
Reduced Order ◽  
Modeling Methodology ◽  
Relative Coordinates

Predicting the influence of cracks on the dynamics of bladed disks is a very important challenge. Cracks change the structural response, which in turn changes the crack propagation characteristics. Hence, accurate and computationally effective means to model the dynamics of cracked bladed disks and blisks is particularly crucial in applications such as prognosis, guidance for repairs, characterization after repairs, design, and structural health monitoring. Most current models of bladed disks exploit cyclic symmetry to gain computational efficiency. However, the presence of cracks and mistuning destroys that symmetry and makes computational predictions much more expensive. In this work, we propose a new reduced order modeling methodology that can speed up computations by several orders of magnitude. There are two key components of the new methodology. First, the displacements and deformations of the crack surfaces are not modeled in absolute coordinates but relative coordinates, which allows for an effective model reduction based on (fixed-interface Craig–Bampton) component mode synthesis (CMS). The use of relative coordinates allows one to define one of the components in CMS as the pristine/uncracked structure (with mistuning). This approach is used in combination with a set of accurate approximations for the constraint modes used in CMS. Second, the effects of mistuning are captured by component mode mistuning, which allows the construction of extremely efficient reduced order models for the pristine/uncracked component with mistuning. The novel proposed method is applied to a finite element model of an industrial blisk. The combined presence of mistuning and cracks is shown to have important effects. Also, the proposed approach is shown to provide accurate predictions for the overall blisk while requiring computations using single-sector models only. The influence of various parameters on the accuracy of the reduced order models is investigated. Overall, the results show a very good agreement between full finite element analyses and the proposed reduced order modeling approach.

Sign in / Sign up

Export Citation Format

Share Document