The Influence of Blade Properties on the Forced Response of Mistuned Bladed Disks

2011 ◽  
Author(s):  
Andreas Hohl ◽  
Benedikt Kriegesmann ◽  
Jo¨rg Wallaschek ◽  
Lars Panning
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Degrees Of Freedom ◽  
Vibrational Energy ◽  
Normal Modes ◽  
Element Model ◽  
Forced Response ◽  
Optimization Approach ◽  
Bladed Disks ◽  
Value Decomposition

In turbomachinery applications bladed disks are subjected to high dynamic loads due to fluctuating gas forces. Dynamic excitation can result in high vibration amplitudes which can lead to high cycle fatigue (HCF) failures. Herein, the blades are almost identical but differ due to wear or small manufacturing tolerances. Especially, after regeneration and repair procedures the properties of the blades can differ with a high variance. These deviations of the blade properties can lead to a localization of the vibrational energy in single blades and even higher risk of HCF. A recently developed substructure model with a combination of the Hurty transformation or Component Mode Synthesis (CMS) and the so called Wave Based Substructuring (WBS) is used to obtain a Reduced Order Model (ROM) with a reasonable low number of degrees of freedom. The CMS of the disk can be calculated with one cyclic disk segment of the underlying finite element model. The WBS is used to describe the numerous coupling degrees of freedom between the disk and the blades with a truncated set of waves. The orthogonal waves are derived by a Singular Value Decomposition or a QR decomposition from the coupling nodes normal modes calculated by a cyclic modal analysis of the full structure. The blade eigenvalues of the clamped blade can be mistuned individually under consideration of the variance as well as the correlation between the different eigenvalues of the blades. Monte-Carlo-Simulations are performed to calculate the effect of these parameters on the forced response of a mistuned bladed disk for blade dominated modes. Furthermore, Monte-Carlo-Simulations and a constraint optimization approach is used to calculate the worst and best case blade patterns for specific blade patterns and blade patterns with distributed blade properties.

Analysis of the Influence of Blade Pattern Characteristics on the Forced Response of Mistuned Blisks With a Cyclic CMS-Based Substructure Model

2010 ◽  
Author(s):  
Andreas Hohl ◽  
Lars Panning ◽  
Jo¨rg Wallaschek
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Vibrational Energy ◽  
Normal Modes ◽  
Element Model ◽  
Forced Response ◽  
Symmetry Approach ◽  
Full Structure ◽  
Value Decomposition

In turbomachinery applications bladed disks and blisks are subjected to high dynamic loads due to fluctuating gas forces. The dynamic excitation results in high vibration amplitudes which can lead to high cycle fatigue failures (HCF). Herein, the blades are almost identical but differ due to wear or small manufacturing tolerances. These small deviations of the blade properties can lead to a localization of the vibrational energy in single blades and even higher risk of HCF. Intentional mistuning, for example an alternating alignment of two different blades AB around the blisk, has been studied in literature to decrease the sensitivity against statistical mistuning. Using a Component Mode Synthesis (CMS) based mistuning model the influence of intentional mistuning on blisks is analyzed in this paper. Therein, the CMS of the disk is calculated with a fast and accurate cyclic symmetry approach. Therefore, the CMS of the disk can be calculated with one disk segment of the underlying Finite Element Model. The so called Wave Based Substructuring (WBS) is used to reduce the (numerous) coupling degrees of freedom between the disk and the blades with a truncated set of waves. The orthogonal waves are derived with a Singular Value Decomposition or a QR decomposition from the normal modes at the coupling degrees of freedom (DOF) calculated by a cyclic modal analysis of the full structure. In a case study the Reduced Order Model (ROM) of a spatial Finite Element Model is used to determine the influence of intentional mistuning with additional statistical mistuning on the forced response of blisks.

A Substructure Based Reduced Order Model for Mistuned Bladed Disks

2009 ◽  
Author(s):  
Andreas Hohl ◽  
Christian Siewert ◽  
Lars Panning ◽  
Jo¨rg Wallaschek
Keyword(s):  
Degrees Of Freedom ◽  
Normal Modes ◽  
Forced Response ◽  
Component Mode Synthesis ◽  
Order Model ◽  
Bladed Disks ◽  
Reduced Order ◽  
Symmetry Approach ◽  
Full Structure ◽  
Value Decomposition

A efficient method for the calculation of the forced response of mistuned bladed disks is introduced. Based on the Component Mode Synthesis techniques the structure is divided into substructures, namely the disk and the blades. The Component Mode Synthesis of the disk is calculated with a fast and accurate cyclic symmetry approach. A recently developed method called Wave Based Substructuring is used to describe the (numerous) coupling degrees of freedom between the disk and the blades. The orthogonal waves are derived with a Singular Value Decomposition or a QR decomposition from the coupling nodes’ normal modes calculated by a modal analysis of the full structure.

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.

Optimization of Intentional Mistuning Patterns for the Reduction of the Forced Response Effects of Unintentional Mistuning: Formulation and Assessment

2002 ◽  
Vol 125 (1) ◽  
pp. 131-140 ◽  
Author(s):  
B.-K. Choi ◽  
J. Lentz ◽  
A. J. Rivas-Guerra ◽  
M. P. Mignolet
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Forced Response ◽  
Second Step ◽  
Bladed Disks ◽  
Screening Technique ◽  
Bladed Disk ◽  
Step Procedure ◽  
Random Mistuning

The focus of the present investigation is on the use of intentional mistuning of bladed disks to reduce their sensitivity to unintentional random mistuning. The class of intentionally mistuned disks considered here is limited, for cost reasons, to arrangements of two types of blades (A and B, say). A two-step procedure is then described to optimize the arrangement of these blades around the disk to reduce the effects of unintentional mistuning. First, a pure optimization effort is undertaken to obtain the pattern(s) of the A and B blades that yields small/the smallest value of the largest amplitude of response to a given excitation in the absence of unintentional mistuning. Then, in the second step, a pattern screening technique based on a recently introduced measure of localization is used to determine which of the patterns does have a large/small sensitivity to random unintentional mistuning. In this manner, expensive Monte Carlo simulations can be eliminated. Examples of application involving both simple bladed disk models and a 17-blade industrial rotor clearly demonstrate the significant benefits of using this class of intentionally mistuned disks.

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.

Optimization of Intentional Mistuning Patterns for the Reduction of the Forced Response Effects of Unintentional Mistuning: Formulation and Assessment

2001 ◽  
Author(s):  
Byeong-Keun Choi ◽  
Jeff Lentz ◽  
Alejandro Rivas-Guerra ◽  
Marc P. Mignolet
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Forced Response ◽  
Second Step ◽  
Bladed Disks ◽  
Screening Technique ◽  
Bladed Disk ◽  
Step Procedure ◽  
Random Mistuning

The focus of the present investigation is on the use of intentional mistuning of bladed disks to reduce their sensitivity to unintentional random mistuning. The class of intentionally mistuned disks considered here is limited, for cost reasons, to arrangements of two types of blades (A and B, say). A two-step procedure is then describe to optimize the arrangement of these blades around the disk to reduce the effects of unintentional mistuning. First, a pure optimization effort is undertaken to obtain the pattern(s) of the A and B blades that yields small/the smallest value of the largest amplitude of response to a given excitation in the absence of unintentional mistuning. Then, in the second step, a pattern screening technique based on a recently introduced measure of localization is used to determine which of the patterns does have a large/small sensitivity to random unintentional mistuning. In this manner, expensive Monte Carlo simulations can be eliminated. Examples of application involving both simple bladed disk models and a 17-blade industrial rotor clearly demonstrate the significant benefits of using this class of intentionally mistuned disks.

scholarly journals Prediction of Isolated Resonance Curves Using Nonlinear Normal Modes

2015 ◽  
Author(s):  
R. J. Kuether ◽  
L. Renson ◽  
T. Detroux ◽  
C. Grappasonni ◽  
G. Kerschen ◽  
...  
Keyword(s):  
Normal Modes ◽  
Resonance Curve ◽  
Element Model ◽  
Nonlinear Normal Modes ◽  
Initial Guess ◽  
Forced Response ◽  
Numerical Continuation ◽  
Continuation Algorithm ◽  
Resonance Curves ◽  
Nonlinear Normal

Isolated resonance curves are separate from the main nonlinear forced-response branch, so they can easily be missed by a continuation algorithm and the resonant response might be underpredicted. The present work explores the connection between these isolated resonances and the nonlinear normal modes of the system and adapts an energy balance criterion to connect the two. This approach provides new insights into the occurrence of isolated resonances as well as a method to find an initial guess to compute the isolated resonance curve using numerical continuation. The concepts are illustrated on a finite element model of a cantilever beam with a nonlinear spring at its tip. This system presents jumps in both frequency and amplitude in its response to a swept sinusoidal excitation. The jumps are found to be the result of a modal interaction that creates an isolated resonance curve that eventually merges with the main resonance branch as the excitation force increases. Excellent insight into the observed dynamics is provided with the NNM theory, which supports that NNMs can also be a useful tool for predicting isolated resonance curves and other behaviors in the damped, forced response.

Comparative Studies of Surrogate Models for Response Analysis of Mistuned Bladed Disks

2020 ◽  
Vol 17 (10) ◽  
pp. 2050012 ◽  
Author(s):  
Shiyuan Deng ◽  
Jianyao Yao ◽  
Linlin Wang ◽  
Jianqiang Xin ◽  
Ning Hu
Keyword(s):  
Degrees Of Freedom ◽  
Surrogate Models ◽  
Forced Response ◽  
Statistical Characteristics ◽  
Kriging Interpolation ◽  
Response Analysis ◽  
Bladed Disks ◽  
Single Output ◽  
Random Mistuning ◽  
Forced Responses

The forced responses of bladed disks are highly sensitive to inevitable random mistuning. Considerable computational efforts are required for the sampling process to assess the statistical vibration properties of mistuned bladed disks. Therefore, efficient surrogate models are preferred to accelerate the process for probabilistic analysis. In this paper, four surrogate models are utilized to construct the relation between random mistuning and forced response amplitudes, which are polynomial chaos expansion (PCE), response surface method (RSM), artificial neural networks (ANN) and Kriging interpolation, respectively. A bladed disk with 2-degrees-of-freedom (2-DOF) each sector is used to validate the effectiveness of the surrogate models. The effects of number of training samples on the surrogate model accuracy are discussed. The responses results of one blade (single output) and maximum response of all blades (multi-output) indicate that PCE and Kriging interpolation could yield accurate and stable predictions of the statistical characteristics of the forced responses. PCE is recommended for the mistuned response predictions due to its accuracy and efficiency.

scholarly journals An Independence Test Based on Symbolic Time Series

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Wiston Adrián Risso
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Time Series Analysis ◽  
Monte Carlo Simulations ◽  
Degrees Of Freedom ◽  
Chaotic Systems ◽  
Small Samples ◽  
Independence Test ◽  
Series Analysis ◽  
Symbolic Time Series Analysis

An independence test based on symbolic time series analysis (STSA) is developed. Considering an independent symbolic time series there is a statistic asymptotically distributed as a CHI-2 with n-1 degrees of freedom. Size and power experiments for small samples were conducted applying Monte Carlo simulations and comparing the results with BDS and runs test. The introduced test shows a good performance detecting independence in nonlinear and chaotic systems.

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.

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