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

2011 ◽  
Author(s):  
Chulwoo Jung ◽  
Akira Saito ◽  
Bogdan I. Epureanu
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Savings ◽  
Forced Response ◽  
Response Analysis ◽  
Reduced Order Models ◽  
Reduced Order

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 un-cracked blades while the cracked blade is considered as a reference (with no mistuning). Next, the resulting (reducedorder) 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.

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

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Chulwoo Jung ◽  
Akira Saito ◽  
Bogdan I. Epureanu
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Savings ◽  
Forced Response ◽  
Response Analysis ◽  
Reduced Order Models ◽  
Reduced Order

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.

scholarly journals Stress Recovery Algorithm for Reduced Order Models of Mechanical Systems in Nonlinear Dynamic Operative Conditions

2021 ◽  
Author(s):  
GIUSEPPE BATTIATO ◽  
CHRISTIAN MARIA FIRRONE
Keyword(s):  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Forced Response ◽  
Response Analysis ◽  
Stress Recovery ◽  
Reduced Order Models ◽  
Technical Literature ◽  
Reduced Order ◽  
Recovery Algorithm ◽  
Safety Margins

Abstract Nonlinear forced response analyses of mechanical systems in the presence of contact interfaces are usually performed in built-in numerical codes on reduced order models (ROM). Most of the cases these derive from complex finite element (FE) models, because of the high accuracy the designers require in meshing the components in commercial FE software. In the technical literature several numerical methods are proposed for the identification of the nonlinear forced response in terms of kinematic quantity (i.e. displacement, velocity and acceleration) at the location where the master degrees-of-freedom are retained in the ROM. In fact, the displacement is the quantity usually adopted to monitor the nonlinear response, and to evaluate the effectiveness of a partially loose friction interface in damping vibrations with respect to a linear case where no friction interfaces exist and no energy dissipation can take place. However, when a ROM is used the engineering quantities directly involved in the mechanical design, i.e. the strains and stresses, cannot be retrieved without a further data processing. Moreover, in the case of a strong nonlinear behavior of the mechanical joints, the distributions of the nonlinear strains and stresses is likely different than the modal ones, meaning that the latter cannot be used to predict the safety margins of the structure working in real (nonlinear) operative conditions. This paper addresses this topic and presents a novel stress recovery algorithm for the identification of the strains and stresses resulting from a nonlinear forced response analysis on a ROM. The algorithm is applied to a bladed disk with friction contacts at the shroud joint, which make the behavior of the blades nonlinear and non-predictable by means of standard linear analyses in commercial FE software.

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

2016 ◽  
Author(s):  
Mauricio Gutierrez Salas ◽  
Ronnie Bladh ◽  
Hans Mårtensson ◽  
Paul Petrie-Repar ◽  
Torsten Fransson ◽  
...  
Keyword(s):  
Structural Modeling ◽  
Forced Response ◽  
Response Analysis ◽  
Reduced Order Models ◽  
Energy Localization ◽  
Order Model ◽  
Foreign Object Damage ◽  
Reduced Order ◽  
Manufacturing Tolerances ◽  
Blade Failure

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 tolerances, corrosion, foreign object damage and in-service wear in general. It has been shown in past studies that mistuning can increase the risk of blade failure due to energy localization. For weak blade to blade coupling, this localization has been shown to be critical and higher amplitudes of vibration are expected in few blades. This paper presents a comparison of three reduced order models for the structural modeling of blisks. Two of the models assume cyclic symmetry while the third model is free of this assumption. The performance of the reduced order models for cases with small and large amount of mistuning will be examined. The benefits and drawbacks of each reduction method will be discussed.

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.

Modal and Forced Response Analysis of Vehicle Systems With Latent Vibration Modes Due to Hydraulic Mounts

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Hyeon Gyu Sakong ◽  
Gyunchul Hur ◽  
Kwang-Joon Kim ◽  
Wonju Jeon
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Time Domain Analysis ◽  
Hydraulic Modeling ◽  
Internal Variable ◽  
Forced Response ◽  
Response Analysis ◽  
Car Body ◽  
Modeling Approaches ◽  
Mechanical Mass

Abstract Hydraulic mounts used in vehicles for better isolation of vibrations were often approximated by lumped or mechanical mass-damper-spring (m-c-k) models, although deficiency in such modeling was pointed out and “hydraulic” modeling was proposed as an alternative. In this paper, a brief review on the mechanical m-c-k modeling and “hydraulic” modeling of the hydraulic mounts is presented. A simplest system consisting of a single mass and a hydraulic mount is used to illustrate both equivalence and difference in a closed form between the two modeling approaches. Then, modal analyses are done on an apparently three degrees-of-freedom (DOF) quarter car with a hydraulic mount, where the key idea is to use an internal variable for the movement of fluid mass which is responsible for a “latent” vibration mode. Equations of motion for the apparently 3DOF system, 4DOF system in fact, by the two modeling are formulated. Modal parameters by the proposed “hydraulic” modeling of the hydraulic mount are compared with those by the m-c-k modeling. Forced responses to transient base excitations are also compared between the two modeling approaches to illustrate how much errors can arise in the frequency and time domain analysis. To be more realistic, the modal and forced response analysis on a full car of an apparently 10DOF (3DOF for powertrain, 3DOF for car body, and 4DOF for knuckles and tires) with two more DOF internally for two hydraulic mounts between the powertrain and car body is presented.

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.

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.

Dynamic Modeling and Vibration Response Simulation for High Speed Rolling Ball Bearings With Localized Surface Defects in Raceways

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Linkai Niu ◽  
Hongrui Cao ◽  
Zhengjia He ◽  
Yamin Li
Keyword(s):  
High Speed ◽  
Degrees Of Freedom ◽  
Surface Defects ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Hertzian Contact ◽  
Ball Bearings ◽  
Rolling Ball ◽  
Vibration Responses

A dynamic model is developed to investigate vibrations of high speed rolling ball bearings with localized surface defects on raceways. In this model, each bearing component (i.e., inner raceway, outer raceway and rolling ball) has six degrees of freedom (DOFs) to completely describe its dynamic characteristics in three-dimensional space. Gyroscopic moment, centrifugal force, lubrication traction/slip between bearing component are included owing to high speed effects. Moreover, local defects are modeled accurately and completely with consideration of additional deflection due to material absence, changes of Hertzian contact coefficient and changes of contact force directions due to raceway curvature variations. The obtained equations of motion are solved numerically using the fourth order Runge–Kutta–Fehlberg scheme with step-changing criterion. Vibration responses of a defective bearing with localized surface defects are simulated and analyzed in both time domain and frequency domain, and the effectiveness of fault feature extraction techniques is also discussed. An experiment is carried out on an aerospace bearing test rig. By comparing the simulation results with experiments, it is confirmed that the proposed model is capable of predicting vibration responses of defective high speed rolling ball bearings effectively.

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

2013 ◽  
Author(s):  
Joseph A. Beck ◽  
Jeffrey M. Brown ◽  
Charles J. Cross ◽  
Joseph C. Slater
Keyword(s):  
Degrees Of Freedom ◽  
Principal Component ◽  
Element Model ◽  
Forced Response ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Eigen Analysis ◽  
Geometric Deviations ◽  
Added Benefit ◽  
Connection Type

New geometric mistuning 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. The developed Reduced Oder Models (ROMs) are formulated 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. A tuned mode approximation has the added benefit of being only calculated once which offers significant computational savings for subsequent analyses. Two configurations of disk-blade connection mistuning are investigated: as-measured principal component deviations and random perturbations to the inter-blade spacing. Furthermore, the perturbation sizes are amplified to investigate the significance of incorporating mistuned disk-blade connection. 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 highly accurate results with a significant reduction in solution time compared to the full FEM. In addition, results indicate that the inclusion of a mistuned disk-blade connection becomes significant as the size of the geometric deviations at the connection become large.

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

2018 ◽  
Vol 34 (3) ◽  
pp. 565-577 ◽  
Author(s):  
Mauricio Gutierrez Salas ◽  
Paul Petrie-Repar ◽  
Hans Mårtensson ◽  
Ronnie Bladh ◽  
Damian M. Vogt
Keyword(s):  
Forced Response ◽  
Response Analysis ◽  
Reduced Order Models ◽  
Reduced Order
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