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.

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.

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.

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.

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

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

2017 ◽  
Vol 139 (6) ◽  
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 (ROMs) 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.

scholarly journals A Reduced Order Model of Mistuning Using a Subset of Nominal System Modes

1999 ◽  
Author(s):  
M.-T. Yang ◽  
J. H. Griffin
Keyword(s):  
Degrees Of Freedom ◽  
Reduced Order Model ◽  
Reduced Order Models ◽  
Order Model ◽  
Disk System ◽  
Element Analysis ◽  
Reduced Order ◽  
Nominal System ◽  
Harmonic Response ◽  
Bladed Disk

Reduced order models have been reported in the literature that can be used to predict the harmonic response of mistuned bladed disks. It has been shown that in many cases they exhibit structural fidelity comparable to a finite element analysis of the full bladed disk system while offering a significant improvement in computational efficiency. In these models the blades and disk are treated as distinct substructures. This paper presents a new, simpler approach for developing reduced order models in which the modes of the mistuned system are represented in terms of a sub-set of nominal system modes. It has the following attributes: the input requirements are relatively easy to generate; it accurately predicts mistuning effects in regions where frequency veering occurs; as the number of degrees of freedom increases it converges to the exact solution; it accurately predicts stresses as well as displacements; and it accurately models the deformation and stresses at the blades’ bases.

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.

Accuracies of Reduced Order Models of a Bladed Rotor With Geometric Mistuning

2013 ◽  
Vol 136 (7) ◽  
Author(s):  
Yasharth Bhartiya ◽  
Alok Sinha
Keyword(s):  
Natural Frequencies ◽  
Domain Analysis ◽  
Forced Response ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
Model Based ◽  
Bladed Rotor

The results from a reduced order model based on frequency mistuning are compared with those from recently developed modified modal domain analysis (MMDA). For the academic bladed rotor considered in this paper, the frequency mistuning analysis is unable to capture the effects of geometric mistuning, whereas MMDA provides accurate estimates of natural frequencies, mode shapes, and forced response.

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