scholarly journals A Reduced-Order Model of Detuned Cyclic Dynamical Systems With Geometric Modifications Using a Basis of Cyclic Modes

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Moustapha Mbaye ◽  
Christian Soize ◽  
Jean-Philippe Ousty
Keyword(s):  
Reduction Method ◽  
Reduced Order Model ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Element Analysis ◽  
Disk Model ◽  
Reduced Order ◽  
Bladed Disk ◽  
Forced Responses ◽  
Sector Matrix

A new reduction method for vibration analysis of intentionally mistuned bladed disks is presented. The method is built for solving the dynamic problem of cyclic structures with geometric modifications. It is based on the use of the cyclic modes of the different sectors, which can be obtained from a usual cyclic symmetry modal analysis. Hence the projection basis is constituted; as well as, on the whole bladed disk, each sector matrix is reduced by its own modes. The method is validated numerically on a real bladed disk model, by comparing free and forced responses of a full model finite element analysis to those of a reduced-order model using the new reduction method.

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.

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

1999 ◽  
Vol 123 (4) ◽  
pp. 893-900 ◽  
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 subset 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.

A Reduced Order Approach for the Vibration of Mistuned Bladed Disk Assemblies

1997 ◽  
Vol 119 (1) ◽  
pp. 161-167 ◽  
Author(s):  
M.-T. Yang ◽  
J. H. Griffin
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Reduced Order Model ◽  
Order Model ◽  
Disk System ◽  
Element Analysis ◽  
Reduced Order ◽  
Bladed Disk

A reduced order approach is introduced in this paper that can be used to predict the steady-state response of mistuned bladed disks. This approach takes results directly from a finite element analysis of a tuned system and, based on the assumption of rigid blade base motion, constructs a computationally efficient mistuned model with a reduced number of degrees of freedom. Based on a comparison of results predicted by different approaches, it is concluded that: The reduced order model displays structural fidelity comparable to that of a finite element model of the entire bladed disk system with significantly improved computational efficiency; and under certain circumstances both the finite element model and the reduced order model predict quite different response from simple spring-mass models.

scholarly journals A Reduced Order Approach for the Vibration of Mistuned Bladed Disk Assemblies

1995 ◽  
Author(s):  
M.-T. Yang ◽  
J. H. Griffin
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Reduced Order Model ◽  
Order Model ◽  
Disk System ◽  
Element Analysis ◽  
Reduced Order ◽  
Bladed Disk

A reduced order approach is introduced in this paper that can be used to predict the steady-state response of mistuned bladed disks. This approach takes results directly from a finite element analysis of a tuned system and, based on the assumption of rigid blade base motion, constructs a computationally efficient mistuned model with a reduced number of degrees of freedom. Based on a comparison of results predicted by different approaches it is concluded that: the reduced order model displays structural fidelity comparable to that of a finite element model of the entire bladed disk system with significantly improved computational efficiency; and under certain circumstances both the finite element model and the reduced order model predict quite different response from simple spring-mass models.

Reduced-Order Model of a Bladed Rotor With Geometric Mistuning

2007 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Coordinate Measurement ◽  
Coordinate Measurement Machine ◽  
Bladed Disk ◽  
Bladed Rotor ◽  
Proper Orthogonal

This paper deals with the development of an accurate reduced-order model of a bladed disk with geometric mistuning. The method is based on vibratory modes of various tuned systems and proper orthogonal decomposition of coordinate measurement machine (CMM) data on blade geometries. Results for an academic rotor are presented to establish the validity of the technique.

On a New Nonlinear Reduced-Order Model for Capturing Internal Resonances in Intentionally Mistuned Cyclic Structures

2020 ◽  
Author(s):  
Samuel Quaegebeur ◽  
Benjamin Chouvion ◽  
Fabrice Thouverez ◽  
Loïc Berthe
Keyword(s):  
Nonlinear Response ◽  
Forced Response ◽  
Reduced Order Model ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Internal Resonances ◽  
Present Material ◽  
Reduced Order ◽  
Modal Synthesis ◽  
Excitation Force

Abstract Cyclic structures such as turbomachinery present material and geometrical variations between sectors. These discrepancies are called mistuning and break the cyclic symmetry of the structure. Computing the forced response of mistuned cyclic structures is thus a numerical challenge. The Component Nonlinear Complex Mode Synthesis (CNCMS) is one of the few nonlinear reduced-order model formulations that allow to compute the nonlinear response of tuned and mistuned structures. It has been validated successfully for friction problems. However, in the presence of geometric nonlinearities, internal resonances may arise and they cannot be captured correctly with the CNCMS method. The purpose of this work is therefore to present a new methodology for developing a nonlinear reduced-order model that can successfully capture internal resonances for tuned and mistuned structures. This method, called Component Mode Synthesis with Nonlinear Re-evaluation (CMSNR), is based on a variation of the CNCMS approach. The final modal synthesis uses a multi-harmonic procedure and a re-evaluation of the nonlinear forces on each sector independently. The performance and limitations of the proposed approach are assessed using a simplified example of a blisk subject to polynomial nonlinearities. Different internal resonances are exhibited and studied depending on the type of excitation force and on the level of mistuning.

Probabilistic Analysis of Geometric Uncertainty Effects on Blade-Alone Forced Response

2004 ◽  
Author(s):  
Jeffrey M. Brown ◽  
Ramana V. Grandhi
Keyword(s):  
Stress Measurement ◽  
Approximation Error ◽  
Leading Edge ◽  
Monte Carlo Sampling ◽  
Forced Response ◽  
Small Sample ◽  
Reduced Order Model ◽  
Order Model ◽  
Element Analysis ◽  
Reduced Order

This paper investigates the effect of manufacturing variations on the blade-alone forced response of a transonic low aspect ratio fan. A simulated set of coordinate measurement machine measurements from a single rotor, representative of actual manufacturing variations, are used to investigate geometric effects. A reduced order model is developed to rapidly solve for the forced response and is based on eigensensitivity analysis and dynamic response mode superposition. An approximation error analysis is conducted to quantify accuracy of the new tool and errors between approximate and full finite element analysis solutions are shown to be small for low order modes with some high order modes having moderate error. A study of the simulated measured blade results show a significant amount of forced response variation along the leading edge of the airfoil. Statistics from this simulated measured rotor are used with Monte Carlo sampling to generate random blades realizations that are solved with the reduced order model. This procedure allows the prediction of the variation across an entire fleet of blades from a small sample of blades. The large variations predicted, up to 40%, could have a significant impact of the blade design process including the procedures to account for foreign object damage damage tolerance, how non-intrusive stress measurement systems are used, and how mistuning prediction algorithms are validated.

Reduced Order Model for Efficient Engineering Analysis

2020 ◽  
Author(s):  
Allan X. Zhong ◽  
Haoyue Zhang
Keyword(s):  
Finite Element ◽  
Design Of Experiments ◽  
Reduced Order Model ◽  
Reduced Model ◽  
Complex Structures ◽  
Engineering Analysis ◽  
Order Model ◽  
Element Analysis ◽  
Reduced Order ◽  
Numerical Design

Abstract Engineering analysis of complex structures or mechanical systems typically involves contact with multiple components, large deformation, and material nonlinearity, which requires the application of nonlinear finite element methods. Despite the advancement of commercial software for finite element analysis (FEA), nonlinear FEA of a multi-component mechanical assembly will take hours to days, and even weeks to complete. It is highly desired to develop a reduced-order model for a family of complex structures that can reduce an original problems’ complexity and degree of freedom but has a reasonably small discrepancy with the full model and significantly reduces the computation time. The typical approach to construct a reduced model includes 1) the response surface method via numerical design of experiments and, 2) the simplified physics approach. In this paper, it is proposed to develop a reduced model through the combination of simplified physics, dimensional analysis [1], and numerical design of experiments. The approach is applied to the construction of a reduced model for the analysis of a downhole plug [2]. The developed reduced model is verified by full-scale FEA models and validated through physical tests. The reduced model is implemented in a spreadsheet and takes only seconds to complete a calculation in contrast to hours using a full FEA model, enabling engineers’ quick evaluation of the corresponding designs.

A Nonlinear Dynamic Reduced-Order Model for a Large Gas Turbine Outer Casing Low Cycle Fatigue Prediction

2021 ◽  
Author(s):  
Aditya Dubey ◽  
Rishi Relan ◽  
Uwe Lohse ◽  
Jaroslaw Szwedowicz
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Gas Turbine ◽  
Nonlinear Dynamic ◽  
Low Cycle Fatigue ◽  
Reduced Order Model ◽  
Cycle Fatigue ◽  
Order Model ◽  
Element Analysis ◽  
Reduced Order

Abstract The secondary stresses that result from nonlinear and transient thermal gradients during the start-up and shut down of the large gas turbine engines drive low-cycle fatigue at specific locations of the outer casing. Typical service inspection of the outer casing is primarily based on finite element analysis estimates, considering various safety factors. However, as finite element analysis includes the worst possible combination of loading scenarios and operating conditions any engine may encounter in actual operation, this results in a conservative estimation of the service interval. Therefore, a generic preventive maintenance plan for the whole fleet often underutilises the casing capability and added cost. Hence, this paper proposes a data-driven nonlinear dynamic reduced-order model developed using the temperature data from low-cycle fatigue critical casing locations, ramp rates, and the percentage load of operation to predict the stresses. As a result, a reduced-order model can assess the damage for low-cycle fatigue critical locations in real-time using the operational data and propose an appropriate service intervention plan for each casing in a fleet.

A Reduced Order Model for Transient Analysis of Bladed Disk Forced Response

2005 ◽  
Author(s):  
J. P. Ayers ◽  
D. M. Feiner ◽  
J. H. Griffin
Keyword(s):  
Transient Analysis ◽  
Critical Value ◽  
Forced Response ◽  
Reduced Order Model ◽  
Transient Effects ◽  
Order Model ◽  
Reduced Order ◽  
Bladed Disk ◽  
Vibratory Response ◽  
Acceleration Rate

A method for predicting the vibratory response of bladed disks under high engine acceleration rates is developed. The method is based on the Fundamental Mistuning Model, an existing reduced order model for predicting the steady-state vibratory response. In addition, a criterion is developed for a critical engine acceleration rate, above which transient effects play a large role in the response. It is shown that military engines operate at acceleration rates above this critical value and therefore transient effects are important in practice.

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