Reduced-Order Model of a Mistuned Multi-Stage Bladed Rotor

2007 ◽  
Author(s):  
Alok Sinha
Keyword(s):  
Degrees Of Freedom ◽  
Maximum Amplitude ◽  
Reduced Order Model ◽  
Order Model ◽  
Mass Model ◽  
Reduced Order ◽  
Multi Stage ◽  
Bladed Rotor ◽  
The Impact ◽  
Three Degrees Of Freedom

This paper deals with a reduced-order model of a multi-stage rotor in which each stage has a different number of blades. In particular, it is shown that a reduced-order model can be developed on the basis of tuned modes of certain bladed disks. The validity of this algorithm is shown for a spring-mass model with three degrees of freedom per sector. In addition, the statistical distributions of the peak maximum amplitude are generated via Monte Carlo simulations, and the impact of mistuning is examined for a two-stage rotor.

Estimation of Forcing Function for a Geometrically Mistuned Bladed Rotor via Modified Modal Domain Analysis

2015 ◽  
Author(s):  
Vinod Vishwakarma ◽  
Alok Sinha
Keyword(s):  
Estimation Algorithm ◽  
Element Model ◽  
Domain Analysis ◽  
Reduced Order Model ◽  
Dynamic Responses ◽  
Order Model ◽  
Mass Model ◽  
Reduced Order ◽  
Forcing Function ◽  
Bladed Rotor

Modified Modal Domain Analysis (MMDA) is a method to generate an accurate reduced order model (ROM) of a bladed disk with geometric mistuning. An algorithm based on MMDA ROM and a state observer is developed to estimate forcing functions for synchronous (including integer multiples) conditions from the dynamic responses obtained at few nodal locations of blades. The method is tested on a simple spring-mass model, finite element model (FEM) of a geometrically mistuned academic rotor and FEM of a bladed rotor of an industrial scale transonic research compressor. The accuracy of the forcing function estimation algorithm is examined by varying the order of reduced-order model and the number of vibration output signals.

Reduced Order Model of a Bladed Rotor With Geometric Mistuning: Comparison Between Modified Modal Domain Analysis and Frequency Mistuning Approach

2011 ◽  
Author(s):  
Yasharth Bhartiya ◽  
Alok Sinha
Keyword(s):  
Degrees Of Freedom ◽  
Domain Analysis ◽  
Forced Response ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Order Model ◽  
Reduced Order ◽  
Young’S Moduli ◽  
Stiffness Matrices ◽  
Bladed Rotor

Mistuning has traditionally been modeled through the changes in Young’s moduli of blades, or equivalently through perturbations in the stiffness matrices associated with blades’ degrees of freedom. Such a mistuning is termed as Frequency Mistuning because it alters the blade alone frequencies without altering the mode shapes component associated with the blades. Many reduced order models have been developed for frequency mistuning [1–7]. Although frequency mistuning has been developed for Young’s Modulus mistuning, it is applied to geometric mistuning in the literature. In this paper frequency mistuning is applied to a geometrically mistuned system and the results from Subset of Nominal Modes (SNM) [5] technique, a reduced order model based on frequency mistuning, are compared with those from Modified Modal Domain Analysis (MMDA). It is shown that frequency mistuning analysis is unable to capture the effects of geometric mistuning in general, whereas MMDA provides accurate estimates of natural frequencies, mode shapes and forced response.

Reduced Order Model of a Multistage Bladed Rotor With Geometric Mistuning via Modal Analyses of Finite Element Sectors

2010 ◽  
Author(s):  
Yasharth Bhartiya ◽  
Alok Sinha
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Element Model ◽  
Reduced Order Model ◽  
Order Model ◽  
Two Stage ◽  
Reduced Order ◽  
Multi Stage ◽  
Bladed Rotor ◽  
The Finite Element Model

An algorithm to generate a reduced order model of a multi-stage rotor in which each stage has a different number of blades has been developed. It is shown that a reduced order model can be developed on the basis of tuned modes of certain bladed disks which can be easily obtained via sector analyses. Further, it is shown that reduced order model can also be obtained when blades are geometrically mistuned. This algorithm is similar to the modified modal domain analysis, which has been recently developed for a single-stage bladed rotor with geometric mistuning. The validity of this algorithm is shown for the finite element model of a two-stage bladed rotor. In addition, the statistical distributions of peak maximum amplitudes and natural frequencies of a two-stage rotor are generated via Monte Carlo simulations for different patterns of geometric mistuning.

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.

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.

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.

Nonlinear Dynamic Analysis of Cantilever Beam Using POD Based Reduced Order Model

2015 ◽  
Vol 786 ◽  
pp. 398-403 ◽  
Author(s):  
Kulkarni Atul Shankar ◽  
Manoj Pandey
Keyword(s):  
Dynamic Analysis ◽  
Large Deformation ◽  
Cantilever Beam ◽  
Nonlinear Dynamic ◽  
Degrees Of Freedom ◽  
Numerical Technique ◽  
Nonlinear Dynamic Analysis ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order

In this paper, a reduced order model is obtained for nonlinear dynamic analysis of a cantilever beam. Nonlinearity in the system is basically due to large deformation. A reduced order model is an efficient method to formulate low order dynamical model which can be obtained from data obtained from numerical technique such as finite element method (FEM). Nonlinear dynamical models are complex with large number of degrees of freedom and hence, are computationally intensive. With formulation of reduced order models (i.e. Macromodels) number of degrees of freedom are reduced to fewer degrees of freedom by using projection based method like Galerkin’s projection, so as to make system computationally faster and cost effective. These macromodels are obtained by extracting global basis functions from fully meshed model runs. Macromodels are generated using technique called proper orthogonal decomposition (POD) which gives good linear fit for the nonlinear systems. Using POD based macromodel, response of system can be computed using fewer modes instead of considering all modes of system. Macromodel is generated to obtain the response of cantilever beam with large deformation and hence, simulation time is reduced by factor of 90 approximately with error of order of 10-4. Further, method of POD based reduced order model is aplied to beam with different loading conditions to check the robustness of the macromodel. POD based macromodel response gives good agreement with FEA model response for a cantilever beam.

Reduced Order Model for the Geometric Nonlinear Response of Complex Structures

2012 ◽  
Author(s):  
Ricardo Perez ◽  
X. Q. Wang ◽  
Andrew Matney ◽  
Marc P. Mignolet
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Behavior ◽  
Reduced Order Model ◽  
Model Parameters ◽  
Complex Structures ◽  
Order Model ◽  
Plate Structures ◽  
Reduced Order ◽  
Nonlinear Static ◽  
Selection Of

This paper focuses on the development of nonlinear reduced order modeling techniques for the prediction of the response of complex structures exhibiting “large” deformations, i.e. a geometrically nonlinear behavior, and modeled within a commercial finite element code. The present investigation builds on a general methodology successfully validated in recent years on simpler beam and plate structures by: (i) developing a novel identification strategy of the reduced order model parameters that enables the consideration of the large number of modes (> 50 say) that would be needed for complex structures, and (ii) extending an automatic strategy for the selection of the basis functions used to represent accurately the displacement field. The above novel developments are successfully validated on the nonlinear static response of a 9-bay panel structure modeled with 96,000 degrees of freedom within Nastran.

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.

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