Geometric Mistuning Identification of Integrally Bladed Rotors Using Modified Modal Domain Analysis

2012 ◽  
Author(s):  
Yasharth Bhartiya ◽  
Alok Sinha
Keyword(s):  
Taylor Series ◽  
Domain Analysis ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Coordinate Measurement ◽  
Stiffness Matrices ◽  
Taylor Series Expansions ◽  
Bladed Rotor ◽  
Forced Responses

Modified Modal Domain Analysis (MMDA) is a novel method for the development of a reduced-order model of a bladed rotor with geometric mistuning. This method utilizes proper orthogonal decomposition (POD) of Coordinate Measurement Machine (CMM) data on blades’ geometries, and sector analyses using ANSYS and solid modeling. In a recent paper, MMDA has been extended to use second order Taylor series approximations of perturbations in mass and stiffness matrices (δM and δK) instead of exact δM and δK. Taylor series expansions of deviations in mass and stiffness matrices due to geometric mistuning give a direct approach for generating the reduced order model from the components of POD features of spatial variations in blades’ geometries. Reversing the process, algorithms for mistuning identification based on MMDA are presented in this paper to calculate the geometric mistuning parameters. Two types of algorithm, one based on modal analyses and the other on the forced responses, are presented. The validity of these methods are then verified through a mistuned academic rotor.

Geometric Mistuning Identification of Integrally Bladed Rotors Using Modified Modal Domain Analysis

2014 ◽  
Vol 136 (12) ◽  
Author(s):  
Yasharth Bhartiya ◽  
Alok Sinha
Keyword(s):  
Taylor Series ◽  
Domain Analysis ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Coordinate Measurement ◽  
Stiffness Matrices ◽  
Taylor Series Expansions ◽  
Bladed Rotor ◽  
Forced Responses

Modified modal domain analysis (MMDA) is a novel method for the development of a reduced order model of a bladed rotor with geometric mistuning. This method utilizes proper orthogonal decomposition (POD) of coordinate measurement machine (CMM) data on blades' geometries, and sector analyses using ansys and solid modeling. In a recent paper, MMDA has been extended to use second order Taylor series approximations of perturbations in mass and stiffness matrices (δM and δK) instead of exact δM and δK. Taylor series expansions of deviations in mass and stiffness matrices due to geometric mistuning give a direct approach for generating the reduced order model from the components of POD features of spatial variations in blades' geometries. Reversing the process, algorithms for mistuning identification based on MMDA are presented in this paper to calculate the geometric mistuning parameters. Two types of algorithm, one based on modal analyses and the other on the forced responses, are presented. The validity of these methods are then verified through a mistuned academic rotor.

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 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.

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.

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

2009 ◽  
Vol 131 (3) ◽  
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 data on blade geometries. Results for an academic rotor are presented to establish the validity of the technique.

Modified Modal Domain Analysis of a Bladed Rotor Using Coordinate Measurement Machine Data on Geometric Mistuning

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Vinod Vishwakarma ◽  
Alok Sinha ◽  
Yasharth Bhartiya ◽  
Jeffery M. Brown
Keyword(s):  
Natural Frequencies ◽  
Domain Analysis ◽  
Reduced Order Modeling ◽  
Forced Response ◽  
Mode Shapes ◽  
Reduced Order ◽  
Coordinate Measurement ◽  
Coordinate Measurement Machine ◽  
Bladed Rotor ◽  
Proper Orthogonal

Modified modal domain analysis (MMDA), a reduced order modeling technique, is applied to a geometrically mistuned integrally bladed rotor to obtain its natural frequencies, mode shapes, and forced response. The geometric mistuning of blades is described in terms of proper orthogonal decomposition (POD) of the coordinate measurement machine (CMM) data. Results from MMDA are compared to those from the full (360 deg) rotor Ansys model. It is found that the MMDA can accurately predict natural frequencies, mode shapes, and forced response. The effects of the number of POD features and the number of tuned modes used as bases for model reduction are examined. Results from frequency mistuning approaches, fundamental mistuning model (FMM) and subset of nominal modes (SNM), are also generated and compared to those from full (360 deg) rotor Ansys model. It is clearly seen that FMM and SNM are unable to yield accurate results whereas MMDA yields highly accurate results.

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.

Model Reduction for the Electrostatically Actuated Silicon Diaphragm Based on Modal-Type Dynamic Condensation

2014 ◽  
Author(s):  
X. Z. Lin ◽  
Z. M. Hu ◽  
J. M. Huang
Keyword(s):  
Dynamic Models ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Stiffness Matrices ◽  
Electric Driving ◽  
Dynamic Condensation ◽  
Simulation Results ◽  
Modal Type

A method for constructing reduced-order models (ROM) of an electrostatically actuated clamped silicon diaphragm is presented. This reduced-order model is constructed by using basis the spatially dependent eigen-functions. A commercial finite element package is firstly used to form the system mass and stiffness matrices representing the model. These matrices are then manipulated in MATLAB™ and reduced using modal type dynamic condensation. The eigen-value problem is then solved for the reduced mass and stiffness matrices and subset of the modes are used to producing low-order but highly accurate models of electrostatically actuated diaphragm. The reduced-order model can accounts for general residual stress and strain hardening and allows for any other electric driving signal simulations. Once the ROM has been generated, it can be reused to simulate the quasi-state and dynamics behaviors of the device over a range of different electric driving waveforms. The calculated results show that the resulting ROM can capture the static/dynamic behaviors of the device very well. The simulation results also show good agreement with the fully meshed dynamic models simulation results, thus the efficiency and accuracy of the modeling technology are valid.

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