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

2013 ◽  
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 degrees) 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 degree) rotor ANSYS model. It is clearly seen that FMM and SNM are unable to yield accurate results whereas MMDA yields highly accurate results.

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.

Vibratory Parameters of Blades From Coordinate Measurement Machine (CMM) Data

2005 ◽  
Author(s):  
Alok Sinha ◽  
Benjamin Hall ◽  
Brice Cassenti ◽  
Gary Hilbert
Keyword(s):  
Finite Element ◽  
Proper Orthogonal Decomposition ◽  
Natural Frequencies ◽  
Orthogonal Decomposition ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Coordinate Measurement ◽  
Coordinate Measurement Machine ◽  
Bladed Rotor ◽  
Proper Orthogonal

This paper deals with the development of a procedure to model geometric variations of blades. Specifically, vibratory parameters of blades are extracted from CMM data on an integrally bladed rotor (IBR). The method is based on proper orthogonal decomposition (POD) of CMM data, solid modeling and finite element techniques. In addition to obtaining natural frequencies and mode shapes of each blade on an IBR, statistics of these modal parameters are also computed and characterized. Numerical results are validated by comparison with experimental results.

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.

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.

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

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.

scholarly journals Component-Centric Reduced Order Modeling of the Dynamic Response of Linear Multibay Structures

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Yuting Wang ◽  
Marc P. Mignolet
Keyword(s):  
Natural Frequencies ◽  
Element Model ◽  
Fixed Number ◽  
Mode Shapes ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Entire Structure ◽  
Similar Mode ◽  
Fixed Interface ◽  
Proper Orthogonal

Component-centric reduced order models (ROMs) are introduced here as small-size ROMs providing an accurate prediction of the linear response of part of a structure (the β component) without focusing on the rest of it (the α component). Craig–Bampton (CB) substructuring methods are first considered. In one method, the β component response is modeled with its fixed interface modes while the other adopts singular value eigenvectors of the β component deflections of the linear modes of the entire structure. The deflections in the α component induced by harmonic motions of these β component modes are processed by a proper orthogonal decomposition (POD) to model the α component response. A third approach starts from the linear modes of the entire structure which are dominant in the β component response. Then, the contributions of other modes in this part of the structure are approximated in terms of those of the dominant modes with close natural frequencies and similar mode shapes in the β component, i.e., these nondominant modal contributions are “lumped” onto dominant ones. This lumping permits to increase the accuracy in the β component at a fixed number of modes. The three approaches are assessed on a structural finite element model of a nine-bay panel with the modal lumping-based method yielding the most “compact” ROMs. Finally, good robustness of the ROM to changes in the β component properties (e.g., for design optimization) is demonstrated and a similar sensitivity analysis is carried out with respect to the loading under which the ROM is constructed.

scholarly journals Comparison Between Calculated and Measured Free-Free Modes for a Flexible Rotor

1998 ◽  
Author(s):  
José A. Vázquez ◽  
Lloyd E. Barrett
Keyword(s):  
Natural Frequencies ◽  
Forced Response ◽  
Modal Testing ◽  
Analytical Models ◽  
Mode Shapes ◽  
Reduced Order Models ◽  
Response Functions ◽  
Flexible Rotor ◽  
Reduced Order ◽  
Response Characteristics

Many industrial machines nowadays are sold based on analysis performed on mathematical models of the rotors, bearings, substructures, and other components. The validity of the analysts therefore depends on the accuracy of the models themselves. When the rotor is available, modal testing may be used to validate the model of the rotor by comparing the calculated and measured free-free natural frequencies and mode shapes. This work presents additional tools for the verification of analytical models against experimental data. These tools use models of the rotor constructed from the measured data and the analytical model. A comparison of the first six calculated and measured free-free natural frequencies and mode shapes for a multi-mass flexible rotor is presented. The natural frequencies compare within 1.8%. The calculated and measured mode shapes were used to construct independent reduced order models of the rotor. These models were used to perform forced response and stability analyses. Forced response functions are presented comparing the forced response characteristics obtained from the two models. This provides a comparison between the measured and calculated forced response functions for the same number of modes. For the stability analysis, identical bearing models were added to both reduced order models. The eigenvalues were calculated using both models for a range of bearing stiffness and damping coefficients and were plotted for comparison.

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.

Reduced Order Modeling of a Bladed Rotor With Geometric Mistuning via Estimated Deviations in Mass and Stiffness Matrices

2011 ◽  
Author(s):  
Yasharth Bhartiya ◽  
Alok Sinha
Keyword(s):  
Reduced Order Modeling ◽  
Orthogonal Decomposition ◽  
Series Expansions ◽  
Computationally Efficient ◽  
Reduced Order ◽  
Stiffness Matrices ◽  
Taylor Series Expansions ◽  
Bladed Rotor ◽  
Proper Orthogonal ◽  
Further Development

This paper deals with further development of Modified Modal Domain Analysis (MMDA), which is a breakthrough method in the reduced order modeling of a bladed rotor with geometric mistuning. The main focus of this paper is to show that deviations in mass and stiffness matrices due to mistuning, estimated by Taylor series expansions in terms of independent Proper Orthogonal Decomposition variables representing geometric variations of blades, can be used for MMDA. This result has rendered Monte Carlo simulation of the response of a bladed rotor with geometric mistuning to be easy and computationally efficient.

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