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: 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.

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.

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.

A Reduced-Order Model for Evaluating the Effect of Rotational Speed on the Natural Frequencies and Mode Shapes of Blades

2003 ◽  
Vol 125 (3) ◽  
pp. 772-776 ◽  
Author(s):  
P. Marugabandhu ◽  
J. H. Griffin
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Finite Element Analyses ◽  
Order Model ◽  
Reduced Order ◽  
Low Aspect Ratio ◽  
Centrifugal Stiffening ◽  
Fan Blade

A reduced-order model has been developed that can be used to accurately and quickly calculate the changes in the natural frequencies and mode shapes of a blade that are caused by centrifugal stiffening. It has been corroborated by comparisons with finite element analyses of a cantilevered tapered plate and with frequencies from a low aspect ratio fan blade.

A Reduced Order Model for Evaluating the Effect of Rotational Speed on the Natural Frequencies and Mode Shapes of Blades

2000 ◽  
Author(s):  
P. Marugabandhu ◽  
J. H. Griffin
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Finite Element Analyses ◽  
Order Model ◽  
Reduced Order ◽  
Low Aspect Ratio ◽  
Centrifugal Stiffening ◽  
Fan Blade

A reduced order model has been developed that can be used to accurately and quickly calculate the changes in the natural frequencies and mode shapes of a blade that are caused by centrifugal stiffening. It has been corroborated by comparisons with finite element analyses of a cantilevered tapered plate and with frequencies from a low aspect ratio fan blade.

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.

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

2011 ◽  
Vol 134 (4) ◽  
Author(s):  
Yasharth Bhartiya ◽  
Alok Sinha
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Element Model ◽  
Reduced Order Model ◽  
Statistical Distributions ◽  
Order Model ◽  
Two Stage ◽  
Reduced Order ◽  
Bladed Rotor ◽  
The Finite Element Model

An algorithm to generate a reduced order model of a multistage 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 the 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.

Natural Frequencies and Mode Shapes of Slacked Carbon Nanotube NEMS Resonators

2010 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammed I. Younis
Keyword(s):  
Natural Frequencies ◽  
Electrostatic Force ◽  
Static Solution ◽  
Reduced Order Model ◽  
Mode Shapes ◽  
Physical Parameters ◽  
Beam Model ◽  
Order Model ◽  
Research Attention ◽  
Reduced Order

Estimating accurately the natural frequencies of electrically actuated carbon nanotubes (CNTs) has been the center of research attention over the past few years. Despite this important topic, a robust knowledge is still missing to understand the role of various physical parameters that affect the natural frequencies, such as the stretching of doubly-clamped CNTs, the DC electrostatic force, and the curvature of CNTs with slacks. In this investigation, we use a 2D nonlinear curved beam model (arch) to simulate the coupled in-plane and the out-of-plane motions of a CNT with curvature (slack). We calculate the variation of its natural frequencies and mode-shapes with the level of slack and the DC electrostatic load. Toward this, we derive a reduced-order model using a multi-mode Galerkin procedure based on the mode shapes of the straight unactuated CNT. We calculate the natural frequencies of the slacked CNT for a given voltage by substituting the static solution into the Jacobian of the reduced-order-model and then finding the corresponding eigenvalues. We show various scenarios of mode crossing and mode veering as the levels of slack and DC load are varied.

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