Reduced-Order Models for Blisks With Small and Large Mistuning and Friction Dampers

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Weihan Tang ◽  
Seunghun Baek ◽  
Bogdan I. Epureanu
Keyword(s):  
Contact Point ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Cyclic Symmetry ◽  
Energy Localization ◽  
Friction Forces ◽  
Frictional Contacts ◽  
Reduced Order ◽  
Random Mistuning ◽  
Forced Responses

In operation, rotating bladed disks (blisks) are often subject to high levels of dynamic loading, resulting in large amplitudes of forced vibrations especially at resonance. Moreover, variations in structural properties of individual sectors, referred to as mistuning, can lead to strain energy localization and can amplify forced responses. To prevent damages caused by high cycle fatigue, various frictional damping sources are introduced to dissipate vibration energy. Due to the nonlinear behavior of frictional contacts, conventional methods to study the dynamics of the blisk–damper systems are based often on numerical time integration, which is time-consuming and can be computationally prohibitive due to the large sizes of commercial blisk models. Existing techniques for model reduction either rely heavily on cyclic symmetry of the blisk–damper system or are based on component mode synthesis (CMS). However, in the presence of mistuning, cyclic symmetry no longer exists. Also, mistuning is random and best studied statistically. Repetitive CMS condensation for a large amount of random mistuning patterns can lead to a computationally formidable task. This paper presents a reduced-order modeling (ROM) technique to efficiently capture the nonlinear dynamic responses of blisk–damper systems with both small perturbations in blade material properties (small mistuning) and significant changes in the blisk geometries (large mistuning). The ROMs are formed by projecting the blisk–damper systems onto a novel mode basis that mimics the contact behavior. This mode basis contains normal mode shapes of the mistuned blisk–damper systems with either sliding or sticking conditions enforced on the contact surfaces. These mode shapes are computed through the N-PRIME method, a technique recently developed by the authors to efficiently obtain mode shapes for blisks with simultaneous large and small mistuning. The resulting modal nonlinear equations of motion (EOM) are solved by a hybrid frequency/time (HFT) domain method with continuation. In the HFT method, the contact status and friction forces are determined in the time domain by a quasi-two-dimensional contact model at each contact point, whereas the modal EOM are solved in the frequency domain according to a harmonic balance formulation. The forced responses computed by the proposed ROMs are validated for two systems with distinct mistuning patterns. A statistical analysis is performed to study the effectiveness of the frictional dampers under random mistuning patterns.

Reduced Order Models for Blisks With Small and Large Mistuning and Friction Dampers

2016 ◽  
Author(s):  
Weihan Tang ◽  
Seunghun Baek ◽  
Bogdan I. Epureanu
Keyword(s):  
Equations Of Motion ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Reduced Order Models ◽  
Cyclic Symmetry ◽  
Friction Forces ◽  
Frictional Contacts ◽  
Reduced Order ◽  
Random Mistuning ◽  
Forced Responses

In operation, rotating bladed disks (blisks) are often subject to high levels of dynamic loading, resulting in large amplitudes of forced vibrations especially at resonance. Moreover, variations in structural properties of individual sectors, referred to as mistuning, can lead to strain energy localization and can amplify forced responses. To prevent damages caused by high cycle fatigue, various frictional damping sources are introduced to dissipate vibration energy. Due to the nonlinear behavior of frictional contacts, conventional methods to study the dynamics of the blisk-damper systems are based often on numerical time integration, which is time-consuming and can be computationally prohibitive due to the large sizes of commercial blisk models. Existing techniques for model reduction either rely heavily on cyclic symmetry of the blisk-damper system, or are based on component mode synthesis (CMS). However, in the presence of mistuning, cyclic symmetry no longer exists. Also, mistuning is random and best studied statistically. Repetitive CMS condensation for a large amount of random mistuning patterns can lead to a computationally formidable task. This paper presents a reduced-order modeling technique to efficiently capture the nonlinear dynamic responses of blisk-damper systems with both small perturbations in blade material properties (small mistuning), and significant changes in the blisk geometries (large mistuning). The reduced-order models (ROMs) are formed by projecting the blisk-damper systems onto a novel mode basis that mimics the contact behavior. This mode basis contains normal mode shapes of the mistuned blisk-damper systems with either sliding or sticking conditions enforced on the contact surfaces. These mode shapes are computed through the N-PRIME method, a technique recently developed by the authors to efficiently obtain mode shapes for blisks with simultaneous large and small mistuning. The resulting modal nonlinear equations of motion are solved by a hybrid frequency/time (HFT) domain method with continuation. In the HFT method, the contact status and friction forces are determined in the time domain by a quasi-two-dimensional contact model at each contact point, whereas the modal equations of motion are solved in the frequency domain according to a harmonic balance formulation. The forced responses computed by the proposed ROMs are validated for two systems with distinct mistuning patterns. A statistical analysis is performed to study the effectiveness of the frictional dampers under random mistuning patterns.

scholarly journals Prediction of the Resonant Response of Frictionally Constrained Blade Systems Using Constrained Mode Shapes

1998 ◽  
Author(s):  
J. J. Chen ◽  
C. H. Menq
Keyword(s):  
Contact Point ◽  
Element Model ◽  
The Other ◽  
Mode Shapes ◽  
Vibration Modes ◽  
Cyclic Symmetry ◽  
Resonant Response ◽  
Friction Contact ◽  
Blade System ◽  
Free Mode

In this paper, the concept of constrained mode shapes is employed to predict the resonant response of a frictionally constrained blade system. For a tuned blade system, the constrained mode shapes can be calculated using a finite element model of a single blade along with the cyclic symmetry constraint that simulates a fully stuck friction contact. The resulting constrained mode shapes are often complex and can be used to obtain the constrained receptance of the frictionally constrained blade. It is shown that by examining each mode’s contribution to the receptance at the friction contact point, the importance of each individual modes to the prediction of the resonant response of a frictionally constrained blade can be determined. Furthermore, by comparing the receptances calculated from free mode shapes and those from constrained mode shapes, it is found that in the neighborhood of the fully slipping region, the prediction of resonant response requires fewer number of modes when using free mode shapes compared to using constrained mode shapes. On the other hand, in the neighborhood of the fully stuck region, it requires fewer number of modes if constrained mode shapes are used. Therefore, when high preload at the friction contact is desirable, such as for shrouded blade systems, using the constrained mode shapes for the prediction of resonant response is preferred. Moreover, the concept of hybrid receptance is introduced so as to yield very accurate prediction of the resonant response based on only very few vibration modes.

Dynamic Analysis of an Elevator Traveling Cable Using a Singularity-Free Beam Formulation

2017 ◽  
Vol 84 (4) ◽  
Author(s):  
W. Fan ◽  
W. D. Zhu
Keyword(s):  
Dynamic Analysis ◽  
Multibody Dynamics ◽  
Natural Frequencies ◽  
Vertical Motion ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Out Of Plane ◽  
Forced Responses ◽  
Free Beam ◽  
Good Agreement

A round elevator traveling cable is modeled using a singularity-free beam formulation. Equilibria of the traveling cable with different elevator car positions are studied. Natural frequencies and the corresponding mode shapes of the traveling cable are calculated and they are in excellent agreement with those calculated by abaqus. In-plane natural frequencies of the traveling cable do not change much with the car position compared with its out-of-plane ones. Dynamic responses of the traveling cable are calculated and they are in good agreement with those from commercial multibody dynamics software recurdyn. Effects of vertical motion of the car on free responses of the traveling cable and those of in-plane and out-of-plane building sways on forced responses are investigated.

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.

Contribution to Free and Forced Vibration Analysis of an Intentionally Mistuned Blisk

2012 ◽  
Author(s):  
Harald Schoenenborn ◽  
Michael Junge ◽  
Ulrich Retze
Keyword(s):  
Amplification Factor ◽  
Travelling Wave ◽  
Free Vibrations ◽  
Rotor Blades ◽  
Mode Shapes ◽  
Fem Model ◽  
Reduced Order ◽  
Random Mistuning ◽  
Forced Vibration Analysis ◽  
Good Agreement

Most of the experimental mistuning studies are performed using a blisk with random mistuning only. Intentional mistuning is often investigated analytically with respect to aeroelasticity, as it is well known that intentional mistuning reduces the flutter risk due to less interaction between the blades. In this paper, an intentionally mistuned test blisk is investigated both analytically and experimentally with respect to free and forced vibrations. First, free vibrations are studied and aliasing effects for the intentionally mistuned blisk are analyzed in comparison with a tuned blisk. A comparison between the experimentally determined dominant nodal diameters and the computed ones shows good agreement. Then, the blisk is experimentally excited by a travelling wave for various engine orders. Similar investigations are performed with a FEM model of the blisk and a reduced-order code. The amplification factor for some modes and several blisks is compared. The influence of the disc onto the blade mode shapes is studied for the tuned and mistuned case without and with aerodynamic coupling effects. Cyclic spacing of vanes is a concept to reduce the vibration level of downstream rotor blades by distributing the excitation onto more engine orders while reducing the overall excitation level. In this paper it is shown for blisks with and without intentional mistuning that care should be taken in applying this concept in the vicinity of veering regions, because the amplification factor in a veering region may become much higher than compared to other nodal diameters.

Dynamic Analysis of an Elevator Traveling Cable Using a Singularity-Free Beam Formulation

2017 ◽  
Author(s):  
W. Fan ◽  
W. D. Zhu
Keyword(s):  
Natural Frequencies ◽  
Vertical Motion ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Normal Strain ◽  
Euler Parameters ◽  
Current Formulation ◽  
Out Of Plane ◽  
Forced Responses ◽  
Free Beam

An elevator traveling cable is modeled using a singularity-free beam formulation and its static and dynamic behaviors are analyzed. The beam is assumed to be an extensible Euler-Bernoulli beam, and the configuration of the beam is described by Euler parameters, which can resolve the singularity problem of Euler angles, and the normal strain of the centroid line of the beam. The position of the centroid line of the beam is integrated from its slope. Governing equations of the beam and constraint equations are derived using Lagrange’s equations for systems with constraints. The current formulation is used to calculate the equilibrium and dynamic responses of an elevator traveling cable with arbitrarily moving ends. Equilibria of a traveling cable with different elevator car positions are calculated. Natural frequencies and corresponding mode shapes of the traveling cable are calculated and they are in excellent agreement with those calculated by ABAQUS. In-plane natural frequencies of the traveling cable do not change much with the car position compared with its out-of-plane ones. Dynamic responses of the traveling cable are calculated using the current formulation and compared with those from commercial multibody dynamics software RecurDyn, and they are in good agreement with each other. Free responses of the traveling cable due to vertical motion of the car and forced responses with inplane and out-of-plane building sways are simulated, and their effects on dynamic responses of the traveling cable are investigated. While the vertical motion of the car can affect the in-plane lateral response of the traveling cable, it has almost no effect on its out-of-plane response. Building sways can affect both lateral and out-of-plane responses of the traveling cable, but they have little effect on its vertical response.

Dynamic Modeling and Projection-Based Reduction Methods for Bladed Disks With Nonlinear Frictional and Intermittent Contact Interfaces

2019 ◽  
Vol 71 (5) ◽  
Author(s):  
Mainak Mitra ◽  
Bogdan I. Epureanu
Keyword(s):  
Dynamic Modeling ◽  
Coulomb Friction ◽  
Bladed Disks ◽  
Friction Forces ◽  
Frictional Contacts ◽  
Reduced Order ◽  
Reduction Methods ◽  
Intermittent Contact ◽  
Critical Components ◽  
Technical Discussion

AbstractTurbine bladed disks or blisks, which constitute critical components of most modern turbomachinery, are known for their complex vibratory behavior. The nonlinear dynamics observed in most operational regimes of blisk with contact interfaces are dominated by one of two typical contact behaviors. Frictional contacts are dominated by Coulomb friction forces, while intermittent contacts are characterized by multiple separation events. Other factors such as the dispersion in material or geometric properties across blades, known as mistuning, also affect the dynamics significantly. Presently, probabilistic analysis is the widely accepted design methodology to account for mistuning, which is unknown prior to manufacture. Thus, reduced order modeling of these blisks is essential as high fidelity models are prohibitively expensive for such simulations. This paper provides a technical discussion of dynamic modeling and reviews projection-based techniques used for creation of reduced models of blisks with contacts.

scholarly journals Slipping–rolling transitions of a body with two contact points

2021 ◽  
Author(s):  
Mate Antali ◽  
Gabor Stepan
Keyword(s):  
Rigid Body ◽  
Contact Point ◽  
Static Friction ◽  
Rigid Body Dynamics ◽  
Contact Forces ◽  
Friction Forces ◽  
Contact Points ◽  
Body Dynamics ◽  
Coulomb Model ◽  
Rigid Surfaces

AbstractIn this paper, the general kinematics and dynamics of a rigid body is analysed, which is in contact with two rigid surfaces in the presence of dry friction. Due to the rolling or slipping state at each contact point, four kinematic scenarios occur. In the two-point rolling case, the contact forces are undetermined; consequently, the condition of the static friction forces cannot be checked from the Coulomb model to decide whether two-point rolling is possible. However, this issue can be resolved within the scope of rigid body dynamics by analysing the nonsmooth vector field of the system at the possible transitions between slipping and rolling. Based on the concept of limit directions of codimension-2 discontinuities, a method is presented to determine the conditions when the two-point rolling is realizable without slipping.

Modal Reduced Order Model for Vision Sensing of IPMC Actuator

2006 ◽  
Vol 326-328 ◽  
pp. 1523-1526
Author(s):  
Il Kweon Oh ◽  
Seong Won Yeom ◽  
Dong Weon Lee
Keyword(s):  
Reduced Order Model ◽  
Mode Shapes ◽  
Computational Time ◽  
Transverse Displacement ◽  
Metal Composite ◽  
Motion Generation ◽  
Order Model ◽  
Lower Mode ◽  
Reduced Order ◽  
Vision Sensing

In order to control the IPMC (Ionic Polymer Metal Composite) actuators, it is necessary to use a vision sensing system and a reduced order model from the vision sensing data. In this study, the MROVS (Modal Reduced Order Vision Sensing) model using the least square method has been developed for implementation of the biomimetic motion generation. The simulated transverse displacement is approximated with a sum of the lower mode shapes of the cantilever beam. The NIPXI 1409 image acquisition board and CCD camera (XC-HR50) are used in the experimental setup. Present results show that the MROVS model can efficiently process the vision sensing of the biomimetic IPMC actuator with cost-effective computational time.

scholarly journals Damage Diagnosis in 3D Structures Using a Novel Hybrid Multiobjective Optimization and FE Model Updating Framework

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Nizar Faisal Alkayem ◽  
Maosen Cao ◽  
Minvydas Ragulskis
Keyword(s):  
Structural Damage ◽  
Model Updating ◽  
Complex Problem ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Fe Model ◽  
Modal Strain Energy ◽  
3D Structures ◽  
Multiobjective Particle Swarm Optimization ◽  
Damage Tracking

Structural damage detection is a well-known engineering inverse problem in which the extracting of damage information from the dynamic responses of the structure is considered a complex problem. Within that area, the damage tracking in 3D structures is evaluated as a more complex and difficult task. Swarm intelligence and evolutionary algorithms (EAs) can be well adapted for solving the problem. For this purpose, a hybrid elitist-guided search combining a multiobjective particle swarm optimization (MOPSO), Lévy flights (LFs), and the technique for the order of preference by similarity to ideal solution (TOPSIS) is evolved in this work. Modal characteristics are employed to develop the objective function by considering two subobjectives, namely, modal strain energy (MSTE) and mode shape (MS) subobjectives. The proposed framework is tested using a well-known benchmark model. The overall strong performance of the suggested method is maintained even under noisy conditions and in the case of incomplete mode shapes.

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