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.

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.

scholarly journals Reduced order system identification for UAVs

2015 ◽  
Vol 119 (1218) ◽  
pp. 961-980 ◽  
Author(s):  
P-D. Jameson ◽  
A. K. Cooke
Keyword(s):  
System Identification ◽  
Equations Of Motion ◽  
Real Data ◽  
Flight Test ◽  
Rate Of Change ◽  
Order System ◽  
Parameter Estimates ◽  
Reduced Order Models ◽  
Test Scenario ◽  
Reduced Order

Abstract Reduced order models representing the dynamic behaviour of symmetric aircraft are well known and can be easily derived from the standard equations of motion. In flight testing, accurate measurements of the dependent variables which describe the linearised reduced order models for a particular flight condition are vital for successful system identification. However, not all the desired measurements such as the rate of change in vertical velocity (Ẇ) can be accurately measured in practice. In order to determine such variables two possible solutions exist: reconstruction or differentiation. This paper addresses the effect of both methods on the reliability of the parameter estimates. The methods are used in the estimation of the aerodynamic derivatives for the Aerosonde UAV from a recreated flight test scenario in Simulink. Subsequently, the methods are then applied and compared using real data obtained from flight tests of the Cranfield University Jetstream 31 (G-NFLA) research aircraft.

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.

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.

Detection of Cracks in Mistuned Bladed Disks Using Reduced-Order Models and Vibration Data

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Chulwoo Jung ◽  
Akira Saito ◽  
Bogdan I. Epureanu
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Savings ◽  
Forced Response ◽  
Response Analysis ◽  
Reduced Order Models ◽  
Reduced Order

A novel methodology to detect the presence of a crack and to predict the nonlinear forced response of mistuned turbine engine rotors with a cracked blade and mistuning is developed. The combined effects of the crack and mistuning are modeled. First, a hybrid-interface method based on component mode synthesis is employed to develop reduced-order models (ROMs) of the tuned system with a cracked blade. Constraint modes are added to model the displacements due to the intermittent contact between the crack surfaces. The degrees of freedom (DOFs) on the crack surfaces are retained as active DOFs so that the physical forces due to the contact/interaction (in the three-dimensional space) can be accurately modeled. Next, the presence of mistuning in the tuned system with a cracked blade is modeled. Component mode mistuning is used to account for mistuning present in the uncracked blades while the cracked blade is considered as a reference (with no mistuning). Next, the resulting (reduced-order) nonlinear equations of motion are solved by applying an alternating frequency/time-domain method. Using these efficient ROMs in a forced response analysis, it is found that the new modeling approach provides significant computational cost savings, while ensuring good accuracy relative to full-order finite element analyses. Furthermore, the effects of the cracked blade on the mistuned system are investigated and used to detect statistically the presence of a crack and to identify which blade of a full bladed disk is cracked. In particular, it is shown that cracks can be distinguished from mistuning.

A New Mistuning Identification Method Based on the Subset of Nominal System Modes Method

2020 ◽  
Vol 142 (2) ◽  
Author(s):  
Christian U. Waldherr ◽  
Patrick Buchwald ◽  
Damian M. Vogt
Keyword(s):  
Finite Element ◽  
Input Data ◽  
Measurement Data ◽  
Computational Effort ◽  
Mode Shapes ◽  
Reduced Order Models ◽  
Identification Procedure ◽  
Reduced Order ◽  
Nominal System ◽  
Identification Method

Abstract The mistuning problem of quasi-periodic structures has been the subject of numerous scientific investigations for more than 50 years. Researchers developed reduced-order models to reduce the computational costs of mistuning investigations including finite element models. One question which has also high practical relevance is the identification of mistuning based on modal properties. In this work, a new identification method based on the subset of nominal system modes method (SNM) is presented. Different to existing identification methods where usually the blade stiffness of each sector is scaled by a scalar value, N identification parameters are used to adapt the modal blade stiffness of each sector. The input data for the identification procedure consist solely of the mistuned natural frequencies of the investigated mode family as well as of the corresponding mistuned mode shapes in the form of one degree-of-freedom per sector. The reduction basis consists of the tuned mode shapes of the investigated mode family. Furthermore, the proposed identification method allows for the inclusion of centrifugal effects like stress stiffening and spin softening without additional computational effort. From this point of view, the presented method is also appropriate to handle centrifugal effects in reduced-order models using a minimum set of input data compared to existing methods. The power of the new identification method is demonstrated on the example of an axial compressor blisk. Finite element calculations including geometrical mistuning provide the database for the identification procedure. The correct functioning of the identification method including measurement noise is also validated to show the applicability to a case of application where real measurement data are available.

Structural Simplification of Jack-Up Rig and Its Dynamic Responses in Regular Waves

1988 ◽  
Vol 32 (02) ◽  
pp. 134-153
Author(s):  
Jong-Shyong Wu ◽  
Cuann-Yeu Chang
Keyword(s):  
Virtual Work ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Dynamic Responses ◽  
Jacobi Method ◽  
Mode Shapes ◽  
Regular Waves ◽  
Static Condensation ◽  
Rigid Joints ◽  
Jack Up

This paper is composed of two main parts: simplification of leg structure of the jack-up rig, and dynamic analysis of the entire rig due to excitation of regular waves. First, the legs of spatial beamlike lattice with rigid joints are replaced by the equivalent beams through application of the theory of static condensation and the principle of virtual work. Then the equations of motion of the entire rig are derived based on the simplified mathematical model, and the natural frequencies and mode shapes are sought by the Jacobi method. Finally, the dynamic behavior of the hinged rig and fixed rig operating in four kinds of water depths (and hence effective leg lengths) and wave heights is studied by means of the mode superposition technique. The phase angles between responses of the legs and the influence on responses of support conditions at the seabed, wave attack angle, and damping ratio are the key points of the investigation.

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 Evaluation of Component Mode Synthesis Methods for the Detection of Modal Interaction Through Rotor Stator Contacts

2009 ◽  
Author(s):  
Alain Batailly ◽  
Mathias Legrand ◽  
Patrice Cartraud ◽  
Christophe Pierre ◽  
Jean-Pierre Lombard
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Time Integration ◽  
Component Mode Synthesis ◽  
Integration Scheme ◽  
Synthesis Methods ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Free Interface ◽  
Fixed Interface

The study of interactions through direct contact between bladetips and outer casings in modern turbomachines may be very time-consuming when the classical finite element method is used. The construction of reduced-order models using component mode synthesis (CMS) methods generally allows for dramatic increase in computational efficiency and may be used in order to improve the knowledge over these interaction phenomena. Among the available approaches, both a fixed-interface method and a free-interface method are considered here in an original manner to reduce the size of a realistic two-dimensional model. The equations of motion are solved using an explicit time integration scheme with the Lagrange multiplier method where friction is accounted for. This method offers energy momentum conserving which is a critical point to ensure the convergence of the algorithm. Moreover, it is shown that even in a non-linear framework the reduced-order models converge to the finite element solution as the number of modes included in the models increases. Considering the fixed-interface method of Craig-Bampton (CB) and the free-interface method of Craig-Chang-Martinez (CCM), it is shown that a method with fast displacement convergence may be less efficient in terms of motion convergence.

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