Active detection of small imperfections in structures with cyclic symmetry

2020 ◽  
pp. 1-28
Author(s):  
Eyal Baruch ◽  
Yoav Vered ◽  
Harel Plat ◽  
Izhak Bucher
Keyword(s):  
Classical System ◽  
Experimental System ◽  
Mode Shapes ◽  
Cyclic Symmetry ◽  
Small Deviations ◽  
Acoustic Resonators ◽  
Cyclic Symmetric ◽  
Gear Wheels ◽  
Low Sensitivity ◽  
Active Detection

Abstract Structures possessing cyclic symmetry such as turbine bladed disks, ultrasonic motors, and toothed gear wheels can experience elevated vibration levels when small deviations from circumferential periodicity exist. Detection of these perturbations via classical system identification approaches is time-consuming, indirect, and exhibits low sensitivity to defects and are affected by measurement noise. The present work utilizes low-level forces that automatically lock onto a weighted rotating projection of the system modes at resonance frequency to enhance the detectability of small structural imperfections. The spatial localization of defects is exploited to identify multiple, localized, isolated defects' locations. The defects' severities are estimated based on the deviation from the circular structure's analytical mode shapes. Fast and enhanced precision of defect identification is obtained by employing the modal filtered Autoresonance technique. To validate the presented method, an experimental system consisting of a ring of coupled Helmholtz acoustic resonators was developed. Experimental results show good agreement with numerical simulations, verifying the method's capabilities to identify the location and severity of multiple defects. Thus, implementation of the suggested method provides fast and precise structural health monitoring of cyclic symmetric systems.

Study of the Effect of Multi-Stage Cyclic Symmetric Modeling on the Natural Frequencies of Bladed Disks of an Aero Engine Rotor System

2015 ◽  
Author(s):  
Siva Srinivas ◽  
Hardik Roy ◽  
Esakki Muthu Shanmugam
Keyword(s):  
Modal Analysis ◽  
Gas Turbine ◽  
Natural Frequencies ◽  
Rotor System ◽  
Mode Shapes ◽  
Computational Time ◽  
Cyclic Symmetry ◽  
Multi Stage ◽  
Cyclic Symmetric ◽  
Multiple Stages

Majority of the failures in Gas turbine Blades are caused by High Cycle Fatigue induced by the vibratory stresses in the rotor blades. The first step in blade design is the prevention of coincidence of natural frequencies of the blades with the frequencies of the fluctuating Gas loads. The forcing frequency is a function of number of upstream and downstream stator blades, and rotational speed. In gas turbines with multiple stages, modal analysis of bladed-disks is individually performed i.e. stage by stage. As the structure is rotationally periodic, cyclic symmetric boundary conditions can be utilized, over 360 degree modeling. The advantage of cyclic symmetry over full model lies in reduced degrees of freedom and hence reduced computational time. In most of the available tools, cyclic symmetry for modal analysis is limited to single stage. As such there is no provision to model and analyze multiple stages at the same time. This leads to inaccurate values of natural frequencies as the flexibility introduced by the adjacent stages is not being taken into consideration. An alternative to this is full 3D modeling and analysis of all the combined stages. Bladh et al. (2003) [1] have shown that interstage coupling can significantly affect the dynamics of the multi-stage assembly and in some cases lead to an underestimation of vibratory levels. Sokolowski et al [2] studied the influence of inclusion of shaft in the model on the natural frequencies and mode shapes of the shrouded bladed discs up to four nodal diameters for first two frequency series (mode shapes). Rzadkowski and Drewczynski (2006) [3] have used full 360 degrees models to study the free and forced dynamics of multi-stage systems. However this method is avoided as the computational cost is prohibitive. Multi stage cyclic symmetry overcomes this obstacle in which each stage is cyclically modeled and an inter-stage coupling is introduced between adjacent stages. The advantage of multi stage cyclic symmetry lies in the significant reduction in the number of elements and therefore computational time. Laxalde et al. (2007) [4] were the first to come up with the method of dynamic analysis of turbo machinery rotors with multi stage cyclic symmetry using interstage coupling. They considered an example of two-stage High Pressure compressor. The results were validated against a complete 360 degrees reference model. Forced response analysis of rotor stages to fluctuating gas loads with and without interstage coupling definition was also presented and compared. In the present work a complete Gas Turbine rotor system with multiple stages of Compressor, Shaft and Turbine were analyzed together.

Dynamic Analysis of a Turbocharger Centrifugal Compressor Impeller

1991 ◽  
Author(s):  
V. Ramamurti ◽  
D. A. Subramani ◽  
K. Sridhara
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Centrifugal Compressor ◽  
Element Model ◽  
Simplified Model ◽  
Cyclic Symmetry ◽  
Compressor Impeller ◽  
Cyclic Symmetric ◽  
The Finite Element Model

Abstract Stress analysis and determination of eigen pairs of a typical turbocharger compressor impeller have been carried out using the concept of cyclic symmetry. A simplified model treating the blade and the hub as isolated elements has also been attempted. The limitations of the simplified model have been brought out. The results of the finite element model using the cyclic symmetric approach have been discussed.

Experimental Study of Blade Vibration in Centrifugal Compressors

2011 ◽  
Author(s):  
Andrew H. Lerche ◽  
J. Jeffrey Moore ◽  
Timothy C. Allison
Keyword(s):  
High Cycle Fatigue ◽  
Axial Flow ◽  
Modal Testing ◽  
Mode Shapes ◽  
Cyclic Symmetry ◽  
Centrifugal Compressors ◽  
Compressor Blades ◽  
Blade Vibration ◽  
Phase Cancellation ◽  
Blade Failure

Blade vibration in turbomachinery is a common problem that can lead to blade failure by high cycle fatigue. Although much research has been performed on axial flow turbomachinery, little has been published for radial flow machines such as centrifugal compressors and radial inflow turbines. This work develops a test rig that measures the resonant vibration of centrifugal compressor blades. The blade vibrations are caused by the wakes coming from the inlet guide vanes. These vibrations are measured using blade mounted strain gauges during a rotating test. The total damping of the blade response from the rotating test is compared to the damping from the modal testing performed on the impeller. The mode shapes of the response and possible effects of mistuning are also discussed. The results show that mistuning can affect the phase cancellation which one would expect to see on a system with perfect cyclic symmetry.

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.

Experimental Verification of Ground-Based Response of a Spinning, Cyclic Symmetric, Rotor Assembled to a Flexible Stationary Housing via Multiple Bearings

2014 ◽  
Author(s):  
W. C. Tai ◽  
I. Y. Shen
Keyword(s):  
Laser Doppler Vibrometer ◽  
Nodal Line ◽  
Spindle Motor ◽  
Housing System ◽  
Mode Shapes ◽  
Coupled Modes ◽  
Spin Speed ◽  
Resonance Frequencies ◽  
Symmetric Rotor ◽  
Cyclic Symmetric

This paper is to present an experimental study that measures ground-based response of a spinning, cyclic, symmetric rotor-bearing-housing system. In particular, the study focuses on rotor-housing coupled modes that are significantly dominated by housing deformation. In the experiments, a ball-bearing spindle motor, carrying a disk with four evenly spaced slots (i.e., the rotor), is mounted onto a stationary housing. The housing is a square plate supported with steel spacers at four corners and fixed to the ground. Two different ways are used to excite the rotor-housing system to measure frequency response functions (FRFs). One is to use an automatic hammer tapping at the disk, and the other is to use a piezoelectric actuator attached to the housing. Vibration of the rotor and housing is measured via a laser Doppler vibrometer and a capacitance probe. The experiments consist of two parts. The first part is to obtain FRFs when the rotor is not spinning. The measured FRFs reveal two rotor-housing coupled modes dominated by the housing. Their mode shapes are characterized by one nodal line in housing and one nodal diameter in the rotor. The second part is to obtain waterfall plots when the rotor is spinning at various speeds. The waterfall plots show that the housing dominant modes split into primary branches and secondary branches as the spin speed varies. The primary branches almost do not change with respect to the spin speed. In contrast, the secondary branches evolve into forward and backward branches. Moreover, their resonance frequencies increase and decrease at four times of the spin speed. The measured results agree well with the predictions found in the authors’ previous theoretical study [1].

Hydro Francis Runner Stability and Forced Response Calculations

2019 ◽  
Author(s):  
Charles Seeley ◽  
Sunil Patil ◽  
Andy Madden ◽  
Stuart Connell ◽  
Gwenael Hauet ◽  
...  
Keyword(s):  
Large Scale ◽  
Forced Response ◽  
Operating Conditions ◽  
Mode Shapes ◽  
Symmetric Model ◽  
Validation Data ◽  
Fea Model ◽  
Forcing Function ◽  
Cyclic Symmetric ◽  
Work Done

Abstract Hydroelectric power generation accounts for 7% of the total world electric energy production. Francis turbines are often employed in large-scale hydro projects and represent 60% of the total installed base. Outputs up to 800 MW are available and efficiencies of 95% are common. Cost, performance, and design cycle time are factors that continue to drive new designs as well as retrofits. This motivates the development of more sophisticated analysis tools to better assess runner performance earlier in the design phase. The focus of this paper is to demonstrate high fidelity and time-efficient runner damping and forced response calculations based on one-way fluid-structure interaction (FSI) using loosely coupled commercial finite element analysis (FEA) and computational fluid dynamics (CFD) codes. The runner damping is evaluated based on the work done by the fluid on the runner. The calculation of the work first involves determining the runner mode shapes and natural frequencies using a cyclic symmetric FEA model with structural elements to represent the runner hardware, and acoustic fluid elements to represent the mass loading effect of the fluid. The mode shapes are then used in a transient CFD calculation to determine the damping which represents the work done by the fluid on the runner. Positive damping represents stability from flutter perspective while negative damping represents unstable operating conditions. A transient CFD calculation was performed on a runner to obtain engine order forcing function from upstream stationary vanes. This unsteady forcing function was mapped to the FEA model. Care is taken to account for the proper inter-blade phase angle on the cyclic symmetric model. The hydraulic damping from flutter calculations was also provided as input to the forced response. The forced response is then determined using this equivalent proportional damping and modal superposition of the FEA model that includes both the structural and acoustic elements. Results of the developed analysis procedure are presented based on the Tokke runner, that has been the basis of several studies through the Norwegian HydroPower Center. Unique features of the workflow and modeling approaches are discussed in detail. Benefits and challenges for both the FEA model and the CFD model are discussed. The importance of the hydraulic damping, that is traditionally ignored in previous analysis is discussed as well. No validation data is available for the forced response, so this paper is focused on the methodology for the calculations.

Ground-Based Vibration Response of a Spinning, Cyclic, Symmetric Rotor With Gyroscopic and Centrifugal Softening Effects

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Hyunchul Kim ◽  
I. Y. Shen
Keyword(s):  
Theoretical Analysis ◽  
Fourier Expansion ◽  
Vibration Response ◽  
Modal Testing ◽  
Mode Shapes ◽  
Stationary Mode ◽  
Spinning Disk ◽  
Phase Index ◽  
Symmetric Rotor ◽  
Cyclic Symmetric

This paper is to study ground-based vibration response of a spinning, cyclic, symmetric rotor through a theoretical analysis and an experimental study. The theoretical analysis consists of three steps. The first step is to analyze the vibration characteristics of a stationary, cyclic, symmetric rotor with N identical substructures. For each vibration mode, we identify a phase index n and derive a Fourier expansion of the mode shape in terms of the phase index n. The second step is to predict the rotor-based vibration response of the spinning, cyclic, symmetric rotor based on the Fourier expansion of the mode shapes and the phase indices. The rotor-based formulation includes gyroscopic and centrifugal softening terms. Moreover, rotor-based response of repeated modes and distinct modes is obtained analytically. The third step is to transform the rotor-based response to ground-based response using the Fourier expansion of the stationary mode shapes. The theoretical analysis leads to the following conclusions. First, gyroscopic effects have no significant effects on distinct modes. Second, the presence of gyroscopic and centrifugal softening effects causes the repeated modes to split into two modes with distinct frequencies ω1 and ω2 in the rotor-based coordinates. Third, the transformation to ground-based observers leads to primary and secondary frequency components. In general, the ground-based response presents frequency branches in the Campbell diagram at ω1±kω3 and ω2±kω3, where k is phase index n plus an integer multiple of cyclic symmetry N. When the gyroscopic effect is significantly greater than the centrifugal softening effect, two of the four frequency branches vanish. The remaining frequency branches take the form of either ω1+kω3 and ω2−kω3 or ω1−kω3 and ω2+kω3. To verify these predictions, we also conduct a modal testing on a spinning disk carrying four pairs of brackets evenly spaced in the circumferential direction with ground-based excitations and responses. The disk-bracket system is mounted on a high-speed, air-bearing spindle. An automatic hammer excites the spinning disk-bracket system and a laser Doppler vibrometer measures its vibration response. A spectrum analyzer processes the hammer excitation force and the vibrometer measurements to obtain waterfall plots at various spin speeds. The measured primary and secondary frequency branches from the waterfall plots agree well with those predicted analytically.

A Parametric Sonic Crystal Modal Analysis Using Finite Element Modeling

2004 ◽  
Author(s):  
Alan C. Leung ◽  
Peter Matic ◽  
Pier Paolo Delsanto ◽  
Martin Hirsekorn
Keyword(s):  
Finite Element ◽  
Single Cell ◽  
Matrix Material ◽  
Mode Shapes ◽  
Property Variation ◽  
Acoustic Damping ◽  
Acoustic Resonators ◽  
Potential Applications ◽  
Sonic Crystal ◽  
Sonic Crystals

Sonic crystals are typically materials with millimeter scale arrays of acoustic resonators embedded in a matrix material. They provide sound attenuation in acoustic band gaps at frequencies approximately two orders of magnitude lower than those predicted by Bragg’s theory of reflection. There are many potential applications of sonic crystals as filters and frequency selective acoustic damping devices. Performance characteristics of single-cell and double cell based sonic crystal structures were computationally evaluated using finite element methods. In this work, the sonic crystal consisted of cylinder inclusions encased in a soft polymer coating and embedded in a block of epoxy matrix material. Parametric studies were performed to evaluate the effects of material properties of the inclusion, coating and matrix. Mode shapes were determined. A preliminary comparison with Local Interaction Simulation Approach (LISA) is presented. The influence of material property variation, without changing geometric features, on single-cell and double-cell sonic crystal performance is discussed.

scholarly journals Photophoretic spectroscopy in atmospheric chemistry – high-sensitivity measurements of light absorption by a single particle

2020 ◽  
Vol 13 (6) ◽  
pp. 3191-3203
Author(s):  
Nir Bluvshtein ◽  
Ulrich K. Krieger ◽  
Thomas Peter
Keyword(s):  
Atmospheric Chemistry ◽  
Single Particle ◽  
Light Absorption ◽  
Radiative Forcing ◽  
Experimental System ◽  
High Sensitivity ◽  
Atmospheric Conditions ◽  
Brown Carbon ◽  
Radiative Balance ◽  
Low Sensitivity

Abstract. Light-absorbing organic atmospheric particles, termed brown carbon, undergo chemical and photochemical aging processes during their lifetime in the atmosphere. The role these particles play in the global radiative balance and in the climate system is still uncertain. To better quantify their radiative forcing due to aerosol–radiation interactions, we need to improve process-level understanding of aging processes, which lead to either “browning” or “bleaching” of organic aerosols. Currently available laboratory techniques aim to simulate atmospheric aerosol aging and measure the evolving light absorption, but they suffer from low sensitivity and precision. This study describes the use of electrodynamic balance photophoretic spectroscopy (EDB-PPS) for high-sensitivity and high-precision measurements of light absorption by a single particle. We demonstrate the retrieval of the time-evolving imaginary part of the refractive index for a single levitated particle in the range of 10−4 to 10−5 with uncertainties of less than 25 % and 60 %, respectively. The experimental system is housed within an environmental chamber, in which aging processes can be simulated in realistic atmospheric conditions and lifetimes of days to weeks. This high level of sensitivity enables future studies to explore the major processes responsible for formation and degradation of brown carbon aerosols.

Analysis of Fabricated Gear Wheels Using Cyclic Symmetry in a PC Environment

1997 ◽  
Author(s):  
V. Ramamurti ◽  
A. Bhattacharya ◽  
S. Manjula
Keyword(s):  
Dynamic Behaviour ◽  
Gear Wheel ◽  
Computer Memory ◽  
Cyclic Symmetry ◽  
Heavy Duty ◽  
Eigen Value ◽  
Computer Aided Analysis ◽  
Computer Aided ◽  
Gear Wheels ◽  
Industrial Problem

Abstract A computer aided analysis of a heavy duty fabricated gear wheel is presented. The concept of CYCLIC SYMMETRY and the SKYLINE APPROACH are exploited to reduce the computer memory and time. Static and Eigen value analyses are conducted. This is followed by a Quasi Static analysis which gives an idea of the Dynamic behaviour of the gear wheel. The emphasis has been on the use of the PC for solving this industrial problem.

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