The Mechanism on Prediction of Transient Maximum Amplitude for Tuned and Mistuned Blisks

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Luohui Ouyang ◽  
Hai Shang ◽  
Hua Chen ◽  
Qingzhen Bi ◽  
Li-Min Zhu
Keyword(s):  
Damping Ratio ◽  
Maximum Amplitude ◽  
Element Model ◽  
Forced Response ◽  
Lumped Parameter Model ◽  
Fundamental Parameter ◽  
Reduced Order ◽  
Lumped Parameter ◽  
Engine Order ◽  
Acceleration And Deceleration

Abstract Blisks are subjected to frequent acceleration and deceleration, which leads to a transient forced response; however, there is limited understanding of this response. In this work, the mechanism on prediction of transient maximum amplitude is found. An analytical link is proposed between the transient maximum amplitude and a fundamental dimensionless parameter which combines the damping ratio, natural frequency, acceleration, and engine order of the system to reveal the mechanism of the transient maximum amplitude. Therefore, the transient maximum amplitudes of tuned and mistuned blisks are predicted analytically. First, a lumped parameter model is used to study the mechanism of the transient maximum amplitude for a tuned blisk, and an approximated analytical expression is derived between the fundamental parameter and the transient amplification factor of a 1DOF (degree-of-freedom) model. The relationship is also applicable to a reduced order, tuned finite element model (FEM). Second, the mechanism of the transient response for a mistuned blisk is studied in the decoupled modal space of the blisk, based on the 1DOF transient relationship. The transient maximum amplitude in a reduced order, mistuned FEM is predicted. Two lumped parameter models and a FEM are employed to validate the prediction.

Effects of Harmonic Intentional Mistuning on the Free Response of Bladed Disks

1999 ◽  
Author(s):  
Michael E. Brewer ◽  
Matthew P. Castanier ◽  
Christophe Pierre
Keyword(s):  
Forced Response ◽  
Lumped Parameter Model ◽  
Free Response ◽  
Bladed Disks ◽  
Nodal Diameter ◽  
Bladed Disk ◽  
Lumped Parameter ◽  
Engine Order ◽  
Bladed Disk Assembly ◽  
Random Mistuning

Abstract In this paper, the free response of bladed disks with intentional mistuning is considered in detail. A simple lumped-parameter model of a bladed disk is employed. Intentional mistuning is included by applying a sinusoidal variation to the nominal blade stiffnesses. It is shown that if the intentional mistuning harmonic number and the number of blades have a common integer factor greater than one, then the eigenvalue problem reduces to a set of smaller problems. It is found that the ratio of intentional mistuning strength to the interblade coupling strength is a key parameter for the free response. As this ratio increases, the modes become localized. More importantly, the modes of the intentionally mistuned system have several non-zero nodal diameter components, in contrast to the tuned system which has pure nodal diameter modes. Furthermore, if only random mistuning is present, each mode of the bladed disk assembly still retains a strong nodal diameter component. However, the modes of the system with intentional mistuning and random mistuning tend to have more evenly distributed nodal diameter components. This shows why intentional mistuning can be effective in reducing the maximum blade forced response for engine order excitation.

scholarly journals Friction Damper Optimisation: Simulation of Rainbow Tests

1999 ◽  
Author(s):  
Kenan Y. Sanliturk ◽  
David J. Ewins ◽  
Robert Elliott ◽  
Jeff S. Green
Keyword(s):  
Harmonic Balance Method ◽  
Lumped Parameter Model ◽  
Friction Damper ◽  
Blade Vibration ◽  
Friction Dampers ◽  
Lumped Parameter ◽  
Engine Order ◽  
Resonance Response ◽  
Theoretical Predictions ◽  
Different Characteristics

Friction dampers have been used to reduce turbine blade vibration levels for a considerable period of time. However, optimal design of these dampers has been quite difficult due both to a lack of adequate theoretical predictions and to difficulties in conducting reliable experiments. One of the difficulties of damper weight optimisation via the experimental route has been the inevitable effects of mistuning. Also, conducting separate experiments for different damper weights involves excessive cost. Therefore, current practice in the turbomachinery industry has been to conduct so-called ‘rainbow tests’ where friction dampers with different weights are placed between blades with a predefined configuration. However, it has been observed that some rainbow test results have been difficult to interpret and have been inconclusive for determining the optimum damper weight for a given bladed-disc assembly. A new method of analysis — a combination of Harmonic Balance Method and structural modification approaches — is presented in this paper for the analysis of structures with friction interfaces and the method is applied to search for qualitative answers about the so-called ‘rainbow tests’ in turbomachinery applications. A simple lumped-parameter model of a bladed-disc model was used and different damper weights were modelled using friction elements with different characteristics. Resonance response levels were obtained for bladed discs with various numbers of blades under various engine-order excitations. It was found that rainbow tests, where friction dampers with different weights are used on the same bladed-disc assembly, can be used to find the optimum damper weight if the mode of vibration concerned has weak blade-to-blade coupling (the case where the disc is almost rigid and blades vibrate almost independently from each other). Otherwise, it is very difficult to draw any reliable conclusion from such expensive experiments.

Nondestructive Evaluation of Parts With Degenerate Modes Using Pseudorepeated Roots

2004 ◽  
Vol 126 (3) ◽  
pp. 498-508 ◽  
Author(s):  
Brandon J. Jellison ◽  
Harold R. Kess ◽  
Douglas E. Adams ◽  
David C. Nelson
Keyword(s):  
Raw Materials ◽  
Element Model ◽  
Lumped Parameter Model ◽  
Mass Distributions ◽  
Lumped Parameter ◽  
Fabrication Procedure ◽  
Modes Of Vibration ◽  
Systemic Problems ◽  
Vibration Tests ◽  
Degenerate Modes

The modes of vibration of manufactured parts can be good indicators of the overall quality of the manufacturing process. That is, deviations in the modal frequencies or modal vectors of mechanical parts can help to identify outlier or systemic problems in the raw materials or fabrication procedure. A novel method for characterizing nonuniformities in homogeneous symmetric parts using pseudorepeated modal frequencies is discussed in this paper. It is demonstrated that the spacing between pseudorepeated roots in dominantly symmetric manufactured parts is a direct indicator of nonuniformities (i.e., inclusions, voids) in the stiffness or mass distributions. Smaller differences between split-peaks indicate less nonuniformity, and hence, higher quality parts. A simple fourth-order lumped parameter model is used to elaborate on this technique analytically, a representative finite element model is used to further this development, root locus techniques are used to study the sensitivity to nonuniformities, and acceleration response data from impact vibration tests on deep drawn hemispherical shells are used to verify the approach experimentally.

Geometric Mistuning Reduced-Order Model Development Utilizing Bayesian Surrogate Models for Component Mode Calculations

2019 ◽  
Vol 141 (10) ◽  
Author(s):  
Joseph A. Beck ◽  
Jeffrey M. Brown ◽  
Alex A. Kaszynski ◽  
Emily B. Carper ◽  
Daniel L. Gillaugh
Keyword(s):  
Periodic Structures ◽  
Model Development ◽  
Element Model ◽  
Forced Response ◽  
Mode Shapes ◽  
Order Model ◽  
Mode Localization ◽  
Reduced Order ◽  
Structural Periodicity ◽  
Computationally Intensive

AbstractIntegrally bladed rotors (IBRs) are meant to be rotationally periodic structures. However, unique variations in geometries and material properties from sector-to-sector, called mistuning, destroy the structural periodicity. This results in mode localization that can induce forced response levels greater than what is predicted with a tuned analysis. Furthermore, mistuning and mode localization are random processes that require stochastic treatments when analyzing the distribution of fleet responses. Generating this distribution can be computationally intensive when using the full finite element model (FEM). To overcome this expense, reduced-order models (ROMs) have been developed to accommodate fast calculations of mistuned forced response levels for a fleet of random IBRs. Usually, ROMs can be classified by two main families: frequency-based and geometry-based methods. Frequency-based ROMs assume mode shapes do not change due to mistuning. However, this assumption has been shown to cause errors that propagate to the fleet distribution. To circumvent these errors, geometry-based ROMs have been developed to provide accurate predictions. However, these methods require recalculating modal data during ROM formulations. This increases the computational expense in computing fleet distributions. A new geometry-based ROM is presented to reduce this cost. The developed ROM utilizes a Bayesian surrogate model in place of sector modal calculations required in ROM formulations. The method, surrogate modal analysis for geometry mistuning assessments (SMAGMA), will propagate uncertainties of the surrogate prediction to forced response. ROM accuracies are compared to the true forced response levels and results computed by a frequency-based ROM.

A Critical Examination of the Hysteresis in Wells Turbines Using CFD and Lumped Parameter Models

2019 ◽  
Author(s):  
T. Ghisu ◽  
F. Cambuli ◽  
P. Puddu ◽  
I. Virdis ◽  
M. Carta ◽  
...  
Keyword(s):  
Turbine Blades ◽  
Unsteady Aerodynamics ◽  
Lumped Parameter Model ◽  
Hysteretic Behavior ◽  
Critical Examination ◽  
Wells Turbine ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Acceleration And Deceleration ◽  
The Common

Abstract The hysteretic behavior of OWC-installed Wells turbines has been known for decades. The common explanation invokes the presence of unsteady aerodynamics due to the continuously varying incidence of the flow on the turbine blades. This phenomenon is neither new nor unique to Wells turbines, as an aerodynamic hysteresis is present in rapidly oscillating airfoils and wings, as well as in different types of turbomachinery, such as wind turbines and helicopter rotors, which share significant similarities with a Wells turbine. An important difference is the non-dimensional frequency: the hysteresis appears in oscillating airfoils only at frequencies orders of magnitude larger than the ones Wells turbines operate at. This work contains a reexamination of the phenomenon, using both CFD and a lumped parameter model, and shows how the aerodynamic hysteresis in Wells turbines is negligible, and how the often measured differences in performance between acceleration and deceleration are caused by the capacitive behavior of the OWC system.

Analysis of mistuned forced response in an axial high-pressure compressor rig with focus on Tyler–Sofrin modes

2019 ◽  
Vol 123 (1261) ◽  
pp. 356-377
Author(s):  
F. Figaschewsky ◽  
A. Kühhorn ◽  
B. Beirow ◽  
T. Giersch ◽  
S. Schrape
Keyword(s):  
Axial Compressor ◽  
Maximum Amplitude ◽  
Forced Response ◽  
Operating Conditions ◽  
Cfd Simulations ◽  
High Pressure Compressor ◽  
Engine Order ◽  
Stator Vane ◽  
Vibration Responses ◽  
The Impact

ABSTRACTThis paper aims at contributing to a better understanding of the effect of Tyler–Sofrin Modes (TSMs) on forced vibration responses by analysing a 4.5-stage research axial compressor rig. The first part starts with a brief review of the involved physical mechanisms and necessary prerequisites for the generation of TSMs in multistage engines. This review is supported by unsteady CFD simulations of a quasi 2D section of the studied engine. It is shown that the amplitude increasing effect due to mistuning can be further amplified by the presence of TSMs. Furthermore, the sensitivity with respect to the structural coupling of the blades and the damping as well as the shape of the expected envelope is analysed.The second part deals with the Rotor 2 blisk of the research compressor rig. The resonance of a higher blade mode with the engine order of the upstream stator is studied in two different flow conditions realised by different variable stator vane (VSV) schedules which allows to separate the influence of TSMs from the impact of mistuning. A subset of nominal system modes representation of the rotor is used to describe its mistuned vibration behaviour, and unsteady CFD simulations are used to characterise the present strength of the TSMs in the particular operating conditions. Measured maximum amplitude vs blade pattern and frequency response functions are compared against the predictions of the aeromechanical models in order to assess the strength of the TSMs as well as its influence on vibration levels.

scholarly journals The Development of a Tympanic Membrane Model and Probabilistic Dose-Response Risk Assessment of Rupture Because of Blast

2020 ◽  
Vol 185 (Supplement_1) ◽  
pp. 234-242
Author(s):  
Anthony E Iyoho ◽  
Kevin Ho ◽  
Philemon Chan
Keyword(s):  
Tympanic Membrane ◽  
Dose Response ◽  
Injury Risk ◽  
Element Model ◽  
Lumped Parameter Model ◽  
Unintended Effects ◽  
Response Curves ◽  
Membrane Rupture ◽  
Lumped Parameter ◽  
Dose Response Curves

ABSTRACT Introduction There is no dose-response model available for the assessment of the risk of tympanic membrane rupture (TMR), commonly known as eardrum rupture, from exposures to blast from nonlethal flashbangs, which can occur concurrently with temporary threshold shift. Therefore, the objective of this work was to develop a fast-running, lumped parameter model of the tympanic membrane (TM) with probabilistic dose-dependent prediction of injury risk. Materials and Methods The lumped parameter model was first benchmarked with a finite element model of the middle ear. To develop the dose-response curves, TMR data from a historic cadaver study were utilized. From these data, the binary probability response was constructed and logistic regression was applied to generate the respective dose-response curves at moderate and severe eardrum rupture severity. Results Hosmer-Lemeshow statistical and receiver operation characteristic analyses showed that maximum stored TM energy was the overall best dose metric or injury correlate when compared with total work and peak TM pressure. Conclusions Dose-response curves are needed for probabilistic risk assessments of unintended effects like TMR. For increased functionality, the lumped parameter model was packaged as a software library that predicts eardrum rupture for a given blast loading condition.

Geometric Mistuning Reduced-Order Models for Integrally Bladed Rotors With Mistuned Disk–Blade Boundaries

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Joseph A. Beck ◽  
Jeffrey M. Brown ◽  
Alex A. Kaszynski ◽  
Charles J. Cross ◽  
Joseph C. Slater
Keyword(s):  
Degrees Of Freedom ◽  
Principal Component ◽  
Element Model ◽  
Forced Response ◽  
Solid Model ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Small Areas ◽  
Eigen Analysis ◽  
Connection Type

New geometric mistuning modeling approaches for integrally bladed rotors (IBRs) are developed for incorporating geometric perturbations to a fundamental disk–blade sector, particularly the disk–blade boundary or connection. Reduced-order models (ROMs) are developed from a Craig–Bampton component mode synthesis (C–B CMS) framework that is further reduced by a truncated set of interface modes that are obtained from an Eigen-analysis of the C–B CMS constraint degrees of freedom (DOFs). An investigation into using a set of tuned interface modes and tuned constraint modes for model reduction is then performed, which offers significant computational savings for subsequent analyses. Two configurations of disk–blade connection mistuning are investigated: as-measured principal component (PC) deviations and random perturbations to the interblade spacing. Furthermore, the perturbation sizes are amplified to investigate the significance of incorporating mistuned disk–blade connections during solid model generation from optically scanned geometries. Free and forced response results are obtained for each ROM and each disk–blade connection type and compared to full finite element model (FEM) solutions. It is shown that the developed methods provide accurate results with a reduction in solution time compared to the full FEM. In addition, results indicate that the inclusion of a mistuned disk–blade connection deviations are small or conditions where large perturbations are localized to a small areas of the disk–blade connection.

Non-linear dynamic simulation of mechanical periodicity of end-diastolic volume of left ventricle under the influence of baroreflex

2006 ◽  
Vol 220 (3) ◽  
pp. 357-366 ◽  
Author(s):  
Q Wang ◽  
S Xu ◽  
D Chen ◽  
M Collins
Keyword(s):  
Left Ventricle ◽  
Vascular System ◽  
Element Model ◽  
Baroreceptor Reflex ◽  
Lumped Parameter Model ◽  
Linear Dynamic ◽  
End Diastolic Volume ◽  
Lumped Parameter ◽  
Non Linear ◽  
Mechanical Periodicity

Mechanical periodicity (MP) of the end-diastolic volume (EDV) of the left ventricle (LV) is closely associated with cardiovascular pathophysiology. On the basis of the Starling's law of the LV and Burattini and Gnudi's four-element model of the vascular system, and considering baroreceptor reflex, a non-linear dynamic lumped-parameter model is proposed. This simulates the MP phenomena of the EDV by solving a series of one-dimensional discrete non-linear dynamic equations. The results demonstrate that excessive deviations of some physiological parameters often induce MP - the unstable phenomena of EDV - and verify that the effects of baroreceptor reflex enhance the ability of the human physiological system to maintain stability.

Modeling the Microslip in the Flange Joint and Its Effect on the Dynamics of a Multistage Bladed Disk Assembly

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Christian M. Firrone ◽  
Giuseppe Battiato ◽  
Bogdan I. Epureanu
Keyword(s):  
Element Model ◽  
Forced Response ◽  
Flange Joint ◽  
Reduced Order ◽  
Bladed Disk ◽  
Simple Geometry ◽  
Bladed Disk Assembly ◽  
Joint Contact ◽  
Turbine Disks ◽  
Complex Architecture

The complex architecture of aircraft engines requires demanding computational efforts when the dynamic coupling of their components has to be predicted. For this reason, numerically efficient reduced-order models (ROM) have been developed with the aim of performing modal analyses and forced response computations on complex multistage assemblies being computationally fast. In this paper, the flange joint connecting two turbine disks of a multistage assembly is studied as a source of nonlinearities due to friction damping occurring at the joint contact interface. An analytic contact model is proposed to calculate the local microslip based on the different deformations that the two flanges in contact take during vibration. The model is first introduced using a simple geometry representing two flanges in contact, and then, it is applied to a reduced finite element model in order to calculate the nonlinear forced response.

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