scholarly journals A Prediction Method with Altering Equivalent Stiffness for Damping Evaluation of Shrouded Bladed Disk Dynamic Systems

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 413
Author(s):  
Shimin Gao ◽  
Yanrong Wang ◽  
Zhiwei Sun ◽  
Siyuan Chen
Keyword(s):  
Contact Surface ◽  
Contact Stiffness ◽  
Damping Ratio ◽  
Characteristic Curve ◽  
Prediction Method ◽  
Blade Vibration ◽  
Stick Slip ◽  
Bladed Disk ◽  
Damping Characteristics ◽  
Vibration Stress

In turbomachinery bladed disks are typical cyclic symmetric structures where high-cycle fatigue of the blades can easily occur. Increasing the shroud structure is an effective blade vibration reduction method using the dry friction of the shroud contact surface to dissipate vibration energy. During one vibration cycle of the blade, the contact surface of the shroud may have one or several states of stick, slip, and separation due to the different amplitude of blade, which affects not only the damping, but also the stiffness of the system. This paper proposes a method to analyze the damping characteristics of blades with shroud considering the change of equivalent contact stiffness of the shroud by using the finite element method. With a 2D contact model, this method calculates the equivalent damping and obtains the damping characteristic curve to evaluate the damping of shroud. During the design phase, the objective is that when resonance occurs, the shroud can provide the optimal damping ratio under the allowable vibration stress of the blade. The parameter sensitivity of the damping characteristic for one bladed disk with parallel shroud is investigated. It is shown that vibration phase angle, contact stiffness, contact force, friction coefficient significantly influence the damping characteristics.

An Energy Method for Assessing the Damping of Turbine Blade Underplatform Damper and Forced Response Verification

2020 ◽  
Author(s):  
Shimin Gao ◽  
Yanrong Wang ◽  
Zhiwei Sun
Keyword(s):  
Energy Method ◽  
Gas Turbines ◽  
Contact Stiffness ◽  
Damping Ratio ◽  
Characteristic Curve ◽  
Turbine Blades ◽  
Time Integration ◽  
Forced Response ◽  
Optimal Damping ◽  
Vibration Stress

Abstract Rotating turbine blades in aircraft gas turbines are subject to high loads which can result in high cycle fatigue (HCF) failure. In order to reduce the vibration of blades, underplatform dampers are widely used to increase the damping by dry friction dissipating the vibration energy. This paper proposes an energy method (EM) for assessing the damping effect of underplatform dampers with the contacts of one cylinder and one flat without calculating the forced response. In this method the characteristic curve of the damping ratio of the damper on the vibration stress of the blade is used to design the damper. The design objective is that the damper can provide an optimal damping ratio on a given range of vibration stress if resonance occurs. This paper proposes a method for calculating the response and the performance plot based on the above characteristic curve to compare with Direct Time Integration (DTI). The effects of parameters such as contact stiffness, modal data and rotation speed, friction coefficient, damper mass on the damping ratio characteristics are analyzed. Based on the allowable vibration stress of the blade, the design process of the underplatform dampers using damping ratio characteristic curve is given. The proposed method is suitable and efficient for situations where the presence of the damper does not greatly affect the mode shape of the blade.

Analysis of Beam-Like Structures With Displacement-Dependent Friction Forces: Part I — Single-Degree-of-Freedom Model

1995 ◽  
Author(s):  
Wayne E. Whiteman ◽  
Aldo A. Ferri
Keyword(s):  
Dry Friction ◽  
Damping Ratio ◽  
Strong Dependence ◽  
Time Integration ◽  
Single Mode ◽  
Stick Slip ◽  
Friction Forces ◽  
Equivalent Damping ◽  
Damping Characteristics ◽  
Parameter Values

Abstract The dynamic behavior of a beam-like structure undergoing transverse vibration and subjected to a displacement-dependent dry friction force is examined. In Part I, the beam is modeled by a single mode while Part II considers multi-mode representations. The displacement dependence in each case is caused by a ramp configuration that allows the normal force across the sliding interface to increase linearly with slip displacement. The system is studied first by using first-order harmonic balance and then by using a time integration method. The stick-slip behavior of the system is also studied. Even though the only source of damping is dry friction, the system is seen to exhibit “viscous-like” damping characteristics. A strong dependence of the equivalent natural frequency and damping ratio on the displacement amplitude is an interesting result. It is shown that for a given set of parameter values, an optimal ramp angle exists that maximizes the equivalent damping ratio. The appearance of two dynamic response solutions at certain system and forcing parameter values is also seen. Results suggest that the overall characteristics of mechanical systems may be improved by properly configuring frictional interfaces to allow normal forces to vary with displacement.

Multiple Solutions in an Amplitude Limited Jeffcott Rotor Including Rubbing and Stick-Slip Effect

2005 ◽  
Author(s):  
Jan-Olov Aidanpa¨a¨
Keyword(s):  
Bifurcation Diagram ◽  
Contact Stiffness ◽  
Damping Ratio ◽  
Slip Effect ◽  
Chaotic Motions ◽  
Stick Slip ◽  
Diagram Method ◽  
Machine Failure ◽  
Jeffcott Rotor ◽  
Stable Solutions

The non-linear behaviour of rub-impact rotors have been studied in several papers. In such systems rich dynamics have been found together with the coexistence of solutions within some specific parameter ranges. In this paper an attempt is made to find all stable solutions for an amplitude limited Jeffcott rotor including rubbing and stick-slip effect. The recently suggested “multi bifurcation diagram method” is used to find and extract stable sets of bifurcation diagrams. A system is chosen where the linear stationary amplitude only exceeds the clearance in a narrow region near the natural frequency. Therefore large regions in frequency are expected to have only the linear stationary response. The results show that it is only for very low frequencies that one single solution exists. Even though periodic motions are dominant, there exist large ranges in frequency with quasi-periodic or chaotic motions. For the studied cases, three coexisting stable solutions are most common. In one case as many as four stable solutions was found to coexist. For rotors with large clearances (no impacts necessary) it is still possible to find several coexisting motions. For all cases the stick motion is the most severe one with large amplitudes and high backward whirl frequencies. In real situations the consequence of this stick motion is machine failure. These high amplitude motions were found to be stable over large frequency ranges. From the stability analysis it was found that this rolling motion can be avoided by low spin speed, low contact stiffness, low coefficient of friction, small ratio of disc radius/clearance or high damping ratio. In a design situation the parameters are seldom known with high accuracy. Therefore, it is of interest to know all solutions for parameter intervals. The multi-bifurcation diagram can be used in such situations to design a robust machine or at least be prepared for unwanted dynamics.

Dynamic Response of Two-Disk Systems With Friction and Misalignment

1998 ◽  
Author(s):  
Ahmed Anabtawi ◽  
Kambiz Farhang
Keyword(s):  
Mathematical Model ◽  
Dynamic Response ◽  
Contact Stiffness ◽  
Stick Slip ◽  
Torsional Response ◽  
Damping Characteristics ◽  
Disk Friction ◽  
Stiffness And Damping ◽  
The Mathematical Model ◽  
Friction Induced Vibration

Abstract Friction induced vibration and noise pose one of the most challenging problems. The complexity of the friction system arises due to the nonlinear nature of friction phenomena and that of contact stiffness and damping. This paper presents a mathematical model for studying the dynamic response of two-disk friction system in the presence of misalignment. The contact stiffness and damping characteristics of the system are represented in the axial as well as the torsional directions. In addition, the axial and torsional responses of the system are coupled by assuming dependency between the torsional response and the normal force between the two disks. Using the mathematical model, various scenarios are examined to study the effect of misalignment. These include cases of symmetric and asymmetric actuation forces as well as forces applied at unequal actuation times. The results suggest that asymmetry in actuation forces has negligible effect on stick-slip behavior of the system.

scholarly journals Predicting drug–target interactions Based on the Ensemble Models of Multiple Feature Pairs

2021 ◽  
Vol 22 (12) ◽  
pp. 6598
Author(s):  
Cheng Wang ◽  
Jun Zhang ◽  
Peng Chen ◽  
Bing Wang
Keyword(s):  
Drug Target ◽  
Essential Feature ◽  
Characteristic Curve ◽  
Prediction Method ◽  
New Drugs ◽  
Good Prediction ◽  
Ensemble Model ◽  
Test Set ◽  
Multiple Feature ◽  
Validation Set

Backgroud: The prediction of drug–target interactions (DTIs) is of great significance in drug development. It is time-consuming and expensive in traditional experimental methods. Machine learning can reduce the cost of prediction and is limited by the characteristics of imbalanced datasets and problems of essential feature selection. Methods: The prediction method based on the Ensemble model of Multiple Feature Pairs (Ensemble-MFP) is introduced. Firstly, three negative sets are generated according to the Euclidean distance of three feature pairs. Then, the negative samples of the validation set/test set are randomly selected from the union set of the three negative sets in the validation set/test set. At the same time, the ensemble model with weight is optimized and applied to the test set. Results: The area under the receiver operating characteristic curve (area under ROC, AUC) in three out of four sub-datasets in gold standard datasets was more than 94.0% in the prediction of new drugs. The effectiveness of the proposed method is also shown with the comparison of state-of-the-art methods and demonstration of predicted drug–target pairs. Conclusion: The Ensemble-MFP can weigh the existing feature pairs and has a good prediction effect for general prediction on new drugs.

Study on the Prediction Method of Tunnel Surrounding Rock Pressure Based on the Theory of Progressive Destruction

2012 ◽  
Vol 446-449 ◽  
pp. 1432-1436
Author(s):  
Suo Wang
Keyword(s):  
Rock Pressure ◽  
Characteristic Curve ◽  
Prediction Method ◽  
Surrounding Rock ◽  
Progressive Damage ◽  
Tunnel Excavation ◽  
Practical Engineering ◽  
Surrounding Rock Pressure ◽  
The Relationship ◽  
Rock Parameters

In order to predict tunnel surrounding rock pressure, this paper puts forward a series of dynamic numerical simulative model on the tunnel excavation. According to the change of rock damage in the construction program, it adjusts dynamically the mechanical material parameters of surrounding rock. So the model achieves the purpose which is controlling and simulating the process of tunnel progressive damage. In accordance with the numerical simulative results, it analyzes the relationship between the rock parameters with the plastic strain, radial displacement. Then this paper proposes a prediction method of tunnel surrounding rock pressure based on the theory of the progressive damage and method of characteristic curve. Finally, it compares the pressure on the numerical simulative models with on the site date, and it proves that the prediction method has practical engineering value.

scholarly journals Improved Reliability of Bladed Disks due to Friction Dampers

1997 ◽  
Author(s):  
Walter Sextro ◽  
Karl Popp ◽  
Ivo Wolter
Keyword(s):  
Dry Friction ◽  
Three Dimensional ◽  
Line Contact ◽  
Two Dimensional ◽  
Centrifugal Forces ◽  
Friction Damper ◽  
Blade Vibration ◽  
Friction Dampers ◽  
Bladed Disk ◽  
Bladed Disk Assembly

Friction dampers are installed underneath the blade platforms to improve the reliability. Because of centrifugal forces the dampers are pressed onto the platforms. Due to dry friction and the relative motion between blades and dampers, energy is dissipated, which results in a reduction of blade vibration amplitudes. The geometry of the contact is in many cases like a Hertzian line contact. A three-dimensional motion of the blades results in a two-dimensional motion of one contact line of the friction dampers in the contact plane. An experiment with one friction damper between two blades is used to verify the two-dimensional contact model including microslip. By optimizing the friction dampers masses, the best damping effects are obtained. Finally, different methods are shown to calculate the envelope of a three-dimensional response of a detuned bladed disk assembly (V84.3-4th-stage turbine blade) with friction dampers.

Preparation and Vibration Damping Characteristics of Wide Frequency Domain PVMQ/IIR Foam Materials

2012 ◽  
Vol 538-541 ◽  
pp. 2298-2303
Author(s):  
Shi Kai Luo ◽  
Guo Fang Ding ◽  
Jing Li Li ◽  
Yan Song Sha ◽  
Qing Min Cheng ◽  
...  
Keyword(s):  
Frequency Domain ◽  
Wide Temperature Range ◽  
Damping Ratio ◽  
Vibration Damping ◽  
Simple Equation ◽  
Structural Damping ◽  
Damping Characteristics ◽  
Damping Materials ◽  
Foaming Technology ◽  
Isoprene Rubber

In this paper, we prepared foaming silicon rubber (PVMQ) /isobutylene-isoprene rubber (IIR) composites with chemical foaming technology. The DMA tests results showed that these foaming materials have effective damping characteristics in a wide temperature range. With the special vibrator, we found that the PVMQ/IIR foams that we prepared were the damping materials which has wide frequency domain, because they can keep high damping ratio in a wide frequency domain. When the preloading was between 1.0 mm and 1.7 mm, the structural damping did not change obviously. According to tests, we found that the damping ratio of these foams was fit to the simple equation .

scholarly journals Mistuning Effects on the Nonlinear Friction Saturation of Flutter Vibration Amplitude

2020 ◽  
Author(s):  
Carlos Martel ◽  
Salvador Rodríguez
Keyword(s):  
Vibration Amplitude ◽  
Gas Flow ◽  
Travelling Waves ◽  
Computational Cost ◽  
Travelling Wave ◽  
Nonlinear Friction ◽  
Blade Vibration ◽  
Bladed Disk ◽  
Spring System ◽  
Mass Spring

Abstract The blade vibration level of an aerodynamically unstable rotor is a quantity of crucial importance to correctly estimate the blade fatigue life. This amplitude is the result of the balance between the energy pumped into the blades by the gas flow, and the nonlinear dissipation at the blade-disk contact interfaces. In a tuned configuration, the blade displacements can be described as a travelling wave consisting of one fundamental nodal diameter and frequency and its higher harmonics, and the problem can be reduced to the computation of a time periodic solution in just one sector. This simplification is no longer valid for a mistuned bladed disk. The resulting nonlinear vibration of the mistuned system is a combination of several travelling waves with different number of nodal diameters, coupled through mistuning. In this case, the complete bladed disk has to be considered, which requires an extremely high computational cost, and, for this reason, reduced order models (ROM) are required to analyze this situation. In this work, we use a 3 DOF/sector mass-spring system to describe the nonlinear friction saturation of the flutter vibration amplitude of a realistic mistuned bladed disk. The convergence of the solution of the mass-spring system is still quite slow because of the presence of many unstable modes with very similar growth rates. In order to speed-up the simulations a simpler asymptotic ROM is derived from the mass-spring model, which allows for much faster integration times. The simulations of the asymptotic ROM are compared with the measurements obtained in the European project FUTURE, where an aerodynamically unstable LPT rotor was tested with different intentional mistuning patterns.

Enhancement of vibration characteristics in filament wound FRP composite shafts using nitinol wires

2018 ◽  
Vol 47 (5) ◽  
pp. 377-385 ◽  
Author(s):  
Kannan Murugesan ◽  
Kalaichelvan K. ◽  
M.P. Jenarthanan ◽  
Sornakumar T.
Keyword(s):  
Natural Frequency ◽  
Damping Ratio ◽  
Filament Winding ◽  
Fiber Reinforced ◽  
Content Type ◽  
Fiber Reinforced Plastic ◽  
Damping Characteristics ◽  
Filament Wound ◽  
Reinforced Plastic ◽  
Hollow Shafts

Purpose The purpose of this paper is to investigate the use of embedded Shape Memory Alloy (SMA) nitinol wire for the enhancement of vibration and damping characteristics of filament-wound fiber-reinforced plastic composite hollow shafts. Design/methodology/approach The plain Glass Fiber-Reinforced Plastic (GFRP) and plain Carbon Fiber-Reinforced Plastic (CFRP) hollow shafts were manufactured by filament winding technique. Experimental modal analysis was conducted for plain hollow shafts of C1045 steel, GFRP and CFRP by subjecting them to flexural vibrations as per ASTM standard C747, with both ends clamped (C-C) end condition to investigate their vibration and damping behavior in terms of first natural frequency, damping time and damping ratio. Nitinol wires pre-stressed at various pre-strains (2, 4 and 6 per cent) were embedded with CFRP hollow shafts following same manufacturing technique, and similar experimental modal analysis was carried out by activating nitinol wires. The first natural frequencies of all the shaft materials were also predicted theoretically and compared with experimental measurements. Findings Among the three materials C1045 steel, plain GFRP and plain CFRP, the vibration and damping behavior were found to be the best for plain CFRP. Hence, CFRP shafts were considered for further improvement by embedding nitinol wires at pre-stressed condition. For CFRP shafts embedded with nitinol wires, the damping time decreased; and damping ratio and first natural frequency increased with increase in percentage of pre-strain. In comparison with plain CFRP, 7 per cent increase in first natural frequency and 100 per cent increase in damping ratio were observed for nitinol embedded CFRP shafts with 6 per cent pre-strain. Theoretical predictions of the first natural frequencies agree well with the experimental results for all the shaft materials. Originality/value The effect of nitinol on vibration and damping characteristics of filament wound hollow CFRP composite shafts with different pre-strains has not been studied extensively by the previous researchers. This paper addresses the effect of embedded nitinol wires pre-stressed at three varied pre-strains, that is, 2, 4 and 6 per cent on the vibration and damping characteristics of composite hollow CFRP shafts manufactured by filament winding technique.

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