scholarly journals Effects of Crack on Vibration Characteristics of Mistuned Rotated Blades

2017 ◽  
Vol 2017 ◽  
pp. 1-18 ◽  
Author(s):  
Hailong Xu ◽  
Zhongsheng Chen ◽  
Yongmin Yang ◽  
Limin Tao ◽  
Xuefeng Chen
Keyword(s):  
Natural Frequency ◽  
Vibration Amplitude ◽  
Crack Detection ◽  
Vibration Characteristics ◽  
Lumped Parameter Model ◽  
Crack Model ◽  
Breathing Crack ◽  
Vibration Localization ◽  
Lumped Parameter ◽  
Amplitude Increase

Rotated blades are key mechanical components in turbine and high cycle fatigues often induce blade cracks. Meanwhile, mistuning is inevitable in rotated blades, which often makes it much difficult to detect cracks. In order to solve this problem, it is important and necessary to study effects of crack on vibration characteristics of mistuned rotated blades (MRBs). Firstly, a lumped-parameter model is established based on coupled multiple blades, where mistuned stiffness with normal distribution is introduced. Next, a breathing crack model is adopted and eigenvalue analysis is used in coupled lumped-parameter model. Then, numerical analysis is done and effects of depths and positions of a crack on natural frequency, vibration amplitude, and vibration localization parameters are studied. The results show that a crack causes natural frequency decease and vibration amplitude increase of cracked blade. Bifurcations will occur due to a breathing crack. Furthermore, based on natural frequencies and vibration amplitudes, variational factors are defined to detect a crack in MRBs, which are validated by numerical simulations. Thus, the proposed method provides theoretical guidance for crack detection in MRBs.

Vibration and Analysis of Multi-Disk Friction Systems

1998 ◽  
Author(s):  
Henric Larsson ◽  
Kambiz Farhang
Keyword(s):  
Frictional Contact ◽  
Vibration Characteristics ◽  
Lumped Parameter Model ◽  
Stick Slip ◽  
Friction Forces ◽  
Lumped Parameter ◽  
Modes Of Vibration ◽  
The Coefficient Of Friction ◽  
Slip Region ◽  
Stiffness And Damping

Abstract The paper presents a lumped parameter model of multiple disks in frictional contact. The contact elastic and dissipative characteristics are represented by equivalent stiffness and damping parameters in the axial as well as the torsional directions. The formulation accounts for the coupling betwen the axial and angular motions by viewing the contact normal force to be the result of axial behavior of the system. The frictional contact of two disks in contact is modeled in two dynamic states (i.e. sticking and slipping state) having individual lumped parameter models and the conditions that control the switching between the two states are established. The friction forces are represented by assuming the coefficient of friction to be a function of the sliding velocity, varying exponentially from its static value at zero relative velocity to its kinetic value at high velocities. A computer simulation of an eight-rotor disk assembly is presented. The torsional vibration characteristics and how it is liked to the axial modes of vibration is analyzed. The vibration characteristics in the transient, steady-state and stick-slip region is compared. In the stick-slip region, the angular velocity of the interfaces in frictional contact is depicted and the sticking and slipping states are defined. It is shown that the duration of slip is approximately constant and the duration of stick increases almost exponentially until a final sticking is achieved.

Vibration Localization Analysis of Bladed Disk with Grouped Blades

2010 ◽  
Vol 139-141 ◽  
pp. 2307-2311
Author(s):  
Ai Lun Wang ◽  
Bo Hai Sun ◽  
Jin Bo Chen
Keyword(s):  
Natural Frequency ◽  
Vibration Localization ◽  
Bladed Disk ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Periodic Groups ◽  
Localization Analysis ◽  
Random Mistuning ◽  
Nature Frequency ◽  
Grouped Blades

Vibration localization of bladed disk turns to be much complex when a number of blades are assembled into periodic groups. This work focused on natural frequency distribution and modal localization of bladed disks with grouped blades based on the lumped parameter models, and effects of the blade number in each group on natural frequency were studied. Then Monte Carlo method was applied to analyze the sensitivity of modal localization to the random mistuning of blade stiffness. The results show that the number of blades in each group influences the nature frequency of bladed disk with grouped blades, and modal localization of tuned bladed disk with grouped blades is found in the closely spaced modal region. Moreover, compared to the bladed disk with free blades, the modal localization of bladed disk with grouped blades is much less sensitive to random mistuning of blade stiffness.

Vibration Amplitudes of Compressor Blades Resulting From Scatter in Blade Natural Frequencies

1969 ◽  
Vol 91 (3) ◽  
pp. 182-187 ◽  
Author(s):  
R. C. F. Dye ◽  
T. A. Henry
Keyword(s):  
Gas Turbine ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Model Analysis ◽  
Lumped Parameter Model ◽  
Compressor Blades ◽  
Lumped Parameter ◽  
Gas Turbine Compressor ◽  
Flexible Disk

Intercoupling between blades mounted on a flexible disk is examined employing a lumped-parameter model incorporating damping. Tests carried out on a gas turbine compressor and blades provide frequency and mass parameters for the model. Analysis of the model shows that vibration, and hence stress, in one or more blades, can be magnified if the distribution of blade natural frequency around the disk is suitably chosen. Feasible distributions are examined, leading to stress increases of up to 180 percent.

The Effect of Group Number and Group Coupling Stiffness on Vibration Response Localization in Tuned Grouped Blade-Disk

2012 ◽  
Vol 226-228 ◽  
pp. 124-128
Author(s):  
Ai Lun Wang ◽  
Hui Long ◽  
Qiang Huang ◽  
Qian Jin Wang
Keyword(s):  
Structural Parameters ◽  
Vibration Response ◽  
Lumped Parameter Model ◽  
Vibration Equation ◽  
Vibration Localization ◽  
Lumped Parameter ◽  
Group Number ◽  
Coupling Stiffness

The group number and group coupling stiffness are important structural parameters of the grouped blade-disk. This work examines how the group number and group coupling stiffness affect the vibration response localization of tuned grouped blade-disk. The lumped parameter model of the grouped blade-disk was established, and the vibration equation was derived. The vibration response localization factors of tuned grouped blade-disks were obtained at the different group number and group coupling stiffness, and the effects of group number and group coupling stiffness on vibration response localization was analyzed. The results show that the vibration localization appears in the tuned grouped blade-disk and the degree of vibration response localization reduces with the increasing of group number and group coupling stiffness. The results can help to completely reveal the localization mechanism of the grouped blade-disk

Theoretical Study of the Vibration Suppression on a Mistuned Bladed Disk Using a Bi-periodic Piezoelectric Network

2018 ◽  
Vol 35 (1) ◽  
pp. 17-28 ◽  
Author(s):  
Lin Li ◽  
Pengcheng Deng ◽  
Jiuzhou Liu ◽  
Chao Li
Keyword(s):  
Vibration Suppression ◽  
Robustness Analysis ◽  
Forced Response ◽  
Lumped Parameter Model ◽  
Modal Assurance Criterion ◽  
Vibration Localization ◽  
Bladed Disk ◽  
Lumped Parameter ◽  
Random Mistuning ◽  
Response Amplification

AbstractThe paper deals with the vibration suppression of a bladed disk with a piezoelectric network. The piezoelectric network has a different period (so called bi-period) from that of the bladed disk and there is no inductor in it. The system is simulated by an electromechanical lumped parameter model with two DOFs per sector. The research focuses on suppressing the amplitude magnification or reducing the vibration localization of the mistuned bladed disk. The dynamic equations of the system are derived. Both mechanical mistuning and electrical mistuning have been taken into account. The Modified Modal Assurance Criterion (MMAC) is used to evaluate the vibration suppression ability of the bi-periodic piezoelectric network. The Monte Carlo simulation is used to calculate the MMAC of the system with the random mistuning. As a reference, the forced responses of the bladed disk with and without the piezoelectric network are given. The results show that the piezoelectric network would effectively suppress amplitude magnification induced by mistuning. The vibration amplitude is even smaller than that of the tuned system. The robustness analysis shows that the bi-periodic piezoelectric network can provide a reliable assurance for avoiding the forced response amplification of the mistuned bladed disk. The amplified response induced by the mechanical mistuning with standard deviation 0.2 can be effectively suppressed through the bi-periodic piezoelectric network.

scholarly journals Analysis and Research on Longitudinal Vibration Characteristics of Deep Sea Mining Pipe Based on Finite Element Method

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Qiang Liu ◽  
Linjing Xiao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Frequency ◽  
Vibration Amplitude ◽  
Longitudinal Vibration ◽  
Excitation Frequency ◽  
Vibration Characteristics ◽  
Wind Condition ◽  
Vibration Intensity ◽  
Element Method

This paper aimed to study the longitudinal vibration characteristics of the 5000 m mining pipe in the ocean under different working wind conditions, offset angle, damping, and ore bin weight. Based on the finite element method, the mining pipe is simplified into beam element and discretized, and the physical and mathematical models of the mining pipe system are established. The Wilson-θ direct integral method is adopted for numerical calculation. The results show that the longitudinal vibration of the mining pipe is irregular, which presents the phenomenon of oscillation. The vibration amplitude decreases first and then increases from top to bottom, the minimum vibration amplitude appears at 1000 m, and the maximum vibration amplitude appears at the top of the mining pipe. Under the same working wind condition, the overall longitudinal vibration amplitude of the mining pipe can be increased by increasing the ore bin weight and the offset angle, but neither of them can change the frequency of the longitudinal vibration. The closer the excitation frequency generated by different working wind conditions is to the natural frequency, the larger the mining pipe longitudinal vibration amplitude is. The closer the vibration frequency generated by the same excitation frequency is to the natural frequency, the stronger the vibration intensity is, and when damping is added, the vibration intensity decreases faster.

Research on Torsional Vibration of Gear-Shafting System Based on an Extended Lumped Parameter Model

2010 ◽  
Vol 143-144 ◽  
pp. 487-492 ◽  
Author(s):  
Xiang Xu ◽  
Rui Ping Zhou
Keyword(s):  
System Dynamics ◽  
Natural Frequency ◽  
Dynamic Simulation ◽  
Torsional Vibration ◽  
Lumped Parameter Model ◽  
Input Frequency ◽  
Analysis Method ◽  
Vibration Equation ◽  
Lumped Parameter ◽  
Marine Propulsion

In this paper, gear-shafting system dynamics theory has been introduced into the torsional vibration calculation of the marine propulsion shaft and the vibration equations of a marine gear-shafting system were established using the lumped parameter model by taking the gear-shafting system in marine propulsion shaft as the research object. In order to solve the problem of vibration equation, dynamic simulation has been done in MATLAB software, in which the natural frequency of the system has been obtained from the simulation curve by changing the input frequency, meanwhile, the conclusion that the gears pair comprehensive meshing error is independent of the system natural frequency has been achieved. Thus, the analysis method presented in this work is available for the torsional vibration calculation of the marine gear-shafting system.

Research on Torsional Vibration of the Propulsion Shafting Gear System Based on an Extended Lumped Parameter Model

2010 ◽  
Vol 37-38 ◽  
pp. 1120-1124 ◽  
Author(s):  
Xiang Xu ◽  
Rui Ping Zhou
Keyword(s):  
Natural Frequency ◽  
Normal Condition ◽  
Torsional Vibration ◽  
Gear System ◽  
Lumped Parameter Model ◽  
Prototype Model ◽  
Analysis Method ◽  
Lumped Parameter ◽  
Marine Propulsion ◽  
Simulation Results

In this paper, gear dynamics theory has been introduced into the torsional vibration calculation of the marine propulsion shafting. The vibration equations of a marine gearbox were established using an extended lumped parameter model through reasonably adjusting the parameters to get the natural frequency of marine gearbox shafting gear system. The solution of the equations shows that under normal condition, the natural frequency of gear meshing transmission is high and the gearbox itself will not affect the torsional resonance. Then a virtual prototype model of marine gearbox was built by the use of ADAMAS software. The simulation results show that the proposed method could reflect the actual torsional vibration correctly. Thus, the analysis method presented in this work is available for the torsional vibration calculation of the marine gearbox.

scholarly journals Investigation of the Influence of Splitter Blades on the Resonance Conditions of Impellers

2019 ◽  
Vol 9 (10) ◽  
pp. 2051
Author(s):  
Kaicheng Liu ◽  
Cheng Yan
Keyword(s):  
Natural Frequency ◽  
Excitation Frequency ◽  
Specific Form ◽  
Lumped Parameter Model ◽  
Hazard Evaluation ◽  
Spatial Harmonic ◽  
Harmonic Response ◽  
Lumped Parameter ◽  
Engine Order ◽  
Harmonic Components

The conventional resonance conditions are derived based on the conventionally designed impellers without splitter blades. This paper proposes the resonance conditions for impellers under the excitation from the impeller–diffuser interaction with attention paid on the influence of splitter blades. A lumped parameter model is established and the modal analysis is carried out. The blade-based representative modal vector (RMV) is defined. The influence of splitter blades on the impeller’s traits of modes is investigated by analyzing the spatial harmonic contents of the RMV. Then, given the specific form of the diffuser-induced engine order excitation acting on the main and splitter blades, the resonance conditions are derived. Tuned and mistuned cases are provided for a practical impeller. The resonance conditions are verified by harmonic response calculations. The applications of the proposed resonance conditions in resonance identification and hazard evaluation of different excitations are given. The differences between the proposed resonance conditions and the conventional ones are discussed. The research indicates that even the RMV of the tuned impeller contains two harmonic components due to the existence of splitter blades. When the excitation frequency equals the natural frequency of the impeller and the excitation order matches with either harmonic index of the two harmonics, the resonance occurs. The results of case studies show that the harmfulness of various engine orders of excitation can be exactly evaluated by the joint use of the spatial harmonic contents analysis result and the proposed resonance conditions; however, analyzing based on the conventional resonance conditions may lead to the misjudgment of the harmfulness of the excitations.

Development of a Novel Algorithm for a Crack Detection, Localization, and Sizing in a Beam Based on Forced Response Measurements

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
M. Karthikeyan ◽  
R. Tiwari ◽  
S. Talukdar
Keyword(s):  
Natural Frequency ◽  
Crack Detection ◽  
Beam Theory ◽  
Crack Size ◽  
Forced Response ◽  
Crack Model ◽  
Beam Model ◽  
Crack Location ◽  
Forced Responses ◽  
Crack Element

The present work aims at the development of a method for the crack detection, localization and sizing in a beam based on the transverse force and response signals. The Timoshenko beam theory is applied for transverse vibrations of the beam model. The finite element method is used for the cracked beam forced vibration analysis. An open transverse surface crack is considered for the crack model, which contains standard five flexibility coefficients. The effect of the proportionate damping is also included. A harmonic force of known amplitude with sine-sweep frequency is used to dynamically excite the beam, up to few flexible modes, which could be provided with the help of an exciter. In practice, linear degrees of freedom (DOFs) can be measured quite accurately; however, rotational DOFs are difficult to measure accurately. All rotational DOFs, except at crack element, are eliminated by a dynamic condensation scheme; for elimination of rotational DOFs at the crack element, a new condensation scheme is implemented. The algorithm is iterative in nature and starts with a presumption that a crack is present in the beam. For an assumed crack location, flexibility coefficients are estimated with the help of forced responses. The Tikhonov regularization technique is applied in the estimation of bounded crack flexibility coefficients. These crack flexibility coefficients are used to obtain the crack size by minimizing an objective function. With the help of the estimated crack size and measured natural frequency, the crack location is updated. The procedure iterates till the crack size and location get stabilized up to the desired level of accuracy. The algorithm has a potential to detect no crack condition also. The crack flexibility and damping coefficients are estimated as a by-product. Numerical examples, with the simply supported and cantilevered beams, are given to justify the applicability and versatility of the algorithm in practice. With the numerically simulated forced responses, which have the noise contamination and the error in the natural frequency measurements, the estimated crack parameters (i.e., the crack location and size) are in good agreement.

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