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.

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.

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 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.

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.

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.

Behavior of Short Lateral Dead Ends on Pipeline Transients: A Lumped Parameter Model and an Analytical Solution

2005 ◽  
Vol 127 (3) ◽  
pp. 529-535 ◽  
Author(s):  
Xiao-Jian Wang ◽  
Martin F. Lambert ◽  
Angus R. Simpson
Keyword(s):  
Analytical Solution ◽  
Side Branch ◽  
Relative Volume ◽  
Lumped Parameter Model ◽  
Efficient Manner ◽  
Lumped Parameter ◽  
Dead End ◽  
Fluid Transients ◽  
Harmonic Components ◽  
The Impact

By integrating the continuity equation over a short lateral dead end, the effects of a short lateral dead end side branch on pipeline fluid transients can be lumped into a node. The analytical solution to a linearized equation shows that a pipeline transient can be expressed as a Fourier series and presence of a lateral dead end reduces the frequencies of the harmonic components. The impact of the lateral dead end on the observed transients depends on a parameter Sd, which is related to the location of the lateral dead end, the relative volume, and the wave speed of the lateral dead end with respect to the pipeline. A lumped parameter approach that can be incorporated into the method of characteristics has also been developed in this paper. It has been found that it is possible to take account of the effects of a short lateral dead end in an accurate and computational efficient manner.

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.

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