Modal and Aeroelastic Analysis of a Compressor Blisk Considering Mistuning

2011 ◽  
Author(s):  
Jens Nipkau ◽  
Arnold Ku¨hhorn ◽  
Bernd Beirow
Keyword(s):  
Equations Of Motion ◽  
Computing Time ◽  
Element Model ◽  
Forced Response ◽  
Lumped Mass ◽  
Aerodynamic Forces ◽  
Mass Model ◽  
Influence Coefficients ◽  
Aeroelastic Analysis ◽  
Lumped Mass Model

Focussing on three basic blade modes the effect of the flow’s influence on the forced response of a mistuned HPC-blisk is studied using a surrogate lumped mass model called equivalent blisk model (EBM). Both measured and intentionally allowed mistuning is considered to find out in principle if the flow contributes to a slowdown of blade displacements with increasing mistuning. In a first step the mechanical properties of the EBM are adjusted to a finite element model and known mistuning distributions given in terms of blade frequencies and damping. Taking into account the flow structure interaction CFD-computations are carried out in order to derive aerodynamic influence coefficients (AIC) which are used to describe the aerodynamic forces coming along with the motion of each blade in the flow. These aerodynamic forces can be included directly in the EBM equations of motion or alternatively be used to calculate aeroelastic eigenvalues from which additional equivalent aerodynamic elements representing the co-vibrating air mass as well as aerodynamic stiffening and damping effects are derived. Both kinds of EBM are applied to study the forced response at least in a qualitative manner aiming to demonstrate some basic effects at low computing time.

Investigation of Working Line Variation Onto Forced Response Vibrations of a Compressor Blisk

2020 ◽  
Author(s):  
Seif ElMasry ◽  
Arnold Kühhorn ◽  
Felix Figaschewsky
Keyword(s):  
Resonance Condition ◽  
Element Model ◽  
Forced Response ◽  
Mode Shapes ◽  
Aerodynamic Forces ◽  
Aerodynamic Damping ◽  
Single Passage ◽  
Influence Coefficients ◽  
Stator Vane ◽  
Operational Range

Abstract This paper aims to study the effect of varying the working line of a compressor onto the forced response vibrations of the blades of an integrally bladed disk (blisk). The investigated rotor belongs to a transonic research compressor, where various probes are placed to measure flow data at all stations and analyze blade vibrations. A single-passage CFD model of all compressor blade-rows is used for steady computations. Using a finite element model, the natural frequencies and mode shapes of the blisk across the operational range of the compressor are predicted. Thus, resonance conditions can be identified from the Campbell diagram. The variation of the compressor working line is investigated at 90% of the maximum shaft speed, where the resonance condition of the 11th blade mode family and the engine order corresponding to the aerodynamic distortion from the upstream stator vane is predicted. Using a single-passage model, time-accurate simulations of the investigated rotor are executed at various operating points, which cover the operational range of the compressor between choke and stall conditions. Aerodynamic damping ratios are calculated using the aerodynamic influence coefficients method at each point, in order to predict the resulting vibration amplitudes of the blades. Relatively high amplitudes of the modal aerodynamic forces are observed at the low working line. A detailed post-processing analysis is performed, as the change of flow incidence contributes largely in the increase of modal aerodynamic forces on the blade. The aerodynamic damping ratios increase with higher working lines, where the rotor achieves relatively higher pressure ratios. However, the damping decreases rapidly close to stall conditions. The trend of the predicted vibration amplitudes is compared to strain gauge measurements from the rig, which are registered during multiple acceleration maneuvers performed over different working lines. A strong correlation between the predicted and measured trends of the forced response vibration is witnessed.

An Efficient Response Analysis Method for a Non-Linear/Parameter Changing System Using Sub-Structure Modes

1993 ◽  
Vol 207 (1) ◽  
pp. 41-52
Author(s):  
H K Kim ◽  
Y-S Park
Keyword(s):  
Equations Of Motion ◽  
Forced Response ◽  
Suggested Method ◽  
Response Analysis ◽  
Synthesis Methods ◽  
Lumped Mass ◽  
State Equations ◽  
Mass Model ◽  
Non Linear ◽  
Forced Responses

An efficient state-space method is presented to determine time domain forced responses of a structure using the Lagrange multiplier based sub-structure technique. Compared with the conventional mode synthesis methods, the suggested method can be particularly effective for the forced response analysis of a structure subjected to parameter changes with time, such as a missile launch system, and/or having localized non-linearities, because this method does not need to construct the governing equations of the combined whole structure. Both the loaded interface free-free modes and free interface modes can be employed as the modal bases of each sub-structure. The sub-structure equations of motion are derived using Lagrange multipliers and recurrence discrete-time state equations based upon the concept of the state transition matrix are formulated for transient response analysis. The suggested method is tested with two example structures, a simple lumped mass model with a non-linear joint and an abruptly parameter changing structure. The test results show that the suggested method is very accurate and efficient in calculating forced responses and in comparing it with the direct numerical integration method.

Application of Annular Damper Reaction Wall in Seismic Isolated LNG Tank

2010 ◽  
Author(s):  
Rui-Fu Zhang ◽  
Da-Gen Weng ◽  
Wei-Bo Ni
Keyword(s):  
Equations Of Motion ◽  
Time Base ◽  
Base Shear ◽  
Lumped Mass ◽  
Mass Model ◽  
Isolation System ◽  
Lead Rubber Bearings ◽  
Lumped Mass Model ◽  
Lng Tank ◽  
Rubber Bearings

Most of the large LNG tanks have a fundamental frequency between 2 and 10 Hz which involves range of resonance of most earthquake ground motions. It is a fact that tanks could be damaged easily in the earthquake, which had been proved in many cases in the past few decades. It is an effective way to reduce the response for an isolation system being used for large LNG storage tanks in the strong earthquake. However, the displacement of the isolation story for actual project is very large in soft site so that the design of connection components is relatively difficult. In order to solve this problem, isolation system which is composed of annular damper reaction wall, viscous dampers, and lead rubber bearings mounted on the top of the piles is presented in this paper. The annular damper reaction wall which is not connected with the piles is embedded into the ground independently. The multi-degree-of-freedom lumped mass model is used to solve the governing equations of motion in which convective, impulsive and rigid masses are included. Simplified model of an actual LNG tank which can contain 160000m3 gases is analyzed by using isolators and annular damper reaction wall. The efficiency of the isolation system is investigated by analyzing various parameters such as displacement of the isolation story, base shear and so on. The results show that isolation system is very effective to control the displacement of isolation story, and at the same time base shear and other parameters are also effectively controlled.

scholarly journals Validation of Numerical Models of a Rotorcraft Crashworthy Seat and Subfloor

Aerospace ◽  
2020 ◽  
Vol 7 (12) ◽  
pp. 174
Author(s):  
Paolo Astori ◽  
Mauro Zanella ◽  
Matteo Bernardini
Keyword(s):  
Numerical Models ◽  
Element Model ◽  
Drop Test ◽  
Reference Scenario ◽  
Lumped Mass ◽  
Mass Model ◽  
Seat Cushion ◽  
Lumped Mass Model ◽  
Energy Absorbers ◽  
Energy Absorbing

The present work explores some critical aspects of the numerical modeling of a rotorcraft seat and subfloor equipped with energy-absorbing stages, which are paramount in crash landing conditions. To limit the vast complexity of the problem, a purely vertical impact is considered as a reference scenario for an assembly made of a crashworthy helicopter seat and a subfloor section, including an anthropomorphic dummy. A preliminary lumped mass model is used to drive the design of the experimental drop test. Some additional static and dynamic tests are carried out at the coupon and sub-component levels to characterize the seat cushion, the seat pan and the honeycomb elements that were introduced in the structure as energy absorbers. The subfloor section is designed and manufactured with a simplified technique, yet representative of this structural component. Eventually, a finite element model representing the full drop test was created and, together with the original lumped mass model, finally validated against the experimental test, outlining the advantage of using both the numerical techniques for design assistance.

scholarly journals Dynamic Analysis of Pantograph-Catenary System considering Ice Coating

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Yongming Yao ◽  
Ning Zhou ◽  
Guiming Mei ◽  
Weihua Zhang
Keyword(s):  
Arc Discharge ◽  
Element Model ◽  
Normal Operation ◽  
Ice Thickness ◽  
Lumped Mass ◽  
Mass Model ◽  
Current Collection ◽  
Coating Method ◽  
Lumped Mass Model

Ice coating on overhead contact system (OCS) will affect the sliding of pantograph, and arc discharge phenomena will occur between pantograph and catenary, which will threaten the normal operation of train. This paper presents a comprehensive model to analyze the dynamics of icing on pantograph-catenary (PAC) system. The finite element model (FEM) is used for building the catenary, the pantograph is modeled as lumped-mass model, and the ice section of the cable is fan-shaped. The increased density method, uniform load method, and combinatorial material method of icing are used to analyze the icing problem of PAC system. The similarities and differences between the three simulation methods are compared. The influence of the ice thickness on the current collection quality between the pantograph and catenary at the different operating speeds calculated by the three methods is basically the same, which fully illustrates the effectiveness of the simulated ice coating method. In comparison, the combinatorial material method is a more reasonable method for calculating the icing of catenary systems. The research also shows that the influence of icing on the current collection quality of PAC system is different when the train runs at different speeds. Specifically, as the speed of trains increases, the effect of ice thickness on the current collection quality of the PAC system is becoming increasingly apparent.

Effect of Mass Models in the Dynamic Analysis of Structures

2010 ◽  
Author(s):  
I˙brahim Korkmaz
Keyword(s):  
Dynamic Analysis ◽  
Dynamic Stiffness ◽  
Equations Of Motion ◽  
Beam Element ◽  
Lumped Mass ◽  
Mass Model ◽  
Comparison Results ◽  
Nodal Coordinates ◽  
Lumped Mass Model ◽  
Computer Calculations

In this research the utilization of distributed, lumped, and consistent mass models in the dynamic analysis of structures is studied, and the results obtained by these models for example problems are compared. In distributed mass model, the dynamic stiffness matrix for a planar beam element is derived by integrating the differential equations of motion. In lumped mass model, the mass of the structure is lumped at the nodal points where translational displacements are defined. However, in the consistent mass model the mass characteristics corresponding to the nodal coordinates of beam element are evaluated by a procedure similar to the determination of the element stiffness coefficients. These mass models are executed for three numerical examples. Results of two examples are compared with analytical solutions. The last example analysis of planar frames with distributed mass model is calculated with using a developed computer program by using two comparison results of other examples. The Fourier series approach is used for the solution of dynamic equations. Numerical results have shown the effectiveness of the dynamic stiffness approach with the distributed mass model. The distributed mass model gives the exact values of the natural frequencies with the exception of numerical errors in computer calculations. This research is different from the other studies that demonstrate the application of the modeling and calculation of the natural frequency values’ accuracy regarding to choose mass model. It is also shows the method to deal with the external excitation.

Analysis of Mistuned Blade Vibrations Based on Normally Distributed Blade Individual Natural Frequencies

2015 ◽  
Author(s):  
Felix Figaschewsky ◽  
Arnold Kühhorn
Keyword(s):  
Probability Distribution ◽  
Development Process ◽  
Structural Model ◽  
Natural Frequencies ◽  
Rotor Blades ◽  
Lumped Mass ◽  
Mass Model ◽  
Influence Coefficients ◽  
Random Mistuning ◽  
Rotor Assembly

With increasing demands for reliability of modern turbomachinery blades the quantification of uncertainty and its impact on the designed product has become an important part of the development process. This paper aims to contribute to an improved approximation of expected vibration amplitudes of a mistuned rotor assembly under certain assumptions on the probability distribution of the blade’s natural frequencies. A previously widely used lumped mass model is employed to represent the vibrational behavior of a cyclic symmetric structure. Aerodynamic coupling of the blades is considered based on the concept of influence coefficients leading to individual damping of the traveling wave modes. The natural frequencies of individual rotor blades are assumed to be normal distributed and the required variance could be estimated due to experiences with the applied manufacturing process. Under these conditions it is possible to derive the probability distribution of the off-diagonal terms in the mistuned equations of motions, that are responsible for the coupling of different circumferential modes. Knowing these distributions recent limits on the maximum attainable mistuned vibration amplitude are improved. The improvement is achieved due to the fact, that the maximum amplification depends on the mistuning strength. This improved limit can be used in the development process, as it could partly replace probabilistic studies with surrogate models of reduced order. The obtained results are verified with numerical simulations of the underlying structural model with random mistuning patterns based on a normal distribution of individual blade frequencies.

A Comparison of Inverse Models for the Estimation of Ice-Induced Propeller Moments on a Polar Vessel

2021 ◽  
Author(s):  
Brendon M. Nickerson ◽  
Anriëtte Bekker
Keyword(s):  
Rotational Speed ◽  
Continuous Model ◽  
Full Scale ◽  
Lumped Mass ◽  
Mass Model ◽  
Inverse Models ◽  
Lumped Mass Model ◽  
Ill Posed ◽  
Shaft Torque ◽  
Measurement Location

Abstract Full-scale measurements were conducted on the port side propulsion shaft the S.A. Agulhas II during the 2019 SCALE Spring Cruise. The measurements included the shaft torque captured at two separate measurement locations, and the shaft rotational speed at one measurement location. The ice-induced propeller moments are estimated from the full-scale shaft responses using two inverse models. The first is a published discrete lumped mass model that relies on regularization due to the inverse problem being ill-posed. This model is only able to make use of the propulsion shaft torque as inputs. The second model is new and employs modal superposition to represent the propulsion shaft as a combination of continuous modes, resulting in a well-posed problem. This new model requires the additional measurement of the shaft rotational speed for the inverse solution. The continuous model is shown to be more consistent and efficient, which allows its use in real-time monitoring of propeller moments.

Coupled Torsional Vibration and Fatigue Damage of Turbine Generator Due to Grid Disturbance

2014 ◽  
Vol 136 (6) ◽  
Author(s):  
Chao Liu ◽  
Dongxiang Jiang ◽  
Jingming Chen
Keyword(s):  
Fatigue Damage ◽  
Torsional Vibration ◽  
Coupled System ◽  
Lumped Mass ◽  
Mass Model ◽  
Turbine Generator ◽  
Failure Prevention ◽  
Lumped Mass Model ◽  
Continuous Mass ◽  
Fatigue Evaluation

Crack failures continually occur in shafts of turbine generator, where grid disturbance is an important cause. To estimate influences of grid disturbance, coupled torsional vibration and fatigue damage of turbine generator shafts are analyzed in this work, with a case study in a 600MW steam unit in China. The analysis is the following: (i) coupled system is established with generator model and finite element method (FEM)-based shafts model, where the grid disturbance is signified by fluctuation of generator outputs and the shafts model is formed with lumped mass model (LMM) and continuous mass model (CMM), respectively; (ii) fatigue damage is evaluated in the weak location of the shafts through local torque response computation, stress calculation, and fatigue accumulation; and (iii) failure-prevention approach is formed by solving the inverse problem in fatigue evaluation. The results indicate that the proposed scheme with continuous mass model can acquire more detailed and accurate local responses throughout the shafts compared with the scheme without coupled effects or the scheme using lumped mass model. Using the coupled torsional vibration scheme, fatigue damage caused by grid disturbance is evaluated and failure prevention rule is formed.

Identification of firefly algorithm-based fluctuation coefficient of the exciting torque for vehicle driveline

2018 ◽  
Vol 233 (2) ◽  
pp. 317-326
Author(s):  
Qiaobin Liu ◽  
Wenku Shi ◽  
Zhiyong Chen
Keyword(s):  
Torsional Vibration ◽  
Firefly Algorithm ◽  
Vibration Response ◽  
Theoretical Modelling ◽  
Lumped Mass ◽  
Mass Model ◽  
Engine Torque ◽  
Lumped Mass Model ◽  
Vibration Performance ◽  
Engine Excitation

The unbalanced excitation force and torque generated by an engine that resonate with the natural frequency of drivetrain often causes vibration and noise problems in vehicles. This study aims to comprehensively employ theoretical modelling and experimental identification methods to obtain the fluctuation coefficients of engine excitation torque when a car is in different gear positions. The inherent characteristics of the system are studied on the basis of the four-degree-of-freedom driveline lumped mass model and the longitudinal dynamics model of vehicle. The correctness of the model is verified by torsional vibration test. The second order's engine torque fluctuation coefficients are identified by firefly algorithm according to the curves of flywheel speed in different gears under the acceleration condition of the whole open throttle. The torque obtained by parameter identification is applied to the model, and the torsional vibration response of the system is analysed. The influence of the key parameters on the torsional vibration response of the system is investigated. The study concludes that proper reduction of clutch stiffness can increase clutch damping and half-axle rigidity, which can help improve the torsional vibration performance of the system. This study can provide reference for vehicle drivetrain modelling and torsional vibration control.

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