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.

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.

An Enhanced Methodology for Estimating the Natural Frequency of Valves Using Raleigh’s Energy Principle

2013 ◽  
Author(s):  
L. Ike Ezekoye ◽  
Ronald S. Farrell ◽  
Preston A. Vock ◽  
Richard J. Gradle
Keyword(s):  
Natural Frequency ◽  
Nuclear Power ◽  
Power Plants ◽  
Natural Frequencies ◽  
Lumped Mass ◽  
Mass Model ◽  
Energy Principle ◽  
Mass System ◽  
Valve Body ◽  
Extended Structure

This paper presents a model for calculating the minimum natural frequency of valve assemblies using the Raleigh’s energy principle. Raleigh’s principle states that the point where the kinetic energy of a multi-mass system and its potential energy are equal defines the minimum natural frequency of the system. This principle was used by Ezekoye to calculate the natural frequency of valve superstructures [1]. The early Ezekoye paper provided the fundamental tools for estimating the natural frequency of valves. However, over the years, with increasing valve testing to support Generation 3 nuclear power plants requirements, where natural frequency testing is required to complement analytical predictions, it has been noted that the Ezekoye simplified model adequately addressed valves with symmetric actuators and valves with minimal center of gravity (CG) offsets but over predicts the natural frequencies of valves with large CG offset actuators. Testing experience shows that a valve’s extended structure has two fundamental natural frequencies whose values are dictated primarily by the structural flexibility in bending and torsion. This paper extends the Ezekoye model by incorporating mass inertia of the structures with the more traditional methods that are based on a lumped mass model to determine displacements. In the process, the flexibility of the extended structure (otherwise referred to as the superstructure) and the valve body itself are considered. The approach covered in this paper combines classical statics, dynamics, and strength of materials techniques to model the natural frequency of a valve assembly. The resultant natural frequencies from the enhanced model are expected to provide better predictions of the minimum natural frequencies of valve assemblies.

Harmonization of new wind turbine rotor blades development process: A review

2014 ◽  
Vol 39 ◽  
pp. 874-882 ◽  
Author(s):  
B. Rašuo ◽  
M. Dinulović ◽  
A. Veg ◽  
A. Grbović ◽  
A. Bengin
Keyword(s):  
Wind Turbine ◽  
Development Process ◽  
Turbine Rotor ◽  
Rotor Blades ◽  
Wind Turbine Rotor

Damage-Involved Structural Pounding in Bridges under Seismic Excitation

2017 ◽  
Vol 754 ◽  
pp. 309-312 ◽  
Author(s):  
Robert Jankowski
Keyword(s):  
Structural Damage ◽  
Structural Model ◽  
Viscoelastic Model ◽  
Time History ◽  
Seismic Wave Propagation ◽  
Seismic Excitation ◽  
Lumped Mass ◽  
Positive Role ◽  
Contact Points ◽  
Elevated Bridge

During severe earthquakes, pounding between adjacent superstructure segments of highway elevated bridges was often observed. It is usually caused by the seismic wave propagation effect and may lead to significant damage. The aim of the present paper is to show the results of the numerical analysis focused on damage-involved pounding between neighbouring decks of an elevated bridge under seismic excitation. The analysis was carried out using a lumped mass structural model with every deck element discretized as a SDOF system. Pounding was simulated by the use of impact elements which become active when contact is detected. The linear viscoelastic model of collision was applied allowing for dissipation of energy due to damage at the contact points of colliding deck elements. The results show that pounding may substantially modify the behaviour of the analysed elevated bridge. It may increase the structural response or play a positive role, and the response depends on pattern of collisions between deck elements. The results also indicate that a number of impacts for a small in-between gap size is large, whereas the value of peak pounding force is low. On the other hand, the pounding force time history for large gap values shows only a few collisions, but the value of peak pounding force is substantially large, what may intensify structural damage.

Determination of the Critical Operating Speeds of Planar Mechanisms by the Finite Element Method Using Planar Actual Line Elements and Lumped Mass Systems

1979 ◽  
Vol 101 (2) ◽  
pp. 210-223 ◽  
Author(s):  
S. Kalaycioglu ◽  
C. Bagci
Keyword(s):  
Dynamic Systems ◽  
Natural Frequencies ◽  
Dynamic Equilibrium ◽  
Large Error ◽  
Free Vibrations ◽  
Lumped Mass ◽  
Critical Speeds ◽  
Rotating Shafts ◽  
Line Elements ◽  
Kinematic Motion

It has been a well-established fact that dynamic systems in motion experience critical speeds, such as rotating shafts and geared systems whose undeformed reference geometry remain the same at all times. Their critical speeds are determined by their natural frequencies of considered type of free vibrations. Linkage mechanisms as dynamic systems in motion change their undeformed geometries as function of time during the cycle of kinematic motion. They do also experience critical operating speeds as rotating shafts and geared systems do, and their critical speeds are determined by the minima of their natural frequencies during a cycle of kinematic motion. Such a minimum occurs at the critical geometry of a mechanism, which is the position at which the maximum of the input power is required to maintain the instantaneous dynamic equilibrium of the mechanism. Actual finite line elements are used to form the global generalized coordinate flexibility matrix. The natural frequencies of the mechanism and the corresponding mode vectors (mode deflections) are determined as the eigen values and eigen vectors of the equations of instantaneous-position-free-motion of the mechanism. Method is formulated to include or exclude the link axial deformations, and apply to any number of loops having any type of planar pair. Critical speeds of planar four-bar, slider-crank, and Stephenson’s six-bar mechanisms are determined. Experimental results for the four-bar mechanism are given. Effect of axial deformations and link rotary inertias are investigated. Inclusion of link axial deformations in mechanisms having pairs with sliding freedoms is seen to predict critical speeds with large error.

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.

Experimental and Numerical Modal Analysis of Composite Laminated Shells

2019 ◽  
Vol 161 (A1) ◽  
Keyword(s):  
Heat Dissipation ◽  
Mass Matrix ◽  
Experimental Studies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Radius Of Curvature ◽  
Lumped Mass ◽  
Auxiliary Equipment ◽  
Mass Model ◽  
Laminated Shells

The presence of cut outs at different positions of laminated shell component in marine and aeronautical structures facilitate heat dissipation, undertaking maintenance, fitting auxiliary equipment, access ports for mechanical and electrical systems, damage inspection and also influences the dynamic behaviour of the structures. The aim of the present study is to establish a comprehensive perspective of dynamic behavior of laminated deep shells (length to radius of curvature ratio less than one) with cut-out by experiments and numerical simulation. The glass epoxy laminated composite shell has been prepared in the laboratory by resin infusion. The experimental free vibration analysis is carried out on laminated shells with and without cut-out. The mass matrix is developed by considering rotary inertia in a lumped mass model in the numerical modeling. The results obtained from numerical and experimental studies are compared for verification and the consistency between mode shapes is established by applying modal assurance criteria.

Vibrations of a Helicopter Rotor-Fuselage System Induced by the Main Rotor Blades in Flight

1955 ◽  
Vol 22 (3) ◽  
pp. 355-360
Author(s):  
M. Morduchow ◽  
S. W. Yuan ◽  
H. Reissner
Keyword(s):  
Theoretical Analysis ◽  
Natural Frequencies ◽  
Rotor Blades ◽  
Helicopter Rotor ◽  
Simplified Model ◽  
Main Rotor ◽  
Numerical Examples ◽  
The Masses

Abstract Based on a simplified model of the hub-fuselage structure, a theoretical analysis is made of the response of the hub and fuselage of a helicopter in flight to harmonic forces transmitted by the rotor blades to the hub both in, and normal to, the plane of rotation. The assumed structure is in the form of a plane framework with masses concentrated at the joints. Simple expressions are derived for the vibration amplitudes of the mass points as functions of the masses and natural frequencies of the hub and the fuselage. The pertinent nondimensional parameters are determined, and simple explicit conditions of resonance are derived. Numerical examples are given to illustrate the results.

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.

Combining Physics-Based and Data-Driven Models for Estimation of WOB During Ultra-Deep Ocean Drilling

2018 ◽  
Author(s):  
Tatsuya Kaneko ◽  
Ryota Wada ◽  
Masahiko Ozaki ◽  
Tomoya Inoue
Keyword(s):  
Hybrid Model ◽  
Numerical Models ◽  
Drill String ◽  
Operating Conditions ◽  
Data Driven ◽  
High Frequency Oscillation ◽  
Lumped Mass ◽  
Unknown Parameters ◽  
Mass Model ◽  
Time Operation

Offshore drilling with drill string over 10,000m long has many technical challenges. Among them, the challenge to control the weight on bit (WOB) between a certain range is inevitable for the integrity of drill pipes and the efficiency of the drilling operation. Since WOB cannot be monitored directly during drilling, the tension at the top of the drill string is used as an indicator of the WOB. However, WOB and the surface measured tension are known to show different features. The deviation among the two is due to the dynamic longitudinal behavior of the drill string, which becomes stronger as the drill string gets longer and more elastic. One feature of the difference is related to the occurrence of high-frequency oscillation. We have analyzed the longitudinal behavior of drill string with lumped-mass model and captured the descriptive behavior of such phenomena. However, such physics-based models are not sufficient for real-time operation. There are many unknown parameters that need to be tuned to fit the actual operating conditions. In addition, the huge and complex drilling system will have non-linear behavior, especially near the drilling annulus. These features will only be captured in the data obtained during operation. The proposed hybrid model is a combination of physics-based models and data-driven models. The basic idea is to utilize data-driven techniques to integrate the obtained data during operation into the physics-based model. There are many options on how far we integrate the data-driven techniques to the physics-based model. For example, we have been successful in estimating the WOB from the surface measured tension and the displacement of the drill string top with only recurrent neural networks (RNNs), provided we have enough data of WOB. Lack of WOB measurement cannot be avoided, so the amount of data needs to be increased by utilizing results from physics-based numerical models. The aim of the research is to find a good combination of the two models. In this paper, we will discuss several hybrid model configurations and its performance.

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