Optimal Design for Damper of Long Blade in Steam Turbine Based on Dynamic Analysis

2007 ◽  
Author(s):  
Yonghui Xie ◽  
Di Zhang
Keyword(s):  
Finite Element ◽  
Dynamic Analysis ◽  
Steam Turbine ◽  
Stiffness Matrix ◽  
Harmonic Wave ◽  
Mass Matrix ◽  
Beam Element ◽  
Friction Damper ◽  
Element Analysis ◽  
Damping Matrix

Adding damped structure can decrease dynamic stress of blade and avoid blade fatigue failure from forced vibration. Based on the structural feature of long blade with friction damper, the numerical model for dynamic analysis of damped blade in steam turbine has been developed. The blade was described by twisted beam element, the usual space beam element was adopted to analyze the frame of damper, and the slip motion between rubbing surface was modeled by a damping connector. The following matrices which are necessary for finite element analysis were obtained: the stiffness matrix, mass matrix and damping matrix of finite element for blade and damper, the stiffness matrix and damping matrix of damping connector. Then the gross finite element motion equation of the blade was got. Meanwhile, harmonic wave propagation method was adopted to improve calculation efficiency. The comparison of calculation results and experimental data of a 360mm blade shows good agreement. The dynamic characteristic of a last stage long blade in steam turbine with damper was analyzed in detail, its responses with different thickness shroud and gap between shrouds were investigated in detail too, then the optimal structure of damped shroud was obtained, the comparison for response between damped blade and freestanding blade shows the maximum response of blade with optimal damper is 42.4% of that of freestanding blade. At last, a tie wire was added to the damped blade, numerical result shows it can decrease blade response further.

Incorporation of Spinal Flexibility Measurements Into Finite Element Analysis

1990 ◽  
Vol 112 (4) ◽  
pp. 481-483 ◽  
Author(s):  
Mack G. Gardner-Morse ◽  
Jeffrey P. Laible ◽  
Ian A. F. Stokes
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Stiffness Matrix ◽  
Beam Element ◽  
Technical Note ◽  
Element Analysis ◽  
Spinal Motion ◽  
Spinal Flexibility

This technical note demonstrates two methods of incorporating the experimental stiffness of spinal motion segments into a finite element analysis of the spine. The first method is to incorporate the experimental data directly as a stiffness matrix. The second method approximates the experimental data as a beam element.

Spline-Based Finite Element Analysis in Composite Laminates Mechanical Properties

2011 ◽  
Vol 138-139 ◽  
pp. 673-680
Author(s):  
Feng Xiang You ◽  
Fei Zhang ◽  
Buo Lei Zuo
Keyword(s):  
Finite Element ◽  
Composite Laminates ◽  
Mass Matrix ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Normal Displacement ◽  
Laminated Plate ◽  
Element Analysis ◽  
Damping Matrix ◽  
Spline Finite Element

The geometric parameters of the composite laminate in the engineering structure tend to have random properties. It is of great significance on how to study sensitivity of random parameters of laminated plates and carry on the optimized analysis to the parameteranalys when accurately estimating the reliability of structural design. According to the first order shear deformation theory, by using the spline finite element method, we can infer and the establish a laminated plate vibration equation, the stiffness matrix, mass matrix, proportional damping matrix, before making solution of the antisymmetric laminated plates response sensitivity formula, and analyzing the normal displacement, the sensitivity, the natural frequency of compound materials laminated plate. The Numerical examples verify the effectiveness of this algorithm.

KED Modeling of PLS Mechanism

2012 ◽  
Vol 268-270 ◽  
pp. 1319-1326 ◽  
Author(s):  
Yong Peng ◽  
Xiao Xu Bai
Keyword(s):  
Time Domain ◽  
Stiffness Matrix ◽  
Mass Matrix ◽  
Mechanical Vibration ◽  
Beam Element ◽  
Matrix Versus ◽  
Damping Matrix ◽  
Lagrange’S Equation ◽  
The Time Domain ◽  
Final System

For the super-size and large flexibility of Pipe Lay-down System, considering the influence on the mechanism from elastic deformation and mechanical vibration during the movements, the kineto-elastodynamics model is established by using the KED theory which is based on the analysis of kinematics. The PLS mechanism is divided into several finite elements. Dynamic equations of beam element are established in the local coordinate by using Lagrange’s equation. In the process of changing from local coordinate into global coordinate, no longer considering the instantaneous structure assumes. In consideration of the first and second derivative of the coordinate transformation matrix versus time are not zero. The mass matrix, damping matrix and stiffness matrix of the final system kinematic differential equation are the function of time. It realizes the continuity of variable in the time domain. Derivation of the results in this paper lays a foundation for the next more accurate and efficient methods being applied to solve the KED equation of PLS mechanism.

Numerical Model and Optimization for Dynamic Characteristic of Damping Blade

2006 ◽  
Author(s):  
Yonghui Xie ◽  
Di Zhang
Keyword(s):  
Finite Element ◽  
Numerical Model ◽  
Dynamic Characteristic ◽  
Dynamic Stress ◽  
Mass Matrix ◽  
Penalty Function Method ◽  
Apparent Effect ◽  
Element Analysis ◽  
Damping Matrix ◽  
Energy Formula

The reliability of blade is very important for steam turbine. Adding damping structure can decrease dynamic stress of blade. Firstly, the numerical model for dynamic analysis of damping blade has been developed. The following matrices which are necessary for Finite Element analysis have been obtained: the stiffness matrix, mass matrix and damping matrix of Finite Element for blade and damper, then the gross Finite Element motion equation of the blade can be obtained. Secondly, the response energy formula of blade has been obtained by analyzing the relation between exciting force and response of blade, the response energy can be taken as optimization goal, POWELL Penalty Function Method is adopted as optimization algorithm. At last, the dynamic characteristic of a real blade is analyzed, some numerical results such as response energy varied with normal press force have been obtained, the normal press force of rubbing surface has an apparent effect on the damp and response energy of blade, it can change the dynamic characteristic of blade, and there is an optimal normal press force, which can lead to the minimum response energy of blade, i.e. the optimal damper for blade.

On real-time creep damage prediction for steam turbine

2022 ◽  
pp. 014233122110689
Author(s):  
Yongjian Sun ◽  
Bo Xu
Keyword(s):  
Finite Element ◽  
Steam Turbine ◽  
Real Time ◽  
Creep Damage ◽  
Element Model ◽  
Turbine Rotor ◽  
Theoretical Research ◽  
Element Analysis ◽  
Damage Prediction ◽  
Time Calculation

In this paper, in order to solve the calculation problem of creep damage of steam turbine rotor, a real-time calculation method based on finite element model is proposed. The temperature field and stress field of the turbine rotor are calculated using finite element analysis software. The temperature data and stress data of the crucial positions are extracted. The data of temperature, pressure, rotational speed, and stress relating to creep damage calculation are normalized. A real-time creep stress calculation model is established by multiple regression method. After that, the relation between stress and damage function is analyzed and fitted, and creep damage is calculated in real-time. A creep damage real-time calculation system is constructed for practical turbine engineering. Finally, a numerical simulation experiment is designed and carried out to verify the effectiveness of this novel approach. Contributions of present work are that a practical solution for real-time creep damage prediction of steam turbine is supplied. It relates the real-time creep damage prediction to process parameters of steam turbine, and it bridges the gap between the theoretical research works and practical engineering.

Steam Turbine Casing Analyses to Determine Pressure and Temperature Limits

2021 ◽  
Author(s):  
Paul T. Smith ◽  
Daniel J. Griffin
Keyword(s):  
Finite Element ◽  
Steam Turbine ◽  
Elevated Temperatures ◽  
Temperature Limit ◽  
Normal Operation ◽  
Working Pressure ◽  
Element Analysis ◽  
Minimum Width ◽  
Joint Contact ◽  
Joint Contact Pressure

Abstract To ensure safe and reliable operation, steam turbine casings must have acceptable stresses and maintain sealing when subjected to internal pressures and temperatures. To show turbine casings acceptable, analysts conduct structural evaluations using finite element analysis (FEA) techniques. This paper outlines the analytical methods used to perform these types of analyses, provides analysis examples, and summarizes the process to create pressure and temperature limit maps. Finite element models of the main casing and steam chest are used to determine stresses and sealing of the casing horizontal split line and steam chest cover during normal operation. The sealing evaluations consider the sealing capabilities of the bolted joints when the casing is subjected to internal steam pressure and consider the effects of bolt stress relaxation at elevated temperatures, joint contact surface separation, and penetration of the internal pressure into the sealing surface. The acceptance criteria for the bolted joint sealing is based on the minimum width of the contacting surface and the minimum joint contact pressure. A series of analyses were conducted on the various models to create pressure and temperature limit maps, so that the design can be applied for the appropriate conditions. These maps plot maximum allowable working pressure (MAWP) versus maximum allowable working temperature (MAWT), and allow an application engineer to easily determine the acceptability of the casing for a particular application. An explanation of the process used to create the limit maps is presented.

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