Cyclic Symmetry Analysis Research Articles

Structure and modal analysis of the last stage blade in steam turbine under low volume flow conditions

To explore the prestressed modal characteristics of the last stage blade in steam turbine under low volume flow conditions, the fluid–structure interaction (FSI) method of ANSYS mechanical + CFX is adopted to consider the effect of flow field on the strength performance of the rotor blade. The cyclic symmetry analysis is adopted to calculate the strength performance and modal characteristics of the rotor blade. The results show that the flow field of the last stage is composed of backflow vortex, separation vortex and tip clearance vortex under low volume flow conditions. The tip clearance vortex has high circumferential velocity and temperature. The maximum deformation of the rotor blade is on the leading edge of the blade at 80% span, and the maximum equivalent stress is on the suction surface at 90% span. With the decrease of the steam flow, the temperature at the blade tip increases significantly, which increases the maximum deformation and the equivalent stress of the rotor blade. The plastic deformation occurs when the steam flow is reduced to 15% turbine heat acceptance (THA). In addition, the elastic modulus of blade material decreases with the increase of temperature, which leads to the decrease of natural frequencies. From 35 %THA to 5% THA condition, the natural frequencies of the blade decrease by 34-136 Hz. This study provides a theoretical reference for the identification, diagnosis and prediction of the vibration of the last stage blade under low volume flow conditions.

Study on the Coupled Vibration Characteristics of a Two-Stage Bladed Disk Rotor System

This paper conducts a coupled vibration analysis of a two-stage bladed disk rotor system. According to the finite element method, the bladed disk rotor system is established. The substructure modal synthesis super-element method (SMSM) with a fixed interface and free interface is presented to obtain the vibration behaviors of the rotor system. Then, the free vibration results are compared with the ones calculated by the cyclic symmetry analysis method to validate the analysis in this paper. The results show that the modes of the two-stage bladed disk not only include the modes of the first- and second-stage bladed disk, but also the coupled modes of the two-stage bladed disk.

A Reduced-Order Model for the Vibration Analysis of Mistuned Blade–Disc–Shaft Assembly

An effective reduced-order model is presented in this paper for the vibration analysis of a mistuned blade–disc–shaft assembly considering the flexibility of the shaft and the rotordynamic effects. For the sake of accurate modeling and quantitative analysis, three-dimensional (3D) finite element models were employed in obtaining the governing equations of motion with the Coriolis force, centrifugal stiffening, and spin softening effects taken into account. Then, an efficient model order reduction technique based on the coordinate projection by normal modes of tuned assembly and cyclic symmetry analysis was developed for mistuned blade–disc–shaft assembly. The criterion of whether one matrix could be incorporated in cyclic symmetry analysis is presented. During the modeling, the mistuning in blade and disc was taken into account and dealt with independently. In mistuning projection, the blade and disc parts were both projected onto their tuned counterparts of the sector model, where the boundary conditions were set to be fixed and free, respectively. Finally, an example of a blade–disc–shaft assembly was employed to validate the effectiveness of the presented method in free and forced vibration analysis.

Vibration characteristics analysis of mistuned bladed disk system based on mobile interface prestressed CMS super-element method

A new mobile interface prestressed component mode synthesis (CMS) super-element method is proposed with the mobile interface prestressed and free interface super-element approach. Analysis accuracy of this method is verified by the cyclic symmetry analysis method and the direct method. The mistuning parameter of real blades is identified by modal testing and finite element method, and the vibration characteristics of the real mistuned bladed disk system are analyzed based on the mobile interface CMS method. The results showed that the maximum relative error of the dynamic frequency of tuned and mistuned examples are 0.0043 % and 0.1466 %, respectively, which can be to meet the requirement of analytical precision. Compared with the cyclic symmetry analysis method, direct method and fixed interface prestressed CMS super-element method, this method is more suitable for analyzing the vibration characteristics of arbitrary mistuned bladed disk system.

Thermal Buckling Analysis of Cyclic Symmetry Mounting Structure

Buckling analysis is a technique used to determine buckling load and buckled mode shape. Buckling load is the critical load at which a structure becomes unstable while buckled mode shape is the characteristic shape associated with a structure's buckled response. In this paper, the elastic thermal buckling of a heated cyclic symmetry structure is carried out by means of finite element method. The buckling cyclic symmetry analysis is focused on a ring-strut-ring structure which is extensively used as a basic element in rotating machines. The linear eigenvalue buckling analysis is adopted to determine the buckling response with the temperature change of the structure.

Analyzing mistuned multi-stage turbomachinery rotors with aerodynamic effects

A great deal of research has been conducted on accurately modeling large cyclic structures such as turbomachinery rotors. Accurate modeling of realistic industrial turbomachinery requires overcoming several challenges. The first is the excessively large size of the finite element models (FEMs) needed, which can contain millions of degrees of freedom per stage of the rotor. The second challenge is the presence of small random variations in the structural properties known as mistuning, which arise from operational wear and/or manufacturing tolerances, and destroy the cyclic symmetry of the FEMs. The third is the complexity of turbomachinery models, which often include multiple stages that often have a mismatched computational grid at the interface between stages. The fourth challenge is associated with modeling the aerodynamic loads on the turbomachinery rotor. Much research has been conducted to overcome the first two challenges. By combining cyclic symmetry analysis and component mode mistuning (CMM), compact single-stage reduced order models (ROMs) can be created to accurately capture the free and forced response of these systems. These highly efficient ROMs can be developed from single sector calculations and can be of the order of the number of sectors in the stage. Recently, the third challenge associated with the complexity of modeling multiple stages has been addressed by the authors. Their method uses cyclic symmetry and CMM to form single-stage ROMs (using only single sector models and single sector calculations), and then combines these single-stage ROMs by projecting the motion along the interface between stages along a set of harmonic shape functions. This method allows for the creation of compact ROMs of multi-stage systems with mistuning using sector only calculations. The fourth challenge has been addressed only for single-stage systems by computing a complex aerodynamic matrix (which contains stiffness and damping terms) using an iterative approach. In this work, some of the effects of the aerodynamics on multi-stage systems are explored. The methodology consists of first creating efficient structural ROMs of a multi-stage rotor using the method previously developed, and then iteratively calculating the complex aerodynamic matrices for each stage. A new way to account for the effects of a shift in frequency due to mistuning on the complex aerodynamic matrix is also proposed. Additionally, a new classification of complex multi-stage aeroelastic modes is introduced. The presented results focus on exploring the influences of the aerodynamics and mistuning on the multi-stage response. A variety of numerical results are analyzed for two stages of an industrial rotor.

Dynamic Characteristic Analysis and Experiment for Integral Impeller Based on Cyclic Symmetry Analysis Method

A cyclic symmetry analysis method is proposed for analyzing the dynamic characteristic problems of thin walled integral impeller. Reliability and feasibility of the present method are investigated by means of simulation and experiment. The fundamental cyclic symmetry equations and the solutions of these equations are derived for the cyclic symmetry structure. The computational efficiency analysis between whole and part is performed. Comparison of results obtained by the finite element analysis (FEA) and experiment shows that the local dynamic characteristic of integral impeller has consistency with the single cyclic symmetry blade. When the integral impeller is constrained and the thin walled blade becomes a concerned object in analysis, the dynamic characteristic of integral impeller can be replaced by the cyclic symmetry blade approximately. Hence, a cyclic symmetry analysis method is effectively used to improve efficiency and obtain more information of parameters for dynamic characteristic of integral impellers.

Reduced-Order Modeling for Nonlinear Analysis of Cracked Mistuned Multistage Bladed-Disk Systems

with small blade-to-blade mistuning and a cracked blade is proposed. The modeling strategy is based on an efficient stagewise reduced-order modeling method based on cyclic symmetry analysis and component mode synthesis. Reduced-order modelsareconstructed forindividual stagesandassembledbyprojecting themotionof theinterface of the neighboring stages onto a set of harmonic shape functions. The analysis procedure allows the stages to have different numbers of blades and mismatched computational grids on the interfaces of the neighboring stages. Furthermore, the modeling framework is independent of the modeling method for each stage, which enables the use of various existing modeling methods of single stages. Moreover, nonlinearity can also be included in the multistage computations, as long as the nonlinearity can be modeled for a single stage. To demonstrate the capability of the modelingprocedure,thenonlineareffectofcrackopeningandclosingisconsidered,inconjunctionwiththeeffectsof small mistuning. The accuracy and efficiency of the proposed methods are discussed.

Dynamics of Multistage Bladed Disks Systems

This paper presents a new and original method for dynamical analysis of multistage cyclic structures such as turbomachinery compressors or turbines. Each stage is modeled cyclically by its elementary sector and the interstage coupling is achieved through a cyclic recombination of the interface degrees of freedom. This method is quite simple to set up; it allows us to handle the finite element models of each stage’s sector directly and, as in classical cyclic symmetry analysis, to study the nodal diameter problems separately. The method is first validated on a simple case study which shows good agreements with a complete 360 deg reference calculation. An industrial example involving two HP compressor stages is then presented. Then the forced response application is presented in which synchronous engine order type excitations are considered.

Modal methods for the analysis of cyclic symmetric structures

In this paper, the modal displacement and modal acceleration methods have been extended to the cyclic symmetry analysis in the semi-complex domain. The study of the influence of forcing frequency on the relative accuracy of the two modal methods is also made. It is shown that only few modes are sufficient to get accurate stresses in the case of modal acceleration method.

STRESS ANALYSIS OF CIRCULAR CYLINDRICAL SHELLS WITH FLANGE AND RIB ASSEMBLY

Static analysis of circular cylindrical shell with ribs and flange assembly subjected to axisymmetric and asymmetric loading is carried out. Finite element method using cyclic symmetric is used. The Potter’s method is modified to solve the simultaneous equation of cyclic symmetry analysis. An experimental model was tested for static axisymmetric and asymmetric loading. The results are compared with the theoretical ones.