Mode localization in a rotating mistuned turbo disk with Coriolis effect

An investigation of the speed effect, i.e., the effects of centrifugal and Coriolis forces, on the mode localization of a mistuned blade-disk is presented in this paper. A disk comprising of periodically shrouded blades is used to simulate the weakly coupled periodic structure. Galerkin method is employed to derive the mode localization equations of the mistuned system with the consideration of Coriolis force. The blades are approximated as cantilever beams, and five axial and lateral modes of each blade are used to present the dynamic behavior of the system. Ten modal coordinates have been considered for each blade. The effects of Coriolis force and the magnitude of disorder on the localization phenomenon of a rotating blade-disk system were investigated numerically. Numerical results obtained herein indicate that the Coriolis force may enhance the localization phenomenon.     

The influence on coupling vibration of a rotor system due to a mistuned blade length

The influence on coupling vibrations among shaft-torsion, disk-transverse and blade-bending of a rotor system with a mistuned blade length was investigated analytically. The shaft–disk–blades system appeared to have four types of coupling vibrations, shaft–blade (SB), shaft-disk-blade (SDB), disk–blade (DB), and blade–blade (BB) mode. The natural frequencies in a mistuned blade were not only found changed but also the types of coupling modes. First, the DB modes in a tuned system disappeared and instead they are replaced by SDB modes. Second, the disk experienced mode localization due to the mistuned blade. The results also showed that every mode's frequency varied with the mistuned error linearly in one direction, either positive or negative, but not in both directions. At last, the effects of rotation on the changes of the rotor's natural frequencies were illustrated. Frequency loci showed merging phenomenon with an increase in the rotational speed.     

Dynamic stability of a rotating asymmetric cross-section blade subjected to an axial periodic force

The finite element method is applied to study the static and dynamic stability of an aerofoil cross-section rotating blade subjected to an axial periodic force. The effects of coupling due to the center of flexure (shear center) distance from the centroid, rotational speed, stagger angle and disk radius on the stability are considered. Critical load parameters are calculated and dynamic instability regions of the blade with different reference values are illustrated graphically. The numerical results indicate that the coupling effect is very important in the third and fourth modes depending on d_Y distance. The increase in stagger angle makes the blade less stable. However, the increase in rotational speed and disk radius make the blade more stable.     

风力发电系统云模型转桨控制器的设计

风能具有能量密度低、随机性和不稳定性等特点,风力发电机组变成了复杂的非线性不确定系统,风力发电系统控制器设计存在困难.本文将云模型应用于风力发电机组桨叶转角控制,其控制器采用一维多规则云发生器进行设计.当风速高于额定风速时,能够有效地调整桨叶转角随着风速的变化而变化,从而调节风力发电机输出功率维持在额定值附近.最后在MATLAB/SIMULINK中进行仿真,结果表明云模型转桨控制器比模糊转桨控制器具有更好的控制效果.     

Flow visualization in the tip region of a rotating blade row

We use flow visualization to examine the end-wall boundary layer as it passes through a rotating blade row of an axial-flow compressor; we find that concentrations of vorticity, such as the trailing vortex shed from the blade tip, or the horseshoe vortex from the blade leading edge, which we may expect to be present in the end-wall boundary layer, are swamped and rapidly dispersed by the large-scale motions in the turbulent end-wall layer. We investigate the effect of varying tip clearance on the boundary layer and find that increasing tip clearance and blade loading both cause the layer to increase in thickness. We also investigate the effect on the boundary layer of an end-wall casing treatment of the radial type; this leads to an increase in large-scale turbulent motions in the end-wall layer and, for a given clearance and blade loading, to an increase in the thickness of the boundary layer. One vortex is evident with either a treated or solid end-wall: this is the scraping vortex due to the ploughing effect of the blade as it passes through the end-wall boundary layer. This vortex remains evident well downstream.     

Effect of number of blades and distribution of cracks on vibration localization in a cracked pre-twisted blade system

A number of several blades can be grouped at their tips to increase their stiffness. This work examines how the effect of number of grouped blades and distribution of cracks affect the mode localization of a mistuned blade system. The pre-twisted blade and the effect of twist angle on localization are also considered in this article. Dynamic characteristics of blades in a blade system are focused to study. Periodically coupled pre-twisted beams were used to approximate shrouded blades. The Euler–Bernoulli beam model was employed to characterize the tapered pre-twisted blade. The mode localization equations associated with the local blade crack defects in the rotating grouped blade system were formulated using Hamilton's principle. The Galerkin method was used to discretize the localization equations of the mistuned system. The numerical results herein reveal that the number of grouped blades and the distribution of multi-disorders in a rotating blade system may markedly affect the localization phenomenon.     

Dynamics of a rotating Rayleigh beam subject to a repetitively travelling force

The dynamics of a rotating Rayleigh beam subject to a force travelling at a constant speed along the axial direction is studied. The beam is chosen as a simple model of the workpiece in the lathing process. A technique is developed for modeling the repetitive cutting force on the workpiece. The amplitude of the cutting force is chosen to be either constant or dependent on the motion of the beam. The discretized equations of motion of the rotating beam are obtained by Galerkin’s method. The time response of the rotating beam subject to the external force is discussed. The possible resonant conditions resulting in divergent solutions are studied. The stability of the response, due to a travelling motion-dependent force, is determined by the method of multiple scales. The effects of varying the rotating frequency, the travelling speed of the external force, and the movement of the force are also investigated.     

Torque and axial force at the surface of a blade in a conical helical anchor

Theoretical formulas are obtained for the torque and axial force at the upper blade surface when a conical helical anchor is screwed into the soil.     

一种新型谐波传动试验台的研制

介绍所研制的一种新型的适于模拟空间环境下的谐波传动试验台--双伺服扭杆加载谐波传动试验台.该试验台采用扭杆作为加载构件,通过扭杆两端的两台伺服电动机控制扭杆的弹性变形,实现扭矩加载;电子测控系统以工控机为控制中心,以PMAC控制扭矩加载,具有简明易用的可视化人机界面;可以实现8种系统特性的自动检测;具有精度高、自动化程度高、环境适应性强等特点.     

Vibration and reliability of a rotating beam with random properties under random excitation

In this paper, vibration and reliability of a rotating beam with random properties under random excitations are studied. The rotating beam is under a stochastic load modeled as a stationary white noise. The cross-sectional area, elasticity modulus, moment of inertia, shear modulus, damping coefficient, mass density and rotational speed are modeled as random variables. To develop the equations of motion, the finite element method and space state analysis are applied. In order to consider the randomness of properties, a second order perturbation method is used. The effects of rotational speed, setting angle, hub radius, variances of random properties, correlation of random variables and damping matrix forms on the vibration and reliability of rotating beams, are studied completely.     

手腕动力参数测试系统的研制

介绍了一种用于手腕动力参数测试的系统，概述了系统的硬件结构、工作原理及其软件设计，该系统为医学研究提供了良好的实验平台。     

Dynamic stability of a rotating pre-twisted asymmetric cross-section Timoshenko beam subjected to an axial periodic force

A finite element model is presented to study the static and dynamic stability of a pre-twisted Timoshenko beam having asymmetric aerofoil cross-section subjected to an axial periodic force. The change in the effects of coupling due to centre of flexure distance from the centroid and the shear coefficient on the stability due to the pre-twist angle is considered. It is concluded from the results that the pre-twist angle has an influence on the effects of coupling and the shear coefficient.     

Vibration suppression of atomic-force microscopy cantilevers covered by a piezoelectric layer with tensile force

In this paper, vibration suppression of a micro-beam covered by a piezoelectric layer is studied. The micro-beam is modeled with the specific attention to its application in AFM. The AFM micro-beam is a cantilever one which is stimulated close to its natural frequency by applying a harmonic voltage to the piezoelectric layer. The beam is an Euler-Bernoulli beam which abbeys Kelvin-Voigt model. Using such model supplies the comparison between elastic and viscoelastic beams; and one of the most important properties of viscoelastic materials, damping effect can readily be investigated. The pump provides an axial load with the result that it suppresses the vibrations. First, the vibration equations are extracted using Lagrangian and extended Hamiltonian method in vertical, longitudinal, as well as torsional directions and are discretized by exploiting the Galerkin mode summation approach. The discretized time-domain equations are solved by the aid of the Runge-Kutta method. The viscoelastic beam is compared with the elastic one, and the effects of damping ratio on vibration responses are presented. Additionally, the effects of micro-pump load, excitation voltage, and initial twist angle are investigated on the amplitude of vibration and natural frequency of system. It is observed that viscoelasticity of beam and axial load of the pump reduce vibrations and provide uniform time-domain responses without beatings.     

Variations of instability in a rotating spindle system with various bearings

To drive the speed of spindle faster and faster, especially for micro-via-drilling, the gas bearing–spindle is a must. However, most investigations of the dynamic characteristics of the spindle system are limited to the ball bearing type of spindle. This work examines the dynamic instability of a rotating spindle system with various bearings to elucidate the difference between the ball and gas bearing–spindle systems. A round Euler–Bernoulli beam is used to approximate the spindle. The Hamilton principle is applied to derive the equation of motion for the spindle system, and the multiple scales perturbation method is employed to solve the instability solution of the system. The effects of bearing types and speeds of rotation on the dynamic characteristics and instability of a rotating spindle system are further studied.     

一种新型计算机电源谐波检测分析系统设计

为实现计算机电源谐波精确检测和分析,引入基于重新定位采样序列同步化的谐波分析算法,设计了一种新型谐波检测与分析系统.开展了新型谐波检测与分析系统的应用领域、工作原理以及结构的分析.为提高数据处理效率,运用线性重新定位采样序列的同步化方法以减小泄漏误差,并采用了实数序列的快速傅里叶变换分析谐波频谱.搭建了一台新型谐波检测...     

Squeeze film due to a rotating curved disk approaching a fixed plane under the action of a force and moment

Squeeze film flow of an incompressible viscous fluid between a rotating curved disk and a plane wall at rest is studied theoretically. The rotating curved disk is assumed to be driven under the action of an axial force and moment, and to have arbitrary axi-symmetrical shape. The equations governing the gap between the rotating disk and the wall, and the angular velocity of the rotating disk, are determined and are solved for the case of a parabolic shape. If the disk is made concave, the approaching velocity and the angular velocity of the moving disk become small. This result is opposite to the convex case.     

A vibration analysis of a turbine blade system damped by dry friction forces

A turbine blade system with dry friction between the shroud ring elements is analysed and results obtained by a finite element method, are presented. Friction forces in the interacting surfaces are described in terms of anisotropic dry friction theory. In the examples, frequencies and mode shapes of undamped free vibrations of the system are analysed. Vibration excitation due to friction and vibration coupling caused by friction anisotropy are described when vibration is initiated by prescribed displacements or velocities.     

Modal analysis of a multi-blade system undergoing rotational motion

A modeling method for the modal analysis of a multi-blade system undergoing rotational motion is presented in this paper. Blades are assumed as cantilever beams and the coupling stiffness which originates from the shroud flexibility is considered for the modeling. To obtain general conclusions from the numerical results, the equations of motion are transformed into a dimensionless form. Dimensionless parameters related to the angular speed, the hub radius, and the coupling stiffness are identified and the effects of the parameters on the modal characteristics of the system are investigated. It is shown that the coupling stiffness especially plays an important role to change the modal characteristics of the system. The range of critical angular speed is also obtained through the numerical analysis. This paper was recommended for publication in revised form by Associate Editor Seockhyun Kim Ha Seong Lim graduated from Department of Mechanical Engineering at Hanyang University in 2006 and received his Master’s degree in 2008. He is currently a technical engineer in STX Offshore & Shipbuilding Company, Seoul, Korea. Hong Hee Yoo graduated from the Department of Mechanical Design and Production Engineering at Seoul National University in 1980 and received his Master’s degree from the same department in 1982. He received his Ph.D. degree in 1989 from the Department of Mechanical Engineering and Applied Mechanics at the University of Michigan at Ann Arbor, U.S.A. He is currently a professor in the School of Mechanical Engineering in Hanyang University, Seoul, Korea.     

Spray characteristics of the rotating fuel injection system of a micro-jet engine

In micro-turbojet engines with less than 350 kW power, it is not easy to find a suitable fuel injector with good spray quality. However, the rotating fuel injection system can potentially provide high atomization quality without the high-pressure fuel pump through the centrifugal forces of the engine shaft. With this motivation, a very small rotating fuel injector with 40 mm diameter is designed for the micro-turbo jet engine. It is directly linked to a high-speed rotational spindle capable of a speed up to 100,000 rpm. The droplet size, velocity, and spray distribution from the PDPA (Phase Doppler Particle Analyzer) system are measured. The spray is also visualized by a high-speed camera. The test results show that the length of liquid column from injection orifice is controlled by the rotational speeds and that SMD (Sauter Mean Diameter) is decreased with increasing rotational speeds. At a rotational speed of 73.3 m/s (35,000 rpm), SMD is lower than 60 μm at the entirety of the measuring space in the case of Type 2 (injection orifice diameter of 1.5 mm) and Type 3 (injection orifice diameter of 2.2 mm). Therefore, conceptually, it is possible to apply this small rotating fuel injection system to the micro-turbojet engine combustor.     

基于ANSYS的旋转床转鼓系统结构优化

为减小旋转床工作过程中转鼓的应力和变形,促进转鼓系统结构的改进,运用ANSYS软件建立旋转床转鼓系统有限元模型,进行静力学分析,得出转鼓正常工作状态下的应力分布。针对应力集中的部位和特点,改变局部结构,提出转鼓结构优化的有效措施。研究结果表明:最大变形在衬套与转鼓座接触处;在衬套中部存在应力集中现象;增大衬套壁厚、减小螺栓孔直径可以削弱该部位载荷。