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.     

Vibration localization of a mistuned rotating multi-packet blade system undergoing external cyclic harmonic force

A multi-packet blade system consists of several blades which are attached to a disk and connected through shrouds. The blades of a multi-packet blade system are usually assumed to be identical. However, there always exists small, random mistuning among the blades due to manufacturing tolerance, in-operation wear and environmental changes. Such mistuning may cause significant increase in the forced vibration responses of some blades in the multi-packet blade system. Critical fatigue problems often occur in mistuned systems since the forced vibration response of a mistuned system is often significantly larger than that of a tuned system. Therefore, it is very important to predict the maximum blade response. In this study, blades are idealized as cantilever beams and the flexibilities of the disk and shrouds are idealized as discrete springs. Equations of motion are derived using the hybrid deformation variable method. To realize vibration localization with random mistuning, transient analysis is carried out for a multi-packet blade system excited by multiple nozzle jet forces.     

汽轮发电机组叶片—轴耦合系统动力响应问题研究

为了深入研究汽轮发电机组叶片弯振和轴扭振在外界扰动下的耦合振动响应问题 ,提出了阻抗匹配法。该法可以用来分析具有任意多个叶片数目的叶片—轴耦合系统动力响应问题 ,可以计算耦合系统稳态或瞬态响应。研究结果表明叶片弯曲振动和轴扭转振动之间具有很强的耦合性。耦合系统中叶片弯振固有频率降低而轴扭转固有频率增大 ,在外界扰动作用下两者会同时被激发出来 ,叶片根部所承受的力和力矩在短时间内有可能会达到一个比较大的峰值 ,从而影响到叶片的安全稳定运行     

失谐对叶片-轮盘结构振动特性的影响

研究了失谐对叶片—轮盘结构系统振动特性的影响。将叶片模拟为固定在轮盘上的悬臂梁模型,采用Hamilton变分原理和Galerkin方法,导出了系统的运动方程表达式。求解状态方程的特征值问题获得系统的特征向量。以一个含16个叶片的叶片—轮盘结构为例,分析了它的振动模态。结果表明,失谐会导致系统的振动模态出现局部化现象。分析了叶片的失谐量和轮盘的转速对结构振动模态局部化的影响。     

Mode localization of a component cooling water heat exchanger

In a nuclear power plant, the tubes of a component cooling water heat exchanger are frequently affected by cold and hot fluid shock waves. Thus, tubes are often found to be worn out. This wear may alter the dynamics of the tubes and introduce mode localization in the heat exchanger. This paper examines mode localization in a component cooling water heat exchanger. A heat exchanger, consisting of periodic cooling tubes is used to simulate as a coupled periodic structure system. Each tube is coupled to the adjacent one through the water, and so the system is weakly coupled. The Galerkin method is employed herein to derive the mode localization equations off the mistuned system, with reference to the fluid effect. Numerical results reveal that the wear may introduce mode localization into a mistuned heat exchanger with fluid.     

Response of large mistuned bladed disk assembly subjected to random excitations

In this study, the effects of large geometric mistuning on blade response are investigated considering the change of mistuning properties and excitation characteristics. The response variations because of large mistuning are negligible under white noise excitations and are highly significant under narrow band excitations. For the different excitation correlations, the responses are represented using non-dimensional variables in order for the results to be comparable to each other. It is shown that the ratio of the modal frequency between the tuned and large mistuned blades determines the propagation direction of the natural frequencies of the mistuned system, therefore, the responses of large mistuned blades depend primarily on their level of modal frequency.     

频率转向特征对失谐叶盘模态局部化的作用

基于叶盘集中参数模型,分析了叶片刚度失谐对频率转向区内的系统固有频率及叶片模态振型的影响,提出了一个描述模态局部化程度的参数,仿真研究了频率转向特征对失谐叶盘模态局部化程度的作用规律。研究表明,频率转向曲线之间关于节径的最小间隙(转向频率间隙)是反映频率转向特征的重要参数,并存在一个转向频率间隙的极小值点,在该极值点附近,频率转向区内的模态对叶片失谐非常敏感,并会导致模态局部化程度剧烈变化。     

Dynamic response of coupled shaft torsion and blade bending in rotor blade system

This study develops a computational model for the dynamic characteristics of a rotor-blade system. The rotor-blade coupled model with pre-twisted blade attached to a rigid disk driven by a shaft is developed using the Lagrange equation in conjunction with the assumed mode method to discretize the blade deformation. The effects of axial shortening due to blade lagging deformation, centripetal force caused by the rotating blade, and gravity are included in the model. The coupled equation of motion is formulated based on the small deformation theory for the blade and shaft torsional deformation to obtain the dynamic characteristics of the system for various system parameters. Numerical simulations show that the pre-twist angle of the blade and the shaft torsional flexibility strongly influence the dynamic behavior of the rotor-blade system.     

Study on localization influences of frequency veering on vibration of mistuned bladed disk

Reduced-order models of the bladed disk of the aero-engine compressor were established by adopting Prestressed component mode synthesis (PCMS) method. The frequency veering characteristics of the tuned bladed disk were analyzed. From the aspect of the strain energy, the forced vibration response of the mistuned bladed disk was analyzed, along with calculation of the contribution degree factors, the localization factors and frequency veering distances, finding the influences of the frequency veering distance, the contribution degree factors and the localization. The results show that frequency veering has significant influence on vibration localization of the mistuned bladed disk; in the region of frequency veering, the degree of vibration localization of the mistuned bladed disk is relatively high; along with the changes of the frequency veering distance, the contribution degree of the strain energy of the blades of localization of the mistuned bladed disk shows the certainty of regularity.     

Non-linear flap-lag-extensional vibrations of rotating, pretwisted, preconed beams including Coriolis effects

The effects of pretwist, precone, setting angle, Coriolis forces and second degree geometric non-linearities on the steady state deflections, coupled frequencies and mode shapes of rotating, torsionally rigid, cantilevered beams are studied in this investigation. The equations governing flap-lag-extensional motion are derived including the effects of large precone (a component of sweep) and retaining geometric non-linearities up to second degree. The Galerkin method, with non-rotating normal modes, is used for the solution of both steady state non-linear equations and linear perturbation equations. The results indicate that the second degree geometric non-linear terms, which vanish for zero precone, can produce frequency changes of engineering significance (of the order of 20% on the fundamental mode, and about ±4% on the second mode). The results further indicate that the linear and non-linear Coriolis effects must be included in analyzing thick blades while these effects can be neglected in analyzing thin blades, typical of advanced turboprop blade configurations. For those cases where the effect is significant, the linear and non-linear Coriolis effects oppose one another, the non-linear effects generally being stronger.     

Modeling and vibration feedback control of rotating tapered composite thin-walled blade

This paper addresses the problem of the modeling and vibration control of tapered rotating blade modeled as thin-walled beams and incorporating damping capabilities. The blade model incorporates non-classical features such as anisotropy, transverse shear, secondary warping and includes the centrifugal and Coriolis force fields. For the rotating blade system, a thorough validation and assessment of a number of non-classical features including the taper characteristics is accomplished. The damping capabilities are provided by a system of piezoactuators bonded or embedded into the structure and spread over the entire span of the beam. Based on the converse piezoelectric effect, the piezoactuators produce a localized strain field in response to a voltage and consequently, a change of the dynamic response characteristics is induced. A velocity feedback control law relating the piezoelectrically induced transversal bending moment at the beam tip with the appropriately selected kinematical response quantity is used and the beneficial effects upon the closed-loop dynamic characteristics of the blade are highlighted.     

叶盘结构频率转向特征及失谐敏感性实验研究

搭建了用于失谐叶盘结构固有特性及失谐敏感性研究的实验平台,对谐调叶盘结构的频率转向现象进行了实验研究,验证了以往理论分析和有限元仿真中发现的频率转向特征和模态振型转换现象;通过在叶尖粘贴不同的质量块,模拟了三种典型的叶片失谐形式,实验研究了失谐叶盘结构的模态局部化问题;针对同一叶片失谐形式下不同的模态密度区域,实验研究了模态密度对失谐敏感性的影响规律。实验结果与有限元实验仿真结果吻合较好。     

定向凝固合金叶片的裂纹与再结晶研究

对定向凝固合金叶片的裂纹进行分析，在断口观察与金相组织分析的基础上，对叶片的失效模式与失效原因进行研究，并提出预防该类故障发生的措施。研究结果表明，定向凝固合金叶片的裂纹是由于叶片表面的再结晶而导致的。叶片表面的再结晶在叶片使用之前就已存在，是由于固溶热处理前叶片的表面存在塑性变形，在固溶热处理过程中形成的。     

大型风力发电机叶片在三维旋转状态下的气动特性分析

为了更准确地研究风力发电机在三维旋转状态下的动态失速特性,分析其气动性能,建立风力机叶片和轮毂的三维气动模型,采用计算流体力学方法,对叶片在三维旋转状态下的气动特性进行了模拟,得到叶片周围流场分布状况。分析结果表明相对于无旋转状态,三维旋转状态下,叶片表面气流有沿叶展方向的运动,改变了叶片表面压力分布,致使气流流动分离延迟,导致叶片出现失速延迟的现象,提高了叶片从风中获得能量的能力。     

金属材料去除对叶片模态变化影响的试验研究

为了考察叶片在加工过程中的固有频率变化,采用光纤位移传感器对不同加工状态的叶片模态进行了测试。试验结果显示,叶片模态频率阶数较多且分布不均匀,随着加工的进行、材料的去除,叶片各阶模态频率都呈现下降趋势,同时阻尼比也降低。结合试验结果与加工实际进行分析,认为主轴转动引起的切削力激励频率与加工开始时的叶片固有频率较接近,引起了共振,导致叶片表面有振纹产生。在实际生产中,应改变主轴转速以避免共振。通过本试验发现:为避免共振,在高速加工薄壁悬臂零件时,需要关注其加工过程中的模态变化。     

水平轴风力机叶片的结构设计与有限元分析

设计了一种1．5MW水平轴风力机叶片模型,运用ANSYS Workbench对叶片模型添加材料属性、划分网格、施加载荷与约束进行有限元分析。进行了叶片在静止状态和有预应力作用两种工况下的结构模态计算,分析了叶片在被施加极限挥舞栽荷作用下的表面应力分布情况,计算了叶片的最小模态频率和最大应力分布情况。     

叶片数对离心泵叶轮失速特性影响研究

为研究叶片数对离心泵叶轮失速特性的影响,以4种不同叶片数的离心泵叶轮为研究对象,采用改进的亚格子模型(Sub-grid scale model,SGS)对叶轮的内部流场进行数值模拟,得到不同叶片数的失速团的运动规律,以及失速频率、失速团个数、转速等特性参数。研究表明,叶片数对叶轮内部失速团的类型有显著影响,当叶片数为偶数时,会发生"交替失速"流动现象;当叶片数为奇数时,会发生"旋转失速"流动现象。另外,叶片数对失速团特征参数也有一定影响。当发生"交替失速"时,叶片数增多,失速团的数量也随之增多,失速频率也随之变化,4叶片叶轮失速团的失速频率约是6叶片的2.4倍;而当发生"旋转失速"时,叶片数增多,失速团的数量也随之增多,转速也随之增大,7叶片叶轮失速团的转速约是5叶片的1.8倍,失速频率是它的3.8倍。     

液力变矩器叶栅系统的三维建模

液力变矩器要求具有良好的动力性和经济性,叶栅系统的设计是液力变矩器设计的关键,直接影响液力变矩器的性能。探讨了液力变矩器叶片三维建模方法,提出了建模方法的基本设计流程。以投影于多圆柱面的等角射影原理为基础,建立了液力变矩器叶栅系统的数学模型。通过求解流线上各分点的坐标,确定叶片在剖分面上的形状,利用直纹面将其连接,从而直接生成叶片形状。这种模型为液力变矩器叶栅系统的设计制造提供了方便,可用于三维流场的数值分析和叶片的快速成型。     

LP compressor blade vibration characteristics at starting conditions of a 100 MW heavy-duty gas turbine

In this paper are presented the blade vibration characteristics at the starting conditions of the low pressure multistage axial compressor of heavy-duty 100 MW gas turbine. Vibration data have been collected through strain gauges during aerodynamic tests of the model compressor. The influences of operating modes at the starting conditions are investigated upon the compressor blade vibrations. The exciting mechanisms and features of blade vibrations are investigated at the surge, rotating stall, and buffeting flutter. The influences of operating modes upon blade dynamic stresses are investigated for the first and second stages. It is shown that a high dynamic stress peak of 120 MPa can occur in the first stage blades due to resonances with stall cell excitations or with inlet strut wake excitations at the stalled conditions.