Steam turbine rotor crack detection using sifting process of EMD and B-spline wavelet on the interval element model

A high-precision identification method for steam turbine rotor crack is presented. By providing the first three measured natural frequencies,contours for the specified natural frequency are plotted in the same coordinate,and the intersection of the three curves predicts the crack location and size. The cracked rotor system is modeled using Bspline wavelet on the interval(BSWI)finite element method,and a method based on empirical mode decomposition(EMD)and Laplace wavelet is implemented to improve the identification precision of the first three measured natural frequencies. Compared with the classical nondestructive testing,the presented method shows its effectiveness and reliability. It is feasible to apply this method to the online health monitoring for rotor structure.

DYNAMIC BEHAVIOR OF A CRACKED FLEXIBLE ROTOR SUPPORTED ON JOURNAL BEARINGS

The dynamic behavior of a cracked flexible rotor supported on three kinds ofjournal bearings is presented. Numerical experiments show that nonsynchronous responseswill happen due to the rotor crack, and the amplitudes of the nonsynchronous componentsbecome larger with the increase of crack. On the other hand, the fluid forces of journalbearings can suppress the nonsynchronous response. The (1/2) × or (3/2) × harmoniccomponent rarely appears for small crack near the rotating speed ratio Ω = 2Ωc or Ω =(2/3)Ωc. In the case of supercritical rotating speed, the additional 0× harmonic component is increased as the crack increases. The bearing parameters affect greatly the occur-rence of the nonsynchronous responses by means of exerting innuence on the critical spedand the stabi1ity of the system.

APPLICATION OF WAVELET TIME-FR EQUENCY ANALYSIS TO IDENTIFICA-TION OF CRACKED ROTOR

Based on the simple hinge crack model and the local flexibility theorem, thecorresponding dynamic equation of the cracked rotor is modelled, the numerical simulation solutionsof the cracked rotor and the uncracked rotor are obtained. By the continuous wavelet time-frequencytransform, the wavelet time-frequency properties of the uncracked rotor and the cracked rotor arediscussed. A new detection algorithm that uses the wavelet time-frequency transform to identify thecrack is proposed. The influence of the sampling frequency on the wavelet time-frequency transformis analyzed by the numerical simulation research. The valid sampling frequency is suggested.Experiments demonstrate the validity and availability of the proposed algorithm in identification ofthe cracked rotor for engineering practices.

Experimental Dynamic Analysis of a Breathing Cracked Rotor

Crack fault diagnostics plays a critical role for rotating machinery in the traditional and Industry 4.0 fac- tory. In this paper, an experiment is set up to study the dynamic response of a rotor with a breathing crack as it passes through its 1/2, 1/3, 1/4 and 1/5 subcritical speeds. A cracked shaft is made by applying fatigue loads through a three-point bending apparatus and then placed in a rotor testbed. The vibration signals of the testbed during the coasting-up process are collected. Whirl orbit evolution at these subcritical speed zones is analyzed. The Fourier spectra obtained by FFF are used to investigate the internal frequencies corresponding to the typical orbit characteris- tics. The results show that the appearance of the inner loops and orientation change of whirl orbits in the experiment are agreed well with the theoretical results obtained previously. The presence of higher frequencies 2X, 3X, 4X and 5X in Fourier spectra reveals the causes of subharmonic reso- nances at these subcritical speed zones. The experimental investigation is more systematic and thorough than previ- ously reported in the literature. The unique dynamic behavior of the orbits and frequency spectra are feasible features for practical crack diagnosis. This paper provides a critical technology support for the self-aware health man- agement of rotating machinery in the Industry 4.0 factory.

SIMULATION OF CRACK DIAGNOSIS OF ROTOR BASED ON MULTI-SCALE SINGUUR-SPECTRUM ANALYSIS

In the diagnosis of rotor crack based on wavelet analysis, it is a painful task to find out an adaptive mother wavelet as many of them can be chosen and the analytic results of different mother wavelets are yet not the same. For this limitation of wavelet analysis, a novel diagnostic approach of rotor crack based on multi-scale singular-spectrum analysis （MS-SSA） is proposed. Firstly, a Jeffcott model of a cracked rotor is developed and the forth-order Runge-Kutta method is used to solve the motion equations of this rotor to obtain its time response （signals）. Secondly, a comparatively simple approach of MS-SSA is presented and the empirical orthogonal functions of different orders in various scales are regarded as analyzing functions. At last, the signals of the cracked rotor and an uncracked rotor are analyzed using the proposed approach of MS-SSA, and the simulative results are compared. The results show that, the data-adaptive analyzing functions can capture many features of signals and the rotor crack can be identified and diagnosed effectively by comparing the analytic results of signals of the cracked rotor with those of the uncracked rotor using the analyzing functions of different orders.

Simulations and Experimental Investigation on Motion Stability of a Flexible Rotor-bearing System with a Transverse Crack

In the classical process for stability studies on the rotor-bearing system with crack faults, the simple discrete model is adopted for research on such problems, which neglect some needful dynamical influence factor, such as the material damping, shearing effect and gyroscopic effects, etc. Therefore, it is necessary to find a precise calculation model for simulation of the rotor-bearing system with cracks faults. In this paper, instead of the traditional simple discrete model, finite element （FE） model is adopted to investigate the motion stability of a nonlinear rotor system with crack fault. According to finite element theory, the FE model of the cracked rotor system is established firstly. It should be pointed out that the element where the crack occurs is modeled by a particular crack element and the supports at both ends are simulated by two nonlinear loads. Then, based on dimensionless and dimensionality reduction, the Newmark-[3 method and the shooting method are employed to study the effect of eccentricity and the depth of crack on instability speed and bifurcation feature. Furthermore, the simulation results are verified by some corresponding experiments. The simulation and experimental results show that instability speed does not change monotonically, but decreases firstly and then increases when the amount of eccentricity increases. Moreover, as the type of instability changes, the instability speed jumps concomitantly. Additionally, the presence of crack fault can disturb the oil whirl, as a result, instability speed tends to increase slightly, but it does not affect the type of instability and jumping phenomenon. This research presents an effective and convenient method which uses the finite element method （FEM） to research the motion stability of the nonlinear rotor-bearing system with cracked faults and other nonlinear force, and the proposed method can provide a theoretical reference for stability analysis and vibration control in more complex relevant rotor-bearing system.

Dynamic Stability Analysis of Periodically Time-Varying Rotor System with a Transverse Crack

Fatigue cracks may appear in horizontal rotating machinery due to periodic stresses imposed to its shaft. The investigation of stability behavior of cracked rotors can lead to proper diagnosis of machinery and to prevent possible accidents caused by the rotor failure. In this study, the dynamic stability of a rotor with a transverse crack is investigated. Models of both open and breathing cracks are developed and then used in the model of a cracked Jeffcot (de Laval) rotor. The stability of rotor motion equations represented by differential equations with periodic coefficients is investigated using Floquet theory. While both crack models show instability regions around the first un-damped frequency, sub-harmonic regions are predicted by the breathing crack models. Compared to perturbation methods frequently used to determine the stability regions, the transition matrix approach used in this study can be applied to complex models of rotors and consequently may help in the identification of cracks in rotating machinery.

Dynamic Characteristics of Multi-degrees of Freedom System Rotor-bearing System with Coupling Faults of Rub-impact and Crack

Extensive studies on rotor systems with single or coupled multiple faults have been carried out. However these studies are limited to single-span rotor systems. A finite element model for a complex rotor-bearing system with coupled faults is presented. The dynamic responses of the rotor-bearing system are obtained by using the rotor dynamics theory and the modern nonlinear dynamics theory in connection with the continuation-shooting algorithm（commonly used for obtaining a periodic solution for a nonlinear system） for a range of rub-impact clearances and crack depths. The stability and Hopf instability of the periodic motion of the rotor-bearing system with coupled faults are analyzed by using the procedure described. The results indicate that the finite element method is an effective way for determining the dynamic responses of such complex rotor-bearing systems. Further for a rotor system with rub-impact and crack faults, the influences of the clearances are significantly different for different rub-impact stiffness. On the contrary, the influence of crack depths is rather small. The instability speeds of the rotor-bearing system increase due to the presence of the crack fault. The results obtained using the new finite element model, presented for computation and analysis of dynamic responses of the rotor-bearing systems with coupled faults, are in accordance with measurements in experiment. The formulations given can be used for diagnosis of faults, vibration control, and safe and stable operations of real rotor-bearing systems.

NONLINEAR DYNAMICS OF A CRACKED ROTOR IN A MANEUVERING AIRCRAFT

The nonlinear dynamics of a cracked rotor system in an aircraft maneuvering with constant velocity or acceleration was investigated. The influence of the aircraft climbing angle on the cracked rotor system response is of particular interest and the results show that the climbing angle can markedly affect the parameter range for bifurcation, for quasi-periodic response and for chaotic response as well as for system stability. Aircraft acceleration is also shown to significantly affect the nonlinear behavior of the cracked rotor system, illustrating the possibility for on-line rotor crack fault diagnosis.

ANALYSIS OF THE CHAOTIC MOTION FOR A ROTOR SYSTEM WITH A TRANSVERSE CRACK

The chaotic motion of an elastic shaft-disk rotor system including thegeometric nonlinearity of the shaft with a transverse crack is investigated. The critical conditionfor the system to enter chaotic state is given by the Melnikov method. Meanwhile, whether the chaosoccurs is determined by the Poincare map, phase portrait and time-displacement history diagram.

IDENTIFICATION OF CRACKED ROTOR BY WAVELET TRANSFORM

The dynamic equation of cracked rotor in rotational frame was modelled, the numerical simulation solutions of the cracked rotor and the uncracked rotor were obtained. By the wavelet transform, the time frequency properties of the cracked rotor and the uncracked rotor were discussed, the difference of the time frequency properties between the cracked rotor and the uncracked rotor was compared. A new detection algorithm using wavelet transform to identify crack was proposed. The experiments verify the availability and validity of the wavelet transform in identification of crack.

Fatigue crack growth rates of rotor steel at elevated temperatures

Low fatigue samples were obtained from the outer edges of rotor steel (30CrlMolV) which had operated under different temperatures conditions. Based on this data, the effects of temperature on fatigue crack growth rates were investigated. This paper presents a derivation of the superposition expression of two natural logarithms governing crack growth rates and also discusses the relationship between a material’s constants and temperature. These results can provide experimental and theoretical references for fatigue life design of rotor steel in steam turbines.

基于Zencrack的汽轮机叶片蠕变断裂分析方法研究

汽轮机高压级次的动叶片承受着高温和离心力的双重作用,叶片的工作环境及其恶劣。叶片在高温环境下长时间工作会产生蠕变,研究叶片的蠕变断裂对于分析和预防叶片事故具有重要意义。文章利用Zencrack模拟了带有初始裂纹的汽轮机叶片在高温和离心力作用下裂纹的扩展问题,并给出了裂纹的扩展方式和最终的形貌。

基于Zencrack的汽轮机叶片疲劳断裂分析方法研究

汽轮机动叶片承受着高离心力和疲劳载荷的双重作用,其安全性一直是设计关注的焦点。汽轮机叶片的断裂将对汽轮机的安全运行产生重大影响。基于断裂力学分析软件Zencrack,并结合有限元分析软件Abaqus研究了具有初始裂纹的叶片在疲劳载荷的作用下其裂纹的扩展问题,得到了裂纹扩展后的最终形态以及裂纹前沿典型节点的扩展位移。该研究方法和思路对于后续分析汽轮机部件的断裂失效问题具有指导意义。

含呼吸裂纹的多盘双转子系统振动特性探究

由于材料、工作环境等因素影响,以航空发动机为代表的旋转机械在工作过程中可能会产生裂纹故障,常见的裂纹类型为呼吸裂纹。为分析该故障对轴系振动特性的影响,基于某型双转子涡扇航空发动机,建立了包含风扇和多个轮盘在内的双转子—支承动力学数值仿真模型,使用Newmark-β法分别对不同裂纹相对深度和不同转速下的系统工况进行了数值仿真求解。结果发现:随着裂纹逐渐加深,转子高频分量愈加明显,系统稳定性下降;随着转速升高,系统出现了2X,3X分量,工频分量在一阶临界转速前后先增大后减小,轴心轨迹由不规则形状逐渐转变为圆形。

滚动轴承支承下松动-裂纹耦合故障转子系统动力学特性分析

支座松动转子因两端刚度不对称而引发振动异常增大,进而可能导致转子出现裂纹故障,裂纹和松动故障耦合下的转子系统呈现强非线性特性.建立滚动轴承支承的支座松动-弓形裂纹转子动力学模型,研究转速、松动间隙、松动质量及裂纹角等对转子系统非线性动力学响应的影响.考虑非线性Hertz接触力,采用分段线性方程描述支座松动的刚度和阻尼,转子横向裂纹采用呼吸裂纹模型来研究,依据拉格朗日方程建立转子系统动力学方程,采用Runge-Kutta法求解方程获得转子振动响应的分岔图、频谱图、轴心轨迹图、Poincaré图等.计算结果表明,当系统转速达到2300rad/s时,松动-裂纹耦合故障系统较仅裂纹系统在1/3分频处有明显的间谐波成分,混沌区域更为宽泛;当裂纹参数恒定时系统随着松动间隙减小会更加稳定;当松动质量m_(s)>41.25kg时,系统振幅剧增,发生“跳跃”现象.研究工作对松动-裂纹转子系统的故障诊断和健康监测具有重要的工程应用价值.

耦合故障转子系统的非线性动力学分析

为研究多故障耦合对转子系统动力学的影响,建立刚性支承下的裂纹-碰摩耦合故障转子系统动力学模型,采用四阶Runge-Kutta方法对方程进行数值求解,对比分析系统在定子刚度以及裂纹深度等参数变化下转子系统的动力学响应。借助系统的分岔图对其非线性动力学行为以及系统稳定性进行分析,得到故障和转速之间的作用规律。结果表明,随着参数的改变,系统会呈现出丰富的动力学行为,包括单周期、多周期、拟周期和混沌等,该研究结果为汽车中驱动电机转子系统的设计和故障诊断提供了理论依据。

基于卷积神经网络和传感器数据的风力发电机转子断裂故障诊断

提出基于卷积神经网络和传感器数据的新能源风力发电机转子断裂故障诊断算法。根据转子运行状态与裂纹轴向刚度之间的关联关系,构建了发电机转子裂纹模型。对多个传感器采集的发电机转子振动数据进行融合处理后,将原始的一维数据转换为m×n二维矩阵的形式,利用多通道卷积神经网络对传感器数据信息进行分析,并将输出结果代入到发电机转子裂纹模型中,实现对转子断裂故障的诊断。在测试结果中,算法对不同数据源下的电机转子断裂故障诊断结果,误差稳定在0.03μm以内。

含半椭圆形裂纹轴的刚度特性研究

运用断裂力学理论,推导了含半椭圆形裂纹轴的刚度计算公式,研究了在全开的静态下半椭圆形前缘直裂纹和45°斜裂纹深度比、裂纹变形比等参数对轴刚度的影响。计算结果表明:裂纹深度的增大使半椭圆形前缘裂纹轴的刚度变化幅度较大,当裂纹深度较小时,刚度变化缓慢;但当裂纹深度大于轴半径一半时,裂纹轴全部载荷作用的影响都要考虑;随着裂纹变形比增大,半椭圆形前缘裂纹的刚度均减小;半椭圆形前缘裂纹垂直方向的位移随裂纹变形比增大而增大。计算结果与实验共同验证了半椭圆形前缘裂纹轴的动力特性。

X12转子钢蠕变-疲劳裂纹扩展行为的研究

在600℃条件下进行蠕变疲劳裂纹扩展速率实验,施加不同的载荷和保载时间,研究力值和保载时间对蠕变疲劳裂纹扩展速率的影响,并通过金相检测观察裂纹扩展路径。结果表明:在低应力条件下,蠕变疲劳裂纹扩展速率随着保载时间缩短而增大;在高应力条件下,蠕变疲劳裂纹扩展速率随保载时间延长而减小;相对含有疲劳成分裂纹而言,蠕变裂纹的扩展路径显得更加圆滑。