离心式风机含裂纹叶片的试验模态分析

针对离心式风机含裂纹叶片振动特性,搭建了风机在自由悬挂状态下的试验模态分析平台,分别在无裂纹和不同裂纹深度等8种情况下对叶片固有频率及模态振型进行了试验研究。经试验研究与数据分析得:离心式风机叶轮结构固有频率随裂纹深度的增加而单调下降;裂纹越深,固有频率下降越快。该结论为风机叶片故障监测与诊断提供了基础。     

基于模态分析的裂纹齿轮特征识别

为辨别裂纹齿轮的故障位置,通过有限元技术和模态曲率对比分析,获得了裂纹齿轮的动力学特性。建立了正常齿轮和裂纹齿轮的精确模型,利用ANSYS软件计算了齿轮的固有频率和振型,并通过差分法获得振型的模态曲率。分析结果表明,裂纹齿轮的弯曲振动模式发生频率分裂现象,固有频率和振型的变化不明显,而模态曲率的变化可明显指出裂纹的位置。     

裂纹对齿轮轮齿结构振动的影响

建立具有裂纹的齿轮轮齿的动力学模型，分析齿轮轮齿发生裂纹后轮齿结构的动力响应及动力特性，并对裂纹出现位置和裂纹尺寸对齿轮结构动力特性的影响进行深入探讨；通过分析计算和有限元数值模拟验证表明，裂纹发生位置对齿轮轮齿振型影响较大，在裂纹发生处振型发生突变；而裂纹大小对其振型和固有频率影响都较大，当裂纹出现后齿轮固有频率发生下降，振型也发生变化，随着裂纹深度的增加，固有频率更加下降，低阶下降显著，而高阶下降缓慢，振型也与无裂纹的情形完全不同。这显示出裂纹对齿轮轮齿结构振动的影响随裂纹尺寸的增加而强烈。     

含任意数目裂纹梁的振动分析

基于递推方法研究多种边界条件下含任意数目裂纹梁的振动分析。将梁的裂纹模拟为无质量的等效扭转弹簧。通过递推方法可以把裂纹梁的特征微分方程转换成递归代数公式,然后利用边界条件和裂纹位置的连续性条件推导可以得到该裂纹梁的无量纲固有频率以及相应的振形函数解析表达式。通过与参考文献中的计算结果相比较,验证了方法的正确性和有效性。文中还给出了具体的算例,计算出了简支梁的模态振型,并分别讨论了裂纹的数量和深度对于固有频率的影响。     

裂纹齿轮动力特性分析与模拟

建立了齿轮的动力学模型 ,分析了齿轮轮齿发生裂纹后的动力特性 (固有频率、振型等 ) ,并对裂纹出现位置和裂纹尺寸等对齿轮动力特性的影响进行了深入探讨和计算机模拟 ,指出裂纹发生位置对齿轮轮齿振型影响较大 ,在裂纹发生处振型发生突变 ;而裂纹尺寸对其振型和固有频率影响都较大 ,当出现裂纹后固有频率发生下降 ,振型也发生变化 ,随着裂纹尺寸增加 ,固有频率下降更加显著 ,各阶幅值下降大小不一 ,振型也与无裂纹的情况完全不同。这对齿轮的损伤监测和诊断具有重要价值     

链式结构系统动力特性的灵敏度分析

提出了一种求解链式结构系统的动力特性灵敏度的解析方法。首先根据结构系统振动的传递矩阵法建立了求解系统动力特性(固有频率和模态振型)的方程,在此基础上对系统动力特性的灵敏度进行了分析,导出了系统固有频率和模态振型对结构参数灵敏度的计算表达式。最后通过算例说明了文中模型的合理性和求解方法的有效性,并获得了一些有意义的结论。     

单输入多自由度系统自然激励技术的解析格式

自然激励技术的提出为大型复杂工程结构环境激励下的模态提取提供了一条新的途径,但对于单输入的情况存在以下问题:白噪声激励下结构系统位移响应的互相关函数公式中的相位角和幅值缺乏解析表达式;当动力荷载恰好作用在系统某阶振型的节点时可能出现的现象缺乏分析和物理解释.发展了单输入自然激励技术,推导了白噪声激励下结构位移响应的互相关函数,给出了其中相位角和幅值的解析表达.研究发现,当单输入动力荷载恰好作用在系统某阶位移模态的节点时,任意两自由度位移响应的互相关函数中将不含有频率值等于该阶模态有阻尼固有频率的简谐成分,即该阶模态的信息在互相关函数中得不到反映.     

流固耦合作用下空间导叶式离心泵叶轮湿模态分析

研究流固耦合作用下流体机械叶轮的湿模态分析,对避免水泵共振和保证水泵的安全运行具有重要意义。本文以某空间导叶式离心泵为研究对象,运用ANSYS Workbench软件,研究了叶轮部件在空气和水环境中的干湿模态特性,分析了流固耦合作用对叶轮部件固有频率和模态振型的影响。同时,结合流体机械动静干涉的原理,讨论了离心泵叶轮的共振特性与原因。研究表明:在水体附加质量和附加阻尼的作用下,叶轮各个阶次的固有频率大幅降低,模态振型的幅值受到水体的抑制作用有所降低;水环境下叶轮降低的固有频率与激振力频率不再相近,进而抑制了叶轮共振模态的激发;叶轮在不同流体环境下的固有频率与流体声速密切相关,声速越低,固有频率越小。     

摆线钢球行星传动自由振动分析

为准确反映摆线钢球行星传动的固有特性,建立了平移-扭转耦合动力学模型,求解了载荷作用时各构件相对位移量,并推导出动力学微分方程,获得了自由振动特征方程,得到了系统固有频率及主振型。分析了结构参数对固有频率的影响,并对理论研究进行了验证。结果表明：机构具有系统全振动模态、输出轴静止振动模态与输出轴扭转振动模态,传动比对固有频率的影响具有不确定性,输出轴支承刚度是影响固有频率的重要参数,验证了理论研究的正确性。     

轴裂纹故障对齿轮耦合系统固有特性的影响

利用SolidWorks软件建立了齿轮-轴系耦合系统的模型,将其导入ABAQUS软件进行模态分析,用Lanczos法提取系统前九阶固有频率和振型,预估结构的振动特性,对系统的动态响应分析提供了理论基础。在从动齿轮轴上定义crack seam,建立了带有裂纹轴的齿轮耦合系统的有限元模型,并分析了其固有振动特性。对比正常耦合系统,分析了裂纹对齿轮耦合系统的固有特性的影响。结果表明,齿轮轴出现裂纹后固有频率降低,对振型的影响也较大,为齿轮轴裂纹故障的监测和识别提供了一定的理论参考。     

受弯梁中开裂纹的位置识别与分析

利用有限元计算判定受弯梁中开裂纹的位置 ,从中得出 :同正常梁相比 ,裂纹梁的固有频率与振型的变化不但与裂纹深度而且与裂纹位置有关 ,因而 ,通过裂纹梁低阶固有频率及振型的变化情况可以判定裂纹的位置。对于裂纹较浅的情况 ,直接利用振型与固有频率的变化很难判定裂纹的位置 ,必须借用一些特征参数来提高识别的敏感性 ,这样 ,裂纹梁中早期裂纹的识别也是可行的     

Crack detection in a beam with an arbitrary number of transverse cracks using genetic algorithms

In this paper, a crack detection approach is presented for detecting depth and location of cracks in beam-like structures. For this purpose, a new beam element with an arbitrary number of embedded transverse edge cracks, in arbitrary positions of beam element with any depth, is derived. The components of the stiffness matrix for the cracked element are computed using the conjugate beam concept and Betti’s theorem, and finally represented in closed-form expressions. The proposed beam element is efficiently employed for solving forward problem (i.e., to gain precise natural frequencies and mode shapes of the beam knowing the cracks’ characteristics). To validate the proposed element, results obtained by new element are compared with two-dimensional (2D) finite element results and available experimental measurements. Moreover, by knowing the natural frequencies and mode shapes, an inverse problem is established in which the location and depth of cracks are determined. In the inverse approach, an optimization problem based on the new finite element and genetic algorithms (GAs) is solved to search the solution. It is shown that the present algorithm is able to identify various crack configurations in a cracked beam. The proposed approach is verified through a cracked beam containing various cracks with different depths.     

A note on elliptical plate vibration modes as a bifurcation from circular plate modes

The exact modes of vibration of a circular plate satisfy the geometrical boundary conditions of uniform elliptical plates in modified polar coordinates. In a previous investigation the exact modes of a clamped circular plate were used as shape functions in the Rayleigh-Ritz method to characterize the vibration of clamped elliptical plates. The mass and stiffness matrices were expressed in closed form and the resulting eigen value problems for the four mode categories of the elliptical plates were solved numerically. In the present investigation the computed variations of the plate frequencies with aspect ratio are used to study the similarities between the elliptical and circular plate modes. It is concluded that as the aspect ratio increases from unity, the axisymmetrical circular plate mode varies as a single elliptical plate mode, whereas the non-axisymmetrical circular plate mode splits up into two distinct elliptical plate modes.     

Four-beam model for vibration analysis of a cantilever beam with an embedded horizontal crack

As one of the main failure modes, embedded cracks occur in beam structures due to periodic loads. Hence it is useful to investigate the dynamic characteristics of a beam structure with an embedded crack for early crack detection and diagnosis. A new four-beam model with local flexibilities at crack tips is developed to investigate the transverse vibration of a cantilever beam with an embedded horizontal crack; two separate beam segments are used to model the crack region to allow opening of crack surfaces. Each beam segment is considered as an Euler-Bernoulli beam. The governing equations and the matching and boundary conditions of the four-beam model are derived using Hamilton's principle. The natural frequencies and mode shapes of the four-beam model are calculated using the transfer matrix method. The effects of the crack length, depth, and location on the first three natural frequencies and mode shapes of the cracked cantilever beam are investigated. A continuous wavelet transform method is used to analyze the mode shapes of the cracked cantilever beam. It is shown that sudden changes in spatial variations of the wavelet coefficients of the mode shapes can be used to identify the length and location of an embedded horizontal crack. The first three natural frequencies and mode shapes of a cantilever beam with an embedded crack from the finite element method and an experimental investigation are used to validate the proposed model. Local deformations in the vicinity of the crack tips can be described by the proposed four-beam model, which cannot be captured by previous methods.     

Identification of multiple cracks in beams under bending

The identification of a transverse crack on a beam is the subject of many investigators. Identifying the crack means to find its position and depth. In many cases there are more than one cracks on a beam. Then the solutions, or the combinations of parameters characterising the cracks are more and the problem becomes more complicated particularly when the crack must be identified using one more parameter, the relative each other angular position.In the present paper the dynamic behaviour of a cracked beam with two transverse surface cracks is studied. Each crack is characterised by its depth, position and relative angle. Both cracks are considered to lie in arbitrary angular positions with respect to the longitudinal axis of the beam and at any distance from the left end. A local compliance matrix of two degrees of freedom, bending in the horizontal and the vertical planes is used to model the rotating transverse crack in the shaft and is calculated based on the available expressions of the stress intensity factors and the associated expressions for the strain energy release rates. The compliance matrix is calculated for the first time at any angle of rotation. Thus, the compliance is given as a function of both the crack depth and the angular location. These expressions are usable, due to the stress intensity function limitations, only for limited regions around the zero angular position of the crack and not for every crack angle. For these cases, B-spline curves are used to interpolate the known points and a function in analytical form is given for every crack depth and angle. It is well known that when a crack exists in a structure, such as a beam, then the natural frequency of vibration decreases. This reduction is studied here for six independent parameters namely the depth, the location, and the rotational angle of each crack. By keeping these six parameters constant, the first three flexural eigenmodes can be computed and plotted.Due to its sensitivity in slope or displacement changes the theory of wavelets is used here to identify the locations of the cracks reducing thus the number of independent parameters. As it is well known the existence of a crack on a beam in bending, creates in the elastic line of the beam a slope discontinuity analog generally to the crack depth and additionally here to the angular position. The wavelet transformation of a vibration mode or of the vibration response of the structure under some circumstances could be used to locate the cracks. If the positions are known, then the depths and the respective angles can be determined. Here the diagrams of the first three eigenvalues versus both the crack depth and the rotational angle, are used to identify the remaining unknown parameters for both cracks.     

Free vibration analysis of Euler-Bernoulli beam with double cracks

In this paper, the influence of two open cracks on the dynamic behavior of a double cracked simply supported beam is investigated both analytically and experimentally. The equation of motion is derived by using the Hamilton’s principle and analyzed by numerical method. The simply supported beam is modeled by the Euler-Bemoulli beam theory. The crack sections are represented by a local flexibility matrix connecting three undamaged beam segments. The influences of the crack depth and the position of each crack on the vibration mode and the natural frequencies of a simply supported beam are analytically clarified for the single and double cracked simply supported beam. The theoretical results are also validated by a comparison with experimental measurements.     

Vibrations of rectangular plates with internal cracks or slits

This work applies the famous Ritz method to analyze the free vibrations of rectangular plates with internal cracks or slits. To retain the important and useful feature of the Ritz method providing the upper bounds on exact natural frequencies, the paper proposes a new set of admissible functions that are able to properly describe the stress singularity behaviors near the tips of the crack and meet the discontinuous behaviors of the exact solutions across the crack. The validity of the proposed set of functions is confirmed through comprehensive convergence studies on the frequencies of simply supported square plates with horizontal center cracks having different lengths. The convergent frequencies show excellent agreement with published accurate results obtained by an integration equation technique, and are more accurate than those obtained by a previously published approach using the Ritz method combined with a domain decomposition technique. Finally, the present solution is employed to obtain accurate natural frequencies and mode shapes for simply supported and completely free square plates with internal cracks having various locations, lengths, and angular orientations. Most of the configurations considered here have not been analyzed in the previously published literature. The present results are novel, and are the first published vibration data for completely free rectangular plates with internal cracks and for plates with internal cracks, which are not parallel to the boundaries.     

柔性差测量科赫分形涡流传感器内部裂纹检测

柔性涡流传感器由于其可变形性有望被用于复杂形貌结构的无损检测。 柔性科赫分形涡流传感器由于其局部微结构 对涡流的调理效果,对各方向短裂纹检测性能的一致性较高,但该传感器对于近表面及内部裂纹的检测还未展开研究。 构建了 差测量传感器的等效电路模型;通过仿真方法研究了涡流分布随深度的演化规律;通过试验方法,研究了传感器对覆盖不同厚 度铝板预制裂纹试块的检测效果。 有限元结果表明,随着深度的增加,涡流密度减小,集中性降低,分布的形态与其在表面差异 越来越大,形态由雪花状向圆形演化。 试验结果表明,传感器输出信号随着覆盖层厚度的增加而减弱;当激励频率为 10 kHz 时,传感器可检测到裂纹时覆盖铝板最大厚度为 2. 0 mm。     

Vibration of clamped elliptical plates using exact circular plate modes as shape functions in Rayleigh-Ritz method

The vibration of clamped uniform elliptical plates is investigated using the exact modes of circular plates as shape functions in the Rayleigh-Ritz method. This paper investigates the behaviour of clamped elliptical plates using modified polar coordinates and the exact modes of circular plates in terms of Bessel and modified Bessel functions. The elements of the mass and stiffness matrices are expressed in closed form using Lommel integrals. The accuracy and the convergence of this approach are validated, and numerical results for natural frequencies for various plate aspect ratios are presented.     

基于双轴 TMR 电磁传感器的裂纹检测方法研究

针对单一激励交流电磁探头检测任意方向裂纹容易出现漏检问题,设计了用于检测奥氏体不锈钢表面斜裂纹的新型双激励传感器,建立了奥氏体不锈钢表面裂纹交流电磁场检测仿真模型,开发了基于新型双激励传感器和高分辨率隧道效应磁阻传感器的金属平板表面裂纹检测系统。基于理论模型和试验系统研究了试件上裂纹走向和裂纹宽度对传感器拾取到磁场分量幅值的影响规律,研究了裂纹检测与方向判定方法。仿真和实验结果表明,利用磁场分量B_x、B_y畸变特征能够以相同的灵敏度检测出试件表面尺寸为15 mm×0.2 mm、深度大于3 mm的微小裂纹,并实现裂纹方向判定。引入宽度补偿参数后减小了横向、纵向裂纹判定误差,判定误差最大为3.9°。