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A comprehensive theoretical, numerical and experimental approach for crack detection in power plant rotating machinery

机译：发电厂旋转机械裂纹检测的综合理论，数值和实验方法

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In order to describe the state-of-the-art on cracked rotor related problems, the current work presents the comprehensive theoretical, numerical and experimental approach adopted by EDF for crack detection in power plant rotating machinery. The work mainly focuses on the theoretical cracked beam model developed in the past years by S. Andrieux and C. Vare and associates both numerical and experimental aspects related to the crack detection problem in either turboset or turbo pump units. The theoretical part consists of the derivation of a lumped cracked beam model from the three-dimensional formulation of the general problem of elasticity with unilateral contact conditions on the crack lips, valid for any shape and number of cracks in the beam section and extended to cracks not located in a cross-section. This leads to the assessment of the cracked beam rigidity as a function of the rotation angle, in case of pure bending load or bending plus shear load. In this way the function can be implemented in a 1D rotordynamics code. An extension of the cracked beam model taking into account the torsion behaviour is also proposed. It is based on the assumption of full adherence between crack lips, when the crack closes, and on an incremental formulation of deformation energy. An experimental validation has been carried out using different cracked samples, both in static and dynamic configurations, considering one or three elliptic cracks in the same cross-section and helix-shaped cracks. Concerning the static configuration, a good agreement between numerical and experimental results is found. It is shown to be equal to 1% maximal gap of the beam deflection. Concerning the dynamical analysis, the main well-known indicator 2 × rev. bending vibration component at half critical speed is approximated at maximum by 18% near the crack position. Our experiments also allowed for the observation of the bending and torsion resonance frequency shifts determined by the extra-flexibility induced by the crack in the shaft. The validated crack model is then applied to predict the dynamical behaviour of large industrial rotating machinery and to verify the crack detection capability based on the vibratory response. With respect to 900 MW turboset units, with cracks affecting LP rotors, a map of crack detection capabilities, based on 1 x rev. and 2 x rev. components as a function of circumferential extension ratio and crack depth, is drawn. If the crack depth is higher than 37% of the rotor diameter, online measurements of 2 × rev. vibratory level shift allow to detect the crack. On the opposite, 1 x rev. monitoring is necessary for cracks with circumferential extension superior to 270°. It is also observed that LP rotor bending mode shift monitoring theoretically allows to detect cracks with depths equal to or greater than 20% of the rotor diameter or with circumferential extension greater than 120°. The difficulties encountered for distinguishing the LP rotor bending mode frequencies, which may also evolve in time, independently from the cracks, limit the industrial application of this latter technique. Therefore new studies will focus on the analysis of torsion dynamic behaviour and on its sensitivity to cracks.
机译：为了描述裂纹转子相关问题的最新技术，本工作介绍了EDF用于发电厂旋转机械裂纹检测的综合理论，数值和实验方法。这项工作主要集中于S. Andrieux和C. Vare在过去几年中开发的理论裂隙梁模型，并将数值和实验方面与涡轮机组或涡轮泵机组中的裂纹检测问题相关联。理论部分包括从裂纹唇的单侧接触条件下弹性的一般问题的三维表示的集总裂纹梁模型的推导，该模型对梁截面中任何形状和数量的裂纹均有效，并扩展到裂纹不位于横截面中。在纯弯曲载荷或弯曲加剪切载荷的情况下，这将导致裂纹梁刚度作为旋转角的函数进行评估。通过这种方式，可以用一维转子动力学代码实现该功能。还提出了考虑到扭转行为的裂纹梁模型的扩展。它基于以下假设：裂纹闭合时，裂纹唇之间完全附着，并基于变形能的递增公式。考虑到相同横截面中的一个或三个椭圆形裂纹和螺旋形裂纹，使用了静态和动态配置的不同裂纹样品进行了实验验证。关于静态配置，数值和实验结果之间找到了很好的一致性。它显示等于光束偏转的最大间隙的1％。关于动力学分析，主要的著名指标2×rev。在裂纹位置附近，半临界速度时的弯曲振动分量最大近似为18％。我们的实验还允许观察弯曲和扭转共振频率变化，该频率变化是由轴上的裂纹引起的超柔韧性决定的。然后将验证的裂纹模型应用于预测大型工业旋转机械的动力学行为，并基于振动响应验证裂纹检测能力。对于900 MW涡轮机组，其裂纹影响LP转子，基于1 x rev的裂纹检测能力图。和2 x转绘制了与周向延伸率和裂纹深度有关的成分。如果裂纹深度大于转子直径的37％，则在线测量为2×rev。振动水平位移允许检测裂纹。相反，1 x转速。对于周向延伸超过270°的裂纹，必须进行监测。还可以观察到，LP转子弯曲模式偏移监控在理论上可以检测深度等于或大于转子直径20％或周向延伸大于120°的裂纹。区分LP转子弯曲模式频率时遇到的困难（也可能随时间而发展）独立于裂纹，这限制了后一种技术的工业应用。因此，新的研究将集中于扭转动态行为的分析及其对裂纹的敏感性。

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