The cross-sectional geometry of a rail is complex, and numerous guided wave modes can be propagated in rails. In order to select a mode which is the most suitable for detecting a specific crack on a rail, a mathematical model of guided wave mode selection is constructed. The model is composed of a modal vibration factor and a modal orthogonal factor. By setting a reasonable vibration coefficient and orthogonal coefficient, the mode with the highest sensitivity to cracks is selected for crack detection. Taking a vertical crack on the rail bottom as an example, mode 1 at a frequency of 60 kHz is selected as the most suitable detection mode. At the same time, mode 7 and mode 11 are selected as comparative modes, and these three modes are simulated to detect rail cracks. Among them, mode 1 is the best, which verifies the correctness of the mode selection model. In addition, vertical cracks are manufactured artificially on the side of the rail bottom. The cracks are successfully detected by mode 1, and the positioning error is 0.07 m. After correction, the error is reduced to 0.02 m. The model can effectively select guided wave modes suitable for detecting arbitrary cracks on rails, which provides a theoretical solution for rail crack detection.

中文翻译：

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超声波导波的铁路裂纹检测模式选择模型

轨道的横截面几何形状很复杂，并且许多导波模式可以在轨道中传播。为了选择最适合检测轨道上特定裂纹的模式，构建了导波模式选择的数学模型。该模型由模态振动因子和模态正交因子组成。通过设置合理的振动系数和正交系数，可以选择对裂纹敏感性最高的模式进行裂纹检测。以钢轨底部的垂直裂缝为例，选择频率为60 kHz的模式1作为最合适的检测模式。同时，选择模式7和模式11作为比较模式，并模拟这三种模式以检测钢轨裂纹。其中，模式1最好，验证模式选择模型的正确性。另外，在钢轨底部的侧面上人为地制造了垂直裂纹。通过模式1成功检测到裂纹，定位误差为0.07 m。校正后，误差减小到0.02 m。该模型可以有效地选择适合检测轨道上任意裂纹的导波模式，为轨道裂纹的检测提供了理论上的解决方案。