混频非线性超声波检测钢轨中裂纹的数值计算方法

Numerical Calculation Method for Detecting Rail Cracks Using Mixed-Frequency Nonlinear Ultrasonic Waves

摘要:

提出一种基于有限元法与谱元法耦合的非线性混频超声检测数值模型，研究非共线混频超声波与钢轨裂纹之间的非线性相互作用机制。通过非共线混频技术激发裂纹界面的非线性响应，结合双谱分析与非线性参数方法，定量表征裂纹尺寸变化对非线性超声响应的影响规律。结果表明，数值计算结果与试验数据有较好的一致性，非线性参数和非线性超声因子的平均绝对误差分别小于1.64%和1.99%。裂纹长度由1 mm增至8 mm时，非线性参数的数值计算与试验值增幅为95%和102%，非线性超声因子增幅为43%和46%，非线性特征参数与裂纹长度呈正相关关系。裂纹长度大于1 mm后回波信号的主波包裂变为多个子波包，双谱表现出明显的和频峰和二次谐波峰。非共线混频技术可有效识别钢轨中1 mm及以上的微裂纹，为钢轨早期伤损的高灵敏度检测提供理论依据与技术支持。

Abstract:

This paper proposes a numerical model combining the finite element method and spectral element method for nonlinear ultrasonic mixing. The nonlinear interaction mechanism between non-collinear mixing ultrasonic waves and rail cracks is systematically investigated. By exciting nonlinear responses at the crack interface via non-collinear mixing and applying bispectral analysis along with nonlinear parameter methods， the effect of crack size variation on the nonlinear ultrasonic response is quantitatively characterized. The results show strong agreement between numerical simulations and experimental data， with average absolute errors below 1.64% for nonlinear parameters and 1.99% for nonlinear ultrasonic factors. As crack length increases from 1 mm to 8 mm， the nonlinear parameter increases by 95% in simulations and 102% in experiments， while the nonlinear ultrasonic factor increases by 43% and 46%， respectively. The nonlinear characteristic parameters are positively correlated with crack length. For cracks longer than 1 mm， the main wave packet of the echo signal splits into multiple sub-packets， and the bispectrum exhibits distinct sum-frequency and second-harmonic peaks. The non-collinear mixing technique effectively identifies micro-cracks of 1 mm and above in rails， providing a theoretical basis and technical support for high-sensitivity detection of early-stage rail damage.