Mechanical Engineering Department, University Carlos III of Madrid, 28911 Leganés, Spain.
Sensors (Basel). 2022 Dec 13;22(24):9777. doi: 10.3390/s22249777.
In this work, a procedure to obtain an accurate value of the critical speed of a cracked shaft is presented. The method is based on the transversal displacements of the cracked section when the shaft is rotating at submultiples of the critical speed. The SERR (Strain Energy Ralease Rate) theory and the CCL (Crack Closure Line) approach are used to analyse the proposed methodology for considering the behaviour of the crack. In order to obtain the best information and to define the procedure, the orbits and the frequency spectra at different subcritical rotational speed intervals are analyzed by means of the Fast Fourier Transform. The comparison of the maximum values of the FFT peaks within the intervals allows the subcritical speed to be determined, along with the value of the critical speed. When verified, the proposed procedure is applied to shafts with the same geometry and material and with cracks of increasing depth. The results show that the critical speed diminishes with the severity of the crack, as expected. A comparison is made between the critical speed obtained using the vertical and the horizontal displacements, finding no remarkable differences, meaning that in practical applications only one sensor for one of the displacements (in the vertical or horizontal direction) is needed to determine the critical speed. This is one of the main contributions of the paper, as it means that the orbits of the shaft are not needed. Finally, after this study we can conclude that the best results are achieved when the critical speed is obtained using data displacement in only one direction within the intervals around 12 or 13 of the critical speed.
在这项工作中，提出了一种获取带有裂纹轴临界转速的精确值的方法。该方法基于轴在亚临界转速的倍数旋转时裂纹部分的横向位移。SERR（应变能量释放率）理论和 CCL（裂纹闭合线）方法用于分析提出的方法，以考虑裂纹的行为。为了获得最佳信息并定义该方法，通过快速傅里叶变换分析不同亚临界旋转速度间隔的轨道和频谱。通过分析间隔内的 FFT 峰值的最大值，可以确定亚临界速度以及临界速度的值。当验证时，将提出的程序应用于具有相同几何形状和材料且裂纹深度增加的轴。结果表明，正如预期的那样，临界速度随着裂纹的严重程度而减小。比较使用垂直和水平位移获得的临界速度，发现没有显着差异，这意味着在实际应用中，仅需一个传感器即可测量一个位移（垂直或水平方向），以确定临界速度。这是本文的主要贡献之一，因为这意味着不需要轴的轨道。最后，通过这项研究，我们可以得出结论，当在围绕临界速度的 12 或 13 的间隔内仅在一个方向上使用数据位移来获得临界速度时，可以获得最佳结果。
