包含频率-幅值-频次的三维谱建立方法研究

doi:10.3901/JME.260480

摘要/Abstract

摘要： 目前通过雨流计数法构建的结构应力谱均为包含幅值和频次的二维谱，此类应力谱未能提取信号的频率信息，无法获得不同频率/频域应力对结构损伤的贡献，因此亟需研究包含信号频率信息的三维谱建立方法。基于雨流计数法，提出获取雨流循环时间间隔和频率的方法，获得了雨流循环对应的频率和幅值，建立包含频率-幅值-频次的三维应力谱。基于北京地铁某线路车辆转向架构架动应力测试数据，研究了动应力信号对应的频域特点，确定有效表达信号频域特征的频率等级，建立构架电机座测点的三维应力谱，验证了所建三维谱的真实性和合理性。研究列车不同运行速度对结构动应力频域影响，构建了测点三个速度等级的三维应力谱，获得了不同速度对等效应力的贡献。结果表明，提出的包含信号频率的三维谱建立方法，能够准确提取信号的频率信息，反映信号不同频域动应力对结构等效应力的贡献。研究结果为进一步研究结构弹性振动对损伤的影响奠定了基础。

关键词: 三维谱, 建立方法, 雨流计数, 频率, 幅值

Abstract: In current studies, stress spectrum constructed using the rainflow counting method are typically two-dimensional, consisting only of amplitude and count. However, such spectrum don’t capture the frequency information of the signal, limiting the ability to assess the contribution of stresses from different frequency domains to structural damage. Therefore, it is necessary to develop a method for constructing a three-dimensional spectrum that incorporates signal frequency. In this paper, we propose a method based on the rainflow counting technique to obtain the time intervals and frequencies of rainflow cycles. This enables us to determine the frequency and amplitude of each rainflow cycle, resulting in the establishment of a three-dimensional stress spectrum that includes frequency, amplitude, and count. Using dynamic stress test data from the bogie frame of a vehicle operating on a specific line of the Beijing Subway, we analyzed the frequency-domain characteristics of the dynamic stress signals. We identified the frequency levels that effectively represent the signal’s frequency-domain features and developed a three-dimensional stress spectrum for the motor hanger on the bogie frame. The validity and accuracy of the proposed three-dimensional spectrum were verified. Additionally, we explored the effect of different train speeds on the dynamic stress frequency domain of the structure and constructed three-dimensional stress spectrum at three distinct speed levels for the measurement point. This analysis allowed us to quantify the contribution of different speeds to the equivalent stress. The results demonstrate that the proposed method for constructing a three-dimensional spectrum incorporating signal frequency can effectively extract frequency information and reflect the contribution of dynamic stresses in different frequency domains to the structure’s equivalent stress. These findings provide a foundation for further research into the impact of elastic vibrations on structural damage.

Key words: 3D spectrum, development method, rainflow counting, frequency, amplitude

中图分类号:

U270

马觉凡, 任尊松, 安睿. 包含频率-幅值-频次的三维谱建立方法研究[J]. 机械工程学报, 2026, 62(14): 347-354.

MA Juefan, REN Zunsong, AN Rui. Study on the Development of Three-dimensional Spectrum Incorporating Frequency-amplitude-count[J]. Journal of Mechanical Engineering, 2026, 62(14): 347-354.

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链接本文: http://www.cjmenet.com.cn/CN/10.3901/JME.260480

http://www.cjmenet.com.cn/CN/Y2026/V62/I14/347

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