Study on the Development of Three-dimensional Spectrum Incorporating Frequency-amplitude-count

doi:10.3901/JME.260480

Abstract

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

CLC Number:

U270

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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URL: http://www.cjmenet.com.cn/EN/10.3901/JME.260480

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

References

[1] 熊峻江. 疲劳断裂可靠性工程学[M]. 北京：国防工业出版社，2008. XIONG Junjiang. Fatigue and fracture reliability engineering[M]. Beijing：National Defence of Industry Press，2008.
[2] 王爱红，徐格宁，高有山. 桥式起重机随机应力谱获取及疲劳剩余寿命估算[J]. 机械工程学报，2012，48(18)：192-198. WANG Aihong，XU Gening，GAO Youshan. Random stress spectrum acquisition and fatigue residual life estimate for overhead travelling crane[J]. Journal of Mechanical Engineering，2012，48(18)：192-198.
[3] WALLBRINK C，HUGHES J M，KOTOUSOV A. Experimental investigation of crack opening loads in an aircraft load spectrum[J]. International Journal of Fatigue，2023，171：107560.
[4] ZHOU Yifu，HE Li，ZHONG Luo. An accelerated editing method of multiaxial load spectrums for durability testing[J]. Engineering Fracture Mechanics，2022，270：108569.
[5] ZHENG Guofeng，WANG Qiongyao，CAI Chuan. Criterion to determine the minimum sample size for load spectrum measurement and statistical extrapolation[J]. Measurement，2021，178：109387.
[6] JIN Tongtong，YAN Chuliang，GUO Jinyan，et al. Compilation of drilling load spectrum based on the characteristics of drilling force[J]. The International Journal of Advanced Manufacturing Technology，2023，124(11-12)：4045-4055.
[7] 陈道云，孙守光，李强. 一种新的高速列车动应力谱分布估计方法[J]. 机械工程学报，2017，53(8)：109-114. CHEN Daoyun，SUN Shouguang，LI Qiang. A new dynamic stress spectrum distribution estimation method of high-speed train[J]. Journal of Mechanical Engineering，2017，53(8)：109-114.
[8] 王宏伟，邢波，骆红云. 雨流计数法及其在疲劳寿命估算中的应用[J]. 矿山机械，2006，34(3)：95-97. WANG Hongwei，XING Bo，LUO Hongyun. Rain-flow count method and application on fatigue life estimation[J]. Mining & Processing Equipment，2006，34(3)：95-97.
[9] MATSUISHI M，ENDO T. Fatigue of metals subjected to varying stress[J]. Japan Society of Mechanical Engineers，Fukuoka，Japan. 1968，68(2)：37-40.
[10] HUANG Gangting，LI Yunfei，LUO Yajun，et al. One-stage extraction four-point algorithm for rainflow cycle counting in fatigue life estimation[J]. Engineering Computations，2023，40(1)：126-148.
[11] CHEN Jie，IMANIAN A，WEI Haoyang，et al. Piecewise stochastic rainflow counting for probabilistic linear and nonlinear damage accumulation considering loading and material uncertainties[J]. International Journal of Fatigue，2020，140：105842.
[12] FIORITI D，SCARPELLI C，PELLEGRINO L，et al. Battery lifetime of electric vehicles by novel rainflow-counting algorithm with temperature and C-rate dynamics: Effects of fast charging，user habits，vehicle-to-grid and climate zones[J]. Journal of Energy Storage，2023，59：106458.
[13] CHENG Tian，LU D D，SIWAKOTI Y P. Circuit-based rainflow counting algorithm in application of power device lifetime estimation[J]. Energies，2022，15(14)：5159.
[14] GUENNEC B，UENO A，SAKAI T，et al. Effect of the loading frequency on fatigue properties of JIS S15C low carbon steel and some discussions based on micro- plasticity behavior[J]. International Journal of Fatigue，2014，66：29-38.
[15] 赵光伟. 基于工况识别的地铁构架疲劳损伤预测方法研究[D]. 北京：北京交通大学，2021. ZHAO Guangwei. Study on fatigue damage rediction method of metro frame based on working condition recognition[D]. Beijing：Beijing Jiaotong University，2021.
[16] 任尊松，曹杰，李玉怡，等. 高速动车组构架载荷特征研究[J]. 工程力学，2021，38(2)：242-256. REN Zunsong，CAO Jie，LI Yuyi，et al. The load characteristics of the bogieframe of High Speed EMUs[J]. Engineering Mechanics，2021，38(2)；242-256.
[17] CAI Yikun，ZHAO Yu，MA Xiaobing，et al. An extended model for fatigue life prediction and acceleration considering load frequency effect[J]. IEEE Access，2018，6：21064-21074.
[18] HUNG J，HOCHENG H. Frequency effects and life prediction of polysilicon microcantilever beams in bending fatigue[J]. Journal of Micro/Nanolithography，MEMS，and MOEMS，2012，11(2)：21206.
[19] 陈道云，王斌杰，肖乾，等. 高速列车转向架构架损伤、等效应力及寿命分布特性研究[J]. 机械工程学报，2020，56(22)：237-246. CHEN Daoyun，WANG Binjie，XIAO Qian，et al. Study on damage，equivalent stress and life distribution characteristics of bogie frame of high-speed train[J]. Journal of Mechanical Engineering，2020，56(22)：237-246.