Research on fatigue life calculation method of droppers in high-speed railway catenary

Hongbo Kou
Infrastructure Inspection Research Institute, China Academy of Railway Sciences Co., Ltd, Beijing 100081, China
Yongming Yao
Infrastructure Inspection Research Institute, China Academy of Railway Sciences Co., Ltd, Beijing 100081, China
Haoshu Lu
Infrastructure Inspection Research Institute, China Academy of Railway Sciences Co., Ltd, Beijing 100081, China
Yunqian Ma
Postgraduate Department, China Academy of Railway Sciences Co., Ltd, Beijing 100081, China

Article ID: 4135

Keywords: catenary dropper; pantograph-catenary coupling system; fatigue load extrapolation; fatigue life calculation method

Abstract

To address the problems that catenary droppers are prone to fatigue failure under the operating environment of high-speed trains and are faced with the shortage of load measurement samples, insufficient extrapolation accuracy, and large dispersion in life evaluation, an optimized fatigue load extrapolation method based on small multiples and multiple iterations is proposed. Firstly, a pantograph-catenary coupling system model is established. After verification, the load-time history of the dropper is obtained through dynamic simulation. Secondly, the rainflow counting method is used to statistically analyze the stress cycles. The bandwidth and range of non-parametric rainflow extrapolation are determined according to the extrapolation multiple, and the reliable load extrapolation to the target multiple is realized through a multi-iteration strategy, which is compared with the traditional amplification method and the large-multiple direct extrapolation method. Finally, the mean stress is corrected based on the Goodman model, and a standard fatigue load spectrum is constructed. Combined with the S-N curve and linear cumulative damage theory, a fatigue life prediction model for high-speed railway droppers is established. This study provides a theoretical basis and data support for life evaluation, maintenance schedule formulation, and reliability design of catenary droppers.

Published

2026-07-22

How to Cite

Kou, H., Yao, Y., Lu, H., & Ma, Y. (2026). Research on fatigue life calculation method of droppers in high-speed railway catenary. Sound & Vibration, 60(4). https://doi.org/10.59400/sv4135

Download Citation

Issue

Vol. 60 No. 4 (2026)

Section

Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

References

[1]Zeng S, Gao S, Yu L, et al. Analysis of External Environmental Operating Risk Factors for Overhead Contact System. In: Proceedings of the 6th International Conference on Electrical Engineering and Information Technologies for Rail Transportation (EITRT) 2023. Springer Nature; 2024. pp. 12–19. doi: 10.1007/978-981-99-9315-4_2

[2]Pan L, Chen L, Xu Y, et al. Study on the Influence of Different Dropper Models in Pantograph–Catenary System on Dropper Load Simulation. Machines. 2025; 13(9): 874. doi: 10.3390/machines13090874

[3]Yang Z, Song Z, Zhao X, et al. Time-domain extrapolation method for tractor drive shaft loads in stationary operating conditions. Biosystems Engineering. 2021; 210: 143–155. doi: 10.1016/j.biosystemseng.2021.08.020

[4]Huang HZ, Gong J, Zuo MJ, et al. Fatigue Life Estimation of an Aircaft Engine Under Different Load Spectrums. International Journal of Turbo & Jet-Engines. 2012; 29(4). doi: 10.1515/tjj-2012-0017

[5]Li Y, Wang Z, Chen YL, et al. Research on compiling fatigue load spectrum of individual aircraft and analysis of fatigue life based on flight data. In: Proceedings of the IEEE 2012 Prognostics and System Health Management Conference (PHM-2012 Beijing); 23–25 May 2012; Beijing, China. pp. 1–5. doi: 10.1109/PHM.2012.6228937

[6]Deng Z, Huang T, Huang H, et al. Study on Load Spectrum of Evolution Accelerated Test for Fatigue Spalling of Angular Contact Ball Bearings under Varying Working Conditions. Journal of Mechanical Engineering, 2024, 60(13): 193–204. (in Chinese)

[7]Yuan Z, Chen X, Ma L, et al. A segmented load spectrum model for high-speed trains and its inflection stress as an indicator for line quality. International Journal of Fatigue. 2021; 148: 106221. doi: 10.1016/j.ijfatigue.2021.106221

[8]Zhang Z, Wu X, Wu S, et al. Investigation on Load Definition of Vibration Fatigue of Railway Vehicle Bogie. Journal of Mechanical Engineering. 2024; 60(22): 311. doi: 10.3901/JME.2024.22.311

[9]Xian C, Zhang H, Kim Y, et al. Programmed system for fatigue life prediction of excavator turntables based on multi-body dynamics and finite element analysis. Heliyon. 2024; 10(12): e33126. doi: 10.1016/j.heliyon.2024.e33126

[10]Fu L, Yu L, Yan D, et al. Fatigue Damage Prediction Framework of The Boom System Based on Embedded Physical Information and Attention Mechanism BiLSTM Neural Network. Journal of Mechanical Engineering. 2024; 60(13): 205. doi: 10.3901/JME.2024.13.205

[11]Parzen E. On Estimation of a Probability Density Function and Mode. The Annals of Mathematical Statistics. 1962; 33(3): 1065–1076. doi: 10.1214/aoms/1177704472

[12]Silverman BW. Density Estimation for Statistics and Data Analysis, 1st ed. Routledge; 1998. doi: 10.1201/9781315140919

[13]Dressler K, Hack M, Krüger W. Stochastic Reconstruction of Loading Histories from a Rainflow Matrix. Journal of Applied Mathematics and Mechanics. 1997; 77(3): 217–226. doi: 10.1002/zamm.19970770315

[14]Wang J, Liu Y, Zeng X, et al. Selection Method for Kernel Function in Nonparametric Extrapolation Based on Multicriteria Decision-Making Technology. Mathematical Problems in Engineering. 2013; 2013: 1–11. doi: 10.1155/2013/391273

[15]Socie D, Pompetzki M. Modeling Variability in Service Loading Spectra. Journal of ASTM International. 2004; 1(2): 1–12. doi: 10.1520/JAI11561

[16]Zheng X, Gao S, Yu L, et al. Method for fatigue program load spectrum compilation of catenary droppers based on adaptive kernel density estimation. Railway Standard Design. 2026; 70(4): 188–195. https://doi.org/10.13238/j.issn.1004-2954.202407240003 (in Chinese)

[17]European Committee for Electrotechnical Standardization. EN 50318:2018/A1:2022: Railway Applications - Current Collection Systems - Validation of Simulation of the Dynamic Interaction Between Pantograph and Overhead Contact Line. European Committee for Electrotechnical Standardization; 2022. Available online: https://standards.iteh.ai/catalog/standards/clc/629314f1-88bd-4d6f-826e-3095fd5a39e1/en-50318-2018-a1-2022?srsltid=AfmBOop4QgsuM9J3mY7kdTMuJDRyofE5SHV-XRxjbXh0btij_7566eej

[18]American Society for Testing and Materials (ASTM). ASTM E1049-85: Standard Practices for Cycle Counting in Fatigue Analysis. ASTM International; 2017.

[19]Conover JC, Jaeckel HR, Kippola WJ. Simulation of Field Loading in Fatigue Testing. SAE Transactions. 1967; 75: 543–556. Available online: http://www.jstor.org/stable/44563657

[20]Wang J, Chen H, Li Y, et al. A Review of the Extrapolation Method in Load Spectrum Compiling. Strojniški vestnik - Journal of Mechanical Engineering. 2016; 62(1): 60–75. doi: 10.5545/sv-jme.2015.2905

[21]Yang X, Zhang J, Ren WX. Threshold selection for extreme strain extrapolation due to vehicles on bridges. Procedia Structural Integrity. 2017; 5: 1176–1183. doi: 10.1016/j.prostr.2017.07.030

[22]Schröder V, Müller C, Esderts A. Extrapolation of load spectra by optimized Kernel Density Estimators using Monte-Carlo-Simulation. International Journal of Fatigue. 2021; 147: 106182. doi: 10.1016/j.ijfatigue.2021.106182

[23]Nasution FP, Sævik S, Berge S. Experimental and finite element analysis of fatigue strength for 300 mm2 copper power conductor. Marine Structures. 2014; 39: 225–254. doi: 10.1016/j.marstruc.2014.07.005

[24]Mars WV. Computed Dependence of Rubber’S Fatigue Behavior on Strain Crystallization. Rubber Chemistry and Technology. 2009; 82(1): 51–61. doi: 10.5254/1.3557006

[25]Miner MA. Cumulative Damage in Fatigue. Journal of Applied Mechanics. 1945; 12(3): A159–A164. doi: 10.1115/1.4009458

Editor-in-Chief

Prof. Jun Yang

Institute of Acoustics, Chinese Academy of Sciences, China

ISSN

1541-0161 (Print)

2693-1443 (Online)

Publication Frequency

Bi-monthly

Indexing

Web of Science Coverage

Emerging Sources Citation Index (IF 4.2, Q1)

Elsevier Solutions

Scopus (2025 CiteScore 2.0);

Portico, etc.

About the Publisher

Academic Publishing insists on taking academic exchange and publication as the main line, carrying out comprehensive management based on science and technology, and fully exploring excellent international publishing resources. Within 5 years, it will form a strategic framework and scale with science (S), technology (T), medicine (M), education (E), and humanities and arts (H) as the main publishing fields. Academic Publishing is headquartered in Singapore and based in Malaysia, with the United States and China providing the main scientific and academic resources. At the same time, it has established long-term good cooperative relations with other publishing companies, scientific research communities, and academic organizations in more than a dozen countries and regions. Academic Publishing uses English and Chinese as its main publishing languages, mainly publishing books, journals, and conference papers in print and online. The vast majority of publications follow the international open access policy, providing stable and long-term quality and professional publications. With the joint efforts of the expert team and our professional editorial team, our publications will gradually be indexed by international databases in stages to provide convenient and professional retrieval for various scholars. At the same time, manuscripts we accept will be subject to the peer review principle, and cutting-edge and innovative research articles will be preferentially accepted for peer reference and discussion. All kinds of our publications are welcome for peer to contribute, access, and download.

more

Member of ASC

Volume Arrangement

Featured Articles

New scaling of critical damping and reduced frequency for mechanically excited systems

This paper introduces a universal framework for understanding the vibration responses of systems subjected to harmonic excitation. By examining a simplified cylinder-spring-damper model, the study refurbishes traditional scaling methods for the excitation frequency ratio and critical damping ratio. The findings indicate that in damped systems, the maximum amplitude of vibration does not align with the natural frequency. This observation leads to the introduction of a new scaling method for reduced frequency. This new approach aligns resonance peaks at the new reduced velocity of 1.0 across different damping ratios, providing a consistent characterization of vibration behavior. A new critical damping ratio of 0.707 is identified for an excited system as opposed to the traditional damping ratio of 1.0 for an unexcited system. Key properties such as maximum amplitude, phase lag, bandwidth, and quality factor are analyzed, demonstrating that the proposed reduced frequency and critical damping ratio effectively capture the dynamics of both damped and undamped excited systems. The findings offer significant insights for practical applications in engineering and various scientific fields.

Ultrasonic wave velocity as a universal metric for defect detection in timber structures: A case study on Japanese cedar wood (Cryptomeria japonica)

This study makes significant contributions to the field of ultrasonic testing (UT) by offering a novel approach to the identification of artificially introduced defects within Japanese cedar wood (Cryptomeria japonica). The findings are of particular relevance for the heritage conservation and construction sectors, where non-invasive defect detection is paramount. The study establishes a robust framework for assessing the structural integrity of timber by correlating ultrasonic wave velocity reductions with defect size and distribution. Big-sized defects led to more substantial decreases in wave velocity. The study establishes a robust framework for assessing the structural integrity of historical timber by correlating ultrasonic wave velocity reductions with defect size and distribution. This framework has the potential to be applicable to diverse wood species and defect types.

Vehicle structural road noise prediction based on an improved Long Short-Term Memory method

The control of vehicle interior noise has become a critical metric for assessing noise, vibration, and harshness (NVH) in vehicles. During the initial phases of vehicle development, accurately predicting the impact of road noise on interior noise is essential for reducing noise levels and expediting the product development cycle. In recent years, data-driven methods based on machine learning have gained significant attention due to their robust capability in navigating complex data mapping relationships. Notably, surrogate models have demonstrated exceptional performance in this domain. Numerous researchers have integrated diverse intelligent algorithms into the study of vehicle noise, leveraging advantages such as the elimination of precise modeling requirements, extensive solution space exploration, continuous learning from data, and robust algorithmic versatility. However, in NVH engineering applications, data-driven models face inherent limitations, particularly in interpretability and stability. To address these issues, this paper introduces an improved Long Short-Term Memory (LSTM) network that combines knowledge and data. Inspired by the physical information neural network concept, this approach incorporates values calculated through empirical formulas into the neural network as constraints. Comparative assessments with traditional LSTM networks highlight the advantages of this deep learning model. By integrating empirical formulas constraints, the model not only enhances interpretability but also achieves robust generalization with fewer data samples. The proposed method is validated on a specific vehicle model, showing significant improvements in prediction accuracy and efficiency.