The pantograph, a critical component of the pantograph-catenary system (PCS), operates in harsh environments and is susceptible to crack failures, which pose risks to current collection quality and operational safety. Despite its importance, its service reliability has not been adequately explored. This study presents a novel approach to developing high-precision three-dimensional (3D) load spectra for key pantograph components. Initially, the pantograph-catenary dynamics model is enhanced to accurately capture 3D dynamic loads. Subsequently, multiple methods are employed to fit load spectrum probability densities, with the TOPSIS method identifying the most effective fitting approach. To improve fatigue test efficiency, extrapolated load spectra for varying operational speeds are synthesized and converted into constant amplitude load spectra, which are then combined to generate comprehensive 3D load spectra. Finally, the damage reduction analyses are conducted to confirm the acceptability of the load-induced damage, thereby validating the method’s effectiveness. This innovative approach provides highly precise foundational data, which can be used for structural design and life prediction of pantographs, significantly enhancing their reliability and operational safety.
ZhangWHZouDTanMY, et al.Review of pantograph and catenary interaction. Front Mech Eng2018; 13(2): 311–322.
2.
ShiJWLiMXZhangSM, et al.Effect of low temperature on aerodynamic performance of pantograph. Journal of Mechanical Engineering2021; 57(2): 190–199.
3.
QingTShaoTMWenSZ. Effects of relative humidity on surface adhesion. Tribology2006; 26(4): 295–299.
4.
LuoQMeiGMChenGX, et al.Study of pantograph-catenary system dynamic in crosswind environments. Veh Syst Dyn2023; 62: 1. DOI: 10.1080/00423114.2023.2199456.
5.
ZhouNWeiHFJiangHY, et al.Fatigue crack propagation model and life prediction for pantographs on High-Speed trains under different service environments. Eng Fail Anal2023; 149: 107065.
6.
PomboJAmbrósioJ. Environmental and track perturbations on multiple pantograph interaction with catenaries in high-speed trains. Comput Struct2013; 124: 88–101.
7.
SongYWangZWLiuZG, et al.A spatial coupling model to study dynamic performance of pantograph-catenary with vehicle-track excitation. Mech Syst Signal Process2021; 151: 107336.
8.
ZhaiWMCaiCB. Effect of locomotive vibrations on pantograph-catenary system dynamics. Veh Syst Dyn1998; 29(S1): 47–58.
9.
YaoYMZouDZhouN, et al.A study on the mechanism of vehicle body vibration affecting the dynamic interaction in the pantograph-catenary system. Veh Syst Dyn2021; 59(9): 1335–1354.
10.
BrambillaECarnevaleMFacchinettiA, et al.Influence of train roof boundary layer on the pantograph aerodynamic uplift: a proposal for a simplified evaluation method. J Wind Eng Ind Aerod2022; 231: 105212.
11.
CarnevaleMFacchinettiARocchiD. Procedure to assess the role of railway pantograph components in generating the aerodynamic uplift. J Wind Eng Ind Aerod2017; 160: 16–29.
12.
YiCWangDZhouL, et al.Evaluation of the influence of pantograph cracks on contact forces in the interaction between pantograph and catenary. Veh Syst Dyn2022; 61(9): 2375–2393.
13.
ZhouNChengYZhangX, et al.Wear rate and profile prediction of cu-impregnated carbon strip for high-speed pantograph. Wear2023; 530-531: 205056.
14.
ZhiXSZhouNChengY, et al.Effect and behaviors of ambient humidity on the wear of metal-impregnated carbon strip in pantograph-catenary system. Tribol Int2023; 188: 108864.
15.
LiuJRZhouNLiY, et al.Hardening and prediction method for suspension system stiffness of pantograph head in electrified railway. J China Railw Soc2022; 44(6): 30–36.
16.
YiCWangDZhouL, et al.A simulation investigation on the influence of pantograph crack defect on graphite contact strip wear. Eng Fail Anal2022; 131: 105889.
17.
ChengYYanJZhangF, et al.Surrogate modeling of pantograph-catenary system interactions. Mech Syst Signal Process2025; 224: 112134.
18.
WangJMeiGZhangW. Sensitivity analysis of flexible upper frame of pantograph with a novel simplified method. Advances in dynamics of vehicles on roads and tracks. Gothenburg, Sweden: Springer Nature Switzerland AG. IAVSD, 2019, pp. 181–188. DOI: 10.1007/978-3-030-38077-9_22.
19.
SchützDLowakHDe JongeJB, et al.A standardised load sequence for flight simulation tests on transport aircraft wing structures. LBF-Report FB-106, NLR-Report TR, 731973.
20.
AicherWBrangerJvan DijkGM, et al.Description of a fighter aircraft loading standard of fatigue evaluation FALSTAFF. Joint publication by F+ W. Emmen (NL): NLR, Darmstadt (DE): LBF, Ottobrunn (DE): IABG1976.
21.
HeulerPKlatschkeH. Generation and use of standardised load spectra and load-time histories. Int J Fatig2005; 27(8): 974–990.
22.
SchützDKlätschkeHHeulerP. Standardized multiaxial load sequences for car wheel suspension components—car loading standard multiaxial—CARLOS multi. Darmstadt (DE): Fraunhofer Institute for Structural Durability and System Reliability LBF. Report No. FB-2011994.
23.
WangSLiuXJiangC, et al.Prediction and evaluation of fatigue life for mechanical components considering an elasticity-based load spectrum. Fatig Fract Eng Mater Struct2021; 44(1): 129–140.
24.
DongQYuYXuG. Fatigue residual life estimation of jib structure based on improved v‐SVR algorithm obtaining equivalent load spectrum. Fatig Fract Eng Mater Struct2020; 43(6): 1083–1099.
25.
ChenDYXiaoQMouMH, et al.Study on establishment of standardized load spectrum on bogie frames of high-speed trains. Acta Mech Sin2019; 35(4): 812–827.
26.
SunJJSunSGLiQ, et al.Compilation method of test load spectrum for bogie frame. J China Railw Soc2021; 43(6): 29–36.
27.
MaSSunSGWangBJ, et al.Estimating load spectra probability distributions of train bogie frames by the diffusion-based kernel density method. Int J Fatig2020; 132: 105352.
28.
YangWJ. Research and application analysis of load spectrum of subway pantograph contact force. Chengdu, China: Southwest Jiaotong University, 2020.
29.
MeiGMLuoQQiaoW, et al.Study of load spectrum compilation method for the pantograph upper frame based on multi-body dynamics. Eng Fail Anal2022; 135: 106099.
30.
YaoYMYangZPWangJ, et al.Analysis of contact force and uplift of pantograph–catenary system in overlap section based on numerical simulations and experimental tests. Veh Syst Dyn2022; 61(10): 2492–2515.
31.
WangJWMeiGMLuLT. Analysis of the pantograph’s mass distribution affecting the contact quality in high-speed railway. Int J Real Ther2023; 11(4): 529–551.
32.
BS EN 50318-2018. Railway applications-current collection system-validation of simulation of the dynamic interaction between pantograph and overhead contact line. Standard Policy and Strategy Committee, UK2018.
33.
ZhouNWeiHFChengY, et al. Study of the dynamics behavior of pantograph-catenary system considering three-dimensional asymmetric characteristics. Veh Syst Dyn2025; 1–28. DOI: 10.1080/00423114.2025.2451711.
34.
WeiHFZhouNChengY, et al.Study of a semi-data-driven high-precision spatial load spectrum fitting method for pantograph design. Proc Inst Mech Eng F J Rail Rapid Transit2025; 239(3): 246–257.
35.
BotevZIGrotowskiJFKroeseDP. Kernel density estimation via diffusion. Ann Stat2010; 38(5): 2916–2957.
36.
CheYLWangXRLvXQ, et al.Study on probability distribution of electrified railway traction loads based on kernel density estimator via diffusion. Int J Electr Power Energy Syst2019; 106(2): 383–391.
37.
XuXYYanZXuSL. Estimating wind speed probability distribution by diffusion-based kernel density method. Elec Power Syst Res2015; 121(3): 28–37.
38.
WangYMLiuPDYaoYY. BMW-TOPSIS: a generalized TOPSIS model based on three-way decision. Inf Sci2022; 607: 799–818.
39.
LiQGZhouZLZhangXJ, et al.Aerial target threat assessment based on combined weighting method and TOPSIS method. Electron Opt Control2022; 29: 39–42.
40.
ZhaoYZhuHChenZT. Failure analysis and improvement of weld cracks in frame of TSG18 pantograph. Electric Locomotives & Mass Transit Vehicles2020; 43(6): 84–87.
41.
ChenMGFengYSunYS. Analysis and improvement of cracks on the frame of high-speed pantograph. Electr Drive Locomot2017; 4: 105–109.
42.
YiDXLvGZZhouXW. Maximal loading calculation for two dimensional fatigue design spectrum under multiple working conditions with probability extrapolation method. Chin J Appl Mech2006; 23(3): 184–487.
43.
ZhaoSBWangZB. Anti-Fatigue Design: Methods and Data. Beijing: China Machine Press, 1997.
