The degradation or failure of spring performance due to stress relaxation can significantly impact the normal operation of the entire system. Physical models are often used to fit the degradation law of spring stress relaxation. However, the error in the prediction process has not yet been emphasized. Therefore, an error compensation model based on PSO-TCN-Attention is proposed in this study. PSO is applied to optimize the TCN-Attention hyperparameters for data at different temperatures. The prediction model is optimized to learn the difference between the empirical equations and the true value, and the prediction error is then compensated for in the empirical equations to achieve a more accurate prediction of spring degradation. The results indicate that the PSO-TCN-Attention model predicts optimally at four temperatures compared to the TCN, RNN, and LSTM models as well as the empirical equation and delay function models. Based on this, the spring’s life at a failure threshold of 0.95 is extrapolated, and the life distribution is obtained. Additionally, the relaxation mechanism of the spring is analyzed using EBSD and TEM at different temperatures before and after pressurization. The results indicate that the relaxation mechanism of the spring is mainly due to dislocation and slip. The proposed algorithmic model effectively describes the spring degradation trend, suggesting its potential for predicting spring performance degradation.
The full text can be downloaded at https://doi.org/10.1007/s40436-024-00538-5
Ting-Ting Zhang
,
Zeng-Gui Gao
,
Zi-Feng Xu
,
Chao-Jia Gao
,
Zhen-Hao Yan
,
Zhong-Sheng Qin
,
Li-Lan Liu
. Stress relaxation behavior and life prediction of 1Cr18Ni9 spring based on PSO-TCN-Attention[J]. Advances in Manufacturing, 2026
, 14(3)
: 774
-788
.
DOI: 10.1007/s40436-024-00538-5
[1] Li J, Wang Y, Chen X et al (2019) Microstructure evolution in stress relaxation behavior of austenite AISI 304 stainless steel spring. Mater Charact 148:266-271
[2] Xiao YH, Guo C (2011) Constitutive modelling for high temperature behavior of 1Cr12Ni3Mo2VNbN martensitic steel. Mater Sci Eng A 528:5081-5087
[3] Zeren A, Zeren M (2003) Stress relaxation properties of prestressed steel wires. J Mater Process Technol 141:86-92
[4] You J, Fu R, Liang H et al (2023) A non-Arrhenius model for mechanism consistency checking in accelerated degradation tests. Actuators 12:319. https://doi.org/10.3390/act12080319
[5] Laidler KJ (1984) The development of the Arrhenius equation. J Chem Educ 61:494. https://doi.org/10.1021/ed061p494
[6] Ronan S, Alshuth T, Jerrams S et al (2007) Long-term stress relaxation prediction for elastomers using the time-temperature superposition method. Mater Des 28:1513-1523
[7] Eitzen A, Flamm M, Steinweger T et al (2018) On the lifetime prediction of rolling lobe air springs. Eng Fail Anal 94:313-326
[8] Yuan M, Yuan HJ, Xu RY et al (2018) Reliability sssessment of Spring based on two degradation modeling methods. In: 2018 12th international conference on reliability, maintainability, and safety (ICRMS). IEEE, Shanghai, pp 390-394
[9] Kong X, Yang J, Hao S (2021) Reliability modeling-based tolerance design and process parameter analysis considering performance degradation. Reliab Eng Syst Saf 207:107343. https://doi.org/10.1016/j.ress.2020.107343
[10] Gill SPA, McColvin G, Strang A (2014) Stress relaxation of nickel-based superalloy helical springs at high temperatures. Mater Sci Eng A 613:117-129
[11] Nong X, Feng W, Gao J et al (2021) Stress relaxation constitutive relations and finite element analysis of T9A Helical compression Spring. Mater Trans 62:962-967
[12] Dong Y, Zhang C, Zhao G et al (2016) Constitutive equation and processing maps of an Al-Mg-Si aluminum alloy: determination and application in simulating extrusion process of complex profiles. Mater Des 92:983-997
[13] Xiao JJ, Li DS (2015) Modeling and simulation for the stress relaxation behavior of Ti-6Al-4V at medium temperature. Rare Met Mater Eng 44:1046-1051
[14] Xia Y, Shu X, Zhang Q et al (2023) Modified arrhenius constitutive model and simulation verification of 2A12-T4 aluminum alloy during hot compression. J Mater Res Technol 26:1325-1340
[15] Huang M, Jiang J, Wang Y et al (2023) Comparison and error evaluation of Arrhenius model and typical machine learning algorithms for high-temperature flow stress prediction of GH3536 superalloy. Mater Lett 349:134754. https://doi.org/10.1016/j.matlet.2023.134754
[16] Adarsh SH, Sampath V (2020) Prediction of high temperature deformation characteristics of an Fe-based shape memory alloy using constitutive and artificial neural network modelling. Mater Today Commun 22:100841. https://doi.org/10.1016/j.mtcomm.2019.100841
[17] Ren J, Wang R, Feng Y et al (2019) Hot deformation behavior and microstructural evolution of as-quenched 7055 Al alloy fabricated by powder hot extrusion. Mater Charact 156:109833. https://doi.org/10.1016/j.matchar.2019.109833
[18] Deng CY, Dong SJ, Tan W (2018) Modelling for the flow behavior of a new metastable beta titanium alloy by GA-based Arrhenius equation. Mater Res Express 6:026544. https://doi.org/10.1088/2053-1591/aaedf7
[19] Zheng Y, Qin C, Lai X et al (2019) A novel capacity estimation method for lithium-ion batteries using fusion estimation of charging curve sections and discrete Arrhenius aging model. Appl Energy 251:113327. https://doi.org/10.1016/j.apenergy.2019.113327
[20] Geng G, He Y, Zhang J et al (2023) Short-term power load forecasting based on PSO-optimized VMD-TCN-Attention mechanism. Energies 16:4616. https://doi.org/10.3390/en16124616
[21] Zhang Y, Shang K, Cui Z et al (2023) Research on traffic flow prediction at intersections based on DT-TCN-Attention. Sensors 23:6683. https://doi.org/10.3390/s23156683
[22] Yang S, Lian H, Xu B et al (2023) Application of robust deep learning models to predict mine water inflow: implication for groundwater environment management. Sci Total Environ 871:162056. https://doi.org/10.1016/j.scitotenv.2023.162056
[23] Chen Q, Liu YB, Ge MF et al (2022) A novel Bayesian-optimization-based adversarial TCN for RUL prediction of bearings. IEEE Sensors J 22:20968-20977
[24] Xue H, Gui X, Wang G et al (2024) Prediction of gas drainage changes from nitrogen replacement: a study of a TCN deep learning model with integrated attention mechanism. Fuel 357:129797. https://doi.org/10.1016/j.fuel.2023.129797
[25] Zhen Y, Fang J, Zhao X et al (2022) Temporal convolution network based on attention mechanism for well production prediction. J Pet Sci Eng 218:111043. https://doi.org/10.1016/j.petrol.2022.111043
[26] Wang Y, Hou D, Xu D et al (2023) Prediction of rolling bearing performance degradation based on sae and TCN-attention models. J Mech Sci Technol 37:1567-1583
[27] Zhang F, Shen Z, Xu M et al (2023) Remaining useful life prediction of lithium-ion batteries based on TCN-DCN fusion model combined with IRRS filtering. J Energy Storage 72:108586. https://doi.org/10.1016/j.est.2023.108586
[28] Kong X, Du X, Xu Z et al (2023) Predicting solar radiation for space heating with thermal storage system based on temporal convolutional network-attention model. Appl Therm Eng 219:119574. https://doi.org/10.1016/j.applthermaleng.2022.119574
[29] Jain M, Saihjpal V, Singh N et al (2022) An overview of variants and advancements of PSO algorithm. Appl Sci 12:8392. https://doi.org/10.3390/app12178392
[30] Zhou Y, Wan M (2018) Comparison of models of stress relaxation in failure analysis for connectorsunder long-term storage. IOP Conf Ser Mater Sci Eng 324:012069. https://doi.org/10.1088/1757-899X/324/1/012069
[31] Li H, Zhan L, Huang M et al (2021) Effects of pre-strain and stress level on stress relaxation ageing behaviour of 2195 Al-Li alloy: experimental and constitutive modelling. J Alloys Compd 851:156829. https://doi.org/10.1016/j.jallcom.2020.156829
[32] Moon J, Hossain MB, Chon KH (2021) AR and ARMA model order selection for time-series modeling with image net classification. Signal Process 183:108026. https://doi.org/10.1016/j.sigpro.2021.108026
