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Editor-in-Chief
Nikiforov
Vladimir O.
D.Sc., Prof.
Partners
doi: 10.17586/2226-1494-2026-26-2-393-401
Prediction of maximum stresses in the shaft–insert system using a neural network
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Article in Russian
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Abstract
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Borovkov A.I., Karchevskaia A.S., Novokshenov A.D., Matveeva A.I., Sherbakov S.S., Klimkovich N.M., Podgayskaya D.A., Poleschuk M.M. Prediction of maximum stresses in the “shaft–insert” system using a neural network. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2026, vol. 26, no. 2, pp. 393–401 (in Russian). doi: 10.17586/2226-1494-2026-26-2-393-401
Abstract
The reliability of machines largely depends on the accuracy of predicting the stress–strain state of components in tribo-fatigue systems, especially under high operating loads. Traditional finite element analysis provides high accuracy but requires significant computational resources and offers limited flexibility for rapid parameter variation. In recent years, machine learning methods have been increasingly applied in engineering practice. Among them, neural networks are of particular interest, as they allow nonlinear relationships between loads and stresses to be captured while significantly reducing computation time compared to traditional models. This work proposes an approach for predicting maximum stresses in the “shaft–insert” system by combining three-dimensional finite element modeling with subsequent neural network training. A database was created containing the results of numerical experiments for different combinations of bending and contact loads. A fully connected neural network with three hidden layers and different activation functions was used for training. The quality of the model was assessed using standard metrics: Mean Squared Error, Mean Absolute Error (MAE), and the coefficient of determination R2. The trained neural network demonstrated high accuracy in predicting maximum stresses both in the shaft and in the insert. For the training set, the R2 value reached 0.99991, and for the test set it was 0.99984, confirming minimal deviations from finite element results. The MAE was less than 0.006, while the maximum relative error in the test set did not exceed 3.2 %. The developed neural network model demonstrated the ability to reproduce the results of finite element analysis for the “shaft–insert” system while providing a substantial reduction in computation time compared to traditional finite element simulations. The model was constructed for a limited range of loads; therefore, further research should focus on expanding the dataset and including additional materials, which will make it possible to evaluate the scalability of the approach and its robustness under more complex conditions.
Keywords: neural networks, machine learning, tribo-fatigue system, stress–strain state, maximum stresses, MONICA, solid mechanics, finite element modeling, contact interaction
Acknowledgements. This work was supported by the Russian Science Foundation (project No. 23-RB-09-27, 15.12.2023) and the Belarusian Republican Foundation for Fundamental Research (project No. T24SPbG-003).
References
Acknowledgements. This work was supported by the Russian Science Foundation (project No. 23-RB-09-27, 15.12.2023) and the Belarusian Republican Foundation for Fundamental Research (project No. T24SPbG-003).
References
1. Sosnovskiy L.A. TRIBO-FATIGUE: Wear-Fatigue Damage and its Prediction. Springer, 2005, 373 p. https://doi.org/10.1007/978-3-540-27027-0
2. Sosnovskiy L.A., Sherbakov S.S., Khonsari M.M., Bogdanovich A.V. From fatigue and tribology to tribo-fatigue. International Journal of Materials and Structural Integrity, 2022, vol. 14, no. 2-4, pp. 164–237. https://doi.org/10.1504/ijmsi.2021.10050854
3. Sosnovskiy L.A., Bogdanovich A.V., Yelovoy O.M., Tyurin S.A., Komissarov V.V., Sherbakov S.S. Methods and main results of Tribo-Fatigue tests. International Journal of Fatigue, 2014, vol. 66, pp. 207–219. https://doi.org/10.1016/j.ijfatigue.2014.04.006
4. Komissarov V.V., Taranova E.S., Drobyshevsky P.S., Zamyatin V.O., Tyurin S.A., Sosnovskiy L.A. About experience of manufacture and maintenance of gears from the new structural material “Monika”. Vestnik IzhGTU imeni M.T. Kalashnikova, 2017, vol. 20, no. 2, pp. 107–112. (in Russian) https://doi.org/10.22213/2413-1172-2017-2-107-112
5. Bendikiene R., Bahdanovich A., Cesnavicius R., Ciuplys A., Grigas V., Jutas A., et al. Tribo-fatigue behavior of austempered ductile iron Monica as new structural material for rail-wheel system. Medziagotyra, 2020, vol. 26, no. 4, pp. 432–437. https://doi.org/10.5755/j01.ms.26.4.25384
6. Meng Y., Xu J., Ma L., Jin Z., Prakash B., Ma T., Wang W. A review of advances in tribology in 2020–2021. Friction, 2022, vol. 10, no. 10, pp. 1443–1595. https://doi.org/10.1007/s40544-022-0685-7
7. Ge Z., Hu Q., Wang R., Fei H., Zhu Y., Wang Z. Machine learning-driven optimization of micro-textured surfaces for enhanced tribological performance: a comparative analysis of predictive models. Coatings, 2024, vol. 14, no. 12, pp. 1539. https://doi.org/10.3390/coatings14121539
8. Nowell D., Nowell P.W. A machine learning approach to the prediction of fretting fatigue life. Tribology International, 2020, vol. 141, pp. 105913. https://doi.org/10.1016/j.triboint.2019.105913
9. Liang L., Liu M., Martin C., Sun W. A deep learning approach to estimate stress distribution: a fast and accurate surrogate of finite-element analysis. Journal of The Royal Society Interface, 2018, vol. 15, no. 138, pp. 20170844. https://doi.org/10.1098/rsif.2017.0844
10. Khorrami M.S., Mianroodi J.R., Siboni N.H., Goyal P., Svendsen B., Benner P., Raabe D. An artificial neural network for surrogate modeling of stress fields in viscoplastic polycrystalline materials. npj Computational Materials, 2023, vol. 9, no. 1, pp. 37. https://doi.org/10.1038/s41524-023-00991-z
11. Kapoor S., Mianroodi J.R., Khorrami M., Siboni N.S., Svendsen B. Comparison of two artificial neural networks trained for the surrogate modeling of stress in materially heterogeneous elastoplastic solids. arXiv, 2022. arXiv:2210.16994. https://doi.org/10.48550/arXiv.2210.16994
12. Jain S., Kapania R.K., Hammerand D.C. Development of a surrogate model for FEM error prediction using deep learning. Proc. of the AIAA Science and Technology Forum and Exposition (AIAA SciTech Forum), 2022, pp. 0972. https://doi.org/10.2514/6.2022-0972
13. Wu J., Du C., Dillenburger B., Kraus M.A. Fast prediction of stress distribution a GNN-based surrogate model for unstructured mesh FEA. Proc. of the IASS Symposium 2024 Redefining the Art of Structural Design. 2024, pp. 1–10.
14. Mokhtari N., Cai Y., Jelovica J. Comparison of deep learning techniques for prediction of stress distribution in stiffened panels. Thin-Walled Structures, 2025, vol. 215, part A, pp. 113494. https://doi.org/10.1016/j.tws.2025.113494
15. Persia J.T., Sung M.K., Lee S., Burns D.E. Neural network-based surrogate model in postprocessing of topology optimized structures. Neural Computing and Applications, 2025, vol. 37, no. 15, pp. 8845–8867. https://doi.org/10.1007/s00521-025-11039-2
16. Marković E., Marohnić T., Basan R. A surrogate artificial neural network model for estimating the fatigue life of steel components based on finite element simulations. Materials, 2025, vol. 18, no. 12, pp. 2756. https://doi.org/10.3390/ma18122756
17. Sosnovskii L.A., Zhmailik V.A., Psyrkov N.V., Zamyatnin V.O., Komissarov V.V. Cast iron with globular graphite and high fatigue resistance. Patent BY 15617, 2012. (in Russian)
18. Bahdanovich A., Sherbakov S., Lis I., Bendikiene R., Cesnavicius R., Grigas V. Some regularities of life time and damage for the new structural material MoNiCA during sliding friction and mechano-sliding fatigue. Solid State Phenomena, 2021, vol. 320, pp. 90–96. https://doi.org/10.4028/www.scientific.net/ssp.320.90
19. Sosnovskiy L.A., Sherbakov S.S. New cast iron MONICA loses its brittleness with increasing strength. International Journal of Materials and Structural Integrity, 2023, vol. 15, no. 1, pp. 24–41. https://doi.org/10.1504/ijmsi.2023.135888
