Vol. 337 No. 8 (2026)
DOI https://doi.org/10.18799/24131830/2026/8/5753
Mathematical models of sorting conveyors with belt and chain carriers
Relevance. This article addresses the problem of improving the reliability and accuracy of sorting timber conveyors with a chain load-bearing element equipped with a variable-frequency asynchronous electric drive. An increase in the length of the working section of an extended timber-sorting conveyor leads to a rise in the mass of moving parts, a stronger influence of the viscoelastic properties of the chain, and greater complexity of transient processes during start-up. As a result, dynamic jerks, wave-like tension fluctuations, and misalignment in the displacement of individual chain sections occur, which reduces equipment durability and impairs the precision of timber delivery to storage bins. The relevance of this study is determined by the need to maintain the design service life of the load-bearing chain (belt) as a key structural element. Aim. To investigate the motion dynamics of chain-type and belt-type sorting conveyors in order to establish the boundary conditions for the operation of the load-bearing section. Results and Conclusions. It has been established that the most hazardous operating mode is rapid conveyor start-up without mechanical vibration damping. The use of a fluid coupling reduces the initial tension peak and proves most effective during short start-ups (up to 10 s), as it smooths abrupt changes in the drive torque and diminishes the intensity of the initial tension wave. However, for extended conveyors, the action of a single fluid coupling is insufficient: in the region of the reflected wave at the end of the load-bearing chain, the systematic error in timber positioning may remain at an unacceptable level. The implementation of an S-shaped ramp function reduces the jerk at the initial start-up stage and, at the final stage, limits tension oscillations while maintaining acceptable sorting performance. To achieve the ultimate sorting accuracy on long conveyors, it is advisable to employ a closed-loop electric drive control system with displacement sensors for timber on the load-bearing chain and wireless data transmission; however, the implementation of such a solution would be technically complex and capital-intensive. The optimal outcome of applying a refined model of the mechanical part of an extended sorting conveyor to reduce excessive oscillations under the climatic conditions of Western and Central Siberia is achieved through coordinated control of the traction variable-speed electric drive in conjunction with an adjustable fluid coupling.
For citation: Kladiev S.N., Sarbassova N.D., Umurzakova A.D., Odnokopylov G.I. Mathematical models of sorting conveyors with belt and chain carriers. Bulletin of the Tomsk Polytechnic University. Geo Assets Engineering, 2026, vol. 337, no. 8, pp. 153–167. http://doi.org/10.18799/24131830/2026/8/5753
Keywords:
belt and chain conveyor, sorting, numerical modeling, parameters of the carrying chain and rubber-fabric belt, reliability of the conveyor mechanical part
References:
1. Mikhaylova A.E., Mushkarova O.M., Zubrin A.A. Digital technology tools to increase the integrated use of wood raw materials. Materials IV International scientific conference on interdisciplinary research. Yekaterinburg, 2023. pp. 122–127. (In Russ.)
2. Mushkarova O.M., Miheeva M.F. Innovative digital products for forestry enterprises. Digital technologies in the forestry sector. Proceedings of the IV All-Russian scientific and technical conf. St Petersburg, October 19–20, 2023. St Petersburg, SPbGLTU Publ., 2023. pp. 70–72. (In Russ.)
3. Polyanskaya O.A., Mikhaylova A.E., Tambi A.A. General characteristics of the economic situation of the Russian forestry industry and development prospects. Modern machines, equipment, and IT solutions for the forestry industry: theory and practice. Proceedings of the All-Russian scientific and practical conference. Voronezh, June 17, 2021. Voronezh, Voronezh State Forest Engineering University Publ., 2021. pp. 101–106. (In Russ.)
4. Starikov A.V., Baturin K.V. Research and analysis of methods of accounting for harvested timber in Russia and foreign countries. Lesotekhnicheskiy Zhurnal, 2015, vol. 20, no. 4, pp. 103–114. (In Russ.) DOI: 10.12737/17408.
5. Soldatov A.V., Gerz E.F., Terinov N.N. Study on photometric method of measering for volume of round timber. Forests of Russia and management in them, 2018, vol. 67, no. 4, pp. 73–77. (In Russ.).
6. Apafaian A.I., Proto A.R., Borz S.A. Performance of a mid-size harvester-forwarder system in integrated harvesting of sawmill pulpwood and firewood. Annals of Forest Research, 2017, vol. 60, no. 2, pp. 227–241. DOI: 10.15287/afr.2017.909.
7. Borz S.A., Proto A.R. Application and accuracy of smart technologies for measurements of roundwood: evaluation of time consumption and efficiency. Computers and Electronics in Agriculture, 2022, vol. 197, pp. 106990. DOI: 10.1016/j.compag.2022.106990.
8. Moskalik T., Tymendorf Ł., Van Der Saar Ja., Trzciński G. Methods of wood volume determining and its implications for forest transport. Sensors, 2022, vol. 22, no. 16, pp. 6028. DOI: 10.3390/s22166028.
9. Achatz J., Lukovic M., Hilt S., Lädrach T., Schubert M. Convolutional neural networks for quality and species sorting of roundwood with image and numerical data. Expert Systems with Applications, 2024, vol. 246, pp. 23117. DOI: 10.1016/j.eswa.2023.
10. Wen H., Hou B., Lin Y., Jin X. Action reliability analysis under random-interval hybrid uncertainty of chain conveyor based on adaptive intelligent extremum surrogate model. Quality and Reliability Engineering International, 2024, vol. 40, no. 4, pp. 1719–1742. DOI: 10.1002/qre.3486.
11. Ma H., Zhang P., Dong Y., Wang X., Xia R., Li B. Study on the rigid-discrete coupling effect of scraper conveyor under different chain speed-load conditions. Simulation Modelling Practice and Theory, 2024, vol. 134, pp. 102943. DOI: 10.1016/j.simpat.2024.102943.
12. Zhang P., Li B., Ma H., Xia R., Dong Y., Wang X. Fatigue life analysis of scraper conveyor chain ring under different chain speeds and loads. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 2024. DOI: 10.1177/09544089241253057.
13. Wieczorek A.N., Wójcicki M., Kalita M., Kandzia R. Problems of wear of the chains used in mine scraper conveyors, caused by friction and corrosion. Scientific Journal of Silesian University of Technology. Series Transport, 2024, vol. 122, pp. 293–304. DOI: https://doi.org/10.20858/sjsutst.2024.122.16.
14. Pásztory Z., Heinzmann B., Barbu M.C. Comparison of different stack measuring methods. Siberian Forestry Journal, 2019, no. 3, pp. 5–13. DOI: 10.15372/SJFS20190301.
15. Jiang S., Huang Sh., Zeng Q., Chen Sh., Lv J., Zhang Yu., Qu W. Dynamic characteristics of the chain drive system under multiple working conditions. Machines, 2023, vol. 11, no. 8. DOI: 10.3390/machines11080819.
16. Wen H., Hou B., Jin X. Fault identification of a chain conveyor based on functional data feature engineering and optimized multi-layer kernel extreme learning machine. Journal of Mechanical Science and Technology, 2023, vol. 37, no. 5, pp. 2289–2300. DOI: 10.1007/s12206-023-0405-x.
17. Zhang X., Ren M., Wang H., Jin L. Simulation study on dynamic characteristics of the chain drive system for mining scraper conveyor driven by the permanent magnet synchronous motor. Processes, 2024, vol. 12, no. 1. DOI: 10.3390/pr12010165.
18. Dong J., Wang J., Bi X., Zheng Y., Wang G., Wang J., Chen Y. Analysis and test of clamp conveying type residual film recycling and film impurity separation mechanism. Processes, 2022, vol. 10, no. 9, pp. 1816. DOI: 10.3390/pr10091816.
19. Zhao Y. Design and experiment of self-propelled seed corn combine harvester. Nongye Jixie Xuebao/Transactions of the Chinese Society for Agricultural Machinery, 2024, vol. 55, no. 5, pp. 121–134. DOI: 10.6041/j.issn.1000-1298.2024.05.011.
20. Sarbassova N., Umurzakova A., Kladiev S. Study of roundwood sorting on the simulation model of longitudinal chain conveyor. International Journal of Power Electronics and Drive Systems, 2024, vol. 15, no. 4, pp. 2068–2079. DOI: 10.11591/ijpeds.v15.i4.pp2068-2079.
21. Kladiev S., Sarbassova N., Umurzakova A. Device for controlling the sorting of round timber. Patent RF, no. 2795741, 2023. (In Russ.)
22. Glazyrin A., Bunkov D., Bolovin E., Isaev Y., Kopyrin V. Kladiev S., Filipas A., Langraf S., Khamitov R., Kovalev V., Popov E., Popov S., Deneko M. Nonlinear algebraic parameter estimation of doubly fed induction machine based on rotor current falling curves. Energies, 2025, vol. 18, pp. 4316. DOI: 10.3390/en18164316.
23. Xie C., Liu Z., Xie M. Dynamic response analysis of scraper conveyor under the condition of chain broken. Journal of Vibroengineering, 2023, vol. 25, no. 6, pp. 1053–1067. DOI: 10.21595/jve.2023.23192.
24. Yin E., Muvengei O., Kihiu J., Njoroge K. Failure analysis on conveyor chain links of a central bucket elevator. Journal of Mechanical and Civil Engineering, 2016, vol. 13, no. 4, pp. 56–63. DOI: 10.9790/1684-1304075663.
25. Glazyrin A.S., Popov E.I., Kopyrin V.A., Popov S.S., Khamitov R.N., Deneko M.V. Development of a mathematical model of a synchronous motor with permanent magnets in discrete time. Dynamics of Systems, Mechanisms and Machines, 2024, vol. 12, no. 1, pp. 36–42. (In Russ.) DOI: 10.25206/2310-9793-2024-12-1-36-42.
26. Glazyrin A.S., Popov E.I., Kopyrin V.A., Popov S.S., Bolovin E.V. Development of an observer of angular velocity and torque resistance on the shaft for synchronous motors with permanent magnets with increased stability to parametric disturbances. Electrical systems and complexes, 2024, no. 4 (65), pp. 47–54. (In Russ.) DOI: 10.18503/2311-8318-2024-4(65)-47-54.
27. Glazyrin A.S., Popov E.I., Kopyrin V.A., Popov S.S., Bolovin E.V., Kovalev V.Z., Khamitov R.N., Timoshkin V.V. Development of an observer of rotor angular velocity and resistance moment on the shaft of an adjustable permanent magnet synchronous motor powered through long cable. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2024, vol. 335, no. 11, pp. 237–257. (In Russ.) DOI: 10.18799/24131830/2024/11/4879.
28. Glazyrin A.S. Transient processes in electricalcomplex of production well with downhole compensator of reactive power. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023. vol. 334, no. 5, pp. 168–180. (In Russ.) DOI: 10.18799/24131830/2023/5/4255.
29. Sarbassova N.D. Algorithm of accurate cargo movement on a physical model of a sorting conveyor. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2024, vol. 335, no. 4, pp. 139–147.
30. Kladiev S.N., Umurzakova A.D., Sarbasova N.D., Khatsevskiy K.V. Simulation modeling of a tracking electric drive of a sorting conveyor. Omsk Scientific Bulletin, 2022, no. 2 (182), pp. 72–76. (In Russ.) DOI: 10.25206/1813-8225-2022-182-72-76.
31. Sorting conveyor with double-sided discharge LT-182. Equipment catalog of Lesmash LLC. (In Russ.) Available at: https://www.lesmash-ekb.com/catalog/lesotransporter-lt-182/ (accessed 20 May 2026).
32. Sorting conveyor LT-86B. Equipment catalog of Lesmash LLC. (In Russ.) Available at: https://www.lesmash-ekb.com/catalog/lesotransporter-lt-86b/ (accessed 20 May 2026).
33. Lewin C. S-curve motion profiles – vital for optimizing machine performance. Performance Motion Devices. Available at: https://www.pmdcorp.com/resources/type/articles/get/s-curve-profiles-deep-dive-article (accessed 20 May 2026).
34. Liu F., Li N., Xiong L., Yang X., Zhao S., Zhai T. Intelligent S-curve acceleration and deceleration algorithm in high-precision servo motion control. Machines, 2026, vol. 14, no. 1, article 91. DOI: 10.3390/machines14010091.
