Keywords
rod magnetization
magnetic forces
integral equation
force visualization
matrix extraction capacity
comparative analysis
energy efficiency двоякоперіодичні структури
намагніченість стрижнів
магнітні сили
інтегральне рівняння
візуалізація силового поля
вилучальна здатність
порівняльний аналіз
енергетична ефективність
How to Cite
Abstract
The paper examines the theoretical and practical aspects of rod-structured matrix filters with double-periodic arrangement of elements, commonly employed in high-gradient magnetic separation technologies, with particular attention to comparative analysis and matrix optimization. An increasing number of studies on the development of highly efficient and lightweight high-gradient systems with reduced energy consumption is noted. The aim of the article is to substantiate and develop a method for optimizing matrix parameters according to the criterion of minimizing the specific energy of the magnetic field in the extraction zone, based on the calculation of local and effective force and energy characteristics of the magnetic field. The efficiency and universality of the proposed method are confirmed by a series of computational experiments with comprehensive consideration of factors influencing the quality of the final product. Specific examples demonstrate that the formation of an array of constant-magnetic-force lines (isodynes) serves as the principal means of investigating the extraction capacity of a matrix. A simple and effective approach to visualizing potential extraction zones is proposed in order to simplify the calculation of their areas. The application of the integral equation method with respect to the magnetization vector of matrix elements is substantiated, as it ensures maximum universality, simplicity, and accuracy in the analysis of complex double-periodic structures. The necessity of determining not only local but also effective magnetic field parameters in energy optimization is demonstrated. The dependence of matrix efficiency on the magnetic field intensity, rod shape and concentration, and their mutual arrangement is illustrated. The developed method is emphasized as being of a theoretical nature and is proposed as an effective complement to experimental analysis methods. It is shown that practical implementation of the method requires consideration of technological characteristics and constraints. Its value lies in the completeness and reliability of the additional information obtained on the basis of operational experience and high-quality experimental studies. References 20, figures 3, table 1.
References
1. Ren L., Zeng S., Zhang Y. Magnetic field characteristics analysis of assembled magnetic medium using ANSYS software. International Journal of Mining Science and Technology. 2015. Vol. 25. No 3. Pp. 479–487. DOI: https://doi.org/10.1016/j.ijmst.2015.03.024.
2. Xuyan Yu, Lei Zhan, Xiubin Wang, Qian Wang, Jiangang Ku. Spatial magnetic force and magnetic energy density analysis of microsphere medium in high gradient magnetic fields: a 3D simulation. Physica Scripta. 2024. Vol. 100. No 1. DOI: https://doi.org/10.1088/1402-4896/ad9180.
3. Ge W., Encinas A., Araujo E., Song Sh. Magnetic matrices used in high gradient magnetic separation (HGMS): A review. Results in Physics. 2017. Vol. 7. Pp. 4278–4286. DOI: https://doi.org/10.1016/j.rinp.2017.10.055.
4. Zheng X., Wang Y., Lu D., Li X. Study on the application of elliptic cross-section matrices for axial high gradient magnetic separation: key considerations for optimization. Physicochemical Problems of Mineral Processing. 2019. Vol. 55. Issue 3. Pp. 655–666. DOI: https://doi.org/10.5277/ppmp18178.
5. Ding L., Chen L.Z., Zeng J.W. Investigation of combination of variable diameter rod elements in rod matrix on high gradient magnetic separation performance. Advanced Materials Research. 2014. Vol. 1030–1032. Pp. 1193-1196. DOI: https://doi.org/10.4028/www.scientific.net/amr.1030-1032.1193.
6. Xia Z., Xing L., Li D., Sheng Z., Yu W., Dong L. Investigation of particle capture by grooved plates with el-liptic teeth for high intensity magnetic separation. Separation and Purification Technology. 2023. Vol. 325. Article no 124685. DOI: https://doi.org/10.1016/j.seppur.2023.124685.
7. Hanyu Lin, Xin Li, Zhongyun Lei, Jiangang Ku, Zhaolian Wang. Developing high gradient magnetic separa-tors for greener production: Principles, design, and optimization. Journal of Magnetism and Magnetic Materials. 2023. Vol. 587. Article no 171260. DOI: https://doi.org/10.1016/j.jmmm.2023.171260.
8. Jiangang Ku, Jun Xia, Jianzheng Li, Xinling Peng, Bao Guo, Hongxiang Ran. Accurate calculation of major forces acting on magnetic particles in a high-gradient magnetic field: A 3D finite element analysis. Powder Technology. 2021. Vol. 394. Pp. 767–774. DOI: https://doi.org/10.1016/j.powtec.2021.08.052.
9. Gerlici J., Shvedchikova I.O., Romanchenko Yu.A., Nikitchenko I.V. Determination of Rational Geometric Parameters of Plate Elements of the Magnetic Matrix of a Polygradient Separator. Electrical Engineering and Electro-mechanics. 2018. No 4. Pp. 58–62. DOI: https://doi.org/10.20998/2074-272X.2018.4.10.
10. Shvedchykova I., Romanchenko J., Nikitchenko I. Comparative analysis of inhomogeneity degree of mag-netic field of polygradient magnetic separators for purification of bulk materials. 2017 International Conference on Modern Electrical and Energy Systems (MEES), Kremenchuk, Ukraine, 15-17 November 2017. DOI: https://doi.org/10.1109/MEES.2017.8248873.
11. Romanchenko Yu.A.. 2d-modeling in multivariate calculations of magnetic induction in matrices of poly-gradient electromagnetic separators. Visnyk Skhidnoukrainskoho natsionalnoho universitetu imeni Volodymyra Dalia. 2024. No 2 (282). Pp. 50-57. DOI: https://doi.org/10.33216/1998-7927-2024-282-2-50-57. (Ukr)
12. Tolmachev S.T., Bondarevsky S.L., Ilchenko A.V. Magnetic Properties of Multicomponent Heterogeneous Media with Bipolar Periodic Structure. Elektrotekhnika I elektromekhanika. 2020. No 1. Pp. 29–38. DOI: https://doi.org/10.20998/2074-272X.2020.1.05. (Rus).
13. Tolmachev S., Ilchenko O. Calculation of Effective Magnetic Properties Rod Matrices of High-Gradient Magnetic Separators. IEEE 4th International Conference on Modern Electrical and Energy System (MEES), Kremen-chuk, Ukraine, 20-23 October 2022. DOI: https://doi.org/10.1109/MEES58014.2022.10005717.
14. Tolmachev S.T., Ilchenko O.V. Mathematical modeling of the magnetic field of high-gradient magnetic separators with a doubly periodic matrix structure. Tekhnichna Elektrodynamika. 2025. No 2. Pp. 3–11. DOI: https://doi.org/10.15407/techned2025.02.003. (Ukr)
15. Zheng X., Wang Y., Lu D. Particle capture of elliptic cross-section matrices for parallel stream high gradient magnetic separation. Compel. 2016. Vol. 35. Issue 1. Pp. 187–199. DOI: https://doi.org/10.1108/COMPEL-03-2015-0140.
16. Liangyu Xia, Fengyu Wang, Lijuan Wang, Xian Li, Junming Chen, Quanliang Cao. Understanding and prediction of magnetization state of elliptic cross-section matrices in high gradient magnetic separation. Minerals Engi-neering. 2021. Vol. 172. Article no 107137. DOI: https://doi.org/10.1016/j.mineng.2021.107137.
17. Xia Z., Li D., Shuang L., Zi J., Dong L., Ke J., Kadir C., Bing P., Yu W. A novel method for efficient re-covery of ilmenite by high gradient magnetic separation coupling with magnetic fluid. Minerals Engineering. 2023. Vol. 202. Article no 108279. DOI: https://doi.org/10.1016/j.mineng.2023.108279.
18. Yu W., Zi X., Xia Z., Dong L., Zi S. Matching relation between matrix aspect ratio and applied magnetic induction for maximum particle capture in transversal high gradient magnetic separation. Minerals Engineering. 2020. Vol. 151. Article no 106316. DOI: https://doi.org/10.1016/j.seppur.2020.116687.
19. Liu J., Dai H., Yu L., Wang C., Feng J., Li P., Xu S. Optimization of the Matrix in a Transverse-Field High-Gradient Magnetic Separator for an Improved Ilmenite Separation. Minerals. 2025. Vol. 15. 114. DOI: https://doi.org/10.3390/min15020114.
20. Zhicheng Hu, Dongfang Lu, Xiayu Zheng, Yuhua Wang, Zixing Xue, Shaohua Xu. Development of a high-gradient magnetic separator for enhancing selective separation: A review. Powder Technology. 2023. Vol. 421. Article no 118435. DOI: https://doi.org/10.1016/j.powtec.2023.118435.
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