This study presents the development and dynamic analysis of a mechanical model representing a multi-component vibratory system consisting of a feeder, a vibratory transporter, and a conveyor-separator. The main goal is to simulate the oscillatory response of a three-mass separator excited by a crank-slider mechanism and analyse its efficiency, focusing on the working body responsible for material separation. The vibratory system is modeled using a set of second-order linear differential equations derived via Lagrange’s second kind formulation. Masses are connected by spring-damper elements, capturing the elastic and dissipative interactions. The excitation is modeled as a kinematically imposed harmonic displacement of the third mass, simulating the crank mechanism’s motion. Frequency-domain and time-domain simulations were conducted in MATLAB to determine displacements, velocities, accelerations, and damping-induced energy losses under harmonic excitation. The model enables the identification of key dynamic characteristics, including resonance frequencies, peak amplitudes, and phase shifts, and the evaluation of amplitude control under industrial constraints. Simulation results show that the system achieves a stable working regime at 15.2 Hz, where the working body reaches the target amplitude of ~4.8 mm, suitable for effective material separation. The energy analysis reveals that more than 90% of the input energy is dissipated through damping. This confirms the dissipative nature of the design, which is advantageous for controlling excess oscillations and achieving stable motion. The model aligns well with industrial reference data and provides a foundation for future optimization of full-process vibratory systems, from feeding to separation. The proposed model demonstrates good agreement with experimental values and industrial references. It provides a solid foundation for further optimization and design of industrial vibratory separators and feeders. Future work may incorporate nonlinear damping effects and control strategies to further enhance system performance under variable loading and operating conditions.
[1] R. Singh, "Vibratory separators still make the grade for screening dry bulk powders", Filtration & Separation, vol. 41, no. 1, pp. 20-21, 2004.
https://doi.org/10.1016/S0015-1882(04)00107-7
[2] G. Filimonikhin, V. Pirogov, M. Hodunko, R. Kisilov, and V. Mazhara, "The dynamics of a resonance single-mass vibratory machine with a vibration exciter of targeted action that operates on the Sommerfeld effect", Eastern-European Journal of Enterprise Technologies, vol. 3, no. 7 (111), pp. 51-58, 2021.
https://doi.org/10.15587/1729-4061.2021.233960
[3] D. Rebot, V. Topilnytskyi, "Nonlinear mathematical model of the five-container vibration system", Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 8, no. 3, pp. 10-18, 2022.
https://doi.org/10.23939/ujmems2022.03.010
[4] G. Filimonikhin, V. Pirogov, V. Amosov, P. Luzan, "Research of antiresonance three-mass vibratory machine with a vibration exciter in the form of a passive auto-balancer", Eastern-European Journal of Enterprise Technologies, vol. 5, no. 7 (107), pp. 89-97.
https://doi.org/10.15587/1729-4061.2020.213724
[5] V. Yatsun, "Experimental Study of Resonance Vibrations of the Vibratory Machine Excited by a Ball Auto-Balancer", Eastern-European Journal of Enterprise Technologies, vol. 2, no. (1 (104)), pp. 32-40, 2020.
https://doi.org/10.15587/1729-4061.2020.201105
[6] S. Ronghua, Z. Liuqing, and P. Chenyu, "AE applied to dynamic optimal design for large-scale vibrating screen", in First ACIS international symposium on cryptography, and network security, data mining and knowledge discovery, E-commerce and its applications, and embedded systems, IEEE, 2010, pp. 316-320.
https://doi.org/10.1109/CDEE.2010.67
[7] N. Anekar, V.V. Ruiwale, Sh. Nimbalkar, P. Rao, "Design and testing of unbalanced mass mechanical vibration exciter" International Journal of Research in Engineering and Technology, vol. 03, no. 08, pp. 107-112, 2014.
https://doi.org/10.15623/ijret.2014.0308017
[8] Т. B. Kurmangaliyev, А. G. Goltsev, М. R. Sikhimbayev, K. Т. Sherov, О. М. Zharkevich, A. K. Sherov, "Analytical and experimental studies of pneumatic vibration exciter in inertia vibroabrasive machining of parts based on beryllium oxide", Vibroengineering, vol. 15, no. 2, pp. 863-871, 2013.
[9] Ž. V. Despotović, M. Jović, "Mathematical model of electromagnetic vibratory exciter with incremental motion", Filtration & Separation, vol. 41, no. 1, pp. 20-21, 2004.
https://doi.org/10.1016/S0015-1882(04)00107-7
[10] V. Korendiy, A. Augousti, O. Lanets, T. Vilchynskyi, V. Kyrychuk, O. Yaniv, R. Protasov, "Novel concepts and designs of inertial vibration exciters for industrial vibratory equipment: a review", Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 10, no. 4, pp. 17-33, 2024.
https://doi.org/10.23939/ujmems2024.04.017
[11] D. Rebot, A. Babii, "Influence of the velocity of the medium layer on its dynamicparameters in the process of vibration separation", Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 8, no. 2, pp. 33-40, 2022.
https://doi.org/10.23939/ujmems2022.02.033
[12] O. Lanets, O. Kachur, V. Korendiy, "Derivation of analytical dependencies for determining stiffness parameters of vibration isolators of vibratory machine", Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 6, no. 3-4, pp. 1-8, 2020.
https://doi.org/10.23939/ujmems2020.03-04.001
[13] Zh. Liu, Ch. Fan, Y. Min, Ch. Liu, Sh. Li, Ya. Li, X. Liang, "An experimental and numerical investigation of influencing factors of gravel vibratory compaction, vol. 473, 2025.
https://doi.org/10.1016/j.conbuildmat.2025.141084
[14] A. Bezpalov, V. Shenbor, V. Korendiy, V. Brusentsov, "Optimization of Structure of Sorting Vibratory Separators", Ukrainian Journal of Mechanical Engineering and Materials Science, vol. 3, no. 1, pp. 97-106, 2017.
[15] S. Oraon, M. L. Chandravanshi, V. Bajpai, "Diagnosis check in the Vibratory Feeder unit using FEA technique", Materials Today: Proceedingsn, vol. 16, no. 2, pp. 329-335, 2019.
https://doi.org/10.1016/j.matpr.2019.05.098
[16] V.N. Doğan, M. Çapar, Ö. Güler, P. Yayla, "Failure Analysis and Prevention of a Heavy-Duty Industrial Vibrating Feeder", Journal of Failure Analysis and Prevention, vol. 24, pp. 1788-1798, 2024.
https://doi.org/10.1007/s11668-024-01958-y
[17] V. Korendiy, O. Lanets, O. Kachur, P. Dmyterko, R. Kachmar, "Determination of inertia-stiffness parameters and motion modelling of three-mass vibratory system with crank excitation mechanism", Vibroengineering Procedia, vol. 36, pp. 7-12, 2021.
https://doi.org/10.21595/vp.2021.21924
[18] O. Kachur and V. Korendiy, "Dynamic behavior of vibratory screening conveyor equipped with crank-type exciter," in Lecture Notes in Mechanical Engineering, pp. 44-53, 2023.
https://doi.org/10.1007/978-3-031-32774-2_5