1. UJMEMS
  2. All Volumes and Issues
  3. Vol. 11, No. 3, 2025
  4. COMPUTER SIMULATION AND EXPERIMENTAL VERIFICATION OF RECTILINEAR MOTION TRAJECTORIES OF A SINGLE-MASS OSCILLATORY SYSTEM ACTUATED BY AN INERTIAL PLANETARY-TYPE VIBRATION EXCITER

COMPUTER SIMULATION AND EXPERIMENTAL VERIFICATION OF RECTILINEAR MOTION TRAJECTORIES OF A SINGLE-MASS OSCILLATORY SYSTEM ACTUATED BY AN INERTIAL PLANETARY-TYPE VIBRATION EXCITER

UJMEMS.
2025;
Volume 11, Number 3
Received: July 22, 2025
Revised: September 12, 2025
Accepted: September 26, 2025
Authors:
  1. Vitaliy Korendiy
  2. Oleh Parashchyn
  3. R. Predko
  4. Oleh Kotsiumbas
  5. Roman Pelo
1
Lviv Polytechnic National University
2
Lviv Polytechnic National University
3
Lviv Polytechnic National University
4
Department of Motor Vehicle Transport, Lviv Polytechnic National University
5
Lviv Polytechnic National University

Problem statement and purpose of research. This study investigates whether a planetary-type inertial exciter can synthesize rectilinear motion trajectories in a single-mass oscillatory system and how the orientation of that trajectory can be programmed mechanically. Methodology. A three-dimensional CAD assembly was created and analyzed using multibody simulations to compute planar displacements, velocities, and accelerations under representative stiffness, damping, and mass properties. The initial carrier-arm angle was used as the primary design variable. A laboratory rig with orthogonal potentiometric sensing measured horizontal and vertical displacements; corresponding trajectories in the vertical plane were reconstructed for multiple geometric configurations. Findings. Simulations predict, and experiments confirm, a one-to-one mapping between the angle being studied and the direction of the straight-line path: horizontal, vertical, or inclined. In all cases, the displacement components are nearly sinusoidal and largely in phase; the component aligned with the target direction dominates in amplitude, while the orthogonal component remains small, causing the Lissajous figure to collapse toward a line. Minor non-smoothness in measured trajectories indicates high-frequency content from non-idealities (e.g., transmission compliance, local resonances), suggesting model extensions but not affecting the primary orientation control. Originality. The work demonstrates mechanism-level trajectory programming of rectilinear motion using a single-DOF planetary exciter, validated experimentally, thereby avoiding multi-actuator synchronization or semi-active control. Practical value. The results provide a simple, reproducible design lever – the initial arm angle – for setting line orientation in vibratory equipment requiring directional impulse transfer with minimal transverse motion. Future scope. Recommended directions of further research include tolerance and robustness analyses, incorporation of gear and belt compliance, and closed-loop trimming strategies to maintain rectilinearity under parameter drift.

planetary-type vibration exciter; rectilinear trajectory; single-mass oscillatory system; trajectory orientation control; multibody simulation; experimental validation

[1] H. Dong, C. Liu, Y. Zhao, and L. Zhao, “Influence of vibration mode on the screening process,” International Journal of Mining Science and Technology, vol. 23, no. 1, pp. 95–98, 2013, doi: 10.1016/j.ijmst.2013.01.014.

[2] Z. Chen, X. Tong, and Z. Li, “Numerical investigation on the sieving performance of elliptical vibrating screen,” Processes, vol. 8, no. 9, p. 1151, Sep. 2020, doi: 10.3390/pr8091151.

[3] V. Korendiy, O. Parashchyn, A. Stetsko, R. Litvin, O. Kotsiumbas, and R. Pelo, “Force analysis of the planetary-type mechanisms of the enhanced vibration exciters,” Vibroengineering Procedia, vol. 54, pp. 28–34, 2024, doi: 10.21595/vp.2024.24029.

[4] V. Korendiy, O. Parashchyn, V. Heletiy, V. Pasika, V. Gurey, and N. Maherus, “Kinematic analysis and geometrical parameters justification of a planetary-type mechanism for actuating an inertial vibration exciter,” Vibroengineering Procedia, vol. 52, pp. 35–41, 2023, doi: 10.21595/vp.2023.23728.

[5] S. S. Rao, Mechanical Vibrations. Harlow, UK: Pearson Education, 2017.

[6] G. Cieplok, “Influence of vibratory conveyor design parameters on the trough motion and the self-synchronization of inertial vibrators,” Open Engineering, vol. 14, no. 1, p. 20220434, Jan. 2024, doi: 10.1515/eng-2022-0434.

[7] V. P. Barbosa, A. L. Menezes, R. Gedraite, and C. H. Ataíde, “Vibration screening: A detailed study using image analysis techniques to characterize the bed behavior in solid–liquid separation,” Minerals Engineering, vol. 154, p. 106383, 2020, doi: 10.1016/j.mineng.2020.106383.

[8] D. Lin, X. Wang, N. Xu, W. Zuo, and Z. Liang, “A method for stabilizing the vibration amplitude of a flip-flow vibrating screen using piecewise linear springs,” Minerals, vol. 14, no. 4, p. 406, Apr. 2024, doi: 10.3390/min14040406.

[9] L. Jia, G. Wang, C. Pan, Z. Liu, and X. Zhang, “Controlled synchronization of a vibrating screen driven by two motors based on improved sliding mode controlling method,” PLoS One, vol. 18, no. 11, p. e0294726, Nov. 2023, doi: 10.1371/journal.pone.0294726.

[10] V. Gurskyi, V. Korendiy, P. Krot, R. Zimroz, O. Kachur, and N. Maherus, “On the dynamics of an enhanced coaxial inertial exciter for vibratory machines,” Machines, vol. 11, no. 1, p. 97, Jan. 2023, doi: 10.3390/machines11010097.

[11] S. Ogonowski and P. Krauze, “Trajectory control for vibrating screen with magnetorheological dampers,” Sensors, vol. 22, no. 11, p. 4225, Jun. 2022, doi: 10.3390/s22114225.

[12] V. Korendiy, O. Kachur, R. Predko, O. Kotsiumbas, R. Stotsko, and M. Ostashuk, “Generating rectilinear, elliptical, and circular oscillations of a single-mass vibratory system equipped with an enhanced twin crank-type exciter,” Vibroengineering Procedia, vol. 51, pp. 8–14, 2023, doi: 10.21595/vp.2023.23657.

[13] H. Yang and X. Ma, “Research on the screening mechanisms of composite vibrating screens based on discrete elements,” PLoS One, vol. 18, no. 10 October, pp. 1–19, 2023, doi: 10.1371/journal.pone.0293205.

[14] C. Duan et al., “Variable elliptical vibrating screen: Particles kinematics and industrial application,” Int. J. Min. Sci. Technol., vol. 31, no. 6, pp. 1013–1022, 2021, doi: 10.1016/j.ijmst.2021.07.006.

[15] V. Korendiy, I. Kuzio, S. Nikipchuk, O. Kotsiumbas, and P. Dmyterko, “On the dynamic behavior of an asymmetric self-regulated planetary-type vibration exciter,” Vibroengineering Procedia, vol. 42, pp. 7–13, 2022, doi: 10.21595/vp.2022.22580.

[16] V. Korendiy, V. Gurey, V. Borovets, O. Kotsiumbas, and V. Lozynskyy, “Generating various motion paths of single-mass vibratory system equipped with symmetric planetary-type vibration exciter,” Vibroengineering Procedia, vol. 43, pp. 7–13, 2022, doi: 10.21595/vp.2022.22703.

[17] V. Korendiy, O. Parashchyn, O. Kotsiumbas, R. Palash, O. Levytska-Revutska, and O. Hrytsun, “Simulation of motion trajectories and kinematic characteristics of an oscillatory system with a planetary-type vibration exciter,” Vibroengineering Procedia, vol. 58, pp. 31–38, May 2025, doi: 10.21595/vp.2025.24973.

[18] A. Radu, I. Grigore, C. Miron, and V. Barna, “Excel Spreadsheets for the Study of Lissajous Figures,” Romanian Reports in Physics, vol. 75, no. 4, pp. 1–16, 2023, doi: 10.59277/RomRepPhys.2023.75.911.