Vibrations in engineering and technology

Serputko Roman - Recipient of the Third Educational and Scientific Level of PMAI, Lviv Polytechnic National University (12 Stepan Bandera Str., Lviv, Ukraine, 79013, e-mail: roman.s.serputko@lpnu.ua), ORCID 0009-0004-9324-0368.

The article presents the results of an experimental study on the performance of a gravitational feeder for bulk materials as a function of its geometric parameters. The main objective of the research was to establish a quantitative relationship between the curvature radius of the chute and its inclination angle, and to determine the optimal combination of parameters that ensure maximum material flow rate and stable operation. To achieve this, a two-factor experimental design with three levels of each factor was applied, providing a reliable data set with high repeatability.

The experiments were conducted on a specially designed laboratory setup that allows adjustment of both chute curvature and inclination angle. Measurements were performed for nine combinations of factors with three replications at each point. The flow rate was calculated from mass and time measurements, and statistical analysis was carried out to evaluate repeatability. The coefficient of variation did not exceed 5%, indicating stable flow and reliable experimental results.

A second-order regression equation was developed to describe the relationship between productivity and the two influencing factors. The obtained coefficient of determination R^2=0,98 confirms the high accuracy and adequacy of the model. The results show that increasing the inclination angle from -10° to +10° increases productivity by 40–45%, while increasing the curvature radius from 120 mm to 160 mm adds another 25%. The maximum productivity of Q=7,5 kg/min is achieved at ρ=160 mm and α=10°. The optimal operating zone is located at ρ=140-150 mm and α=8-12°.

Graphical interpretation using linear plots, contour diagrams and histograms supports the obtained results. The practical significance of this study lies in the possibility of applying the derived mathematical model and experimentally established patterns for the design and optimization of gravitational feeders in agricultural, food and construction industries, as well as for the development of automated dosing control systems.

1. Nedderman, R. M., (1992). Statics and Kinematics of Granular Materials. Cambridge University Press. https://doi.org/10.1017/CBO9780511600043 [in English].

2. Schulze, D., (2008). Powders and Bulk Solids: Behavior, Characterization, Storage and Flow. Springer. https://doi.org/10.1007/978-3-540-73768-1 [in English].

3. Pouliquen, O. (1999). Scaling laws in granular flows down rough inclined planes. Physics of Fluids, 11(3), 542–548. https://doi.org/10.1063/1.870009 [in English].

4. Forterre, Y., Pouliquen, O. (2008).Flows of dense granular media. Annual Review of Fluid Mechanics, 40, 1–24. https://doi.org/10.1146/annurev.fluid.40.111406.102142 [in English].

5. Jop, P., Forterre, Y., Pouliquen, O. A. (2006). Constitutive law for dense granular flows. Nature, 441(7094), 727–730. https://doi.org/10.1038/nature04801 [in English].

6. Beverloo, W. A., Leniger, H. A., Van de Velde, J. (1961). The flow of granular solids through orifices. Chemical Engineering Science, 15(3–4), 260–269. https://doi.org/10.1016/0009-2509(61)85030-6 [in English].

7. Box, G. E. P., Wilson, K. B. (1951). On the Experimental Attainment of Optimum Conditions. Journal of the Royal Statistical Society. Series B (Methodological), 13(1), 1–45. https://doi.org/10.1111/j.2517-6161.1951.tb00067.x [in English].

8. Box, G. E. P., Hunter, W. G., Hunter, J. S. (1978). Statistics for Experimenters. Wiley. https://doi.org/10.1002/0471718130 [in English].

9. Montgomery, D. C. (2017). Design and Analysis of Experiments. Wiley. [in English].

10. Myers, R. H., Montgomery, D. C., Anderson-Cook, C. M. (2016). Response Surface Methodology. Wiley. [in English].

11. Aguilera Mena, D. A. (2013). Dynamic weighing liquid flow calibration system. Flow Measurement and Instrumentation, 33, 65–71. [in English].

12. Pope, J. G., Wright, J. D., Mattingly, G. E. (2021). Liquid Flow Meter Calibrations with NIST’s 15 kg/s Facility. NIST Special Publication 250-98. https://doi.org/10.6028/NIST.SP.250-98. [in English].

13. Bembenyk, M., Dmytriv, V., Banga, V., Horodniak, R. (2024). Dozator-zmishuvach sypkykh materialiv. Teoriia i praktyka [Feeder-Mixer of Bulk Materials. Theory and Practice]. Lviv: SPOLOM, 172. [in Ukrainian].

14. Dmytriv, I. V. (2017). Teoriia ta tekhnolohii naukovykh doslidzhen: mekhanichna inzheneriia [Theory and Technologies of Scientific Research: Mechanical Engineering]. Lviv: SPOLOM, 212. [in Ukrainian].

15. Dmytriv, I. V. (2017). Avtomobilnyi transport. Teoriia i praktyka naukovykh doslidzhen [Automotive Transport. Theory and Practice of Scientific Research]. Lviv Polytechnic National University. Lviv: SPOLOM, 212. [in Ukrainian].