Analytical study of auto-balancing within the framework of the flat model of a rotor and an auto-balancer with a single cargo

Authors

DOI:

https://doi.org/10.15587/1729-4061.2021.227583

Keywords:

passive auto-balancer, rotor, automatic balancing, static balancing, motion stability, static imbalance

Abstract

This paper reports the analytically established conditions for the onset of auto-balancing for the case of a flat rotor model on isotropic elastic-viscous supports and an auto-balancer with a single load. The rotor is statically unbalanced, the rotation axis is vertical. The auto-balancer has a single cargo – a pendulum, a ball, or a roller. The balancing capacity of the cargo is equal to the rotor imbalance.

The physical-mathematical model of the system is described. The differential equations of motion are recorded in dimensionless form relative to the coordinate system that rotates synchronously with the rotor. The so-called main movement has been found; in it, the cargo synchronously rotates with the rotor and balances it. The differential equations of motion are linearized in the neighborhood of the main movement. A characteristic equation has been constructed. It helped investigate the stability of the main movement (an auto-balancing mode) for the cases of the absence and presence of resistance forces in the system.

It was established that in the absence of resistance forces in the system:

– the rotor has three characteristic rotational speeds, and the first always coincides with the resonance frequency;

– auto-balancing occurs when the rotor rotates at speeds between the first and second ones, and above the third characteristic speed;

– the value of the second and third characteristic speeds is significantly influenced by the ratio of weight to the mass of the system;

– the second and third characteristic speeds monotonously increase with an increase in the ratio of cargo weight to the mass of the system.

Resistance forces significantly affect both the values of the second and third characteristic speeds and the conditions of their existence. Small resistance forces do not change the quality behavior of the system. With high resistance forces, the number of characteristic speeds decreases to one.

The paper reports the results applicable to an auto-balancer with many cargoes when it balances the imbalance that equals the balancing capacity of the auto-balancer

Author Biographies

Gennadiy Filimonikhin, Central Ukrainian National Technical University

Doctor of Technical Sciences, Professor, Head of Department

Department of Machine Parts and Applied Mechanics

Lubov Olijnichenko, Central Ukrainian National Technical University

PhD, Senior Lecturer

Department of Machine Parts and Applied Mechanics

Guntis Strautmanis, Riga Technical University

Doctor of Science Engineering, Associate Professor

Department of Railway Engineering

Antonina Haleeva, Mykolayiv National Agrarian University

PhD, Associate Professor

Department of Tractors and Agricultural Machinery, Operating and Maintenance

Vasyl Hruban, Mykolayiv National Agrarian University

PhD, Associate Professor

Department of Tractors and Agricultural Machinery, Operating and Maintenance

Olexandr Lysenko, Central Ukrainian National Technical University

PhD, Associate Professor

Department of Metal Cutting Machines and Systems

Mareks Mezitis, Transport Academy

Doctor of Technical Sciences, Professor, Head of Scientific Institute

Ivan Valiavskyi, Central Ukrainian National Technical University

PhD, Associate Professor

Department of Metal Cutting Machines and Systems

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Published

2021-04-30

How to Cite

Filimonikhin, G., Olijnichenko, L., Strautmanis, G., Haleeva, A., Hruban, V., Lysenko, O., Mezitis, M., & Valiavskyi, I. (2021). Analytical study of auto-balancing within the framework of the flat model of a rotor and an auto-balancer with a single cargo. Eastern-European Journal of Enterprise Technologies, 2(7 (110), 66–73. https://doi.org/10.15587/1729-4061.2021.227583

Issue

Section

Applied mechanics