Empirical criterion for the occurrence of auto-balancing and its application for axisymmetric rotor with a fixed point and isotropic elastic support

Authors

DOI:

https://doi.org/10.15587/1729-4061.2016.79970

Keywords:

rotor, auto­balancer, auto­balancing, the criterion for the occurrence of auto­balancing, main motion, stability of motion

Abstract

We formulated the empirical criterion for the occurrence of auto­balancing for the rotors balanced by passive auto­balancers. The criterion is applicable for rigid and elastic rotors on ductile supports and for elastic rotors on rigid supports. The criterion is intended to answer the question if it is possible in principle, and under what conditions, to automatically balance a particular rotor n by passive auto­balancers of any type in n planes of correction. In accordance with the criterion, the possibility of applying passive auto­balancers for rotor balancing (in “zero approximation”) is determined not by the type of auto­balancers, but by rotor itself. In this case, reaction of rotor to the elementary imbalances, applied in the required planes of correction, is essential. That is why the criterion makes it possible to obtain universal conditions for the occurrence of auto­balancing, applied for any types of auto­balancers.

The criterion is applied in the following sequence.

1. A physical­mechanical model of rotor with elementary imbalances, located in the required planes of correction, is described.

2. Differential equations of motion of the unbalanced rotor are derived.

3. Steady motion of a rotor, which corresponds to the applied elementary imbalances, is searched for.

4. A functional of the criterion for the occurrence of auto­balancing is built. As a rule, this is a quadratic form from elementary imbalances.

5. By analysis of the functional (sign definiteness of the obtained quadratic form), conditions for the occurrence of auto­balancing are determined. The result is conditions of two types. The first ones set limitations to the mass­inertia rotor characteristics. The second ones are a range of angular speeds of rotor rotation, at which auto­balancing will occur provided the first conditions are met.

The criterion is used for the axisymmetric rotor with a fixed point and isotropic elastic support. It was found that auto­balancing will occur only in the case of a long rotor, relative to the point O, independent of the number of auto­balancers (planes of correction) at the speeds, which exceed the only resonance speed of rotor rotation.

Author Biographies

Gennadiy Filimonikhin, Kirovograd National Technical University University ave., 8, Kirovograd, Ukraine, 25006

Doctor of Technical Sciences, Professor

Department of Machine Parts and Applied Mechanics

Irina Filimonikhina, Kirovograd National Technical University University ave., 8, Kirovograd, Ukraine, 25006

PhD, Associate Professor

Department of Mathematics and Physics

Kostyantyn Dumenko, Kirovograd National Technical University University ave., 8, Kirovograd, Ukraine, 25006

Doctor of Technical Sciences, Associate Professor

Department of Operation and Repair of Machines

Mihail Lichuk, Kirovograd National Technical University University ave., 8, Kirovograd, Ukraine, 25006

PhD, Associate Professor

Department of Mathematics and Physics

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Published

2016-10-31

How to Cite

Filimonikhin, G., Filimonikhina, I., Dumenko, K., & Lichuk, M. (2016). Empirical criterion for the occurrence of auto-balancing and its application for axisymmetric rotor with a fixed point and isotropic elastic support. Eastern-European Journal of Enterprise Technologies, 5(7 (83), 11–18. https://doi.org/10.15587/1729-4061.2016.79970

Issue

Vol. 5 No. 7 (83) (2016): Applied mechanics

Section

Applied mechanics

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Copyright (c) 2016 Gennadiy Filimonikhin, Irina Filimonikhina, Kostyantyn Dumenko, Mihail Lichuk

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