System Analysis of Automatic Balancing (Self-Balancing) Machine Rotors with Liquid Working Bodies

Abstract

This article deals with automatic balancing (self-equalizing) of rotors with vertical axis of rotation by means of liquid. There used to be a statement claiming that automatic balancing was possible only after first critical (above resonance) rotation zone of rotors. However in 1995 the phenomenon of automatic balancing with liquid in both below resonance zone of rotor rotation and in the resonance itself was registered using the method of high speed video shooting. The paper suggests theoretical explanation of the phenomenon stated by means of carried out experiments.

Investigation of Small Motions of Liquid in Cylindrical Chamber of Auto-Balancing Device

“…3. Let us suppose that a simplified flat task is considered (since the geometric dimensions of the ABD have a ratio R>>h [10]); that the liquid involves into the cylinder chamber of the ABD and rotates with the rotor as a single solid, and that, when neglected by gravitational forces, it has the form of a ring with an internal radius R1 and external -R. We shall consider the small translational motion of the cylinder in the plane of rotation (z = z(t) and y = y(t) are the generalized coordinates of the cylinder axis). In this case, the movement of the liquid in relation to the cylinder is also considered as small one.…”

“…Reducing the radius of the free surface and correspondingly increasing the thickness of the liquid layer at a constant radius of the chamber R does not cause a shift in the centre of the mass of the system, since the centre of the free surface of the liquid coincides with the centre of the mass of the system. In the change of the unbalanced state of the rotary system, a thin layer of fluid is involved, which is close to the magnitude of the double displacement of the centre of the mass of the rotor [10,13]. Another liquid only increases the mass of the system, located concentrically around the axis of rotation.…”

“…Experimental fluid balancer studies have been carried out by Kasahara [3] and Nakamura [4]. As to mathematical models, simple lumped mass models have been considered by Bae [5], Jung [6], Majewski [7], Chen [8], and Urbiola-Soto and Lopez-Parra [9]. The first and the last two of these papers include experimental studies a swell.…”

“…The characteristic features of the process of automatic balancing of liquid under stationary conditions of rotor movement with a vertical axis of rotation is that automatic fluid balancing is effective for elastically deformable rotors, on elastic supports ones, where there is a phase difference between the direction of force from the imbalance and the rotor deflection or the displacement of the rotor, as well as the fact that in the auto-balancer device chamber the liquid tends to set against an imbalance not only in the above resonance but also in the preresonant area of rotation of the rotor and at the resonance itself [10]. However, there is no theoretical verification of fluid behavior in the auto-balancing device (ABD) chamber under non-stationary conditions of rotor rotation.…”

Operation of Passive Fluid Self-Balancing Device at Resonance Transition Regime

“…At the next Phase the mechanical system of a solid body with a cylindrical chamber partly filled with a fluid is investigated, and mathematical model of its stationary motion is derived [9].…”