Empirical criterion for the occurrence of auto-balancing and its application for axisymmetric rotor with a fixed point and isotropic elastic support - Filimonikhin, Gennadiy; Filimonikhina, Irina; Dumenko, Kostyantyn; Lichuk, Mihail (Eastern-European Journal of Enterprise Technologies, 2016)
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.