Abstract
The conditions for the occurrence of auto-balancing for the rigid axisymmetric rotor on two isotropic elastic supports, balanced by any quantity of passive auto-balancers of any type, are defined. The empirical criterion for the occurrence of auto-balancing is applied. It is established that the dynamic auto-balancing of the rotor (in two or more correction planes by several passive auto-balancers) is possible only in the case of the long rotor. There can be any quantity of auto-balancers. The long rotor has two resonant rotational speeds. The auto-balancing occurs at above resonance speeds. The static auto-balancing of the rotor (in one correction plane) is possible at any quantity of auto-balancers in such cases. If the rotor is long, then it has two resonant speeds and one additional speed, located between the resonant ones. The auto-balancing occurs between the first resonant speed of rotor rotation and additional speed, and over the second resonant speed. If the rotor is spherical, then it has one resonant speed and the additional speed, which is higher than the resonant one. The auto-balancing occurs between the resonant and additional speeds. If the rotor is short, then the conditions for the occurrence of auto-balancing depend on the distance between the rotor center of mass and the correction plane. If this distance does not exceed the certain boundary size, then the rotor has the only resonant speed and the auto-balancing occurs at above resonance speeds. Otherwise, the rotor has one resonant and one additional speed, which is higher than the resonant one. The auto-balancing occurs between these speeds. The additional speed is due to the installation of the auto-balancers on the rotor. Upon transition to it, the behavior of auto-balancers changes. At slightly lower rotor rotational speeds, the auto-balancers reduce the rotor imbalance, and at slightly higher ones – increase it.
Highlights
Paper [11] proposed the empirical criterion of stability of the main motion in the case of rotor balancing by several auto-balancers of a particular type
The purpose of this work is to obtain the conditions under which several passive automatic balancers of any type will balance statically or dynamically a rigid axisymmetric rotor on two isotropic elastic supports
The dynamics of the rotor with the elementary unbalances applied at the future points of the suspension of auto-balancers, mounted on two isotropic elastic supports, is described by a system of four linear differential equations of motion
Summary
For balancing of high-speed rotors in motion, in the process of exploitation, passive auto-balancers are applied [1, 2]. Paper [2] proposed the engineering (empirical) criterion for the occurrence of auto-balancing with the balancing of the rotor by an auto-balancer of any type in one correction plane. Analytical conditions for the occurrence of auto-balancing were obtained when balancing of rotor that performs planar, spherical, spatial motions by one auto-balancer of any type. Paper [11] proposed the empirical criterion of stability of the main motion in the case of rotor balancing (both elastic and rigid) by several auto-balancers of a particular type. In the paper [12] the empirical criterion of stability of the main motion was modernized for obtaining conditions for the occurrence of auto-balancing, suitable for any type of auto-balancers. It is expedient to balance them with several autobalancers, including multi-row balancers
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