Necessary Self-Balancing Robustness Conditions for a Two-Bearing Rotor Taking Unbalance Mass into Account

The paper derives the necessary conditions that make self-balancing of an unbalanced rotor moving in three dimensions possible. We considered the system dynamics taking the rotor unbalance mass into account. We derived analytical expressions for the necessary conditions using an engineering phase criterion for self-balancing robustness. We show that there are two rotor speed ranges within which self-balancing is possible. Critical rates of transverse and torsional rotor vibrations together with critical anti-resonance angular speed form the boundaries of these ranges. We detected the parameters that affect self-balancing conditions. We show that self-balancing of long rotors is possible within two angular speed ranges, while self-balancing of spherical and short rotors only happens within a single angular speed range. We determined that long and nearly spherical rotors are most sensitive to unbalance mass. We analysed the necessary self-balancing conditions for the case of high angular speeds. The results presented in this paper should be considered during design and operation of rotary machines equipped with a self-balance system

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