This paper is to study how vibration modes of a stationary asymmetric rotor evolve when it is assembled to a flexible housing via multiple bearing supports. Prior to the assembly, vibration modes of the rotor are classified as "balanced modes" and "unbalanced modes." Balanced modes are those modes whose natural frequencies and mode shapes remain unchanged after the rotor is assembled to the housing via bearings. Otherwise, the vibration modes are classified as "unbalanced modes." In this paper, we first develop two mathematical criteria to identify balanced modes. For the first criteria, the rotor is subjected to fixed boundary conditions at the bearings prior to assembly. In this case, a vibration mode will be a balanced mode if the reactions at the fixed boundary vanish. For the second criterion, the rotor is subjected to free boundary conditions (including the bearing points) prior to assembly. In this case, a vibration mode will be a balanced mode if the bearing locations are nodal points of the vibration mode. These mathematical criteria are then applied to a rotor consisting of a rigid hub supporting a flexible structure, which appears in many practical applications. For balanced modes, the criteria lead to a conclusion that surface integrals of modal forces and moments at the flexible-rigid rotor interface will vanish. Moreover, these surface integrals can be conveniently calculated using finite element methods. To validate the mathematical criteria, modal testing was conducted on a disk with 4 pairs of brackets mounted on a rigid spindle, a ballbearing spindle and a fluid-dynamic bearing spindle.
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