3D model-based evaluation of the vibration characteristics of a rotor with a transverse crack on rigid supports
Keywords:
rotor, oscillations, transverse crack, finite element model, crack faces, contact, resonanceAbstract
The rotor of the intermediate-pressure cylinder of steam turbine Т-250/300-240 is used for investigating the influence of a transverse crack on its vibration condition with account of faces contact. The rotor is considered in the rotating coordinate system and modelled as a 3D body resting on rigid supports. The finite-element method is used, whereas the crack is modelled using a technique allowing to create on an arbitrary surface a layer of double nodes belonging to different faces of the crack. The matrices in the motion equation are built for a completely open crack, whereas the contact conditions on the crack faces are satisfied by introducing contact forces applied in the double nodes. The time solution of the problem is based on the Newmark scheme, and at each time step iterations determine the distribution of contact forces on the crack faces.
The basic variant for numerical investigations with different rotational speeds was a rotor with a 50 % deep crack located in the middle of the rotor body between the discs. In other variants, the crack location over the length of the rotor and the crack depth were changed. It was found that the first natural frequencies of an integral rotor and the segregated natural frequencies of a rotor with a crack when faces contact was not accounted for are lower than the working frequency. According to estimates, a rotor with a "breathing" crack acquires periodic vibrations with a complex spectrum of harmonic components where one can distinguish the first, second and third harmonics. At a rotational speed close to one-half of the lowest natural frequency of an integral rotor, the 2/1 resonance of the second harmonic component is observed. Above this rotational speed, the harmonics are redistributed, and the first harmonic becomes predominant. In the frequency range close to natural frequencies with the first mode of flexural vibrations, the fundamental resonance for the rotational component occurs. The amplitudes of harmonics decrease with an increase of the rotational speed to the running one. If the location of a crack and its depth change, the differences in the values of vibration characteristics can be significant, though the qualitative pattern of results changes insignificantly.
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