PSI - Issue 60

Ashish Kumar et al. / Procedia Structural Integrity 60 (2024) 364–371 A. Kumar, Y.V.N. Bhat, S.Patri, P.A.Kumar, S.I.S.Raj, S.S.Kumar, B.K.Sreedhar / Structural Integrity Procedia 00 (2019) 000–000 7

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It is observed from Table 2 that when the IGT and OGT are constrained to each other by two or more connections between them (Sl. No. 3, 4, and 5 1 ), the natural frequency of the combined system is in the range of 31 – 33 Hz. This value is in close agreement with the measured value obtained using the modified experimental setup and it confirms that 33 Hz corresponds to an integral IGT – OGT, connected at multiple locations below the O–Ring. The probable reason for such connections may be the tilt of LMP about the spherical seat. LMP, as shown in figure 1 and 2, is provided with a special feature that enables its rotor assembly and intermediate casing to tilt about a spherical seat to compensate for the differential thermal expansion between the pump’s top and bottom portions. The pump shaft and intermediate casing are assembled with a tilt of certain degrees w.r.t. vertical during installation at room temperature so that it gets aligned vertically under nominal operating conditions. As a result of this inclined assembly, the IGT below the shield box also tilts along with the LMP, while the OGT always remains vertical. The difference in angles between the IGT and OGT at the tilt junction may cause the IGT to touch the OGT at multiple locations. It is further seen from the analytical results that the first mode shape, in which the portion of IGT lying below the shield box vibrates at a lower natural frequency (28.7 Hz), did not get captured during the measurements. This may be because the IGT portion lying below OGT does not respond to impact excitation given at the top, or IGT’s lower portion responses are not captured by the sensors mounted on the top. Harmonic analyses with two sets of BCs were carried out to confirm these hypotheses with the modified model. In both cases, connections between IGT and OGT were the same as in Sl. No. 5 of Table 2, the only difference was that in the first harmonic analysis, simple supports were provided at six locations of the IGT. In contrast, in the second harmonic analysis, no supports were provided in IGT below the shielding box location. OGT remained fixed at the two weld locations in both analyses. With these connections and BCs, the top portion of IGT was excited using a sinusoidal force of magnitude 10 N and frequencies ranging from 1 Hz to 50 Hz. A constant damping ratio of 2% was used to get finite displacements during resonance, because from practical applications, it has been revealed that the damping ratio is equal to 2% for welded steel structures, Fatma Nur Kudu et. al. (2015). The frequency response under both cases peaked at 33 Hz. The peak in frequency response spectrum was also accompanied by a phase angle change of 180° as shown in Figure 11. This indicates that 33 Hz is the combined natural frequency of the IGT and OGT irrespective of the bottom support conditions of the IGT. It can be hence surmised that the bottom portion of the IGT does not get excited or the amplitude of such excitations is negligible when the impulse is given on the top portion of the IGT.

Fig. 11. Frequency and phase response plots for harmonic analysis of combined IGT-OGT system

1 Increasing the number of connections between IGT and OGT beyond Sl. No. 5 of Table 2 did not alter the natural frequencies of the system any more.