PSI - Issue 60

Ashish Kumar et al. / Procedia Structural Integrity 60 (2024) 364–371

365

2 A. Kumar, Y.V.N. Bhat, S.Patri, P.A.Kumar, S.I.S.Raj, S.S.Kumar, B.K.Sreedhar / StructuralIntegrity Procedia 00 (2019) 000–000

assembled from the top. Insertion of the slender IGT in the pump is a blind operation, and it passes through seven supports spaced along the stationary part of the pump. Proper assembly of IGT is a prerequisite for ensuring error free reading of the probe and eliminating unwanted flow-induced vibrations and stresses during pump operation. An indirect approach to confirm proper IGT assembly is measuring its natural frequency and comparing it with analytical values, Thompson (1993) and French (1973). Analytical estimation of natural frequencies of IGT and OGT was made, followed by in-situ experiments on the as-assembled ECFM in the LMP. However, the experimental results did not match the analytical ones. The unanticipated experimental results called for further analyses and experiments, culminating finally in better insight and understanding of vibration characteristics of assembled slender components under close tolerances. This paper discusses in detail, the experiments and analytical studies done to understand and conclude the support conditions acting on IGT.

2. Methodology

The exercise of confirming proper assembly of IGT is divided into two parts; the first part is the estimation of the theoretical natural frequencies of IGT in the properly assembled condition (with all the supports acting on it), while the second part involves experiments to measure the natural frequency of IGT in as-assembled condition, which is shown in figure 1. The next step is comparing the measured values with the analytical ones and concluding on the state of support of IGT. While the similarity in both the values would confirm proper IGT assembly, deviations/mismatches in the results would call for further experiments and studies, followed by a conclusion.

3. Analytical natural frequencies of IGT and OGT

Assembly details of IGT in OGT, and OGT in the shield box of the LMP are shown in figure 2. Commercially available Finite Element (FE) based software was used to obtain the natural frequencies of IGT and OGT, which were modelled using solid elements. The material of construction of IGT and OGT is AISI SS 304, and the following properties were used for the material model at 35°C as per RCC-MR.

: 1.95 × 10 11 Pa

Young’s Modulus

: 7958 kg/m 3

Density

Poison’s Ratio

: 0.3

3.1. Estimation of natural frequencies of IGT

The top portion of IGT butts on OGT’s top ring flange, as shown in figure 3, the remaining portion of IGT are supported laterally at seven different locations below the shield box, as shown in figure 1.

Boundary Conditions for IGT To estimate the natural frequencies of IGT, following BCs were provided:- (i) IGT top portion which rests on OGT was provided with fixed support, i.e. U x = U y = U z = 0, and

R x = R y = R z = 0; where ‘U’ represents displacement Degree of Freedom (DOF) and ‘R’ represents rotational DOF; x, y and z are the three directions in Cartesian co-ordinate system.

(ii) IGT was simply supported at seven lateral support locations. i.e. Ux= Uz= 0,

Under these BCs, the first three natural frequency of IGT were found to be 16.3 Hz , 31.3 Hz and 35.5 Hz .

3.2. Estimation of natural frequencies of OGT

The OGT is welded to the top and bottom surfaces of shield box of LMP using fillet welds.

Boundary Conditions for OGT Fixed BCs were provided on the OGT at the weld locations, and with these BCs, first three natural frequencies of