2 Correlation of Non-contact Full-Field Dynamic Strain Measurements with Finite Element Predictions 13 (a) (b) (c) 5 10 15 20 2 4 6 8 10 12 14 16 18 20 FE Modes Test Modes Modal Assurance Criterion (%) 10 20 30 40 50 60 70 80 90 Fig. 2.2 (a) Compressor blade FE model, (b) Measurement grid used displacement mode shapes, (c) resulting auto-MAC plot sampled at measurement nodes are compared to themselves. Cross-mode correlation amplitudes as evident from trivial offdiagonal terms (all below 10%) suggest that all measured modes should be uniquely identifiable. Measurement grid for the strain mode shapes is significantly denser than the one for displacement mode shapes. This is required to capture the local strain variations faithfully. Note that by this stage the modes are already identified through correlation of displacement mode shapes. As such autoMAC check performed for displacements is not necessary to repeat for strain. 2.4 Correlation of Mode Shapes Measurement grid given above was identified for the displacement mode shapes using the full deformation field. In other words all X, Y and Z displacement DOFs were used at each measurement grid as the same DOFs would be captured from the tests. Measurement of all DOFs at each point is a requirement for strain measurements but it is not essential for displacement mode shapes. In fact 1-D SLDVs, measuring a projection of total deformation field in the line of sight, have been used for decades. Nevertheless, availability of all DOFs brings significant advantages in the form of increased independent information which even in the case of displacement mode shapes can make a big difference. Figure 2.3 shows a particular mode measured on the intermediate pressure turbine blade by 1-D and 3-D SLDV systems, together with the predicted FE mode shape where FE and the 3-D measured mode shape are almost identical. Although the 1-D measurement appears to be very different, a direct comparison is inappropriate. 1-D SLDV measures a projection of overall response in the viewing direction whereas distributions shown for the FE and the 3-D SLDV are for the resultant displacements from all DOFs computed and measured. A correct correlation in the case of 1-D SLDV measurements would be with FE predictions projected in a similar way to reflect the operation of 1-D SLDV system. Having said that, the fact remains that the 3-D SLDV provides a lot more information (three times as much) about the deformation field, which in return allows better identification of measured mode shapes. This is demonstrated in Fig. 2.4. Here there are two correlation scenarios shown where mode shapes captured by 1-D and 3-D SLDV systems are correlated in the form of Modal Assurance Criterion (MAC) with their corresponding FE predictions in Fig. 2.4a and b, respectively. Significant off-diagonal values in 1-D SLDV case which lead to difficulties in identifying mode shapes unambiguously are greatly reduced in the 3-D case where the identification of the modes is now straight forward. Displacement mode shape measurement campaign performed on the compressor blade is summarised in Fig. 2.5. As evident from the sub-set of measured and predicted mode shapes given in Fig. 2.5a, not only the global behaviour but also the local variations are extremely closely matched. MAC matrix given in Fig. 2.5b shows a remarkable degree of correlation between measurements and the predictions with MAC values at 95% and above, and, with all off-diagonal values below 10%. It is worth noting the extraordinary similarity between autoMAC plot generated in Fig. 2.2c and the MAC plot given in Fig. 2.5b. As such the FE model is demonstrated to be a good representation of the measurement hardware from mode shapes point of view. This level of accuracy in the resultant correlation also demonstrates that tests are carried out as planned and that the alignment of FE model and the test model is performed adequately. The latter is a critical factor, particularly for mode shapes
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