Figure 7: Combining FEM and LPM to evaluate total response Sawalhi et al. in [22] evaluated the total response by expanding both the physical and modal responses back to the slave DOFs of interest which also represented a virtual sensor corresponding to a physical accelerometer location used in the experimental testing (Approach A, Fig 7). Using this approach, the results were valid only up to 4 kHz (100 modes). In order to improve the accuracy of the combined LPM-reduced model and extend this to a higher frequency range, the forces from the LPM-reduced casing model were extracted and convolved with the impulse response of the gearbox (Approach B, Fig 7). This approach of extracting the forces and convolving them with the impulse response was earlier proposed in [5]. However, when this was done for the LPM model, the dynamic interaction was not fully accounted for in the low frequency region. By reducing the model and then convolving the LPMreduced forces with the impulse responses, we achieve a more interactive approach which has a higher valid frequency range. This is also viable as at high frequency the main focus is on the modal density rather than the individual modes, and also on the response to local rather than extended faults, already shown to be well modeled by the simpler models. Hence, in this paper the combination of the LPM and FE reduced model was achieved by extracting the bearing forces from the LPM model and convolving them with the impulse responses corresponding to the frequency response functions (FRFs) of the casing [5] (Fig 7). The FRFs were extracted from the FE model by synthesizing them from the natural frequencies and mode shapes in the LMS Virtual Lab ® environment which compute the FRFs based upon the modal superposition of the selected mode set. The FRFs were calculated between the bearing force location (input points) and accelerometer position (output point) located on the casing directly above the faulty bearing. 405
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