15 Frequency Based Model Mixing for Machine Condition Monitoring 159 Thus, the solution for the coupled system can be formulated as: Y (ab) coupled =Y −YBT(BYBT)−1 BY. (15.1) Equation 15.1 uses the complex admittances Y = u f with system responses u to external forces f of the uncoupled subsystems a and b in block diagonal form. Here, Bcontains the coupling DoF between rotor and housing expressed by a signed Boolean matrix. For detailed information about LM FBS, the authors refer to [3]. Thus, we get a coupled FRF matrix describing the blower system(ab), comprising rotor and housing. 15.3 Modal Expansion In order to refine the model approximation, the numerical solution is mixed with experimentally determined transfer functions. Therefore, we perform frequency response measurements using the test set up illustrated in Fig. 15.3. Force impacts are applied with the automatic modal hammer AMimpact [4] and system responses sensed by piezoelectric accelerometers (Kistler 8688A). Siemens LMS Test Lab is used for data acquisition to set up an experimental FRF-matrix with 6×4 DoF (x- and y-direction only). This FRF-matrix represents our overlay model within performing the SEMM method. In this case, all these measured DoF are considered as boundary DoF for mixing with the numerical model. One ability of SEMM is to expand the experimental determined dynamics to internal DoF at the rotor, which cannot be measured. Herewith, we close the gap between accessible housing measurement locations and all rotor positions of interest via the hybrid SEMM model. The numerical FRF-matrix is used as parent model with all DoF kept for SEMM. Here, the numerical subset FRF-matrix with 6×4 DoF contains the boundary DoF between numerical simulation and experimental model. The 8×4 DoF subset FRF-matrix contains 6 “measurement” DoF (4 at the rotor and 2 at the housing, see Fig. 15.3). Furthermore, it implies 4 “excitation” DoF (2 at the rotor and 2 at the housing, see Fig. 15.3) The remainder is kept as internal DoF subset. According to SEMM implementation, we perform the fully extended interface method with the associated single-line Y SEMM= Y(ab) − Yik Yib Ybk Ybb (ab) Ybk Ybb rem + Y rem bb −Y ov bb Ykb Ybb rem + Yki Ykb Ybi Ybb (ab) (15.2) with internal DoFi, boundary DoFb and kept DoFk, removed model “rem” and the overlay model “ov”. Z X Y Fig. 15.3 Partial blower representation with measurement set up. Blue force impacts (arrows) and triaxial accelerometers are used for modal expansion. The orange schematic accelerometer represents the validation measurement point at the rotor shaft end
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