of simulating the structure using a limited number of degrees-of-freedom (DOF), which facilitates studying the behavior of gears and bearings in the presence of nonlinearities and geometrical faults [1, 2]. However, it is difficult to account for the casing flexibility in the LPM models, which is an important consideration in lightweight structures such as in aircraft applications and this results in poor spectral matching over a wide frequency range. In the case of continuous elastic systems, where masses are distributed over the structure (gearbox casing), other methods, such as finite element analysis (FEA), are often used to study the behavior of the structure. The use of FEA results in a large number of DOF, which in turn complicates simulating the whole system’s response to the presence of nonlinearities and to gear and bearing faults. This in turn limits the validity of the simulated results and restricts their later usage in the diagnostics and prognostics of the gears and bearings. Hence there is a growing trend to use FE model reduction methods to create accurate low order dynamic models before calculating eigenfrequencies and eigenmodes [3]. Model reduction is applied to large FE models to give faster computation of the natural frequencies and mode shapes and at the same time compute the static and dynamic responses correctly. Model reduction also plays a role in experimental modal analysis since the mass and stiffness matrices may also be used to compare the analytical and experimental modes by using orthogonality checks [4]. In this paper, a dynamic reduction technique, the so-called Craig–Bampton reduction technique, is used to reduce the finite element model of the UNSW gearbox casing. The reduced model is valid only within a certain frequency range, subject to the number of modes retained in the analysis. The reduced model is then connected to a lumped parameter model of the internals (shafts, gears and bearings) which has the capacity to simulate faults. The combined model is run in Simulink environment with extended inner race faults. Thus the total response will not only include the contributions of the dynamics of the internals but also the flexibility and the dynamics of the casing. This makes this approach very attractive as the finite element model has been dramatically reduced from over a hundred thousand degrees of freedom to only 124 DOF. In order to extend the validity of the combined /reduced model, the forces are extracted from combined/reduced model and convolved with the impulse responses corresponding to the FRFs of the whole gearbox (casing and internals). The approach of convolving the forces with the impulse response of the FE model was earlier proposed [5, 6], but only applied to the forces extracted from the LPM model. The current approach has the advantage of maintaining a dynamic interaction in the low/mid frequency regions and improves the validity at higher frequency where it is the modal density rather than the individual modes that are of interest. 2. UNSW Gearbox The gearbox test rig (Fig.1) under investigation was built by Sweeney [7] to investigate the effect of gear faults on transmission error. 400
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