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In computational fluid dynamic (CFD) and computational aeroacoustics (CAA) simulations, the wall surface is normally treated as a purely reflective wall. However, some surface treatments are usually applied in experiments. Thus, the acoustic simulations cannot be validated by experimental results. One of the major challenges is how to define acoustically boundary conditions in a well-posed way. In aeroacoustics analysis, impedance is a quantity to characterize reflectivity and absorption of an acoustically treated surface, which may be introduced into the numerical models as a frequency-domain boundary condition. However, CFD and CAA simulations are time-domain computations, meaning the frequency-domain impedance boundary condition cannot be adopted directly. Several methods, including the three-parameter model, the z-transform method and the reflection coefficient model, were developed.

Nested planetary gear trains, which consist of two integrated co-axial single-stage planetary gearsets, have recently been widely implemented in automobile transmissions and various other applications. In the current study, a non-destructive vibrational and acoustical monitoring technique is developed to detect a common type of gear grinding defect for a complex nested gear train structure. A nested gear train which has an unground pinion with unpolished teeth profile is used to exemplify the developed methodology. An experimental test stand with an open and vertical mounting configuration has been designed to acquire both vibrational and acoustical data. The measured data are investigated using several signal processing techniques to identify unground pinions in the gear system. A general frequency spectrum analysis is performed initially, which is then followed by a peak finding algorithm to identify the peaks in the spectrum.