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Early detection of tooth cracks is crucial for effective condition-based monitoring and decision making. The scope of this work was to bring more insight into the vibration behavior of spur gears in the presence of single and multiple simultaneous tooth cracks. The investigation was conducted in both time and frequency domains. A finite element analysis was performed to determine the variation in stiffness with respect to the angular position for different combinations of crack lengths. A simplified nonlinear lumped parameter model of a one-stage gearbox with six degrees of freedom was then developed to simulate the vibration response of faulty external spur gears. Four different multiple-crack scenarios were proposed and studied. The performances of various statistical fault detection indicators were considered and investigated. The simulation results obtained via MATLAB indicated that, as the severity of a single crack increases, the values of the time domain statistical indicators increase also, but at different rates. Moreover, the number of cracks was found to have a negative effect on the values of all the performance indicators, except for the RMS. The number and amplitude of the sidebands in the frequency spectrum were also considered, while assessing the severity of the faults in each scenario. It was observed that, in the case of consecutive tooth cracks, the number of spectrum peaks and the number of cracks were consistent in the frequency range of 4-5 kHz. The main finding of this study was that the peak spectral amplitude was the most sensitive indicator of the number and severity of cracks.

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The knowledge of wave scattering and power flow in waveguide structures is important for many engineering applications. In this paper, power flow and scattering in a straight-helical-straight waveguide structure are investigated using the wave and finite element (WFE) method. For simple (straight or helical) waveguides, wave scattering (and subsequently the power flow and scattering) can be resolved analytically. This is not the case for complex waveguides such as laminated or sandwiched waveguides or waveguides with noncanonical cross-sections. In such cases, the WFE method is used to model the wave behavior in each waveguide in the structure. The power flow is then studied by considering how waves reflect and transmit at the boundaries that join the straight waveguides with the helical waveguide. We present three numerical examples but analytical solutions can be obtained for the first example only; for the second and third examples, the WFE is used in earnest since the wave behavior and subsequently the power flow would at best be extremely difficult to formulate analytically.

In this paper a model of the sound transmission characteristics of a conventional circumaural passive ear protector is presented for low frequency noise. It includes the effects of porous sound absorption material within the device as well as sound leakage. A theoretical study based on the model shows that the presence of sound absorption material effectively acts to increase the volume compliance of the system, thus decreasing its resonance frequency. The role of leakage on the other hand is mainly to shift the resonance to a higher frequency depending on the equivalent leakage diameter. Experimental results are provided in support of the theoretical predictions. The model is useful in providing an understanding of the mechanisms of conventional passive ear defenders and can be employed to guide their design. The modelling can also be extended to study and aid in the development of communication and active noise control ear protectors.