Impact of predicted parabolic crack paths on the natural frequencies of functionally graded transmission gears

The application of advanced materials in transmission gears is crucial because these components constantly work under substantial loads, making their stability and durability a primary concern. This article uses the finite element analysis (FEA)-based numerical method to study the free vibration behavior with a predicted crack following a parabolic curve path in functionally graded transmission gears (FGGs). The FGG consists of 18 equal layers, aligning equally to the gear tooth profile, where material properties vary radially according to power-law function, with the metal in the inner most core and the ceramic at the outer surface, respectively. Two types of predicted cracks are considered, both following a parabolic curve path: one propagating towards the gear root and the other towards the gear body. The proposed solution is validated using available literature, and good agreement is found. The effect of cracks with constant width and depth reaching various layers, along with different angle propagation directions and power indices on the first three natural frequency values are described in detail. The results show a significant impact on the natural frequency values for both gear root and gear body crack paths.