Architecture-dependent modal sensitivity of linearly cracked functionally graded spur gears

In this study, the free-vibration behavior of linearly cracked spur gears made from functionally graded materials is investigated by finite element analysis. The gear is modeled with equally spaced concentric layers following the tooth profile, with material properties varying according to a power-law function from a metallic core to a ceramic outer surface. Two material architectures are investigated, a fully graded gear and a hybrid half-metal/half-graded gear. Mesh convergence is verified with a variation of no more than 0.05% in the first three natural frequencies. Each gear model has a linear crack at the tooth root with varying depth and crack propagation angle. The comparison shows that the substitution of the fully graded architecture with the hybrid architecture results in a gradation index dependent variation of the first three natural frequencies, instead of a constant reduction. From the parametric study, it is found that the crack depth is the most influential factor which causes an approximately 5.7% decrease in frequency, followed by the gradation index which causes a nonlinear trend of around 4%. The crack propagation angle causes frequency changes of less than 0.3%. Normalized tooth-path mode-shape profiles are also used to compare the deformation behavior of the two material architectures under the same crack condition. The results provide guidelines for designing appropriate functionally graded gear architectures and a reference for future vibration studies of functionally graded gears.