Quantitative assessment for tooth crack of the sun gear in a planetary gearbox

Abstract The sun gear in a planetary gearbox is prone to generate tooth crack due to its much more severe load conditions than other gears. The cracked sun gear will evolve into distinct tooth breakages and thus may deteriorate the operation status and even cause catastrophic loss of the whole transmission system. To avoid tooth crack induced malfunction of the planetary gearbox, the tooth crack of sun gear should be accurately identified during the early stage. Therefore, a novelty quantitative assessment methodology for tooth crack damage is proposed, which is a mathematical model for crack propagation of the sun gear in planetary gearboxes based on vibration acceleration signal. Firstly, the quantitative relationship between the crack propagation parameters along the gear thickness and width directions and the time-varying mesh stiffness is analytically formulated. The analytical time-varying mesh stiffness formulation is incorporated into a translational–torsional dynamic model to reveal the effects of crack propagation on the vibration signal of internal and external meshing pairs in the planetary gearbox. Secondly, a quantitative mapping function is established by taking the cracked section area as the variable and the residual of the summed envelope spectrum amplitude of the vibration acceleration signal as the assessment index. Finally, a numerical simulation as well as an experimental test is conducted and compared to verify the correctness of the proposed assessment methodology. We believe that the established model and the corresponding index provide a physically intuitive yet mathematically quantitative reference for diagnosing tooth crack in planetary gearboxes.