Estimation of gear crack size using embedded modeling and prognosis of gear crack propagation using fracture mechanics

Gearboxes are mechanical subsystems designed to transmit power from one place to another and change speed and/or direction. They are usually critical to the safety and functionality of the systems they belong to. For example, a crash and a loss of live are almost inevitable when the main transmission of a helicopter fails. One of the most common causes of gear failure in gearboxes is tooth root fatigue crack due to cyclic loading. It results in progressive damage to gear teeth and ultimately leads to complete failure of the gear. Hence the ability for early detection, diagnosis, and prognosis of gear tooth fatigue crack in a gearbox has always been one of the major technical challenges for safe and economic operation of machinery containing them. This study proposes an embedded modeling methodology for identifying gear meshing stiffness from measured gear torsional vibration such as angular displacement or transmission error. An embedded model integrating a physical-based model of the gearbox and a parametric representation, in the form of truncated Fourier series, of meshing stiffness is established. A solution method is then used to find the meshing stiffness that minimizes the discrepancy between the model output and the measured output. Furthermore, an algorithm is developed to estimate the size of tooth crack from identified meshing stiffness. Both simulation and experimental studies were conducted to evaluate if and how accurately gear meshing stiffness can be identified and the size of the tooth crack can be estimated from identified tooth meshing stiffness. Additionally, a gear residual life prognosis methodology was established by integrating the embedded modeling method which identifies the meshing stiffness and then crack size, a gearbox dynamic simulator which estimates tooth load, and a failure model based on FEM and a Paris crack growth model. Experimental data were acquired to validate results of crack diagnosis and prognosis.