An Evolution-Based Uncertainty Analysis Method for Bending Fatigue Failure of Involute Spur Gears

An evolution-based uncertainty analysis model of bending fatigue failure of involute spur gears is presented. The fluctuation of transmit torque and rotational velocity of gears are introduced to the mild wear model of gear flanks. Then a novel simulation model of tooth profile evolution is developed to describe the change of meshing parameters, which include the tooth load, load angle and bending moment arm. The critical tooth-root bending stress is influenced by these time-varying parameters. Based on the evolution-based uncertainty analysis method, the load is approximately obeying logarithmic normal distribution, the load angle and bending moment arm are approximately obey geometric Brownian motion. Then the critical tooth-root bending stress is calculated as a logarithmic normal distribution quantity over time. Finally, the prediction model of time dependent reliability of the bending load capacity of spur gears is proposed.