Reliability Analysis of Gear Under Multiple Failure Modes Based on Time‐Dependent Mixed Copula Function

Gears are subjected to alternating loads during operation and are prone to various failure modes. In addition, the mutual influence of gear stress states and the cumulative effect of fatigue damage can lead to the correlation between failure modes on the gear, thereby affecting the confidence level of reliability assessments. To address this, the performance degradation of gears over their lifecycle is considered, and time‐dependent limit state functions for contact and bending fatigue failures are established. The Kendall rank correlation coefficient is also employed to characterize the time‐dependent correlation between failure modes. A time‐dependent mixed Copula function is developed to analyze the reliability of gears, elucidating the evolution of reliability throughout the gear's operational lifecycle.