Reliability optimization design of wind power gear considering the influence of deformation

Addressing the reliability challenges faced by wind turbine planetary gearboxes—such as strength degradation and coupled multi-failure modes under complex operating conditions—this study proposes a reliability optimization method that integrates dynamic degradation modeling and multi-failure correlation analysis. A strength degradation model is established by combining the Probability-Stress-Life (P-S-N) curve with the Wiener process. A dynamic reliability framework, which adopts the quadratic fourth-order moment method to improve accuracy compared with traditional second-order approaches, is developed to evaluate the bending and contact fatigue reliability over a 15-year service life. A novel mixed Copula function is utilized to quantify the time-dependent correlations between different failure modes. An optimization model is formulated to minimize the joint failure probability, with constraints including transmission parameters, modulus, tooth width, volume, and deformation, and solved using the Dung Beetle Optimizer (DBO) algorithm. Optimization results show that the system volume is reduced by 4.2% (to 1.13 × 10 9 mm 3 ) and the deformation of critical components is decreased by over 75%. After 15 years of service, the bending fatigue reliability reaches 0.9568 (sun gear), 0.9414 (planetary gear), and 0.9671 (ring gear), while the contact fatigue reliability achieves 0.9504, 0.9316, and 0.9377, respectively. This approach overcomes the limitations of static models by addressing strength degradation and failure coupling, providing a theoretical and technical basis for designing lightweight, high-stiffness, and long-life gearboxes, thereby enhancing the reliability of wind turbines.