A method to balance root stresses of planetary geartrains considering nonlinear damage accumulation

Abstract Planetary gear sets are considered the optimal arrangement for power transmission needs in many automotive and aerospace applications. However, the design criteria for durability can become more complex as compared to parallel axis arrangements due to the addition of more gearing components and the prevalence of using different materials and heat treatment for the ring component as compared to the sun and planet components. While there has been development in experimental methodologies to characterize fatigue strengths of gears there is little guidance in best practices for how to apply the experimental characterizations particularly within the context of a complex, multi-material system such as planetary gear arrangements. In this study, a general kinematics formulation is applied to determine loading frequencies of gear teeth in various planetary geartrains. These kinematic relationships are combined with Stress-Life (S-N) relationships considering mean stress and material effects along with linear and nonlinear cumulative damage formulations to describe fatigue damage on each planetary component. This fatigue damage is then leveraged to develop a generalized formulation to balance the relative allowable maximum tooth root stresses amongst the gear components of a planetary geartrain such that each gear in the system has the same bending fatigue life expectancy.