Optimization of gear teeth in the wind turbine drive train with gear contact’s uncertainty using the reliability-based design optimization

Although gear teeth give lots of advantages, there is a high possibility of failure in gear teeth in each gear stage in the drive train system. In this research, the authors developed proper gear teeth using the basic theorem of gear failure and reliability-based design optimization. A design variable characterized by a probability distribution was applied to the static stress analysis model and the dynamics analysis model to determine an objective function and constraint equations and to solve the reliability-based design optimization. For the optimization, the authors simulated the torsional drive train system which includes rotational coordinates. First, the authors established a static stress analysis model which gives information about endurance limit and bending strength. By expressing gear mesh stiffness in terms of the Fourier series, the equations of motion including the gear mesh models and kinematical relations in the drive train system were acquired in the form of the Lagrange equations and constraint equations. For the numerical analysis, the Newmark Beta method was used to get dynamic responses including gear mesh contact forces. From the results such as the gear mesh contact force, the authors calculated the probability of failure, arranged each probability and gear teeth, and proposed a reasonable and economic design of gear teeth