Flexible Multibody Dynamic Modeling of a Horizontal Wind Turbine Drivetrain System

A mathematical model of a horizontal wind turbine drivetrain is developed by applying the flexible multibody dynamics theory based on the Lagrange formulation. The proposed model accounts for the variation in the number of teeth in contact and support bearing elasticity, which are known to influence the dynamic behavior of drivetrain significantly. The derivation of the system governing equation by Lagrange equations requires the formulations of the kinetic energy terms of both orbiting and rotating gears, the potential energy terms of time-varying tooth stiffness and bearing compliance, and the work from input torque. From the resultant governing equations, the natural frequencies and modes of interest are calculated, and the effect of bearing stiffness on those modes is examined. The rotational vibrations of the sun gears as well as the tooth contact forces between the sun and planet and the ring and planet are analyzed in detail. Result of the dynamic transmission error as a function of gearbox speed is also predicted to understand the overall dynamic behavior of the drivetrain system.