Multibody Dynamics Model for Predicting the Vibration Response and Transient Tooth Loads for Planetary Gear Systems

A high-fidelity multibody dynamics model for predicting the transient response of planetary gear trains is presented. The model supports an arbitrary number of gears, stages and arms. The model accurately accounts for the effects of gear tooth stiffness/damping/friction and tooth backlash. The multibody system representing the system is modeled using rigid bodies, revolute joints and rotational actuators. A penalty model is used to impose the joint and normal contact constraints. The normal contact penalty stiffness and damping are used to model the tooth stiffness and damping. The contact model detects contact between discrete points on the surface of a gear tooth (master contact surface) and a polygonal surface representation of the mating gear tooth (slave contact surface). A recursive bounding box/bounding sphere contact search algorithm is used to allow fast contact detection. An asperity friction model or an elasto-hydrodynamic lubrication model can be used for the contact friction forces. The governing equations of motion are solved along with joint/constraint equations using a time-accurate explicit solution procedure. The model is partially validated by comparing its predictions of the resonant frequencies of a planetary gear train to those of a previously published steady-state dynamic model. The model can help improve the design of planetary gear boxes including increasing the range of operating speeds, torque capacity and durability.