Modeling and Analysis of Transmission Efficiency for 3K Planetary Gearbox with Flexure-Based Carrier for Backdrivable Robot Joints

A high-gear-ratio anti-backlash 3K planetary gearbox with a preloaded flexure-based carrier is a suitable reducer for robot joints owning to its compact design and high transmission accuracy. However, to design such a 3K planetary gearbox with high bidirectional efficiencies for backdrivable robot joints, it is critical to develop an accurate transmission efficiency model to predict the effects of the preloaded flexure-based carrier on the efficiency of the 3K planetary gearbox. To determine the meshing forces of gear pairs in the 3K planetary gearbox, a quasi-static model is formulated according to tangential displacements of planet gears resulting from the preloaded flexure-based carrier. Considering the reverse meshing forces in the anti-backlash 3K planetary gearbox, a modified efficiency model is developed and the bidirectional transmission efficiencies are analyzed. Simulation results show that both forward and backward transmission efficiencies of the anti-backlash 3K planetary gearbox decrease as the preload increases, while they all increase with the increasing load torque. It is also revealed that the preload primarily affects the meshing efficiency of the sun–planet gear pair. Four different carrier prototypes are fabricated for experiments. The average errors between the predicted and measured results for forward and backward transmission efficiencies are 2.30% and 4.01%, respectively.