A quick stress calculation method for flexspline in harmonic actuators based on the finite element method

Abstract The harmonic drive (HD) is increasingly used due to its outstanding advantages, especially for equipment requiring high precision and a large gear ratio. This research is based on the Finite Element Method (FEM) and mechanical analysis to investigate stress calculation methods for the flexspline (FS), a significant component of HD transmission, providing a basis for assessing the durability and failure of the FS. First, the FS deformation and stress analysis model based on the FEM is proposed. Since the two boundary elements of the model have the form of a rotation and translational joint, which have not been provided, based on the stiffness matrix of the fixed beam to build the stiffness matrix for these elements, which completes the proposed analytical model. Then, the structures of an HD reduced are designed and applying the proposed force analysis model, the deformation and stress distributions of the FS are obtained. Finally, the theoretical safety factor is calculated and analyzed. The results of the simulation completely coincide with the theoretical calculation and show that the most concentrated stress is at the root of the teeth, which is the leading cause of the FS failure. So, the study as reference material for rapidly evaluating the stress state and calculating the safety when designing and optimizing the FS.