A Novel Rapid Design Framework for Tooth Profile of Double-Circular-Arc Common-Tangent Flexspline in Harmonic Reducers

Due to its small size, high transmission ratio and precision, the harmonic reducer is widely used. The design of the flexspline tooth profile is crucial for the transmission accuracy and service life of harmonic reducers. However, the numerous design parameters and the lack of a unified design standard for the flexspline tooth profile make it challenging to accurately determine these parameters. This can lead to issues such as tooth profile interference and excessive stress on the gear teeth during transmission. To address these issues, we propose a novel rapid design framework for the tooth profile of a double-circular-arc common-tangent flexspline in harmonic reducers. Firstly, the mathematical formula for the flexspline tooth profile with a double-circular-arc common-tangent and its conjugate circular spline tooth profile is derived. Then, two-dimensional and three-dimensional parametric finite element models of the harmonic reducer are established, and radial and axial profile modifications of the flexspline are carried out. Based on the parametric two-dimensional finite element model of the harmonic reducer, the optimized Latin hypercube experimental design method is employed to determine the flexspline tooth profile parameters. The method proposed can be implemented using Python language code and integrated into the Abaqus 2019 software, offering the advantage of meeting the requirements for rapid engineering development. Finally, a case study is presented to verify the effectiveness of the proposed design method.