A general mathematical modeling and finite element analysis of a strain wave gear possessing a double-circular-arc-with-a-common-tangent profile

In this study, the characteristics of a strain wave gear (SWG) with a double-circular-arc with a common tangent (DCACT) profile were simulated using two-dimensional (2D) and three-dimensional (3D) finite element analysis (FEA). First, theoretically generated tooth profiles for the flexible spline (FS) and circular spline (CS) of an SWG were developed according to the theory of gearing. An automated mesh-generating computer program was developed in Visual C++ to establish 2D and 3D finite element models of the SWG based on its derived geometry. An FEA was then performed to explore the meshing characteristics, including the stress distribution, torsional angle, torsional stiffness, and number of engaged teeth, of the SWG. Continuous meshing of multiple tooth pairs between the FS and CS from the 2D FEA verified the conjugation of tooth profiles. The coning effect on the FS during assembly of the SWG was also predicted and discussed from the 3D FEA results. The 3D FEA produced more accurate and practical results than the 2D FEA did. Additionally, 3D FEAs of a modified (with longitudinal crowning) and unmodified (without longitudinal crowning) FS were performed and compared. Finally, a 3D FEA of a modified FS was successfully conducted to predict cyclic contact stress, root stress, and transmission error.