The parametric design of double-circular-arc tooth profile and its influence on the functional backlash of harmonic drive

The aim focuses on the use of double-circular-arc common-tangent tooth profile (DCTP) in harmonic drive (HD). To enable more teeth to participate in meshing, a complete method to design tooth profile and its backlash assessment in an HD is presented. The parametric equations are expressed for all segments of the DCTP. Using envelope theory, the conjugate tooth profile (CTP) in the conjugate existent domain (CED) is deduced. In order to realize continuously conjugated transmission in the entire engagement region, the influence of the DCTP parameters on the CTP and CED was studied. An algorithm of arc interpolation is used to obtain the position of points on the CTP. The backlash is deduced as an assessment method for the interpolation of the CTP. To verify the effectiveness and correctness of the research, the Finite Element Method (FEM) is employed to verify the distribution and the magnitude of the backlash. The influences of the double-circular-arc common-tangent tooth profile parameters on these quantities are also studied. The results demonstrate the high precision of the proposed method for a specific calculated section.