Concave-convex design of basic tooth profile for flexspline and its optimization on meshing performance

• The paper proposes curvature-vector-based active design method for harmonic tooth profile. • The paper systematically investigates the influence of motion and curve parameters on the meshing phenomenon. • The paper using a single circular-arc convex tooth profile of flexspline with double enveloping as example, the prescribed meshing-active zone is realized. • The paper investigates the influence of curvature vector on tooth shape and meshing performance. • The paper proposes parameter selection suitable for different working conditions based on the finite element analysis results. The tooth profile of a harmonic drive (HD) is a key factor in determining the load-carrying capacity and meshing accuracy. Conventional design methods that passively rely on curve mapping significantly limit the tooth profile shape and meshing performance. Thus, based on the existence conditions for conjugating tooth profiles and flexspline (FS) kinematics, an active tooth profile design method is proposed in which the curvature vector of the basic-profile convex curve is parameterized to control the existence and quality of the envelope. The conjugation process between the FS convex tooth profile (FCTP) and circular spline (CS) concave-convex profile is formulated, enabling the control of meshing phenomena through the interaction between the curve and motion parameters. The proposed tooth design method is verified using a circular-arc FCTP, and a concave-convex meshing pair is constructed through double enveloping. The effects of the minimum pressure angle and concave-convex profile ratio on the tooth profile shape and meshing performance are further investigated through theory and finite element analysis (FEA). Under matched conditions, the results demonstrate that the proposed method enables the regulation of the effective meshing-active zone, mitigates the maximum von-Mises stress, and realizes multi-tooth engagement and dual-point conjugation. This study provides a flexible design method for the tooth profile and improves meshing characteristics of HDs.