Modeling of sliding speed of harmonic reducer based on double-circular-arc tooth profile

The two main failure modes of harmonic reducers are wear and contact friction between the tooth profile of the circular spline (CS) and the flexible spline (FS). The sliding speed of the meshing point is a key factor affecting friction and wear processes of the CS and FS and should therefore be accurately determined. Herein, envelope theory is used to deduce the FS trajectory and the envelope track is divided into two segments according to whether or not the meshing point is outside the top circle of the CS. The velocity of the meshing point in the second meshing stage is essentially the vector sum of the FS velocity in three directions. When the CS is fixed, the relative sliding velocity is the instantaneous velocity of the FS along the tangential direction of the enveloped tooth profile. To verify the proposed model, the finite element method (FEM) and laser sensor experiments were performed and a relationship between the angle of rotation of the wave generator (WG) and the velocity of the FS was established. The results show that the sliding speed is sensitive to the radial displacement coefficient and has a linear relationship with the rotational speed of the WG.