A new harmonic drive model considering the geometry, internal interactions and assembly error of key parts is proposed in this paper. In this model, a single tooth pair is used to represent the transmission mechanism of harmonic drive. The meshing stiffness between the flexspline and the circular spline, the torsional stiffness of the flexspline cylinder, and the radial stiffness of the thin-walled ball bearing are included and formulated. The kinematic error is fitted using a lowvelocity test, and its generating mechanism is analysed. The friction of the harmonic drive is formulated at the tooth meshing section and at the ball bearing, where its parameters are identified based on experimental results. Based on the new model, velocity step simulations are conducted. For comparison, velocity step experiments at eight different velocities from 60 to 3000 r/min are performed, and the simulation results are in good agreement with the experimental results. The new model reveals the dynamic behaviour of the harmonic drive system; therefore, it will be useful for the dynamic design and precision control of harmonic drive systems.

To highlight the key factors which influence the dynamic performance of the harmonic drive, a refined harmonic drive model considering nonlinear stiffness, kinematic error, and friction of the critical components is established. A dedicated experimental apparatus based on double motor twisting is constructed to measure the characteristics of harmonic drive, and the attribute parameters of the proposed model are identified. A series of experiments on the dynamic transmission error at different driving velocities are carried out to verify the proposed model. Based on the proposed model, the influence of different component stiffness on the velocity step response of the harmonic drive is analyzed. The results show that the influence of the component stiffness on the system dynamic response is more significant at high driving velocity, the increase of the stiffness of each component will decrease the dynamic transmission accuracy of harmonic drive, and the bearing radial stiffness is the most sensitive parameter to system’s dynamic response among all the stiffness factors.

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To suppress the abrupt and unexpected turning velocity fluctuation of the industrial robot under the condition of trajectory tracking, a flexible robotic joint experimental setup with the harmonic drive was established. The measured friction with Stribeck effect and velocity were modeled by a simple polynomial fit method. Two friction compensation control strategies of feedforward and feedback were designed. The friction compensation experiments were carried out on the dSPACE system, the good restraint effect of fluctuation on the turning velocity was verified and the control accuracy of feedback compensation control strategy proved better.

Purpose Because of the compact structure, short flexspline (FS) harmonic drive (HD) is increasingly used. The stress calculation of FS is very important in design and optimization of HD system. This paper aims to study the stress calculation methods for short FS, based on mechanics analysis and finite element method (FEM). Design/methodology/approach A rapid stress calculation method, based on mechanics analysis, is proposed for the short FS of HD. To verify the stress calculation precision of short FS, a complete finite element model of HD is established. The results of stress and deformation of short FS in different lengths are solved by FEM. Findings Through the rapid calculation method, the analytical relationship between circumferential stress and length of cylinder was obtained. And the circumferential stress has proportional relation with the reciprocal of squared length. The FEM results verified that the rapid stress calculation method could obtain accurate results. Research limitations/implications The rapid mechanics analysis method is practiced to evaluate the strength of FS at the design stage of HD. And the complete model of HD could contribute to improving the accuracy of FEM results. Originality/value The rapid calculation method is developed based on mechanics analysis method of cylinder and equivalent additional bending moment model, through which the analytical relationship between circumferential stress and length of cylinder was obtained. The complete three-dimensional finite element model of HD takes the stiffness of bearing into consideration, which can be used in the numerical simulation in the future work to improve the accuracy.