Research on dynamic transmission error of harmonic drive with uncertain parameters by an interval method

Transmission error is one of the most important performance indicators for evaluating harmonic drives, and can have crippling effects on positioning accuracy and stability of industrial robots. However, most of the existing error analysis methods focus on a single factor, and do not consider the uncertainty of dynamic parameters, leading to evident limitations. In the present study, static transmission error (caused by manufacturing and assembly error) and dynamic transmission error (generated by static transmission error and dynamic parameters) of a harmonic drive are modeled. An interval method is developed and used to numerically express uncertain dynamic parameters of the system. Chebyshev polynomials are used to approximate the dynamic differential equations of the harmonic drive, and then the distribution of dynamic transmission error and its relationship with uncertain parameters are discussed in detail. In addition, a global sensitivity analysis is carried out to intuitively demonstrate how much impact each parameter has on dynamic transmission error. Our results suggest that the moment of inertia J_in and the torsional stiffness coefficient k₁ have a large influence on dynamic transmission error. Finally, the proposed method is validated by experiment. The method can be adopted to determine the upper and lower bounds of dynamic transmission error of dynamic systems under the influence of uncertain parameters and provides a theoretical basis for transmission error optimization and compensation.