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.

传输误差是评估谐波驱动器最重要的性能指标之一，并且可能对工业机器人的定位精度和稳定性产生严重影响。但是，大多数现有的误差分析方法只关注单个因素，而不考虑动态参数的不确定性，从而导致明显的局限性。在本研究中，对谐波传动的静态传动误差（由制造和装配误差引起）和动态传动误差（由静态传动误差和动态参数产生）建模。提出了一种区间方法，并将其用于数值表示系统的不确定动态参数。Chebyshev多项式用于近似谐波驱动的动态微分方程，然后详细讨论了动态传输误差的分布及其与不确定参数的关系。另外，进行了全局灵敏度分析以直观地证明每个参数对动态传输误差有多大影响。我们的结果表明，惯性矩J _in和扭转刚度系数k ₁对动态传递误差有很大的影响。最后，通过实验验证了该方法的有效性。该方法可以确定不确定参数影响下动态系统动态传输误差的上限和下限，为传输误差的优化和补偿提供理论依据。