A High-Fidelity Harmonic Drive Model

In this paper, a new model of the harmonic drive transmission is presented. The purpose of this work is to better understand the transmission hysteresis behavior while constructing a new type of comprehensive harmonic drive model. The four dominant aspects of harmonic drive behavior—nonlinear viscous friction, nonlinear stiffness, hysteresis, and kinematic error—are all included in the model. The harmonic drive is taken to be a black box, and a dynamometer is used to observe the input/output relations of the transmission. This phenomenological approach does not require any specific knowledge of the internal kinematics. In a novel application, the Maxwell resistive-capacitor hysteresis model is applied to the harmonic drive. In this model, sets of linear stiffness elements in series with Coulomb friction elements are arranged in parallel to capture the hysteresis behavior of the transmission. The causal hysteresis model is combined with nonlinear viscous friction and spectral kinematic error models to accurately represent the harmonic drive behavior. Empirical measurements are presented to quantify all four aspects of the transmission behavior. These measurements motivate the formulation of the complete model. Simulation results are then compared to additional measurements of the harmonic drive performance.