Harmonic drive

Abstract: Harmonic drives can exhibit very nonlinear dynamic behavior. In order to capture this behavior, not only must dynamic models include accurate representations of transmission friction, compliance, and kinematic error, but also important features of harmonic-drive gear-tooth geometry and interaction must be understood. In this investigation, experimental observations were used to guide the development of a model to describe harmonic-drive operation. Unlike less detailed representations, this model was able to replicate many of the features observed in actual harmonic-drive dynamic response. Unfortunately, since model parameters can only be derived from careful analysis of experimental dynamic response, it seems unlikely that any comparably sufficient representation can be constructed with parameter values obtained from catalogs or simple experimental observations.

Abstract: Harmonic drive gears are widely used in space applications, robotics, and precision positioning systems because of their attractive attributes including near-zero backlash, high speed reduction ratio, compact size, and small weight. On the other hand, they possess an inherent periodic positioning error known as kinematic error responsible for transmission performance degradation. No definite understanding of the mechanism of kinematic error as well as its characterization is available in the literature. In this paper, we report analytical and experimental results on kinematic error using a dedicated research Harmonic Drive Test Apparatus. We first show that the error referred to in the literature as kinematic error actually consists of a basic component, representing ‘‘pure’’ kinematic error, colored with a second component resulting from inherent torsional flexibility in the harmonic drive gear. The latter component explains the source of variability in published kinematic error profiles. The decomposition of the kinematic error into a basic component and a flexibility related component is demonstrated experimentally as well as analytically by matching a mathematical model to experimental data. We also characterize the dependence of the kinematic error on inertial load, gear assembly, and rotational speed. The results of this paper offer a new perspective in the understanding of the mechanism of kinematic error and will be valuable in the mechanical design of harmonic drive gears as well as in the dynamic modeling and precision control of harmonic drive systems. @DOI: 10.1115/1.1334379#

Abstract: In my research, I have performed an extensive experimental investigation of harmonic-drive properties such as stiffness, friction, and kinematic error. From my experimental results, I have found that these properties can be sharply non-linear and highly dependent on operating conditions. Due to the complex interaction of these poorly behaved transmission properties, dynamic response measurements showed surprisingly agitated behavior, especially around system resonance. Theoretical models developed to mimic the observed response illustrated that non-linear frictional effects cannot be ignored in any accurate harmonic-drive representation. Additionally, if behavior around system resonance must be replicated, kinematic error and transmission compliance as well as frictional dissipation from gear-tooth rubbing must all be incorporated into the model.

Abstract: The unique performance features of harmonic drives, such as high gear ratios and high torque capacities in a compact geometry, justify their widespreaa industrial application. However, harmonic drive can exhibit surprisingly more complex dynamic behavior than conventional gear transmission. In this paper a systematic way to capture and rationalize the dynamic behavior of the harmonic drive systems is developed. Simple and accurate models for compliance, hysteresis, and friction are proposed, and the model parameters are estimated using least-squares approximation for linear and nonlinear regression models. A statistical measure of variation is defined, by which the reliability of the estimated parameter for different operating condition, as well as the accuracy and integrity of the proposed model is quantified. By these means, it is shown that a linear stiffness model best captures the behavior of the system when combined with a good model for hysteresis. Moreover, the frictional losses of harmonic drive are modeled at both low and high velocities, The model performance is assessed by comparing simulations with the experimental results on two different harmonic drives. Finally, the significance of individual components of the nonlinear model is assessed by a parameter sensitivity study using simulations.