Prediction and Control of Harmonic Gear Backlash Considering Multi-Source Error Sensitivity and Force-Thermal Effect

As a core transmission component in precision robotics, the harmonic drive relies on backlash as a pivotal indicator determining system accuracy and technical performance. However, the inherent flexibility of the flexspline renders backlash highly sensitive to manufacturing tolerances and force-thermal loads, making the ideal backlash state difficult to sustain under actual operating conditions. Consequently, this study proposes a comprehensive backlash analysis model aimed at quantifying the sensitivity of backlash to multi-source errors under complex conditions. First, a virtual assembly model based on the Monte Carlo method is established to perform sensitivity analysis on geometric tolerances, identifying the fit clearance between the flexible bearing, the flexspline, and the wave generator as the dominant error source. Furthermore, a force-thermal coupled model is constructed to evaluate the combined effects of torsional stiffness—accounting for the flexspline warping effect—and thermal deformation on backlash. Finally, fit parameters are optimized using a Genetic Algorithm (GA). The results demonstrate that the optimized design reduces the backlash under rated torque to 8.04 μm, decreases backlash fluctuation by 73.1%, and successfully controls static backlash to within 30″. This study provides quantitative guidance for tolerance allocation and offers a robust design strategy for manufacturing high-precision harmonic gears, aiming to minimize backlash variability under complex operating conditions.