人形机器人的运行工况日趋复杂, 加剧了其谐波减速器的碰撞风险, 该文提出一种新型接触冲击力计算方法以表征谐波减速器的抗冲击性能。该方法基于Hertz接触理论模型, 精准计算带载荷的谐波齿轮传动的多个啮合冲击点, 确定齿侧间隙下的初始相对速度, 并结合Hunt-Crossley含阻尼系数的滞后模型, 计算出谐波传动碰撞过程中的接触力。运用瞬态动力学对理论冲击力模型进行验证。系统探讨柔轮凸圆弧半径、凸齿圆心偏移量、凸齿圆心移距量、齿根壁厚等齿廓参数对冲击力的影响机制。结果表明, 凸圆弧半径对啮合冲击力的影响最大, 齿根壁厚对啮合冲击力的影响最小。该研究成果为谐波减速器抗冲击性能提升提供理论支撑。

Objective: With the increasing complexity of operating conditions in humanoid robots, the risk of collision and impact failure in harmonic reducers has considerably increased. A critical issue arising from severe working environments is the generation of excessive impact forces inside the reducer. Such excessive forces not only accelerate gear wear and degrade transmission precision but also trigger a series of related faults, which in turn directly undermine the service life and operational reliability of the robot. Methods: To address this issue, this study proposes a novel calculation method for contact impact force to evaluate the impact resistance of harmonic gear drives. First, a common-tangent double-circular-arc flexspline tooth profile is constructed. On this basis, the circular spline tooth profile is established using the improved kinematic method. Thereafter, the initial assembled meshing model is built in accordance with the kinematic principles of the harmonic gear drive mechanism. Subsequently, based on this model, the meshing common normal line equation and backlash equation are established. All actual meshing impact points of the harmonic gear drive under load conditions are calculated, and the relative contact velocity under backlash conditions is derived. Based on the law of conservation of energy, the proposed method integrates the Hertzian contact theory with the Hunt-Crossley hysteretic damping model to establish an accurate contact-impact force prediction framework. Transient dynamic analysis is conducted to validate the proposed theoretical model. A comprehensive parametric study was subsequently conducted to quantify the effects of critical flexspline geometric parameters (convex arc radius, convex tooth center offset, convex tooth center displacement, and root wall thickness) with respect to the impact characteristics. Results: By calculating the parameters for the harmonic gear drive system, the following results are derived: (1) when the harmonic gear drive mechanism is subjected to a load torque of 92.95 Nm, with increasing contact time of the harmonic gear drive, the contact force of each tooth initially increases and then decreases, which is consistent with the meshing-in impact process between the flexspline and circular spline. (2) As the contact time increases continuously, the contact force of each tooth initially increases and then decreases. The maximum contact deformation occurs at Tooth No. 11, with a value of 2.03×10^-4 mm, which is consistent with the amped collision model proposed by Hunt and Crossley. (3) In a dynamic calculation using the theoretically constructed model, as the impact velocity increases, the meshing force of the loaded tooth profile pairs gradually increases. The error for Tooth No. 8 is 4.65%, while that for Tooth No. 11 is 11.95%. Finite element analysis verifies the accuracy of the dynamic meshing force theory and calculation method. (4) The results of the parametric study reveal that the convex arc radius exerts the most pronounced effect on the peak impact force, whereas the root wall thickness has the least influence. Conclusions: This study not only provides a reliable analytical framework for predicting the evolution of the meshing impact in harmonic drives but also offers practical design guidelines for improving the load-carrying capacity and impact resilience of the drives in humanoid robotic joints and other precision transmission systems.