[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.
Key words
harmonic gear drive /
improved kinematic method /
tooth engagement impact /
tooth flank backlash /
transient dynamics
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