Rotary vector reducer (RV reducer) serves as a crucial drive train component in industrial robots, and its time varying torsional stiffness significantly impacts the dynamic characteristics, vibration and transmission accuracy. Existing methods for calculating the torsional stiffness suffer from two limitations: (1) considering only the time varying meshing stiffness of the gear pair or the time varying radial stiffness of the bearings as a single factor, and (2) the calculated results according to the traditional initial meshing clearance formula of the cycloid pin gear do not align with the definition of tooth side clearance. To comprehensively and accurately analyze the time varying torsional stiffness, this study proposes a method for the reducer, taking into full consideration the time varying characteristics of gear meshing stiffness and radial stiffness of bearings. To analyze the time varying meshing stiffness of the cycloid pin gear pair, a novel initial meshing clearance formula is derived. Firstly, a new calculation model was constructed to accurately obtain the initial meshing clearance of cycloid pin gear single tooth pair in the low-speed stage. The time varying meshing stiffness of the cycloid pin gear was calculated by determining the number of teeth engaging in meshing simultaneously. Secondly, the time varying meshing stiffness of the involute modified gear in the high-speed stage was simulated employing the weber energy method. Then, time varying radial stiffness of the crankshaft, arm bearings, and supporting bearings was analyzed utilizing finite element method. Finally, by equivalating the time varying meshing stiffness of the two-stage gear mechanism and the time varying radial stiffness of bearings to the output end, the time varying torsional stiffness of the reducer was calculated. The experimental results of the torsional stiffness have only a 3.81% difference compared to the simulated value, which validates the accuracy of this method.

中文翻译：

---

RV减速器时变扭转刚度分析


旋转矢量减速器（RV reducer）是工业机器人中至关重要的传动系统部件，其时变扭转刚度对动态特性、振动和传动精度有重大影响。现有的扭转刚度计算方法存在两个局限性：（1）仅将齿轮副的时变啮合刚度或轴承的时变径向刚度视为单个因素，以及（2）根据摆线针轮的传统初始啮合间隙公式计算的结果与齿侧间隙的定义不一致。为了全面、准确地分析时变扭转刚度，本文提出了一种充分考虑轴承齿轮啮合刚度和径向刚度的时变特性的减速机方法。为了分析摆线针轮副的时变啮合刚度，推导了一种新的初始啮合间隙公式。首先，构建新的计算模型，准确获取摆线针轮单齿副在低速阶段的初始啮合间隙;通过确定同时啮合的齿数来计算摆线针轮的时变啮合刚度。其次，采用 Weber 能量法模拟了渐开线改进齿轮在高速阶段的时变啮合刚度;然后，利用有限元方法分析了曲轴、臂轴承和支撑轴承的时变径向刚度。 最后，将两级齿轮机构的时变啮合刚度与轴承的时变径向刚度对输出端进行等效，计算出减速器的时变扭转刚度。扭转刚度的实验结果与模拟值相比仅相差 3.81%，验证了该方法的准确性。