面向载荷分布优化及啮入冲击抑制的RV减速器摆线齿拓扑修形研究

Cycloid-pin gear transmission mechanism is the key component of RV reducer. Uneven load distribution and meshing-in impact caused by poor tooth modification of cycloidal gear lead to a series of problems to RV reducer, such as abrupt change of transmission error, decline of accuracy preservation and so on. Firstly, the project intends to establish a comprehensive deformation and torsional stiffness model of cycloid-pin tooth pair. The mathematical representation of load distribution state of meshing gears is studied to explore the influence of spatial meshing clearance on load distribution and transmission performance. A quasi-statics model of corner meshing-in impact of cycloid-pin gear transmission under multi-teeth meshing is established. The fluctuation of transmission error and impact load is obtained by using perturbation method. Then an evaluation model of meshing-in impact characteristics is established. Combined with the mathematical representation of load distribution, the optimal design criterion of modified tooth surface of cycloidal gear is obtained. By introducing the topology theory, the parametric formula of the surface coordinate curve related with spatial meshing clearance is constructed. By taking the performance index of RV reducer as a constraint, a discretization method based on curvature is proposed to optimize the surface coordinate curve, then the optimized tooth surface of cycloidal gear is determined. A transmission performance test rig of RV reducer is built to verify the theoretical results of load distribution and meshing-in impact characteristics. Finally, the topological modification theory of cycloid gear is developed. The research results will provide theoretical and technical support for improving the product quality of RV reducer.

摆线针齿传动机构是RV减速器的关键部件，摆线齿修形不良将引起载荷分布不均及啮入冲击加剧，进而导致RV减速器传动误差突变、精度保持性下降等问题。本项目拟建立摆线针齿啮合副的综合变形及扭转刚度模型，研究齿轮载荷分布状态的数学表征方法，揭示空间啮合侧隙对载荷分布规律及传动性能的影响机制。建立多齿啮合下摆线针齿传动的线外啮入冲击准静力学模型，采用摄动法求解传动误差波动量及啮入冲击载荷，从而构建啮入冲击特性评估模型，结合载荷分布状态数学表征，建立摆线齿的修形优化设计准则。引入拓扑理论，以空间啮合侧隙为参量,构建修形齿面的坐标曲线参数式。提出曲率离散点分布设计方法，以RV减速器性能指标为约束，优化设计修形齿面的坐标曲线，从而确定摆线齿修形模型。搭建RV减速器传动性能实验台，对载荷分布状态及啮入冲击性能进行实验验证，最终形成摆线齿拓扑修形理论。研究成果将为本质上提高RV减速器产品质量提供理论和技术支撑。

摆线针齿行星传动机构是RV减速器实现运动功能的核心部件，摆线轮齿廓曲线与机构参数的设计直接决定了RV减速机的整机性能，设计不当将引起承载能力不足及啮合冲击加剧，进而导致RV减速机传动误差突变、精度寿命下降等问题。本项目建立了多齿啮合载荷分布、最大接触应力和扭转刚度模型，提出了摆线针齿传动机构载荷分布状态表征模型，揭示了摆线轮齿廓修形参数与机构设计参数对载荷分布状态的影响机制。通过计算啮合齿轮的理论啮入点与实际啮入点，阐明了摆线针齿传动机构的啮入冲击产生机理。运用H-C接触碰撞模型，并结合迟滞阻尼系数，提出了摆线针齿传动机构的啮入冲击力模型，系统研究了摆线轮齿廓修形参数与机构设计参数对多齿啮合冲击力的影响规律。在此基础上，建立啮入冲击指数模型，以评价多齿啮合冲击特性，并通过曲面拟合方法，获得修形量与冲击指数的映射关系。然后，以承载能力最优和啮入冲击最小为优化目标，运用遗传算法优化了摆线轮齿廓与机构设计参数，最终形成了摆线轮齿廓修形理论和机构优化设计方法。最后，通过有限元仿真分析与对比实验，验证了摆线轮齿廓修形理论的正确性。研究成果为本质上提高RV减速机传动性能和精度寿命提供了理论与技术支撑。