面向谐波传动薄壁柔轮轴向偏载改善的新齿形设计方法研究

Harmonic Drive is the core component of an industrial robot to realize the movement function. The axial partial load of flexspline resulted by large deformation of thin wall and synthetical error leads to a series of problems, such as deterioration of the transmission quality, retention of precision and the decline of fatigue life. Firstly, this project will make basic assumptions and analysis based on the principle of harmonic drive. The cause of axial partial load of flexspline in the process of harmonic transmission will be identified. The mathematical representation of periodic spatial elastic deformation of flexspline under action of wave generator and load will be researched. Then the influence of deformation of flexspline and synthetical error on the axial partial load will be explored. Secondly, the coordinate transformation relation of harmonic drive under axial partial load will be established. Based on improved deformation function of double arc tooth profile and instantaneous center line, Scientific problems such as the mathematical representation of double arc envelopes and mapping relation of tooth surface interference under axial partial load will be solved. Thirdly, the distribution function of backlash of different section and tooth profile coincidence model will be established. A optimization design method for improving tooth surface load distribution by deviation correction method will be formed. Numerical simulation and experimental analysis are used to verify the effect of axial partial load. Finally, On the basis of the concept of axial partial load index proposed, the engagement state parameters of conjugate teeth will be introduced, and a evaluation method of homogenization of tooth surface load of flexspline will be formed. The research results will provide theoretical basis and technical support for solving the problem of comprehensive performance deterioration of Harmonic Drive caused by axial partial load of flexspline.

谐波减速器是工业机器人实现运动功能的核心部件，其薄壁大变形及综合误差引起的柔轮轴向偏载现象严重，导致了传动质量恶化、精度保持性及疲劳寿命下降等一系列问题。项目拟基于谐波传动原理进行基本假设与分析，明晰谐波传动过程柔轮轴向偏载成因，研究波发生器和负载作用下柔轮周期性空间弹性变形的数学表征方法，探索柔轮变形及综合误差对轴向偏载的影响规律；建立轴向偏载作用下谐波传动运动标架，基于改进的双圆弧齿廓和瞬心线变形函数，解决偏载条件下双圆弧包络齿廓数学表征方法及齿面干涉量映射关系的科学问题；建立啮合过程各截面侧隙分布函数和齿廓重合度模型，形成一种以偏差修正法改善齿面负载分布的优化设计方法，结合数值模拟与实验分析对轴向载荷均化效果进行验证，在提出的偏载指数概念基础上引入共轭齿对啮合状态参量形成柔轮齿面负载均化评估方法。研究成果将为解决柔轮轴向偏载引起的谐波减速器整机综合性能恶化问题提供理论基础与技术支持。

谐波减速器作为先进制造技术的基础装备，其制造和发展水平反映了我国制造能力、国民经济水平和综合国力，也是衡量国家工业发展水平的重要标志。谐波减速器柔轮轴向偏载现象导致了传动质量恶化、精度保持性及疲劳寿命下降等一系列问题。本项目基于谐波传动原理进行基本假设与分析，引入柔轮轴向变形参量，明晰了谐波传动过程柔轮轴向偏载成因，研究了波发生器和负载作用下柔轮周期性空间弹性变形的数学表征方法，探索了柔轮变形及综合误差对轴向偏载的影响规律，对不同工况下的柔轮弹性变形函数进行求解，并进行实验验证；建立了轴向偏载作用下谐波传动运动标架，基于改进的双圆弧齿廓和瞬心线变形函数，建立柔性化处理后的刚-柔轮碰撞接触模型，研究偏载条件下柔轮瞬心线随输出负载的变化规律，形成负载量、偏载量与齿面干涉量的映射关系，解决了偏载条件下双圆弧包络齿廓数学表征方法及齿面干涉量映射关系的科学问题；以刚-柔轮啮合对齿廓啮合全过程为研究对象，通过侧隙分布函数和重合度数学模型表征齿面啮合载荷的分布状况，得到实际啮合位置的齿面线位移和角位移偏差，形成了以偏差修正法进行齿廓修形的设计方法，结合数值模拟与实验分析对轴向载荷均化效果进行了验证，在提出的偏载指数概念基础上引入共轭齿对啮合状态参量，结合侧隙和重合度模型建立了负载均化设计的评价体系。研究成果为解决柔轮轴向偏载引起的谐波减速器整机综合性能恶化问题提供了理论基础与技术支持。本项目按照计划书完成了相关研究内容，达到了既定研究目标。应用本研究提出的啮合过程设计方法和模型，为企业相关产品齿形设计、产品加工和性能验证等方面提供了技术支持，解决了柔轮轴向偏载引起的谐波减速器整机综合性能恶化等问题。在该项目及北京市科技计划项目等课题支撑下，突破了谐波减速器设计、制造和检测整套关键技术，实现了重大成果转化。