基于线接触的谐波齿轮三圆弧空间齿廓设计与负载啮合性能研究

The key component of harmonic drives (HDs) - flexspline usually encounters fatigue failure and leads to fault of the whole transmission system. How to design a conjugated tooth profile which has large numbers of engaged teeth and engagement contact area based on spatial deformation of the flexspline is a key problem to increase the transmission capacity and durability. A calculation model which describes more accurate spatial deformation of the flexspline, and a conjugate equation based on exact algorithmic movement of the tooth profile are built based on a modified stretch of the neutral layer of the flexspline in this project. According to the analysis of multiple roots of the conjugate equation, the influence of the tooth profile parameters to the conjugate existent domain and the shape of conjugate tooth profile, a design method of three-circular-arc tooth profile will be proposed where continuous line contact conjugate engagement is realized in the whole engage region. A backlash calculation method between the tooth profiles is present to assess the engagement property under empty transmission loading condition. An iterative calculation method of engaged forces based on finite element contact model and the distribution of backlash between the engaged teeth is present to quantitatively evaluate the transmission capacity property. By analyzing the distributions of the engaged forces in different transmission state, an improvement of the structural parameters of flexspline to decrease the working stress under load conditions can be achieved. Based on the simulation verification of the design method and the theoretical model, physical prototypings of HD will be constructed to verify the engagement property experimentally. The research will provide theoretical support for design method and quantitative assessment of engagement property of high transmission capability and long life HD system, and has wide application prospects in robot, aeronautics and astronautics, instrument and meter area.

柔轮作为谐波齿轮的关键构件，易发生疲劳破坏而引起传动系统失效。如何基于柔轮空间变形特征设计共轭齿廓以增加啮合齿对数和接触面是提高谐波齿轮承载能力及耐用性的关键问题。本项目通过修正柔轮中性层几何学伸长变形，建立更准确表征柔轮空间变形的计算模型，及轮齿运动精确算法的共轭方程；根据共轭方程多解特征分析、齿廓参数对共轭区间大小及共轭齿廓形状影响研究，提出整个啮合区间上线接触连续共轭啮合的三圆弧空间齿廓设计方法；建立齿廓侧隙计算方法以评价空载啮合特性；为定量评价其负载啮合特性，提出基于有限元接触模型和齿间侧隙分布的啮合力迭代计算方法；通过齿间啮合力分布分析，改进设计以减小负载工况下的柔轮应力。在对理论模型及其设计方法进行仿真验证的基础上，试制实物样机进行啮合性能实验验证。项目研究为长寿命、高承载能力的谐波齿轮设计及工作性能评价提供理论依据。项目成果在机器人、航空航天和仪器仪表等领域具有广阔应用前景

谐波齿轮传动中的柔轮易发生疲劳破坏引起传动系统失效，本项目以增加啮合齿对数和齿面接触面面积以提高谐波齿轮承载能力及耐用性为研究目标。为更准确表征柔轮在波发生器作用下的变形，提出基于几何学条件和大变形接触条件的中面曲线表达方法，建立波发生器作用下柔轮中性层伸长模型，实现大包角条件下更准确的轮齿定位。在此基础上建立基于精确算法的轮齿啮合运动的共轭方程；依据共轭齿廓存在条件构造三圆弧齿廓以改进原始齿廓的啮合特性，揭示三圆弧柔轮齿廓参数及空间变形特征参数对共轭齿廓存在性和可用性的影响规律。以主截面上包络存在区间最大为准则，考虑干涉和侧隙合理分布，基于柔轮齿圈的锥度变形特征，提出在整个啮合区间上连续线接触共轭啮合的三圆弧空间齿廓设计方法；相比于双圆弧齿廓，三圆弧齿廓具有更宽的包络存在区间和更均匀的侧隙分布，能有效增加啮合齿数和啮合接触面。建立三圆弧齿廓谐波齿轮侧隙的计算方法以评价空载啮合特性；为定量评价负载啮合特性，提出基于有限元接触模型的啮合刚度算法及啮合力迭代计算方法；对揭示谐波齿轮的整机扭转刚度特性、齿体的负载强度、负载齿廓设计和结构设计奠定理论基础。建立基于理论公式和有限元变形的谐波齿轮装配模型，仿真空载和负载啮合状态。在对理论模型及其设计方法进行仿真验证的基础上试制实物样机，对传动误差、回程误差、扭转刚度、传动效率和过载跑合的精度下降量等指标进行实验测试。仿真分析和实验测试发现：本项目的物理样机在扭转刚度和承载能力上好于日本产品，表明本项目设计的三圆弧齿廓通过增大啮合区间增加了啮合齿数，实现了提高谐波齿轮传动的承载能力和耐用性的预期目标。部分样机的测试传动精度已接近日本产品，表明多齿啮合的齿廓设计能有效冲抵齿面加工误差。尽管目前同批次样机测试数据的一致性不够稳定，可能与加工精度和测试精度有关，许多设计和工艺细节还有待研究。项目成果在机器人、仪器仪表等领域具有广阔应用前景。