少齿差锥齿轮章动减速器多源误差扰动机制与精度退化机理研究

As a key component in high-grade mechanical devices, the transmission precision of gear units significantly affects the overall service performances. A meshing model of bevel gears including coupled random directional errors is developed and emerged into an analytical nonlinear dynamic model of the transmission system that considers internal and external excitations. By solving the motion equations, the dynamic behaviors of the nutation drive containing multi-source errors are revealed with which an indexing framework is constructed to precisely evaluate the drive’s transmission precision. On this basis, the probability distribution of various errors is simulated through statistical analysis to derive the quantative mapping between the multi-source errors and the precision indices. According to this mapping, the tolerances and modifications of key components can be determined in an economical way. Finally, a dynamic wear model of bevel gears with small tooth number difference is developed by considering the effects of micro-geometries as well as lubrication conditions. With this model, the surface wear of bevel gears subjecting to non-stationary payload can be predicted and its influence on the nutation drive’s transmission precision is analyzed. After revealing the relationships among non-stationary load, surface wear and transmission precision, the precision degradation of a nutation drive at given payload can be predicted precisely; and vice versa, the matched payload can be decided according to the expected precision lifespan.

精密齿轮传动作为高端机械装备的核心部件，其传动精度直接影响整机性能。本项目聚焦国产精密传动精度保持性差的问题，开展少齿差锥齿轮章动减速器传动精度表征方法、误差扰动机制与精度退化机理研究，希冀建立该类传动的精度设计方法并助推其工业应用。首先将计入矢量性、随机性与耦合性误差的锥齿轮啮合模型融入考虑内、外激励的传动系统非线性动力学模型，借助完备的动力学分析揭示多源误差作用下系统的动特性，以构建准确表征传动精度的指标体系。然后运用统计学方法模拟各误差的概率分布，从数学层面揭示多源误差与精度指标间的映射关系，并据此制定经济的零件公差与修形策略。最后通过建立计入齿面形貌、润滑状态的少齿差锥齿轮动态磨损模型，预估变载荷工况下章动传动的齿轮磨损进程并分析磨损量对传动精度的影响。在明晰载荷—磨损—精度三者间传递特性的基础上，准确预估既定载荷下章动减速器的精度退化历程及根据精度寿命反向寻求合理的减磨延寿方案。

精密齿轮传动部件是制约我国制造业质量提升和装备创新发展的痛点。突破精密齿轮传动部件的技术瓶颈，研发具有自主知识产权的高性能、精密、长寿命传动产品迫在眉睫。本项目以自主研发的双圆弧锥齿轮章动减速器为研究对象，开展了章动传动系统的多源误差扰动机制和传动精度退化机理研究。首先，溯源出影响双圆弧锥齿轮章动传动精度的六类误差源，即齿面设计几何误差、轮齿弹性变形误差、轮齿制造误差、齿轮副装配误差、系统振动误差和齿面磨损误差。其次，设计了具有高承载能力和高重合度的双圆弧锥齿轮副，并探明了齿面设计几何误差和轮齿弹性变形误差对双圆弧锥齿轮章动运动副传动精度的影响规律。在此基础上，建立了以齿面接触分析为基础的双圆弧锥齿轮副传动误差模型，分析了典型制造/装配误差对系统传动精度的耦合扰动规律，形成了基于传动精度可靠性的关键零部件公差设计方法。再次，提出了计及时变啮合刚度、时变传动误差、啮合阻尼和齿侧间隙的章动传动非线性动力学模型，并基于所建模型开展了系统动力学特性分析，揭示了误差随机性与系统振动对动态传动精度的耦合扰动规律。然后，提出了基于改进Archard磨损模型的双圆弧锥齿轮副的准静态齿面磨损计算模型，揭示了循环次数、负载和系统误差对齿面磨损深度的影响规律，探明了双圆弧锥齿轮副的齿面磨损进程，并确定了合理的齿面磨损迭代计算阈值。最后，研制了两款锥齿轮章动减速器样机，搭建了精密减速器综合性能测试台架并开展了相关性能测试。通过上述工作，项目组探明了少齿差锥齿轮章动减速器的误差扰动机制与精度退化机理，构建了该型传动装置的精度设计方法，掌握了构型创新、结构设计、受力分析、精度综合和性能测试等关键技术。本项目的研究方法及相关成果对其他类型精密齿轮传动装置的精度实现同样具有理论指导意义。