精密齿轮传动系统精度特性的多重共轭复合模型

Taking an actual precision gear drive as the research object, each of components in the gear drive is equivalent to a combination of an internal anisotropic elastic body and rigid geometric feature surface, to explore the geometric mapping, elastic mapping and motion transformation relationships of the geometric characteristic on the components surfaces through static or dynamic connection; the geometry error of the components is effectively mapped to conjugate profile of gear or cam, and the elasticity and deformation of the components assembly is effectively mapped to the conjugate profile, the supporting elasticity and its displacement, a compound model with multiple conjugation for the accuracy and characteristics of precision gear drives is then established. Thus, the analysis and design of the accuracy and characteristics for a precision gear drive are transformed into the analysis and synthesis of the new compound mechanism with multiple elastic conjugation, whose mechaninism is composed of a pair of teeth conjugate of gears supported by two floating shafts with conjugate-cam. The kinematic analysis of the mechanism is corresponding to the kinematic analysis of the precision gear drive, and the synthesis of the compound elastic conjugate profiles are corresponding to the distribution and design of the precision gear drive. The compound model with multiple conjugation truly expresses that the integration of comprehensive geometric error and kinematic geometry with elastic deformation in the actual precision gear drive. This research project will provide a theory and method for studying the accuracy and characteristics of precision gear drives, the accuracy distribution of the components, as well as conjugate tooth profiles synthesis and design, and intension of the traditional rigid conjugate theory well be expanded.

以实际精密齿轮传动系统为研究对象，将其零件等效为内部各向异性弹性体与刚性几何特征表面的组合体，探寻零件表面几何特征通过静动联接面的几何映射、弹性映射及运动变换关系，把齿轮等零件的几何误差等效映射为凸轮及齿轮共轭轮廓，而零件组合体的弹性及其变形等效映射到共轭轮廓、支承弹性及其位移，构建实际精密齿轮传动系统精度特性的多重共轭复合模型；将一对精密齿轮传动系统精度特性的分析与设计问题转换为两组共轭凸轮悬浮轴共同支撑的齿轮齿廓共轭所形成的多重弹性共轭复合新机构的分析与综合问题，其机构的位移、运动以及力分析对应精密齿轮传动系统的精度与精度特性分析，而弹性复合共轭轮廓的综合对应于精密齿轮传动系统的精度分配与设计；该模型真实反映了精密齿轮传动系统综合几何误差、弹性变形下的运动几何学，为研究精密齿轮传动系统精度及其特性、零件精度分配、共轭齿廓形状设计等提供理论与方法，拓展传统的刚性共轭理论的内涵。

本项目以精密齿轮传动系统为对象，基于刚体运动几何学和实际零部件的弹性与误差运动，统筹考虑了齿轮传动系统的齿轮啮合精度特性与支承轴系的精度特性，创造性地将齿轮啮合的弹性共轭模型与支承轴系的弹性冗余机构模型耦合，形成了精密齿轮传动系统精度特性的多重共轭复合机构模型；同时，结合齿轮传动系统输入与输出轴系的六自由度回转误差运动性质及其不变量精度，阐明了齿轮、转轴、轴承等零部件几何误差、弹性变形以及中心距、支持轴系跨距等结构参数对精密齿轮传动系统精度的影响，首次提出了浮动支撑多重共轭复合机构的等效方法，表达了齿轮啮合高副与轴系弹性支撑回转运动副的运动变换性质和综合弹性与误差映射的本构关系，揭示了齿轮啮合高副与回转副的运动变换性质与综合弹性映射规律，形成零件几何精度特征在运动结合面的等效方法。完成了 “齿轮传动零件精度运动联接的运动变换与综合弹性映射模型”、“齿轮传动系统多重共轭复合机构研究”、“实际精密齿轮传动系统精度特性模型”以及“精密齿轮传动系统精度分析与设计”等项目研究内容，并在“精密齿轮传动系统精度特性的多重共轭复合机构模型的建模与分析方法”、“弹性多重共轭复合机构静力学与运动几何分析方法”以及“精密齿轮传动系统精度及其特性分析”等方面取得创新与突破。同时，基于上述理论和方法，以单轴、多轴的机床、机器人关节、齿轮和行星传动等为对象，提出了误差运动测量方法，并对运动精度和特性进行了评价。本项目的研究为精密齿轮传动系统精度特性分析、测试、评价以及设计等提供了理论模型与方法，也为进一步研究精密齿轮传动系统的动态精度特性提供了基础。