弹性冗余空间机构性能与机器精度模型研究

A spatial mechanism, with elastic constraints and redundant degree of freedom, is firstly presented to set up a mathematical model of machine accuracy in the project. In traditional way, a mechanism consists of links and kinematic pairs, which are rigid bodies and ideal geometric surfaces respectively without any error. However, a practical machine consists of elastic machine-parts with irregular surfaces, so a practical mechanism does. It means that an error is produced by the elastic links,or non-ideal kinematic pairs. An elastic link, a machine part, is taken as a combined body of a rigid surface with the special geometric characteristic and an inner elastic body. The elastic kinematic geometry is set up to study the deformation of the surface of an elastic machine-part with different load cases. Based on it, an elastic mapping function is established from one surface to another, in which it includes static joints, deals with connection version, structure parameters and load cases. On the other hand, a non-ideal kinematic pair, or a practical kinematic pair is comprised of several kinematical joints, is designed as a sub-spatial kinematic chain with cam-springs, which contains few cams with a special geometrical surface and several springs with elastic over constraints. The springs with redundant degree of freedom are corresponding to elastic contacts between two surfaces of a kinematic joint, while the profile of a cam denotes the geometrical combination of two surfaces of a kinematic joint. Thus, a sub-spatial kinematic chain with cam-springs can transfer and convert the geometrical accuracy and kinematic characteristics from one elastic machine-part to another. Its performance depends on the types, structure, and combination of kinematical joints for a kinematical pair. Therefore, a novel spatial mechanism with elasticity-redundance readily appears, which are comprized of combined bodies with rigid surface and elastic inner, elastic mapping functions and sub-spatial kinematic chain with cam-springs. It is essential to build up the relationship among the geometry, physics, structure, assembly, kinematics and load of a machine as well as its parts. In the meanwhile, the approach of construction, kinematic and static analysis for a spatial mechanism with elasticity-redundance has to be deeply studied since it is a new spatial mechanism in the literal. As a result, a mathematical model of precision for a practical machine can be represented by the new spatial mechanism. Therefore, resolution of kinematics and statics of a spatial mechanism with elasticity-redundance has an obviously geometrical and physical meaning corresponding to geometrical accuracy, kinematic precision and static stiffness of a machine. Finally, a three-axis precision machine tool is taken as an example to conduct numerical calculating and experimental test.

以实际机器零件为对象，把零件转化为内部各向异性弹性体与表面几何特征刚性体的组合体, 讨论零件几何表面在工况载荷下的弹性运动几何学，阐述零件精度特征弹性映射与零件几何结构、材料物理性能与工况载荷等因素的关系；揭示静联接面的零件精度弹性映射函数效应，并探讨静联接方式、结构参数、工况载荷与弹性映射函数的内在联系；总结运动副的实际结构类型与组合特征，研究其弹性约束与弹性冗余自由度、几何精度与运动特征的传递及合成规律等，建立实际运动副的空间运动子链的结构构型方法；由弹性刚性组合体零件、弹性映射函数、空间运动子链等组合而成弹性冗余空间机构，构建机器整机与零件的几何、物理、结构、装配、运动、载荷之间的耦合关系，深入研究弹性冗余空间机构的组成原理、运动学与静力学及其求解方法，结合多轴精密机床整机样机与零件的数值计算与试验测试分析，形成机器整机精度及其特性的弹性冗余空间机构建模与分析方法。

本项目以机构运动几何学方法研究精密机床工业机器人/等高端装备及其精密主轴、轴承、导轨等关键功能部件的精度特性分析、设计、测量与评价，创造性建立了运动副/运动链精度特性的弹性冗余空间机构模型，首次获得运动副离散误差运动的不变量及其性质，建立了机器精度及其特性的弹性冗余空间机构分析方法。以运动几何学理论研究了运动副及其组成部件（轴承、导轨等零件）表面几何形状及误差分布对误差运动规律的影响，引入典型固定联接结构的装配工艺参数，建立过盈联接、螺栓联接等固定联接结构的精度传递与映射模型，实现机器零件及静联接组件精度特性分析与等效。将运动几何学局部性质发展到整体性质，研究了回转运动与平移运动的点、线运动轨迹整体几何性质与充要条件，讨论回转/移动离散误差运动的不变量，建立了回转副/移动副精度特性分析及评价的不变量方法。以此为基础，研究了真实回转副/移动副的结构、尺度、约束形式、零件几何误差、刚度以及载荷等因素对运动副精度及其特性的影响规律，构建了回转副/移动副精度特性的弹性冗余空间机构模型，揭示了机器精度特性与几何、物理因素之间的本构关系，讨论了机构几何参数、物性参数与各运动副精度特性影响因素之间的对应关系与等效计算方法，以机构运动学与准静力学方法进行真实运动副的精度特性分析与设计。同时，基于上述理论和方法，以三轴/五轴机床及机器人等为对象，研究了整机/运动副误差运动的不变量性质，提出了单/多轴误差运动的不变量精度新概念与不变量测量方法，减少或消除了被测零件几何形状、测量位置及测量仪器安装方式对运动精度评价结果的影响。因此，本项目将刚体运动几何学发展到离散运动几何学，创立了机器/运动链/运动副精度特性的弹性冗余空间机构分析方法，为机器精度及其特性的分析、设计、测量与评价等提供了理论基础，不仅丰富和发展了机构学理论和方法，也为开辟了新的应用领域提供依据。