机构运动精度的弹性冗余约束模型与试验反演研究

A novel elastic redundant constraint dynamic model is firstly proposed in the project for analyzing, testing and designing kinematic accuracy of mechanisms. . Firstly, the constraint structure of actual kinematic pair is equivalent to be as an elastic contact state among multiple geometric surfaces with rolling/sliding, frictions and geometrical errors. Nonlinear dynamic differential equations with elastic error constraint are established, and the functions are studied for revealing relationships among the coefficient of differential equations and the structure of components, geometric errors, assembly parameters and operating conditions. . Then, properties of nonlinear differential equations with elastic error constraints are analyzed and their numerical solutions are discussed. Based on kinematic parameters measured, an inverse method is presented to identify the equivalent parameters of the dynamic model. The actual kinematic parameters of an actual kinematic pairs are studied. . At last, an equivalent testing mechanism is proposed to describe the kinematic parameters of the moving objection measured. The kinematic geometry properties of equivalent testing mechanism are discussed. The theoretical value and actual value of the moving objection measured are mapped into the positive solution and inverse solution of the equivalent testing mechanism. The kinematic parameters (displacement, velocity, acceleration) are described in kinematic invariants and the kinematic accuracy is evaluated by invariants errors, which provide a new method to design the new instruments for testing the kinematic accuracy of typical actual kinematic pairs and mechanisms. . Based on the above proposals, the analysis and improvement of kinematic accuracy of both CNC machine tools and high-speed precision press machines will be achieved; the internal relation between the static accuracy and kinematic accuracy of the mechanism will be revealed. All of these works in the project will develop the theory of machine and mechanisms, which provide a theoretical basis for testing, analyzing and designing kinematic accuracy of the machine and mechanisms.

首次提出机构运动精度的等效弹性冗余约束动力学模型，将实际运动副约束结构抽象为多对几何误差曲面间具有滚滑摩擦状态的弹性接触，建立系统的非线性动力学微分方程组，探讨微分方程组系数和零件结构、几何误差、装配参数、运行工况之间的映射关系。研究弹性误差约束非线性微分方程组的性质与数值解法，探索基于运动参数测试数据的反演解法，揭示实际运动副的约束特性与被约束构件的真实运动规律。提出将机构运动参数测试系统演化为等效测试机构，研究其运动几何学性质，将被测运动参数的理论值和实际值转化为等效测试机构的正解和反解，探讨被测构件的运动参数（位移、速度、加速度）不变量表述与运动精度评价方法，探索典型运动单元、运动副和机构的运动精度检测新技术、新方法与新仪器。据此，分析和改进高档数控机床与精密压力机运动精度，揭示机构运动精度与机构静态精度的内在联系，丰富和发展机构学理论，为机构运动精度分析与设计提供理论依据。

本项目以机构运动几何学方法研究真实机构及其运动副（如机床、主轴、导轨）的弹性误差运动特性，提出了误差运动不变量精度的评测方法。建立了真实运动副精度及其特性的弹性冗余约束模型，分析了结构参数、制造误差及装配工艺参数对移动副不变量精度及其特性的影响规律；构建了移动副装配工艺参数优化模型，利用预装配测量数据反演真实运动副参数与制造误差，针对不同装配工艺方案和装配工艺参数进行优化求解，从而指导移动副装配工艺获得预期的装配精度，为移动副（导轨、滑块、工作台等）装配工艺参数设计提供了理论基础与检测评价方法。提出了机床运动副精度测量的运动几何学原理——运动测量三要素和闭环矢量方程，分析了机床运动副装配精度的常规测量方法，从理论上阐述完备性测量的条件，常规测量多为非完备性简化测量，往往存在原理性误差。提出了两轴联动机床运动精度球杆仪测量的运动几何学原理——将被测机床运动链与球杆仪抽象为两自由度刚柔复合空间PPSPS五杆机构模型，把机构运动精度测量、评价和误差辨识转化为空间PPSPS五杆机构的运动学正解和反解问题，利用球杆仪测量机床精度的实际数据，反演机构结构参数与运动副误差；当机床为理想运动时，机构模型输出运动数据为理想值，否则，机构模型输出机床误差运动函数值，从而为机床运动精度测量获得理想基准值。.本项目丰富机构运动几何学研究内容，发展了机构学研究方法，拓展了机构学理论与方法的应用领域。