工件定位的几何定理及定位误差的程式化计算方法

The normal line at the contact point of workpiece and fixture is named locating normal, Depending on the number and their geometric relationships of the normals, geometrical theorems judging workpiece locating state can be summarized. The theorems make judgment method of workpiece locating state more rigorous, intuitive and perfects locating theory of the workpiece..Taking theoretical benchmark as breakthrough and the specific and accurate definition of locating error as the starting point, a set of stylized calculation method of locating error can be established. Based on the "benchmark is independent of dimension " and "extreme ideology", the determination method of theoretical benchmark of workpiece in various locating states can be summarized. The locating error is due to the geometric error between the process benchmark and the theoretical benchmark. So the locating error can be characterized as geometric error between the specific point, line and surface,which unify and simplify calculation method of locating error. This method is suitable for computer-aided analysis and calculation of locating error..The geometric relationship between all process benchmarks and theoretical benchmarks can be described by using benchmark relationship graph. The locating error of all geometric quantities including allowances can be got from locating error calculation model. Considering each geometric quantity and allowence precision which satisfy the process requirements, A new method for optimizing workpiece locating scheme can be established..By studying the influence rule of blank geometry benchmark to loacting error, the new method of blank geometry benchmark design can be established from the perspective of reducing the locating error.

将工件与夹具接触点处的法线命名为定位法线，根据定位法线的数量及其几何关系归纳出判断工件定位状态的几何定理，使工件定位状态的判断方法更加严谨、直观，完善工件的定位理论。.以理论基准为突破口，定位误差具体准确的定义为切入点，建立一套定位误差的程式化计算方法：基于“基准与定位要素尺寸无关”与“极限思想”概括出工件在各种定位状态下理论基准的确定方法；将定位误差归结为工序基准与理论基准之间的几何误差，并由此将定位误差明确为具体的点、直线、平面之间的几何误差，统一并简化各类定位误差的计算方法，适合计算机辅助定位误差的分析与计算。.用基准关联图描述全部工序基准与理论基准之间的几何关系，获得包括加工余量在内的全部几何量的定位误差计算模型，综合考虑工序要求的各几何量精度，建立一种优化工件定位方案的新方法。.研究毛坯几何基准对定位误差的影响规律，从减小定位误差的角度建立毛坯几何基准设计的新方法。

基于两刚体在其接触点处的公法线方向无相对运动这一事实，建立了一组判断 “刚体自由度数量及其性质”与“法线数量及其几何关系”之间关联的几何定理。将工件在夹具中的定位简化成点约束，用几何定理能准确判断工件在夹具中的自由度及其性质，使工件定位理论更加完善，自由度计算方法简单且无局限，能有效化解工件的复杂、疑难定位问题，也便于工件定位方案的优化。.将机构中各个构件之间的约束简化成点约束，根据约束点在其法线方向相对于机架是否运动，将法线分为动法线与静法线；建立了“机构中虚约束数量”与“法线性质、数量及其几何关系”之间关系的几何定理，给出机构中虚约束总数量的计算方法，通过建立机构中全部构件约束总数量与自由度总数量的平衡方程，得到具有普适性的机构自由度通用计算公式，为空间复杂并联机构、多环耦合机构自由度计算提供一种简单有效的计算方法。.针对目前定位误差的定义繁多、不具体、不严谨等问题，提出理论基准概念，根据定位误差的本质特征，将定位误差定义为“工序基准与理论基准在工序几何量方向上的误差”，由此可简化、规范、统一定位误差的计算方法，适合计算机辅助定位误差计算；基于定位误差新定义，对毛坯尺寸基准进行了研究，指出毛坯尺寸基准选择应考虑其机械加工工艺，否则将导致粗加工余量误差增大、加工面与非加工面之间误差过大等问题，由此提出了毛坯尺寸基准设计原则，这对提高零件加工精度、降低材料消耗有积极作用。. 本项目的研究，发表SCI论文5篇、机械工程学报中文版发表论文4篇、授权发明专利1项、公示发明专利4项。