基于关键装配特性的离散化夹具概念设计算法研究

From the viewpoint of both automated design and engineering application, the mapping relationship from key workpiece assembly characteristics to fixture configuration scheme is deep investigated by converting equivalently workpiece fixturing into workpiece-fixture system assembling. First of all, through constructing the quantitative description of the determination index as well as the hierarchical structure model of locating reference selection, the analytic hierarchy process method of selecting the locating reference is discussed. Secondly, according to the relationship between the the workpiece practical constraints, which are supplied by the locating point scheme, and the workpiece machining requirments, the inherent law between the workpiece motion status and the locating determination is investigated to establish the motion constraint algorithm for arranging the locating points on the selected locating references. Thirdly, the rubber band principle is studied to equivalently turn the arbitrary contact between workpiece and fixture elements into the point contact. By analyzing either the fixturing stability or the workpiece deformation at all mesh notes of clamping surface and at every variation of clamping force magnitude with the given step length, the iterative planning method is explored to determine the placement of clamping force. The reverse increment degression method can further be established to find the critical magnitude of clamping force. Finally, the decomposition of a clamping sequence into the hostorical application steps of clamping forces is revealed. Thus, the force super-ellipsoid volume increment of the rigid workpiece and minimum total complementary energy increment of the elastic workpiece between two adjacent clamping steps can be calculated. A relay shift algorithm is constructed to select the clamping sequence. The successful accomplishment of above stated creative suggestions can systematically build up the discrete algorithm for the conceptual fixture design. It can not only supply the basic theory and methodology for automated fixture design, but also provide the technical support for the fixturing scheme of workpieces with complex surfaces.

从自动化设计与工程应用的角度出发，通过将工件装夹等效为工件-夹具的系统装配，研究工件关键装配特性到夹具结构方案的映射关系。通过构造定位基准选择的层次结构模型及其决策指标的定量描述，研究选择定位基准的层次分析方法；根据定位点方案对工件的实际约束与加工要求的关系，揭示工件运动状态与定位确定性之间的内在规律，构建布局定位点的运动约束法；研究工件与夹具之间任意接触等效为点接触的橡皮筋原理，通过分析夹紧表面网格节点处与夹紧力大小按步长发生变化时的装夹稳定性与工件变形，寻求确定夹紧点的递推设计算法，建立搜索临界夹紧力大小的反向增量递减法；通过夹紧顺序分解为夹紧力作用步骤的历史过程，分析相邻夹紧步骤间刚性工件的力超椭球体积增量与柔性工件的最小总余能增量，构建规划夹紧顺序的接力切换法。从而构建系统的离散化夹具概念设计算法，拓展与完善自动化夹具设计的基础理论与方法，为复杂工件装夹方案的合理设计提供技术支持。

装夹布局离散型规划方法的内容主要包括下列四个方面：.（1）定位点布局规划方法 .通过构建定位基准选择的层次结构模型，利用标度法构造相邻两层的判断矩阵。反复验证判断矩阵的一致性，通过后特征矢量即为层权矢量。通过层权矢量的逐层相乘，所获得的组合权矢量即为定位基准选择的决策指标。综合定位确定性的总体数目条件、局部数目条件以及定位基准的决策方法，构建定位方案的迭代规划算法。.（2）夹紧点布局规划方法 .通过提出装夹稳定性的判断依据及其解算方法，实现工件“稳不稳”的定量描述；定义超椭球体积为装夹稳定量度，用以描述工件装夹时“有多稳”的问题；引入离散化思想，构建了以使装夹稳定量度达到最大为目标的复杂工件装夹布局规划模型，根据每一代的装夹稳定性，定义个体的适应度评价函数，提出装夹布局规划模型的遗传算法求解技术。.（3）单个夹紧力的变向增量递减算法.通过构建力的存在性分析模型及其求解方法，实现夹紧力是否有解的判断。再由力的可行性分析模型及其判断标准，实现给定的夹紧力是否合理的判断。考虑夹紧力的取值范围，以一定步长正向从最小值开始取值，根据当前值与上一次取值之间可行性的差异，确定下一次取值的步长及其方向，直至步长的绝对值在阈值范围之内。.（4）多重夹紧力的变向增量递减算法.针对仅有一个夹紧力的装夹布局，离散化夹紧表面为夹紧点后，起始于第一个网格节点，在具有力封闭的前提下，以一定步长选取相邻的两个夹紧力，根据力可行的差异确定步长系数的递减性，步长递减至阈值范围之内获得第一个夹紧点处的夹紧力，反复迭代计算直至最后一个网格节点，构建“1-夹紧力”的迭代规划算法。将多重夹紧力转化为一个极径和多个极角的描述方法，通过逐个离散化极角为微角，然后在每个微角处调用“1-夹紧力”设计算法形成“n-夹紧力”的迭代规划算法。.此外，在该项基金资助下，课题组对残余应力的产生机理、加工变形随应力释放的演变机制作了初步研究。