基于多色集合理论的产品装配规划建模与算法研究

Product Assembly Planning Modeling and Algorithm Based on Polychromatic Sets

采用多色集合理论建立了一种用数组元素表示的装配关系模型,它包括表示定位关系的定位基准模型和表示装配通道关系的可能位移模型.通过定位基准方程组和可能位移方程组给出了这种装配关系模型的数学表达形式,并提出了它们的求取算法,从而将装配过程中的定位关系和装配通道关系这2种约束关系用简单的逻辑方程式表示出来,方便了计算机的编程.同时,提出的各级装配单元的生成算法和在装配单元基础上建立递阶结构图的算法,为用计算机编程实现装配序列的自动生成提供了基础.与传统的装配规划模型相比较,用多色集合理论进行装配规划建模,便于描述装配过程中的约束关系,具有形式化水平高、避免“组合爆炸”和易于编程等优点.

Adopting polychromatic sets, a kind of assembly relation models represented by array elements are established, including locating datum model to demonstrate the locating relations and possible displacement model to determine the assembly channel relations. The mathematic equations of this assembly relation model are demonstrated via the locating datum equations and possible displacement equations, and the corresponding algorithms are proposed. Thus, these two relations are expressed with simple logic equations to facilitate programming. The generation algorithms of all levels assembly units and the constructing algorithms of hierarchical graph are presented based on the assembly units to realize the automatic generation of the assembly sequence. Compared with the conventional assembly planning models, the newly proposed one is easy to describe the restriction relations in assembly with a higher formalization level to avoid ＇ combinatorial explosion＇.