基于表面网格离散化与遗传算法的复杂工件装夹布局规划方法

A Planning Method of Fixturing Layout for Complex Workpieces Based on Surface Discretization and Genetic Algorithm

装夹是工件加工过程中首先面临的问题,而稳定装夹则是保证工件加工质量与生产安全的必要条件。为此系统地提出了基于稳定性指标与稳定量度的工件装夹布局优化模型及其遗传算法求解技术。根据静力平衡条件与线性规划技术,提出装夹稳定性的判断依据及其解算方法,实现装夹时工件'稳不稳'的定量描述;依据力的超椭球方程,将超椭球体积定义为装夹稳定量度,用以描述工件装夹稳定时'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。提出的基于稳定性指标与稳定量度的装夹布局规划方法,由于只涉及接触点的坐标及其法矢量信息,不仅适用于具有复杂表面的工件,而且能够避免工件处于非稳定状态下优化模型的求解过程,提高了计算效率,为复杂工件装夹布局方案的合理设计提供了基础理论。

Fixturing is firstly confronted in the workpiece machining process. It is more important, stable fixturing is prerequisite to guarantee the machining quality and safety manufacturing. Therefore, an optimal model of fixturing layout and its genetic algorithm-based solution technology are proposed according to the fixturing stability index and stability measurement. Both the conditions for static equilibrium and the linear programming technology above all are employed to conclude the judgment criterion of fixturing stability and the corresponding solution algorithm. Thus, it is possible to describe whether a workpiece is stable in the fixturing process. Secondly, based on the equation of super elliptical sphere of forces, the volume of the super elliptical sphere is defined as the fixturing stability measurement which can measure how stable the workpiece is when it is stable. Finally, the surface discretization is introduced to formulate the optimal model of fixturing layout with the objective of maximizing the fixturing stability measurement. According to the fixturing stability of each generation, the evaluation function is defined for the fitness of the individual. Thus, the genetic algorithm can be skillfully developed to solve the optimal model of fixturing layout. The presented planning methodology for fixturing layout only concern on the coordinates and normal vectors of contact points. Again, it can also avoid the solution of the optimal model under the condition of the workpiece in unstable fixturing. So the proposed method can not only carry out for complex workpieces, but also improve the calculation efficiency. It can provide a basic theory of fixturing layout design for the complex workpiece.