The flowchart of the proposed approach is given in Fig。 5。

Fixture layout optimization is implemented using developed software written in Delphi language named GenFix。 Displacement values are calculated in ANSYS software [24]。 The execution of ANSYS in GenFix is simply done by WinExec function in Delphi。 The interaction between GenFix and ANSYS is implemented in four steps:

(1) Locator and clamp positions are extracted from binary string as real parameters。

(2) These parameters and ANSYS input batch file (modeling, solution and post processing commands) are sent to ANSYS using WinExec function。

(3) Displacement values are written to a text file after solution。

(4) GenFix reads this file and computes fitness value for current locator and clamp positions。

In order to reduce the computation time, chromosomes and fitness values are stored in a library for further evaluation。 GenFix first checks if current chromosome’s fitness value has been calculated before。 If not, locator positions are sent to ANSYS, otherwise fitness values are taken from the library。 During generating of the initial population, every chromosome is checked whether it is feasible or not。 If the constraint is violated, it is eliminated and new chromosome is created。 This process creates entirely feasible initial population。 This ensures that workpiece is stable under the action of clamping and cutting forces for every chromosome in the initial population。 

The written GA program was validated using two test cases。 The first test case uses Himmelblau function [21]。 In the second test case, the GA program was used to optimise the support positions of a beam under uniform loading。

5。 Fixture layout optimization case studies

The fixture layout optimization problem is defined as: finding the positions of the locators and clamps, so that workpiece deformation at specific region is minimized。 Note that number of locators and clamps are not design parameter, since they are known and fixed for the 3-2-1 locating scheme。 Hence, the design parameters are selected as locator and clamp positions。 Friction is not considered in this paper。 Two case studies are given to illustrate the proposed approach。

6。 Conclusion

In this paper, an evolutionary optimization technique of fixture layout optimization is presented。 ANSYS has been used for FE calculation of fitness values。 It is seen that the combined genetic algorithm and FE method approach seems to be a powerful approach for present type problems。 GA approach is particularly suited for problems where there does not exist a well-defined mathematical relationship between the objective function and the design variables。 The results prove the success of the application of GAs for the fixture layout optimization problems。

In this study, the major obstacle for GA application in fixture layout optimization is the high computation cost。 Re-meshing of the workpiece is required for every chromosome in the population。 But, usages of chromosome library, the number of FE evaluations are decreased from 6000 to 415。 This results in a tremendous gain in computational efficiency。 The other way to decrease the solution time is to use distributed computation in a local area network。

The results of this approach show that the fixture layout optimization problems are multi-modal problems。 Optimized designs do not have any apparent similarities although they provide very similar performances。 It is shown that fixture layout problems are multi-modal therefore heuristic rules for fixture design should be used in GA to select best design among others。

摘要：工件变形的问题可能导致机械加工中的空间问题。支撑和定位器是用于减少工件弹性变形引起的误差。支撑、定位器的优化和夹具定位是最大限度的减少几何在工件加工中的误差的一个关键问题。本文应用夹具布局优化遗传算法（GAs）来处理夹具布局优化问题。遗传算法的方法是基于一种通过整合有限的运行于批处理模式的每一代的目标函数值的元素代码的方法，用于来优化夹具布局。给出的个案研究说明已开发的方法的应用。采用染色体文库方法减少整体解决问题的时间。已开发的遗传算法保持跟踪先前的分析设计，因此先前的分析功能评价的数量降低大约93%。结果表明，该方法的夹具布局优化问题是多模式的问题。优化设计之间没有任何明显的相似之处，虽然它们提供非常相似的表现。