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1、附 錄Machining fixture locating and clamping position optimization using genetic algorithmsNecmettin Kaya*Department of Mechanical Engineering, Uludag University, Go¨ru¨kle, Bursa 16059, Turkey Received 8 Jul

2、y 2004; accepted 26 May 2005Available online 6 September 2005AbstractDeformation of the workpiece may cause dimensional problems in machining. Supports and locators are used in order to reduce the error caused by elastic

3、 deformation of the workpiece. The optimization of support, locator and clamp locations is a critical problem to minimize the geometric error in workpiece machining. In this paper, the application of genetic algorithms (

4、GAs) to the fixture layout optimization is presented to handle fixture layout optimization problem. A genetic algorithm based approach is developed to optimise fixture layout through integrating a finite element code run

5、ning in batch mode to compute the objective function values for each generation. Case studies are given to illustrate the application of proposed approach. Chromosome library approach is used to decrease the total soluti

6、on time. Developed GA keeps track of previously analyzed designs; therefore the numbers of function evaluations are decreased about 93%. The results of this approach show that the fixture layout optimization problems are

7、 multi-modal problems. Optimized designs do not have any apparent similarities although they provide very similar performances.Keywords: Fixture design; Genetic algorithms; Optimization1. IntroductionFixtures are used to

8、 locate and constrain a workpiece during a machining operation, minimizing workpiece and fixture tooling deflections due to clamping and cutting forces are critical to ensuring accuracy of the machining operation. Tradit

9、ionally, machining fixtures are designed and manufactured through trial-and-error, which prove to be both expensive and time-consuming to the manufacturing process. To ensure a workpiece is manufactured according to spec

10、ified dimensions and tolerances, it must be appropriately located and clamped, making it imperative to develop tools that will eliminate costly and time-consuming trial-and-error designs. Proper deformation of the workpi

11、ece. Roy andLiao[4]developed a heuristic method to plan for the best supporting and clamping positions. Tao et al.[5]presented a geometrical reasoning methodology for determining the optimal clamping points and clamping

12、sequence for arbitrarily shaped workpieces. Liao and Hu[6]presented a system for fixture configuration analysis based on a dynamic model which analyses the fixture–workpiece system subject to time-varying machining loads

13、. The influence of clamping placement is also investigated. Li and Melkote[7]presented a fixture layout and clamping force optimal synthesis approach that accounts for workpiece dynamics during machining. A combined fixt

14、ure layout and clamping force optimization procedure presented.They used the contact elasticity modeling method that accounts for the influence of workpiece rigid body dynamics during machining. Amaral et al. [8] used AN

15、SYS to verify fixture design integrity. They employed 3-2-1 method. The optimization analysis is performed in ANSYS. Tan et al. [9] described the modeling, analysis and verification of optimal fixturing configurations by

16、 the methods of force closure, optimization and finite element modeling. Most of the above studies use linear or nonlinear programming methods which often do not give global optimum solution. All of the fixture layout op

17、timization procedures start with an initial feasible layout. Solutions from these methods are depending on the initial fixture layout. They do not consider the fixture layout optimization on overall workpiece deformation

18、. The GAs has been proven to be useful technique in solving optimization problems in engineering [10–12]. Fixture design has a large solution space and requires a search tool to find the best design. Few researchers have

19、 used the GAs for fixture design and fixture layout problems. Kumar et al. [13] have applied both GAs and neural networks for designing a fixture. Marcelin [14] has used GAs to the optimization of support positions. Vall

20、apuzha et al. [15] presented GA based optimization method that uses spatial coordinates to represent the locations of fixture elements. Fixture layout optimization procedure was implemented using MATLAB and the genetic a

21、lgorithm toolbox. HYPERMESH and MSC/NASTRAN were used for FE model. Vallapuzha et al. [16] presented results of an extensive investigation into the relative effectiveness of various optimization methods. They showed that

22、 continuous GA yielded the best quality solutions. Li and Shiu [17] determined the optimal fixture configuration design for sheet metal assembly using GA. MSC/NASTRAN has been used for fitness evaluation. Liao [18] prese

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