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1、附录Machining fixture locating and clamping position optimizationusing genetic algorithms Necmettin Kaya* Department of Mechanical Engineering, Uludag University, Goru kle, Bursa 16059, Turkey Received 8 July 2004; accepted 26 May 2005 Available online 6 September 2005 Abstract Deformation of the work
2、piece may cause dimensional problems in machining. Supports and locators are used in order to reduce the error causedby elastic deformation of the workpiece. The optimization of support, locator and clamp locations is a critical problem to minimize the geometricerror in workpiece machining. In this
3、paper, the application of genetic algorithms (GAs) to the fixture layout optimization is presented to handlefixture layout optimization problem. A genetic algorithm based approach is developed to optimise fixture layout through integrating a finiteelement code running in batch mode to compute the ob
4、jective function values for each generation. Case studies are given to illustrate theapplication of proposed approach. Chromosome library approach is used to decrease the total solution time. Developed GA keeps track of previouslyanalyzed designs; therefore the numbers of function evaluations are de
5、creased about 93%. The results of this approach show that the fixture layoutoptimization problems are multi-modal problems. Optimized designs do not have any apparent similarities although they provide very similarperformances. Keywords: Fixture design; Genetic algorithms; Optimization 1. Introducti
6、on Fixtures are used to locate and constrain a workpiece duringa machining operation, minimizing workpiece and fixturetooling deflections due to clamping and cutting forces arecritical toensuring accuracy of the machining operation.Traditionally, machining fixtures are designed and manufacturedthrou
7、gh trial-and-error, which prove to be both expensiveand time-consuming to the manufacturing process. To ensure aworkpiece is manufactured according to specified dimensionsand tolerances, it must be appropriately located and clamped,making it imperative to develop tools that will eliminate costlyand
8、time-consuming trial-and-error designs. Proper workpiecelocation and fixture design are crucial to product quality interms of 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 1 页，共 15 页 - - - - - - - - - precision, accuracy and finish of the machined part. Theoreticall
9、y, the 3-2-1 locating principle can satisfactorilylocate all prismatic shaped workpieces. This method providesthe maximum rigidity with the minimum number of fixtureelements. To position a part from a kinematic point of viewmeans constraining the six degrees of freedom of a free movingbody (three tr
10、anslations and three rotations). Three supports arepositioned below the part to establish the location of theworkpiece on its vertical axis. Locators are placed on twoperipheral edges and intended to establish the location of theworkpiece on the x and y horizontal axes. Properly locating theworkpiec
11、e in the fixture is vital to the overall accuracy andrepeatability of the manufacturing process. Locators should bepositioned as far apart as possible and should be placed onmachined surfaces wherever possible. Supports are usuallyplaced to encompass the center of gravity of a workpiece andpositione
12、d as far apart as possible to maintain its stability. Theprimary responsibility of a clamp in fixture is to secure the partagainst the locators and supports. Clamps should not be expectedto resist the cutting forces generated in the machining operation. For a given number of fixture elements, the ma
13、chiningfixture synthesis problem is the finding optimal layout orpositions of the fixture elements around the workpiece. In thispaper, a method for fixture layout optimization using geneticalgorithms is presented. The optimization objective is to searchfor a 2D fixture layout that minimizes the maxi
14、mum elasticdeformation at different locations of the workpiece. ANSYSprogram has been used for calculating the deflection of the partunder clamping and cutting forces. Two case studies are givento illustrate the proposed approach. 2. Review of related works Fixture design has received considerable a
15、ttention in recentyears. However, little attention has been focused on theoptimum fixture layout design. Menassa and DeVries1usedFEA for calculating deflections using the minimization of theworkpiece deflection at selected points as the design criterion.The design problem was to determine the positi
16、on of supports.Meyer and Liou2 presented an approach that uses linearprogramming technique to synthesize fixtures for dynamicmachining conditions. Solution for the minimum clampingforces and locator forces is given. Li and Melkote3used anonlinear programming method to solve the layout optimizationpr
17、oblem. The method minimizes workpiece location errorsdue to 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 2 页，共 15 页 - - - - - - - - - localized elastic deformation of the workpiece. RoyandLiao4developed a heuristic method to plan for the bestsupporting and clamping
18、 positions. Tao et al.5presented ageometrical reasoning methodology for determining theoptimal clamping points and clamping sequence for arbitrarilyshaped workpieces. Liao and Hu6presented a system forfixture configuration analysis based on a dynamic model whichanalyses the fixture workpiece system
19、subject to time-varyingmachining loads. The influence of clamping placement is alsoinvestigated. Li and Melkote7presented a fixture layout andclamping force optimal synthesis approach that accounts forworkpiece dynamics during machining. A combined fixturelayout and clamping force optimization proce
20、dure presented.They used the contact elasticity modeling method that accountsfor the influence of workpiece rigid body dynamics duringmachining. Amaral et al. 8 used ANSYS to verify fixturedesign integrity. They employed 3-2-1 method. The optimizationanalysis is performed in ANSYS. Tan et al. 9 desc
21、ribedthe modeling, analysis and verification of optimal fixturingconfigurations by the methods of force closure, optimizationand finite element modeling. Most of the above studies use linear or nonlinearprogramming methods which often do not give global optimumsolution. All of the fixture layout opt
22、imization procedures startwith an initial feasible layout. Solutions from these methods aredepending on the initial fixture layout. They do not consider thefixture layout optimization on overall workpiece deformation. The GAs has been proven to be useful technique in solvingoptimization problems in
23、engineering 10 12. Fixture designhas a large solution space and requires a search tool to find thebest design. Few researchers have used the GAs for fixturedesign and fixture layout problems. Kumar et al. 13 haveapplied both GAs and neural networks for designing a fixture.Marcelin14has used GAs to t
24、he optimization of supportpositions. Vallapuzha et al. 15presented GA basedoptimization method that uses spatial coordinates to representthe locations of fixture elements. Fixture layout optimizationprocedure was implemented using MATLAB and the geneticalgorithm toolbox. HYPERMESH and MSC/NASTRAN we
25、reused for FE model. Vallapuzha et al. 16 presented results of anextensive investigation into the relative effectiveness of variousoptimization methods. They showed that continuous GAyielded the best quality solutions. Li and Shiu17 determinedthe optimal fixture configuration design for sheet metala
26、ssembly using GA. MSC/NASTRAN has been used forfitness evaluation. Liao 18 presented a method to automaticallyselect the optimal numbers of 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 3 页，共 15 页 - - - - - - - - - locators and clamps aswell as their optimal positio
27、ns in sheet metal assembly fixtures.Krishnakumar and Melkote19developed a fixture layoutoptimization technique that uses the GA to find the fixturelayout that minimizes the deformation of the machined surfacedue to clamping and machining forces over the entire tool path.Locator and clamp positions a
28、re specified by node numbers. Abuilt-in finite element solver was developed. Some of the studies do not consider the optimization of thelayout for entire tool path and chip removal is not taken intoaccount. Some of the studies used node numbers as designparameters. In this study, a GA tool has been
29、developed to find theoptimal locator and clamp positions in 2D workpiece.Distances from the reference edges as design parameters areused rather than FEA node numbers. Fitness values of realencoded GA chromosomes are obtained from the results ofFEA. ANSYS has been used for FEA calculations. Achromoso
30、me library approach is used in order to decreasethe solution time. Developed GA tool is tested on two testproblems. Two case studies are given to illustrate the developedapproach. Main contributions of this paper can be summarizedas follows: (1) developed a GA code integrated with a commercial finit
31、eelement solver; (2) GA uses chromosome library in order to decrease thecomputation time; (3) real design parameters are used rather than FEA nodenumbers; (4) chip removal is taken into account while tool forces movingon the workpiece. 3. Genetic algorithm concepts Genetic algorithms were first deve
32、loped by John Holland.Goldberg 10 published a book explaining the theory andapplication examples of genetic algorithm in details. A geneticalgorithm is a random search technique that mimics somemechanisms of natural evolution. The algorithm works on apopulation of designs. The population evolves fro
33、m generationto generation, gradually improving its adaptation to theenvironment through natural selection; fitter individuals havebetter chances of transmitting their characteristics to latergenerations. In the algorithm, the selection of the natural environment isreplaced by artificial selection ba
34、sed on a computed fitness foreach design. The term fitness is used to designate thechromosomes chances of survival and it is essentially theobjective function of the optimization problem. The chromosomesthat define characteristics of biological beings arereplaced by strings of numerical values repre
35、senting the 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 4 页，共 15 页 - - - - - - - - - designvariables. GA is recognized to be different than traditional gradient basedoptimization techniques in the following four major ways10: 1. GAs work with a coding of the desig
36、n variables andparameters in the problem, rather than with the actualparameters themselves. 2. GAs makes use of population-type search. Many differentdesign points are evaluated during each iteration instead ofsequentially moving from one point to the next. 3. GAs needs only a fitness or objective f
37、unction value. Noderivatives or gradients are necessary. 4. GAs use probabilistic transition rules to find new designpoints for exploration rather than using deterministic rulesbased on gradient information to find these new points. 4. Approach 4.1. Fixture positioning principles In machining proces
38、s, fixtures are used to keep workpiecesin a desirable position for operations. The most importantcriteria for fixturing are workpiece position accuracy andworkpiece deformation. A good fixture design minimizesworkpiece geometric and machining accuracy errors. Anotherfixturing requirement is that the
39、 fixture must limit deformationof the workpiece. It is important to consider the cutting forces aswell as the clamping forces. Without adequate fixture support,machining operations do not conform to designed tolerances.Finite element analysis is a powerful tool in the resolution ofsome of these prob
40、lems 22. Common locating method for prismatic parts is 3-2-1method. This method provides the maximum rigidity with theminimum number of fixture elements. A workpiece in 3D maybe positively located by means of six points positioned so thatthey restrict nine degrees of freedom of the workpiece. Theoth
41、er three degrees of freedom are removed by clamp elements.An example layout for 2D workpiece based 3-2-1 locatingprinciple is shown in Fig. 4. 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 5 页，共 15 页 - - - - - - - - - Fig. 4.3-2-1 locating layout for 2D prismatic wo
42、rkpiece The number of locating faces must not exceed two so as to avoid a redundant location. Based on the 3-2-1fixturing principle there are two locating planes for accurate location containing two and one locators. Therefore, there are maximum of two side clampings against each locating plane. Cla
43、mping forces are always directed towards the locators in order to force the workpiece to contact all locators. The clamping point should be positioned opposite the positioning points to prevent the workpiece from being distorted by the clamping force. Since the machining forces travel along the mach
44、ining area, it is necessary to ensure that the reaction forces at locators are positive for all the time. Any negative reaction force indicates that the workpiece is free from fixture elements. In other words, loss of contact or the separation between the workpiece and fixture element might happen w
45、hen the reaction force is negative. Positive reaction forces at the locators ensure that the workpiece maintains contact with all the locators from the beginning of the cut to the end. The clamping forces should be just sufficient to constrain and locate the workpiece without causing distortion or d
46、amage to the workpiece. Clamping force optimization is not considered in this paper. 4.2. Genetic algorithm based fixture layout optimization approach In real design problems, the number of design parameters can be very large and their influence on the objective function can be very complicated. The
47、 objective function must be smooth and a procedure is needed to compute gradients. Genetic algorithms strongly differ in conception from other search methods, including traditional optimization methods and other stochastic methods 23. By applying GAs to fixture layout optimization, an optimal or gro
48、up of sub-optimal solutions can be obtained. 名师资料总结 - - -精品资料欢迎下载 - - - - - - - - - - - - - - - - - - 名师精心整理 - - - - - - - 第 6 页，共 15 页 - - - - - - - - - In this study, optimum locator and clamp positions are determined using genetic algorithms. They are ideally suited for the fixture layout optimiz
49、ation problem since no direct analytical relationship exists between the machining error and the fixture layout. Since the GA deals with only the design variables and objective function value for a particular fixture layout, no gradient or auxiliary information is needed 19. The flowchart of the pro
50、posed 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 betw