夾具類外文翻譯-采用遺傳算法優化加工夾具定位和加緊位置【中文4477字】【PDF+中文WORD】

夾具類外文翻譯-采用遺傳算法優化加工夾具定位和加緊位置【中文4477字】【PDF+中文WORD】,中文4477字,PDF+中文WORD,夾具,外文,翻譯,采用,遺傳,算法,優化,加工,定位,加緊,位置,中文,4477,PDF,WORD Machining fixture locating and clamping position optimizationusing genetic algorithmsNecmettin Kaya*Department of Mechanical Engineering,Uludag University,Go ru kle,Bursa 16059,TurkeyReceived 8 July 2004;accepted 26 May 2005Available online 6 September 2005AbstractDeformationoftheworkpiecemaycausedimensionalproblemsinmachining.Supportsandlocatorsareusedinordertoreducetheerrorcausedby 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 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 objective function values for each generation.Case studies are given to illustrate theapplicationofproposedapproach.Chromosomelibraryapproachisusedtodecreasethetotalsolutiontime.DevelopedGAkeepstrackofprevioslyanalyzed designs,therefore the number of function evaulations are decreased 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.#2005 Elsevier B.V.All rights reserved.Keywords:Fixture design;Genetic algorithms;Optimization1.IntroductionFixtures are used to locate and constrain a workpiece duringa machining operation,minimizing workpiece and fixturetooling deflections due to clamping and cutting forces arecritical to ensuring accuracy of the machining operation.Traditionally,machining fixtures are designed and manufac-tured through 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 time-consuming trial-and-error designs.Proper workpiecelocation and fixture design are crucial to product quality interms of precision,accuracy and finish of the machined part.Theoretically,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 translations 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 theworkpiece 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 andpositioned as far apart as possible to maintain its stability.Theprimary responsibility of a clamp in fixture is to secure the partagainstthelocatorsandsupports.Clampsshouldnotbeexpectedto resist the cutting forces generated in the machining operation.For a given number of fixture elements,the machiningfixture 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 maximum elasticdeformation at different locations of the workpiece.ANSYSprogram has been used for calculating the deflection of the in Industry 57(2006)112120*Tel.:+90 224 4428176;fax:+90 224 4428021.E-mail address:necmiuludag.edu.tr.0166-3615/$see front matter#2005 Elsevier B.V.All rights reserved.doi:10.1016/pind.2005.05.001under clamping and cutting forces.Two case studies are givento illustrate the proposed approach.2.Review of related worksFixture design has received considerable attention in recentyears.However,little attention has been focused on theoptimum fixture layout design.Menassa and DeVries 1 usedFEA for calculating deflections using the minimization of theworkpiece deflection at selected points as the design criterion.The design problem was to determine the position of supports.Meyer and Liou 2 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 Melkote 3 used anonlinear programming method to solve the layout optimiza-tion problem.The method minimizes workpiece location errorsdue to localized elastic deformation of the workpiece.Roy andLiao 4 developed a heuristic method to plan for the bestsupporting and clamping positions.Tao et al.5 presented ageometricalreasoning methodologyfor determining theoptimal clamping points and clamping sequence for arbitrarilyshaped workpieces.Liao and Hu 6 presented a system forfixture configuration analysis based on a dynamic model whichanalyses the fixtureworkpiece system subject to time-varyingmachining loads.The influence of clamping placement is alsoinvestigated.Li and Melkote 7 presented a fixture layout andclamping force optimal synthesis approach that accounts forworkpiece dynamics during machining.A combined fixturelayout and clamping force optimization procedure 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 optimiza-tion analysis is performed in ANSYS.Tan et al.9 describedthe modeling,analysis and verification of optimal fixturingconfigurations by the methods of force closure,optimizationand finite element modeling.Mostoftheabovestudiesuselinearornonlinearprogramming methods which often do not giveglobal optimumsolution.All of the fixture layout optimization procedures startwith an initial feasible layout.Solutionsfrom these methods aredepend on the initial fixture layout.They do not consider thefixture layout optimization on overall workpiece deformation.The GAs have been proven to be useful technique in solvingoptimization problems in engineering 1012.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.Marcelin 14 has used GAs to the optimization of supportpositions.Vallapuzhaetal.15presentedGAbasedoptimization 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 wereusedforFEmodel.Vallapuzhaetal.16 presentedresults ofanextensive investigation into the relative effectiveness of variousoptimization methods.They showed that continuous GAyielded the best quality solutions.Li and Shiu 17 determinedthe optimal fixture configuration design for sheet metalassembly using GA.MSC/NASTRAN has been used forfitness evaulation.Liao 18 presented a method to auto-matically select the optimal numbers of locators and clamps aswell as their optimal positions in sheet metal assembly fixtures.Krishnakumar and Melkote 19 developed 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 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 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.Achromosome library approach is used in order to decreasethe solution time.Developed GA tool is tested on two testproblems.Two case studies are givento illustrate the developedapproach.Main contributions of this paper can be summarizedas follows:(1)developed a GA code integrated with a commercial finiteelement 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 conceptsGenetic algorithms were first developed 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 from 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 based 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 chromo-somes that define characteristics of biological beings areN.Kaya/Computers in Industry 57(2006)112120113replaced by strings of numerical values representing the designvariables.GA is recognized to be different than traditional gradient-basedoptimizationtechniquesinthefollowingfour major ways10:1.GAs work with a coding of the design variables andparameters in the problem,rather than with the actualparameters themselves.2.GAs make use of population-type search.Many differentdesign points are evaluated during each iteration instead ofsequentially moving from one point to the next.3.GAs need only a fitness or objective function 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.Algorithm of the basic GA is given as follows:1.Initial population:Generate random population of chromo-somes.2.Fitness:Evaluate the fitness of each chromosome in thepopulation.3.Test:If the end condition is satisfied,stop,and return the bestsolution in current population.4.New population:Create a new population by repeatingfollowing steps until the new population is complete.Reproduction:Select two parent chromosomes from thepopulation according to their fitness.Crossover:With a crossover probability,crossover theparents to form a new offspring(children).If no crossoverwas performed,offspring is an exact copy of parents.Mutation:With a mutation probability,mutate new offspringat each locus(position in chromosome).5.Replace:Use new generated population for a further run ofalgorithm.6.Loop:Go to step 2.3.1.Individual representationThe first andmostimportantstep in preparing anoptimization problem for a GA solution is that of defining aparticular coding of the design variables and their arrangementinto a string of numerical values to be used as the chromosomeby the GA.In most GAs,finite length binary coded strings of ones andzeros are used to describe the parameters for each solution.In amultiparameter optimization problem,individual parametercoding are usually concatenated into a complete string which isshown in Fig.1.In this paper,real representation of binary string is used.Thelength of the string depends on the required precision.Themapping from a binary string to a real number is completed intwo steps:Step 1:Find code length for xi(i=1,.,n):c xmaxi?xmini?rwhere r is the required precision(101,102,103,.).Code length for xiis as follows:lxi n 1where,2nc2n1Total string length is given by:l Xni1lxiStep 2:Mapping from a binary string to a real number:xi xminixmaxi?xmini2n?1Xnj1qij2j?1where qij2 0,1.In order to generate the chromosomes,the length of thechromosome is calculated first.Then random numbers in therange of 0,1aregenerated toform the chromosome.Randomfunction is used in Delphi programming language as a randomnumber generator.3.2.Genetic operatorsEstablishing the GA parameters is very crucial in anoptimization problem because there are no guidelines 20.Thegenetic algorithms contains several operators,e.g.reproduc-tion,crossover,mutation,etc.3.2.1.ReproductionThe reproduction operator allows individual strings to becopied for possible inclusion in the next generation.Afterassesingthefitness valuefor eachstringinthe initialpopulation,only a few strings with high fitness value are considered in thereproduction.There are many different types of reproductionoperatorswhichareproportionalselection,tournamentselection,ranking selection,etc.In this study,tournament selection isselected,since it has better convergence and computational timecomparedtoanyotherreproductionoperator11.Intournamentselection,two individuals are choosen from the population atrandom.Then the string which has best fitness value is selected.This procedure is continued until the size of the reproductionpopulation is equal to the size of the population.3.2.2.CrossoverCrossoveristhenextoperationinthegeneticalgorithm.Thisoperation partially exchanges information between any twoN.Kaya/Computers in Industry 57(2006)112120114Fig.1.Binary representation in GA.selected individuals.Crossover selects genes from parentchromosomes and creates new offsprings.Like reproductionoperator,thereexistanumberofcrossoveroperatorsinGA.Inasingle-point crossoveroperator which is used in this paper,bothstrings are cut at an arbitrary place and the right-side portion ofboth strings are swapped among themselves to create two newstrings,as illustrated in Fig.2.In order to carry out the crossover operation,two individualsare selected from the population at random.Then a randomnumber in the range of 0,1 is generated.If this randomnumber is less than the probability of crossover then theseindividuals are subjected to crossover,otherwise they arecopiedtonewpopulationastheyare.Alsothecrossoverpointisselected at random.Probability of crossover(Pc)is selectedgenerally between 0.6 and 0.9.3.2.3.MutationThis is the process of randomly modifying the string withsmall probability.Mutation operator changes 10 and viceversa with a small probability of mutation(Pm).The need formutation is to keep diversity in the population 11.This is toprevent falling all solutions in population into a local optimumof solved problem.Fig.3 illustrates the mutation operation atseventh bit position.In order to determine whether a chromoseme is to besubjectedtomutation,arandomnumberintherangeof0,1isgenerated.If this random number is less than the probability ofmutation,selected chromosome will be mutated.Probability ofmutation should be selected very low as a high mutation willdestroy fit chromosomes and degenerate the GA into a randomwalk.Pmshould be selected between 0.02 and 0.06 21.3.2.4.Constraint handlingIn most application of GAs to constrained optimizationproblems,the penalty function method has been used.In thisstudy a method proposed by Deb 12 is used.Although apenalty term is added to the objective function,this methoddiffers from conventional GA implementations.The methodproposes to use a tournament selection operator,where twosolutions are compared at a time and the following criteria arealways enforced:-Any feasible solution is preferred to any infeasible solution.-Among two feasible solutions,the one having better fitnessvalue is preferred.-Among two infeasible solutions,the one having smallerconstraint violation is preferred.3.2.5.Elitist strategyIn this strategy,some of the best individuals are copied intothe next generation without applying any genetic operators.Elitist strategy always clones the best individuals of the currentgeneration into the next generation.This guarantees that thebest found design is never lost in future generations.4.Approach4.1.Fixture positioning principlesIn machining process,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 fixture must limit deformationoftheworkpiece.Itisimportanttoconsiderthecuttingforcesaswell 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 problems 22.Common locating method for prismatic parts is 3-2-1method.This method provides the maximum rigidity with theminimum number of fixture elements.Aworkpiece in 3D maybe positively located by means of six points positioned so thatthey restrict nine degrees of freedom of the workpiece.Theother three degrees offreedom are removed by clamp elements.An example layout for 2D workpiece based 3-2-1 locatingprinciple is shown in Fig.4.The number of locating faces must not exceed two so as toavoid a redundant location.Based on the 3-2-1 fixturingprinciple there are two locating planes for accurate locationcontainingtwoand onelocators.Therefore,thereare maximumof two side clampings against each locating plane.Clampingforces are always directed towards the locators in order to forcethe workpiece to contact all locators.The clamping pointN.Kaya/Computers in Industry 57(2006)112120115Fig.2.Illustration of crossover operator.Fig.3.Illustration of mutation operator.Fig.4.3-2-1 locating layout for 2D prismatic workpiece.should be positioned opposite the positioning points to preventthe workpiece from being distorted by the clamping force.Since the machining forces travel along the machining area,it is necessary to ensure that the reaction forces at locators arepositive for all the time.Any negative reaction force indicatesthat theworkpiece is free from fixture elements.In other words,loss of contact or the separation between the workpiece andfixture element might happen when the reaction force isnegative.Positive reaction forces at the locators ensure that theworkpiece maintains contact with all the locators from thebeginning of the cut to the end.The clamping forces should bejust sufficient to constrain and locate the workpiece withoutcausing distortion or damage to the workpiece.Clamping forceoptimization is not considered in this paper.4.2.Genetic algorithm based fixture layout optimizationapproachIn real design problems,the number of design parameterscan be very large and their influence on the objective functioncan be very complicated.The objective function must besmooth and a procedure is needed to compute gradients.Genetic algorithms strongly differ in conception from othersearch methods,including traditional optimization methodsand other stochastic methods 23.By applying GAs to fixturelayout optimization,an optimal or group of sub-optimalsolutions can be obtained.In this study,optimum locator and clamp positions aredetermined using genetic algorithms.They are ideally suitedfor the fixture layout optimization problem since no directanalytical relationship exist between the machining error andthe fixture layout.Since the GA deals with only the designvariables and objective function value for a particular fixturelayout,no gradient or auxiliary information is needed 19