[棱镜座]本体压铸件压铸模具设计-带抽芯压铸模具设计
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ORIGINAL ARTICLEAn intelligent system for low-pressure die-cast processparameters optimizationLiqiang Zhang&Rongji WangReceived: 29 July 2011 /Accepted: 20 April 2012#Springer-Verlag London Limited 2012Abstract Low-pressure die-cast (LPDC) is widely used inmanufacturing thin-walled aluminum alloy products. Sincethe quality of LPDC parts are mostly influenced by processconditions, how to determine the optimum process condi-tions becomes the key to improve the part quality. In thispaper, a combining artificial neural network and geneticalgorithm (ANN/GA) method is proposed to optimize theLPDC process. In this method, considering the more com-plicated preparation process of thin-walled casting, an ANNmodel combining learning vector quantization and back-propagation (BP) algorithm is proposed to map the complexrelationship between process conditions and quality indexesof LPDC. Meanwhile, the orthogonal array design and nu-merical simulation is applied to obtain the training samplesinstead of carrying out a real experiment for the sake of costsaving. The genetic algorithm is employed to optimize theprocess parameters with the fitness function based on thetrained ANN model. Then, by applying the optimizedparameters, a thin-walled component of 300 mm in length,100 mm in width, and 1.5 mm in thickness is successfullyprepared. The results indicate that the proposed intelligentsystem is an effective tool for the process optimization ofLPDC.Keywords LPDC.Processparameters.Artificialneuralnetwork.Geneticalgorithm.Numericalsimulation1 IntroductionOwing to its ability to produce low-porosity and semiauto-matic production, thus high quality casting and high pro-ductivity, the low-pressure die-casting (LPDC) process istaken as the dominant forming technology for casting alu-minum alloy. The evolution of the LPDC process and itsdevelopment as a major manufacturing process has beendiscussed by a number of researchers 14. A LPDC ma-chine usually includes a pressurized melt furnace locatedbelow the die table with a feeding tube running from thefurnace to the bottom of the die. A schematic diagram of aLPDC machine is shown in Fig. 1 in the present paper. Theprocess is an application of Pascals pressure theory. Thesurface of molten metal in the furnace is pressed by a dryprotective gas at relatively low pressure to overcome thedifference of metallic pressure between the die and thesurface of the molten metal. Molten metal is then forced torise through the riser tube, feeder, and gating system, andconsequently feeds the die cavity. When the die cavity isfull, the exerting pressure is increased to pressurize thecasting and improve the feeding of shrinkage during solid-ification. Once the casting is completely solidified, the ex-ternal pressure is released, and the molten metal not yetsolidified in the feeder and the riser tube flow back downto the furnace by the action of gravity.During the last decade, the numerical simulation technol-ogy has been rapidly developed and applied successfully inmany casting industries to improve the product quality andreduce the manufacturing cost 57. However, numericalsimulation is often insufficient to yield the appreciate valuesL. Zhang:R. Wang (*)College of Mechanical and Electrical Engineering, Central SouthUniversity of Forestry and Technology,Changsha 410004, Hunan, Peoples Republic of Chinae-mail: L. Zhange-mail: L. ZhangState Key Laboratory of Advanced Design and Manufacturingfor Vehicle Body, Hunan University,Changsha 410082, Hunan, Peoples Republic of ChinaInt J Adv Manuf TechnolDOI 10.1007/s00170-012-4190-4of process parameters, especially in cases where a largenumber of parameters need to be examined with even alow number of possible values to cover their intended rangeof variation. In addition, the large number of simulation runscoupled with lengthy execution times per run (on the orderof hours or even days depending on computing power andpart complexity) may render such investigations totally im-practical 8. Therefore, advanced methods are highlydemanded to model and optimize the LPDC process withthe purpose of high quality casting and productivity. Inrecent years, the researchers have shown keen interests indeveloping artificial intelligence (AI) system for fast andaccurate prediction of process parameters during the casting9, 10. AI techniques like ANN and GAs have been widelyused for solving complicated and multivariable manufactur-ing problems. Both ANN and GAs are the most promisingnatural computation techniques 11, 12.Yarlagadda 13 developed an integrated neural networksystem to predict the process parameter in metal injectionmolding. The integrated system was implemented in Mat-LAB environment by using neural networks toolbox. In hiswork, the feed-forward type of neural network was used andthen constructed with four neurons (melt temperature, moldtemperature, cavity thickness, and flow path length) in theinput layer and one neuron (injection time) in the outputlayer. Shen et al. 14 proposed a combining artificial neuralnetwork and genetic algorithm (ANN/GA) method to opti-mize the injection molding process. In his method, a BPneural network model was developed to map the complexnonlinear relationship between process conditions and qual-ity indexes of the injection molded parts, and a GAwas usedin the process conditions optimization with the fitness func-tion based on an ANN model. The quality index of thevolumetric shrinkage variation in the part was successfullyimproved by using the proposed ANN/GA method.Krimpenis et al. 9 tried to develop a hybrid model compris-ing of ANN and GA for the optimal selection of pressure die-castingprocessparameters.Here,basedonDoEresults,atotalof 16 data sets (obtained from ProCAST simulations) wereused to train two independent neural network configurationspredicting solidification time and defects (i.e., filling/in-complete filling) with achieved mean relative error of 8.9and 15 %, respectively. In the recent work of Rai et al.10, a physical model called neural network based castingprocess model (NN-CastPro) was developed for real timeestimation of optimal HPDC process parameters. By sub-mitting a set of four process parameters, namely (a) inletmelt temperature, (b) mold initial temperature, (c) inletfirst phase velocity, and (d) inlet second phase velocityas input to the NN-CastPro, values for filling time, solid-ification time, and porosity were obtained simultaneously.Thus, the proposed artificial neural network (ANN) modelwas trained using data generated by ProCAST (a FEM-based simulation software). The obtained prediction accu-racy of NN-CastPro demonstrated the capabilities of ANNin modeling complex multivariable problems as involvedin various other manufacturing processes.From the above review of the AI system applications, itcan be concluded that the AI system can be adopted in thesolving of complicated and multivariable manufacturingproblems. However, they were mostly applied in the areaof the injection molding and the pressure die-casting pro-cess. There is not yet the case for LPDC and there is still alack of comprehensive models for taking into account thecomplex relations among the overall molding processvariables.This paper reports a combining ANN/GA approach pro-posed for modeling and optimizing the LPDC processparameters of A356 thin-walled aluminum with permanentmold. Learning vector quantization (LVQ) and back-propagation (BP) algorithm is simultaneously used in theANN model to map the complex relationship between pro-cess conditions and quality indexes of LPDC. Moreover, theorthogonal array design and numerical simulation technol-ogy are applied to obtain the training data for ANN systeminstead of carrying out a real experiment. The main advan-tage of the proposed system over previous works is that itprovides three outputs, namely defect existence, filling time,and maximum temperature difference from a single config-uration with better prediction accuracy.Fig. 1 Schematic diagram ofLPDC machineInt J Adv Manuf Technol2 LPDC experimentIn this paper, an L-shape thin-walled casting of 300 mm inlength, 100 mm in width, and 1.5 mm in thickness wasstudied, shown in Fig. 2. The experimental materials,A356 alloy, were melted in an electrically heated furnaceusing a graphite crucible. Its chemical composition is shownin Table 1. The sketch map of the model section is shown inFig. 3. It can be seen that the cooling channels and gatingsystem were located in the bottom of the die. And consid-ering the poor filling ability of the thin-walled casting andentrapment of gas in the casting filling die cavity, someessential vents are designed at the interface of top die andbottom die. For experimental need, a small type of LPDCmachine is selected as the experimental equipment. TheLPDC process parameters are obtained by combiningANN/GA method. The procedure of combining ANN/GAoptimization is shown in Fig. 4. It involves a selection ofLPDC process parameters and quality indexes, preparationof training samples, creation of predictive ANN models, andoptimization of process parameters via a genetic algorithm.3 Selection of LPDC process parametersIn LPDC process, many process parameters are very impor-tant to improve the casting quality, such as filling pressure,filling speed, holding pressure, pressure holding time, cast-ing temperature, die temperature, etc. As to the thin-walledcasting, the influence of these process parameters becomesmore significant on the defect formation (such as cold shutand short fills) due to its poor filling ability during moltenmetal filling. For instance, if the casting and die temperatureare too low, the casting is easier to form the cold shut andshort fills, with the casting filling ability decreasing. How-ever, too high temperature would shorten the die life. Ingeneral, casting temperature is selected between 680 and750C. For the die, the temperature is assumed to be at auniform temperature of 450550C 1517. Another cru-cial part of the LPDC operation is the control of the exertingpressure in the crucible to ensure a laminar flow of moltenmetal through the feed tube into the die. If die filling is notappropriately controlled, the casting will suffer from fill-related defects such as short fills or gas porosity. In actualoperations, filling speed is controlled by the pressure.Therefore, in the present work, inlet melt temperature,initial mold temperature, and exerting pressure velocitywere considered as ANN inputs, and defect prediction,filling time, and maximum temperature difference in thecasting as ANN outputs.4 Neural network modelsAn ANN model is referred to as a type of computationalmodels that consists of hidden-layer neurons connectedbetween the input and output neurons. The connectionsbetween the neurons are described by weights which are tobe determined through training. The nonlinear hyperbolicfunctions are usually used as the activation functions toincrease the modeling flexibility. In this work, a learningvector quantization (LVQ) ANN model was applied to pre-dict defect existence in the casting. Defect existence inLPDC products constitutes an important criterion in charac-terizing the manufacturing process as successful or not. TheANN models with back-propagation (BP) algorithm wereused to map the relationship between filling time, maximumtemperature difference, and process parameters. BP networkFig. 2 3-D appearance of castingTable 1 Chemical compositions of A356 alloy used in the presentstudyElementSiMgCuMnSrTiOthersAlContent(%)0.030.10.15Bal.Fig. 3 The model section sketch mapInt J Adv Manuf Technolis a typical ANN that has been widely used in many researchfields 18, 19. Implementation was carried out in the appli-cation toolbox of MatLAB. Table 2 shows the influence ofthe number of neurons in BP network.4.1 Defect prediction through LVQ ANN implementationOwing to its predominance in classifying problems, theLVQ ANN model in this work was used to predict defectexistence in the casting 4. This is a two-class problem,where the first, denoted with “1” in Table 3, implies perfectfilling, and the second, denoted with “2”, implies a defect inthe casting.Using a LVQ ANN, modeling needs to determine thefollowing:&the minimum and maximum input values&the number of neurons in the competitive layer&the percentage of class participation in the trainingsubset&the training rateMinimum and maximum input values and percentage ofclass participation in the training subset can be calculatedfrom the training samples. Neurons in the competitive layerand training rate practically represent the ANN architectureand training algorithm, respectively. Four competitive layerneurons and a training rate of 0.001 are used in the LVQANN model, where they are determined by train trails. Inaddition, in order to speed up the training phase and enhancetraining algorithm behavior, the values of exerting pressurevelocity are multiplied by 10,000.4.2 Prediction of filling time and maximum temperaturedifference through BP ANN implementationThe ANN model was trained using the BP algorithm to mapthe relationship between filling time, maximum temperaturedifference, and process parameters. The ANN architectureadopted in the model is shown in Fig. 5. It consists of threelayers: an input layer, a hidden layer, and an output layer.The input and output layers have three and two neurons,respectively. Neurons in input layer correspond to melttemperature, mold temperature, and exerting pressure veloc-ity. Output layer corresponds to filling time and maximumtemperature difference. However, the determination of thenumber of neurons in hidden layer is usually quite compli-cated. If the architecture of ANN model is too simple, thetrained network might not have sufficient ability to learn theprocess correctly. Conversely, if the architecture is too com-plex, it may not converge during training or the trained datamay be overfitted. In general, the number of neurons isdetermined according to the experience. In this study, thehidden layer is determined to have seven neurons by thetrail-and-error method. Based on this method, the influenceof the various numbers of neurons on the training andtesting error has been analyzed, and the result is shown inTable 2. It can be well known that the training and testingresults are the best when the number of neurons is seven.During the ANN training, the smooth sigmoid function isadopted as the transfer function in ANN model as follows:f vj 11 e?vj1where vjis the state variable of the weights, which imply theconnection strength between the neurons. The weightedsignals are summed up in vjand transformed into the outputsignal through the transfer function. Moreover, it is quitesignificant to conduct the input and the output data unifica-tion before training for effectively training the ANN model.Therefore, the input and output data in the present work areFig. 4 Flow chart of combining ANN/GA optimizationTable 2 The influence of the number of neurons in BP networkNumber56789Trainingerror0.19910.19200.18390.18260.1879Testingerror0.47411.03260.36520.61940.5110TrainingepochNo convergence69344123Int J Adv Manuf Technolnormalized before training ANN model by using the follow-ing formula:cici? cimincimax? cimin2whereximinandximaxare the minimal and maximal values ofthe ith input valuexi, respectively, in the sample data set.xiisthe normalized value of parameter x ranging between 0 and1. The outputs can be normalized in exactly the same way.5 Optimization of process parameters via a geneticalgorithmA genetic algorithm is a stochastic optimization procedure,which can solve complex problems by imitating Darwinstheory of evolution on a computer 2022. The conceptbehind the creation of genetic algorithms is the global opti-mization of an objective function in a complex multimodalsearch space. Solution of the optimization problem withgenetic algorithm begins with a set of chromosomes thatare randomly selected. The entire set of these chromosomesconstitutes a population. The chromosomes evolve duringseveral iterations or generations. New generations (off-spring) are generated using the crossover and mutationtechnique. Crossover involves splitting two chromosomesand then combining one-half of each chromosome with theother pair. Mutation involves flipping a single bit of achromosome. The chromosomes are then evaluated using acertain fitness criteria, and the best ones are kept while theothers are discarded. This process is repeated until onechromosome has the best fitness. That chromosome is takenas the best solution of the problem.The optimized objective function based on the geneticalgorithm is formulated according to the simulation functionobtained by ANN in the previous section:f X 10;000 ? netlvqX ? 1 netbpX3where X is the process parameter values, netlvq(X) is theoutput value of the LVQ ANN model for defect existence, andnetbq(X) is the output value of the BPANN model for fillingtime and maximum temperature difference. The problem asdefined previously is optimized by floating point-coded GA.The population size is 30, and maximum number of genera-tionsis80.Thecrossoverrateandthemutationrateare0.8and0.05, respectively.6 Results and discussionsThe primary objective of the present research is to study thepossibility of modeling and predicting the quality of LPDCparts and optimizing the process conditions so as to improvethe part quality by using the combining of ANN/GA meth-od. A commercial finite-element package, ProCAST, wasused to calculate and obtain the training samples instead ofcarrying out a real experiment for the sake of cost saving.The other advantage of finite-element method is that thetime required to train a network is much less than that withreal experiments because there is no noise existing in thecomputation data compared to the experimental data 9.Orthogonal array design of three parameters with five levelswas employed to obtain the training samples. The orthogo-nal array is a procedure to systematically organize experi-ment runs in order to improve processes in the mostTable 3 Comparison of simulation results to the ANN prediction model (perfect filling is denoted by 1 and defect existence, by 2)Melt temperature(C)Mold temperature(C)Exerting pressure velocity(MPa/s)PerfectfillingFilling time(s)Temperaturedifference (C)ANNpredictions7264930.0412.9873.5Simulationresults7264930.0413.3906.0Absolute error0.4032.5Relative error11.9 %41.7 %Fig. 5 Neural network architecture used in this studyInt J Adv Manuf Technoleffective way, which results in conducting a minimum num-ber of experiments without losing significant information23. The selected parameters for the LPDC process are asfollows:&670Cmelt temperature730C;&350Cmold temperature550C; and&0.01 MPa/sexerting pressure velocity0.05 MPa/s.Based on orthogonal array design, a total of 25 sets ofexperimental samples were generated. Among these sam-ples, 20 samples were used to train the ANN as shown inFigs. 6 and 7. Figure 6 shows the training error versusepochs of LVQ ANN. Given the sizes of training and testingsubsets, the performance achieved is considered to be ade-quate. Figure 7 shows the training error during training ofBPANN. The mean square error of all 20 training samples is0.00099426. The remaining five samples were then used totest the performance of the ANN. ANN prediction is also ingood agreement with the simulation results. This indicatesthat the ANN has a good performance, and it can accuratelymap the relationship between process conditions and qualityindexes of the casting.The common LPDC process parameters include pouringtemperature, die temperature, filling pressure, etc. In thisstudy, by applying the combining ANN/GA method basedon ProCAST, the optimized parameters are obtained throughanalyzing the filling state of casting and the major influencefactors of the casting quality. Figure 8 shows the evolutionof the generations based on a genetic algorithm. It is obviousthat convergence is achieved approximately in the 30thgeneration. The optimized process conditions are as thefollowing: the melt temperature is 726C, the mold temper-ature is 493C, and exerting pressure velocity is 0.04 MPa/s.Accordingly, as ANN outputs, the filling is perfect, and thefilling time and maximum temperature difference in thecasting is 2.987 s and 3.5C, respectively, as shown inTable 3. Table 3 shows the comparison of numerical calcu-lated results to the ANN prediction model. The numericalcalculated data are obtained by applying the optimizedprocess parameters as the initial condition of numericalsimulation. Then, the evolution of filling state at differentfilling time during LPDC and the corresponding temperaturefield can be calculated. Through analyzing these results, thefilling state, the filling time, and the maximum temperatureFig. 6 Training error versusepochs for the LVQ ANNFig. 8 Objective function values for the best chromosome in eachgenerationFig. 7 Training error versus epochs for the BP networkInt J Adv Manuf Technoldifference can be obtained, as shown in Table3. Itcan beseenin Table 3 that the relative error is a little high, but absoluteerrors offilling time and maximum temperature difference arelow, at 0.403 and 2.5, respectively. During the ANN training,the training samples is obtained by the commercial finite-element software, ProCAST, instead of carrying out a realexperiment for the sake of cost saving. This may be a majorreason why the relative errors are so high. However, the lowabsolute errors demonstrate enough the accuracy of using theANN modeling and GA searching techniques to model andoptimize LPDC process.Figure 9 shows the result of LPDC experiment. It illus-trates that a sound casting of 300 mm in length, 100 mm inwidth, and 1.5 mm in thickness is successfully preparedusing the optimized LPDC process parameters. It can beseen that the surface of the casting is smooth, and noobvious defects such as shrinkage, gas porosity, distortion,and crack are found, which verify further the feasibility ofusing the ANN modeling and GA searching techniques tomodel and optimize LPDC process.7 ConclusionsThe LPDC process parameters of A356 aluminum thin-walled component with permanent mold are optimized us-ing the combining ANN/GA method. The optimized processparameters are in the following: melt temperature 726C,die temperature 493C, and exerting pressure velocity0.04 MPa/s. By applying the parameters, a thin-walledcomponent of 300 mm in length, 100 mm in width, and1.5 mm in thickness has been successfully prepared. Inaddition, no obvious casting defects such as shrinkage, gasporosity, distortion, and crack can be found in the compo-nent. The results indicate that the intelligent system pro-posed in this paper is an effective tool for mapping thecomplex relationship between process parameters and partquality indexes and optimizing the LPDC process parame-ters. The proposed method also shows the great potential incomplicated industrial applications.AcknowledgmentsThe research supports from the Open ResearchFund Program of the State Key Laboratory of Advanced Design andManufacturing for Vehicle Body (No.31115009), the Initial ScientificResearch foundation of Central South University of Forestry & Tech-nology for the introduction of talents (No.104-0206), and the YouthScientific Research Foundation of Central South University of Forestry& Technology are gratefully acknowledged.References1. Fu PH, Luo AA, Jiang HY, Peng LM (2008) Low-pressure diecasting of magnesium alloy AM50: response to process parame-ters. J Mater Process Technol 205:2242342. Cleary PW (2010) Extension of SPH to predict feeding, freezingand defect creation in low pressure die casting. Appl Math Model34:318932013. Zhang LQ, Li LX, Zhu BW (2009) Simulation study on the LPDCprocess for thin-walled aluminum alloy casting. Mater ManufProcess 24:134913534. Zhang B, Maijer DM, Cockcroft SL (2007) Development of a 3-Dthermal model of the low-pressure die-cast (LPDC) process ofA356 aluminum alloy wheels. Mat Sci Eng A 464:2953055. Wu SP, Li CY, Guo JJ (2006) Numerical simulation and experi-mental investigation of two filling methods in vertical centrifugalcasting. T Nonferr Metal Soc 16:103510406. Vijayaram TR, Sulaiman S, Hamouda AMS (2006) Numericalsimulation of casting solidification in permanent metallic molds.J Mater Process Technol 178:29337. Dobrzanski LA, Krupinski M, Sokolowski JH (2005) Computeraided classification of flaws occurred during casting of aluminum.J Mater Process Technol 167:4564628. Shi HZ, Gao YH, Wang XC (2010) Optimization of injectionmolding process parameters using integrated artificial neural net-work model and expected improvement function method. Int JAdv Manuf Technol 48:9559629. Krimpenis A, Benardos PG, Vosn
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