附录
The Optimal Design of a Cooling System for a Die-Casting Die With a Free Form Surface
Abstract
This study is on the finite element and abductive networkmethod application to die-casting dies with free-form surfaces.The study aims to find the optimal cooling system parametersand decrease in deformation of a die-casting die. In order toavoid the numerous influencing factors, the free-form surfaceof a die-casting die is created as a non-linear Eq. of apolynomial function. The parameters of the cooling system,including the channel space and channel diameter, are adjustedaccording to the non-linear Eq.. An abductive network has been built for modelling the diecastingcooling parameters. The abductive network is composedof a number of functional nodes. Once the cooling systemparameters are given, this network can predict the deformationof the die-casting accurately. A simulated annealing optimizationalgorithm with a performance index is then applied tothe neural network for searching for the optimal cooling systemparameters and to obtain a satisfactory result.
Keywords ：Die-casting die；Free-form ；Neural network；Simulatedannealing
1. Introduction
The typical, traditional die-casting process includes high-pressurefilling, cooling, solidification and ejection stages. The coolingstage is of great importance because it significantly affectsboth the productivity and the quality of the die-cast part. It iswell known that about 80% of the cycle time of die-castingis spent in cooling the hot melt sufficiently so that the castpart can be ejected without warp. The design of a successfuldie can be considerably affected by perfect filling, whichreduces the cooling time, reduces warp and in turn increasesthe quality of the part. The main aim of the
cooling processis to maintain a uniform temperature of the filling and cooling cycle. Accordingly, there are at least two important conceptsfor the designer when considering the cooling system and inestablishing cooling processing conditions:
(1) achieving uniformtemperature and.
(2) mini-mising the cycle time.
To achieve these two aims, the designer may need an optimalcomputer-aided design system to achieve a rapid and uniformcooling system. The design of an optimal system needs analysisof 3D heat transfer during the filling and cooling processes.The thermal analysis tool should predict the temperature gradientand deformation of the die-body.
Generally speaking, traditional die design still depends onexperience, due to the lack of analytic ability in mould flowand heat transfer, so the designer is unable to evaluate andhandle the deformation resulting from material and thermalexpansion and shrinkage of the die. The parameters of differentcooling systems can cause large temperature gradients, anddifferent deformations.
Although FEM software is capable of analysing the fillingflowand coolingconditions of pressure-injected metal and theheat stress, heat strain and temperature distribution conditionsof a die-casting die under various cooling systems, the establishmentof an analytic model is very difficult, especiallyfor 3D free-form geometry. Besides understanding therequirements of multi-cavity dies, and the metal flow andsolidification process, the designer should be fullyacquaintanted with the basic finite element software. Integrationcan be achieved and can save a lot of money and time onlyif a complete understanding of the process of die manufacturingis available and eliminate the annoyance caused by movingof personnel.
Initially, consider the design of the vent gate and overflowgate in the process of injection and flow to fill the die cavityduring cold room die-casting as investigated by simulation byGarber [2]. When metal casting using a plunger into a cavity,he considered the change occurring in the metal, and thereplacement of the air in the cavity by molten metal. Subsequently,Garber [3,4] showed that too large or too small aplunger speed will affect the cast quality. Groenevelt andKaiser [5] studied and discussed the influence of the speed ofinjection of the molten metal into the cavity, and flow distanceand cavity temperature on the quality of product after casting.According to the experiment, the distance of molten metalflow increases linearly as the die-casting speed increases, asdoes the die temperature. The range of temperature is approximately121–288ºC. Other studies [6,7] proposed the importanceof initial temperature (pre-heat temperature) of the die, andpointed out that too low a pre-heat
temperature would tend tocause failure in filling up the cavity inside the die by thedie-casting liquid, and result in formation failure. A highertemperature may increase the cooling time and reduce productivity.Truelove [8] used a cooling system to control theoverall temperature of the die, in order to obtain an optimalheat transmission characteristic, and reduce the occurrence ofhard pointphenomena in the cast piece, thereby improving thequality of the piece.
Jong et al. [9] developed a mathematical Eq. for the flowand solidification of molten metal during high-pressure diecasting,in order to analyse the temperature conditions andsolidification strain of die-cast components in the cavity.
Kenichiro et al. [10] used a finite element method to analyseand design the die; the result was not only improved accuracy,but the factors to be considered are increased too, and thepressure of die-casting, the speed of molten liquid flow, viscosity,and the mechanical nature of the material changed withtemperature and phase.
This study uses CAD\CAE error software for a systemicdesign process of a die, in order to minimise human error indie design [11–13]. It uses the CAD software to create a freeformmodel, and the finite element software to analyse theconditions of die-cast processing. It simulates the temperaturedistribution of the die-body and deformation after casting undervarious parameters (cooling-line distance R, channel centerdistance L, channel diameter D), as shown in Fig. 1. Ituses an abductive network to establish the relationship of theFig. 1. Relationship between cooling channel and free-form die.deformation and the cooling system parameters model. Basedon the abductive modelling technique, it is able to representthe complicated and uncertain relationships between the inputand the output variables.
Once the abductive network has constructed the relationshipsof the input and output die-casting variables, an appropriateoptimisation algorithm with a performance index is able tosearch for the optimal casting parameters. In this paper, asound optimisation method of simulated annealing [14] isadopted. The simulated annealing algorithm is a simulation ofthe annealing process for minimising the performance index.It has been successfully applied to die-casting die design [15],etc. The basic theory can be widely applied.
2. Die-Casting Flow Theory
In the die-casting process about 80% of the time is spent incooling cycle. The deformation of the die-casting die is causedby the non-uniform temperature distribution of the castingprocessing, which affects the quality of casting part. Thedesigner of the
cooling system has to think about the totalcycle and compute the deformation at every stage of the diecastingprocess. The die-casting process analysis includes threemajor stages: (1) filling stage; (2) cooling and solidificationstage; (3) ejection, i.e. stress residue stage. Firstly, the castingprocessing has to ensure that the melt fills the cavity. Themajor die-casting flow equations are divided into five stages.In the filling stage, the mould cavity fills with molten plasticfluid under high pressure.
3. Create the Relationship BetweenCooling System and Die-Casting DieDeformation
The die-casting pressure for high-pressure injection in Al alloydie-casting is approximately 30–150 Mpa; generally the injectionpressure varies with time. To examine the influence ofthe processing pressure, Dochler and Borton used a cathoderay oscilloscope and camera to analyse the pressure variationin the die-casting process, i.e. high-pressure filling, coolingand ejection.
Design of a die-casting die involves the design of a runner,cavity balance, analysis of life span of the die (residue stress),cooling system, etc. The purpose of this study is to find theoptimal cooling system of a die-casting die for casting anyworkpiece. The assumed casting conditions are: die-castingpressure 120 Mpa, casting speed 2.8 m/s, die-casting cyclingtime 20 s/cycle, pre-heat die temperature 150ºC, injectiontemperature 700ºC. The basic assumption for the flow in thecavity is: (1) 3D flow; (2) Newton fluid;
(3) laminar flow; (4)incompressible fluid; (5) zero speed of fluid in the vertical andhorizontal wall directions.
According to the different cooling parameters in the closedsection of the part surface, there are 15 sets of data to simulatedie-casting processing. The basicconfiguration is a free-formsurface according to mould flow analysis of the 3D flow model.The surface temperature is set at the pre-heat temperature(150ºC) of the die, while the temperature of the molten metalis 700ºC. The different cooling parameters of the coolingsystem produce a total of 15 sets, as shown in Table 1.
The method for heat transfer and deformation analysis isidentical, the set injection temperatures are all 700ºC, so it isonly necessary to maintain a temperature of 700ºC at theinjection gate. The mould temperature is 150ºC, cooling watertemperature is 40ºC, and other temperatures are obtained usingfinite element analysis for the temperature at the instant offilling up, as shown in Figs 2 and 3.
Fig. 2. Temperature gradient.Fig. 3. Deformation distribution.
The deformation analysis uses a solid model analysed by3D flow and non-linear conditions, for finding its temperatureat the boundary condition required for performing the analysis.The configured temperature of each node is input as the initialcondition. Making the injection gate a boundary constraintcondition serves as a 3D thermal strain condition. The mechanicalproperties change with the accompanying the change oftemperature. It is obtained from an analysis of the non-linearstable stage. The results of the cavity flow analysis discussedabove performed by the strain analysis stage are shown inTable 1.
The parameters of the die-casting process are complicatedand hard to control. There is no definite determination in therelation of each parameter and target function. It is differentwhen using experimental and statistical methods for the conditionof the actual die-casting. There is much restriction inthe application. This study employs a neural network to learnand train the network for the deformation of the die-castingdie, and the deformation of the die in the die-casting process,and uses this neural network to perform further analysis oneach parameter.
Similarly, the establishment of the relation of the inputparameter (cooling system parameters: R, cooling line distance;D, channel diameter; L, channel-centre distance) and outputparameter (deformation) during the die-casting process is shownin the Appendix. To build a complete abductive network, thefirst requirement is to train the database. The information givenby the input and output data must be sufficient. Thus thetraining factor (cooling system parameters) for the abductivenetwork training should be good and make defect-free product.Table 1 illustrates the cooling system parameters and themaximum deformation of the die-casting die obtained from 3Dmould-flow analysis.
Based on the development of the die-casting model, threelayerabductive networks,
which are composed of coolingsystem parameters and the casting results (deformation),
aresynthesised automatically. The process is capable of predictingaccurately the die-casting die deformation under various controlparameters. All polynomial equations used in this network arelisted in the Appendix (PSE = 5.43 X 10_7).
Table 2 compares the error predicted by the abductive modeland the simulation case. The simulation case is excluded fromthe 20 sets of simulation cases for establishing the model. Thisset of data is used to test the appropriateness of the modelestablished above. We can see from Table 2 that the error isapproximately 2%, which shows that the model establishedabove is suitable for this purpose.
带自由面压铸模具冷却系统的最优设计
摘要
这个研究是关于有限元法和运用到带自由表面压铸模具的推断网络法。研究的目的是发现最佳的冷却系统参数和减少压铸模具的变形。为了避免众多的影响因素，压铸模具的自由表面采用等价的多项式函数非线性的结构。根据非线性函数，包括空间开槽和孔道直径的冷却系统参数被适当调整了。一个模仿压铸冷却参数的推断网络系统已经被构造出来。这个推断网络包括许多函数节。一旦这冷却系统的参数被给定，这个网络系统便可以精确地预测压铸件的变形量。一个带有性能指标的模拟退火最佳化算法然后被应用到神经网络，目的是探索最优的冷却系统参数和获得一个满意效果。
关键词：压铸模具；自由形态的；神经网络；模拟退火
1. 引言
典型的传统压力铸造法包括高气压的充填，冷却，凝固和顶出阶段。冷却阶段具有非常的重要性，因为它能较大地影响生产能力继而影响压铸件的数量。众所周知压模铸件大约有八成的循环时间被花费于对热熔进行充分地冷却，目的是使铸件可以被没有翘曲的顶出。一个成功的冷却系统的设计可以显著地减小各种因数影响，它可以减少冷却时间、减少翘曲和相应地增加部件的质量。冷却过程的主要目的是维持充填和冷却的均匀温度。
相应地, 当考虑冷却系统和建立冷却过程条件时至少有二个重要的准则供设计师参考：1、达到均匀温度；2、缩小循环时间。要实现这两个目标，设计师可能需要一个最佳的计算机辅助设计系统来完成一个快速和均匀的冷却体系。在充填和冷却过程期间，最优系统设计需要进行热传递分析。这个热分析工具将预测压铸件的温度梯度和变形。
一般而言，传统的压模设计仍然依靠经验，由于缺乏铸造流动和热传递的有利分析，设计师不能评价和控制由于压铸材料、膨胀和收缩引起的变形。不同冷却系统参数可以引起大的温度梯度和不同的变形。虽然有限元法软件能够分析一个在不同的冷却系统的压铸模具的注射金属压力和热应力、热膨胀和温度分布情况的填充流动和冷却条件，分析模型的建立是很难的，特别是三维自由形态的几
何学。除了了解多腔模、金属流动和固化过程非常必要，设计师还应该完全地掌握基本的有限元软件。只要完全的了解压出板制造是能有效避免人员移动麻烦的过程，引用软件就可以达到和节省大量金钱和时间。
首先，对冷室压模铸件注射和压铸型腔填充排气孔和溢流口进行设计。当金属铸件使用一个活塞进入到一个腔内，他会考虑金属发生的变化和型腔内的空气被熔化的金属置换。随后Garber 将会显示太大的或太小的活塞速度可能影响铸件的质量Groenevelt 和Kaiser 研讨了注射入型腔内熔融金属的速度的影响、流经距离和腔内产品铸件上表面的温度。根据压铸件不同的浇注初始温度实验可得太低的预先加热温度可能引起铸塑料液堵塞流道，从而发生故障。但较高的温度可能增加冷却时间和减少生产能力。Truelove 使用一个冷却系统控制压铸过程的整个温度，目的是获得一最佳的传热特征，减少压铸件的热节问题的发生，从而改善铸件的质量。
Jong 和一些人发明了一个用于熔融金属在高气压压铸期间流动和凝固数学方程，以便分析型腔内压铸元件的温度情况和冷却应力。kenichiro 和一些人使用有限元法分析和设计压铸模；结果不仅改善精度，但被考虑的因素还有许多，如压模铸件的压力、浇铸的液体的流动速度、粘性和材料随温度和相变化的机械特性。使用CAD\CAE故障软件对压出板的系统设计过程的研究，目的是减少压模设计过程中的人为误差。它使用CAD 软件创造一个形式自由的模型、使用有限元软件分析压铸过程的情况。它模拟压铸件和在不同参数（冷却线长度R 、开槽中心距L 、孔道直径D ）下的铸件变形的温度分布，如图1所示。它使用一个推断系统建立了关系图1，冷却通道和自由形态压出板之间的关系，变形和冷却系统参数模型之间的关系。根据推断模拟方法，它能描绘输入和输出变量之间的复杂的和不确定的关系。
一旦推断系统构造出输入和输出压力铸造参数的关系，一个合理的带有性能指标的优选法能探索出最佳的铸造参数。在这里，一个模拟退火的测深优化方法被采用。这个模拟退火算法是通过模拟退火过程来减少性能指标。它已经被成功地应用到压铸模具设计中等。这个基础理论可以被广泛地应用。
2. 压铸流动理论
在压铸过程中大约80%的时间花费在冷却过程中。压模铸件的变形是由于浇铸过程中不均匀的温度分布引起的，它影响铸件的质量。冷却系统的设计者不得不考虑整体循环和计算压铸过程中不同阶段的变形。铸造过程分析包括三主要阶段：第一，浇铸过程必须保证浇铸充满型腔。主要的压模铸件流动方程被分成五阶段。在填充阶段，模槽在高压下充满浇铸的塑性流体。
3. 建立冷却系统和压铸模具变形之间的关系
高气压注射铝合金压铸的铸造压力大约是30–150 Mpa；通常注射压力随时间而变。为了研究铸造过程压力的影响，Dochler 和Borton 使用阴极射线示波器和照相机分析铸造过程中的气压变化，那就是说高压充填、冷却和顶出。压铸模具的设计包括流道、均匀的型腔布置、分析压铸模具的寿命（残余应力）、冷却系统等等。
这个研究结果的目的是找到适合铸造任何工件的压铸模具的最佳冷却系统。假定铸造条件是：压铸压力120 Mpa、浇注速度2.8 m / s、压铸循环时间20s 每次、预先加热温度150oC 、注射温度700oC 。对流入型腔的液体的基本假定：1、三维流动；2、牛顿流体；3、层流；4、不可压缩流体；5、流体在垂直的和水平方向无流速差别。根据在零件面的闭合截面不同的冷却参数，有15个设计数据用于模拟压铸过程。根据三维流动模型的模型流动分析，基本布局是一个自由形态的表面。压铸模具的表面温度被预先加热到一定温度(150度) ，熔融金属的温度被控制在700度。注射口的温度特别需要维持在700度。模具的温度是150度、冷却水温度是40度、其它的温度在填充时需要即时使用有限元分析控制，如图2和3所示。
因为获得其临界温度条件需进行分析，变形分析使用三维流动和非线性条件对实体模型进行分析。各节点的配置温度作为初始条件被输入。使注射口的边界约束。条件充当三维热应变条件。机械性能随温度变化而变。它是从非线性稳定阶段分析中获得。上面讨论的型腔流动分析结果用应变分析阶段执行显示在表格1上。铸造过程中的参数是很复杂的和难以控制的。在各参数和指标函数之间的关系很难明确决定。用于实际压铸条件的实验方法和统计法是不同的。在实际运用中有很多地限制。研究使用一个神经网络去学习和培养一个系统，它用于压铸件的变形和铸造过程中的变形，使用这个神经网络完成各参数的进一步地分析。
图2、温度梯度图3 变形分布
同样地，输入参数关系的建立（冷却系统参数： R, 冷却线距离: D,孔道直径: L,开槽中心距）和在铸造过程期间输出参数（变形）被显示在附录上。建设一个完整的推断系统，第一个必要条件是建立数据库。由输入和输出产生的信息必须足够的多。因而推断网络训练的导流因素（冷却系统参数）应该完美和制造没有缺点的产品。表格1阐明了从三维模型流动分析获得的压铸件的冷却系统参数和极限变形。
根据压铸模型的发展，三层推断系统能自动地综合处理，它由冷却系统参数和铸件结果（变形）组成。不同的控制参数被用于这个系统，它能够预先模拟压铸模型在不同的控制参数下面的变形。全部的多项式方程被登记在附录（PSE =
5.43 X 10_7）。表格2比较这些出错预测的模型和模拟情况。这模拟情况是从因为建立这个模型进行压铸模拟试验而设置的20个装置中得到的这个数据集被用来检定这模型建立的合理性。我们看得见来源于表2的故障大约2% ，则可以得到建立这模型的目的。
附录
The Optimal Design of a Cooling System for a Die-Casting Die With a Free Form Surface
Abstract
This study is on the finite element and abductive networkmethod application to die-casting dies with free-form surfaces.The study aims to find the optimal cooling system parametersand decrease in deformation of a die-casting die. In order toavoid the numerous influencing factors, the free-form surfaceof a die-casting die is created as a non-linear Eq. of apolynomial function. The parameters of the cooling system,including the channel space and channel diameter, are adjustedaccording to the non-linear Eq.. An abductive network has been built for modelling the diecastingcooling parameters. The abductive network is composedof a number of functional nodes. Once the cooling systemparameters are given, this network can predict the deformationof the die-casting accurately. A simulated annealing optimizationalgorithm with a performance index is then applied tothe neural network for searching for the optimal cooling systemparameters and to obtain a satisfactory result.
Keywords ：Die-casting die；Free-form ；Neural network；Simulatedannealing
1. Introduction
The typical, traditional die-casting process includes high-pressurefilling, cooling, solidification and ejection stages. The coolingstage is of great importance because it significantly affectsboth the productivity and the quality of the die-cast part. It iswell known that about 80% of the cycle time of die-castingis spent in cooling the hot melt sufficiently so that the castpart can be ejected without warp. The design of a successfuldie can be considerably affected by perfect filling, whichreduces the cooling time, reduces warp and in turn increasesthe quality of the part. The main aim of the
cooling processis to maintain a uniform temperature of the filling and cooling cycle. Accordingly, there are at least two important conceptsfor the designer when considering the cooling system and inestablishing cooling processing conditions:
(1) achieving uniformtemperature and.
(2) mini-mising the cycle time.
To achieve these two aims, the designer may need an optimalcomputer-aided design system to achieve a rapid and uniformcooling system. The design of an optimal system needs analysisof 3D heat transfer during the filling and cooling processes.The thermal analysis tool should predict the temperature gradientand deformation of the die-body.
Generally speaking, traditional die design still depends onexperience, due to the lack of analytic ability in mould flowand heat transfer, so the designer is unable to evaluate andhandle the deformation resulting from material and thermalexpansion and shrinkage of the die. The parameters of differentcooling systems can cause large temperature gradients, anddifferent deformations.
Although FEM software is capable of analysing the fillingflowand coolingconditions of pressure-injected metal and theheat stress, heat strain and temperature distribution conditionsof a die-casting die under various cooling systems, the establishmentof an analytic model is very difficult, especiallyfor 3D free-form geometry. Besides understanding therequirements of multi-cavity dies, and the metal flow andsolidification process, the designer should be fullyacquaintanted with the basic finite element software. Integrationcan be achieved and can save a lot of money and time onlyif a complete understanding of the process of die manufacturingis available and eliminate the annoyance caused by movingof personnel.
Initially, consider the design of the vent gate and overflowgate in the process of injection and flow to fill the die cavityduring cold room die-casting as investigated by simulation byGarber [2]. When metal casting using a plunger into a cavity,he considered the change occurring in the metal, and thereplacement of the air in the cavity by molten metal. Subsequently,Garber [3,4] showed that too large or too small aplunger speed will affect the cast quality. Groenevelt andKaiser [5] studied and discussed the influence of the speed ofinjection of the molten metal into the cavity, and flow distanceand cavity temperature on the quality of product after casting.According to the experiment, the distance of molten metalflow increases linearly as the die-casting speed increases, asdoes the die temperature. The range of temperature is approximately121–288ºC. Other studies [6,7] proposed the importanceof initial temperature (pre-heat temperature) of the die, andpointed out that too low a pre-heat
temperature would tend tocause failure in filling up the cavity inside the die by thedie-casting liquid, and result in formation failure. A highertemperature may increase the cooling time and reduce productivity.Truelove [8] used a cooling system to control theoverall temperature of the die, in order to obtain an optimalheat transmission characteristic, and reduce the occurrence ofhard pointphenomena in the cast piece, thereby improving thequality of the piece.
Jong et al. [9] developed a mathematical Eq. for the flowand solidification of molten metal during high-pressure diecasting,in order to analyse the temperature conditions andsolidification strain of die-cast components in the cavity.
Kenichiro et al. [10] used a finite element method to analyseand design the die; the result was not only improved accuracy,but the factors to be considered are increased too, and thepressure of die-casting, the speed of molten liquid flow, viscosity,and the mechanical nature of the material changed withtemperature and phase.
This study uses CAD\CAE error software for a systemicdesign process of a die, in order to minimise human error indie design [11–13]. It uses the CAD software to create a freeformmodel, and the finite element software to analyse theconditions of die-cast processing. It simulates the temperaturedistribution of the die-body and deformation after casting undervarious parameters (cooling-line distance R, channel centerdistance L, channel diameter D), as shown in Fig. 1. Ituses an abductive network to establish the relationship of theFig. 1. Relationship between cooling channel and free-form die.deformation and the cooling system parameters model. Basedon the abductive modelling technique, it is able to representthe complicated and uncertain relationships between the inputand the output variables.
Once the abductive network has constructed the relationshipsof the input and output die-casting variables, an appropriateoptimisation algorithm with a performance index is able tosearch for the optimal casting parameters. In this paper, asound optimisation method of simulated annealing [14] isadopted. The simulated annealing algorithm is a simulation ofthe annealing process for minimising the performance index.It has been successfully applied to die-casting die design [15],etc. The basic theory can be widely applied.
2. Die-Casting Flow Theory
In the die-casting process about 80% of the time is spent incooling cycle. The deformation of the die-casting die is causedby the non-uniform temperature distribution of the castingprocessing, which affects the quality of casting part. Thedesigner of the
cooling system has to think about the totalcycle and compute the deformation at every stage of the diecastingprocess. The die-casting process analysis includes threemajor stages: (1) filling stage; (2) cooling and solidificationstage; (3) ejection, i.e. stress residue stage. Firstly, the castingprocessing has to ensure that the melt fills the cavity. Themajor die-casting flow equations are divided into five stages.In the filling stage, the mould cavity fills with molten plasticfluid under high pressure.
3. Create the Relationship BetweenCooling System and Die-Casting DieDeformation
The die-casting pressure for high-pressure injection in Al alloydie-casting is approximately 30–150 Mpa; generally the injectionpressure varies with time. To examine the influence ofthe processing pressure, Dochler and Borton used a cathoderay oscilloscope and camera to analyse the pressure variationin the die-casting process, i.e. high-pressure filling, coolingand ejection.
Design of a die-casting die involves the design of a runner,cavity balance, analysis of life span of the die (residue stress),cooling system, etc. The purpose of this study is to find theoptimal cooling system of a die-casting die for casting anyworkpiece. The assumed casting conditions are: die-castingpressure 120 Mpa, casting speed 2.8 m/s, die-casting cyclingtime 20 s/cycle, pre-heat die temperature 150ºC, injectiontemperature 700ºC. The basic assumption for the flow in thecavity is: (1) 3D flow; (2) Newton fluid;
(3) laminar flow; (4)incompressible fluid; (5) zero speed of fluid in the vertical andhorizontal wall directions.
According to the different cooling parameters in the closedsection of the part surface, there are 15 sets of data to simulatedie-casting processing. The basicconfiguration is a free-formsurface according to mould flow analysis of the 3D flow model.The surface temperature is set at the pre-heat temperature(150ºC) of the die, while the temperature of the molten metalis 700ºC. The different cooling parameters of the coolingsystem produce a total of 15 sets, as shown in Table 1.
The method for heat transfer and deformation analysis isidentical, the set injection temperatures are all 700ºC, so it isonly necessary to maintain a temperature of 700ºC at theinjection gate. The mould temperature is 150ºC, cooling watertemperature is 40ºC, and other temperatures are obtained usingfinite element analysis for the temperature at the instant offilling up, as shown in Figs 2 and 3.
Fig. 2. Temperature gradient.Fig. 3. Deformation distribution.
The deformation analysis uses a solid model analysed by3D flow and non-linear conditions, for finding its temperatureat the boundary condition required for performing the analysis.The configured temperature of each node is input as the initialcondition. Making the injection gate a boundary constraintcondition serves as a 3D thermal strain condition. The mechanicalproperties change with the accompanying the change oftemperature. It is obtained from an analysis of the non-linearstable stage. The results of the cavity flow analysis discussedabove performed by the strain analysis stage are shown inTable 1.
The parameters of the die-casting process are complicatedand hard to control. There is no definite determination in therelation of each parameter and target function. It is differentwhen using experimental and statistical methods for the conditionof the actual die-casting. There is much restriction inthe application. This study employs a neural network to learnand train the network for the deformation of the die-castingdie, and the deformation of the die in the die-casting process,and uses this neural network to perform further analysis oneach parameter.
Similarly, the establishment of the relation of the inputparameter (cooling system parameters: R, cooling line distance;D, channel diameter; L, channel-centre distance) and outputparameter (deformation) during the die-casting process is shownin the Appendix. To build a complete abductive network, thefirst requirement is to train the database. The information givenby the input and output data must be sufficient. Thus thetraining factor (cooling system parameters) for the abductivenetwork training should be good and make defect-free product.Table 1 illustrates the cooling system parameters and themaximum deformation of the die-casting die obtained from 3Dmould-flow analysis.
Based on the development of the die-casting model, threelayerabductive networks,
which are composed of coolingsystem parameters and the casting results (deformation),
aresynthesised automatically. The process is capable of predictingaccurately the die-casting die deformation under various controlparameters. All polynomial equations used in this network arelisted in the Appendix (PSE = 5.43 X 10_7).
Table 2 compares the error predicted by the abductive modeland the simulation case. The simulation case is excluded fromthe 20 sets of simulation cases for establishing the model. Thisset of data is used to test the appropriateness of the modelestablished above. We can see from Table 2 that the error isapproximately 2%, which shows that the model establishedabove is suitable for this purpose.
带自由面压铸模具冷却系统的最优设计
摘要
这个研究是关于有限元法和运用到带自由表面压铸模具的推断网络法。研究的目的是发现最佳的冷却系统参数和减少压铸模具的变形。为了避免众多的影响因素，压铸模具的自由表面采用等价的多项式函数非线性的结构。根据非线性函数，包括空间开槽和孔道直径的冷却系统参数被适当调整了。一个模仿压铸冷却参数的推断网络系统已经被构造出来。这个推断网络包括许多函数节。一旦这冷却系统的参数被给定，这个网络系统便可以精确地预测压铸件的变形量。一个带有性能指标的模拟退火最佳化算法然后被应用到神经网络，目的是探索最优的冷却系统参数和获得一个满意效果。
关键词：压铸模具；自由形态的；神经网络；模拟退火
1. 引言
典型的传统压力铸造法包括高气压的充填，冷却，凝固和顶出阶段。冷却阶段具有非常的重要性，因为它能较大地影响生产能力继而影响压铸件的数量。众所周知压模铸件大约有八成的循环时间被花费于对热熔进行充分地冷却，目的是使铸件可以被没有翘曲的顶出。一个成功的冷却系统的设计可以显著地减小各种因数影响，它可以减少冷却时间、减少翘曲和相应地增加部件的质量。冷却过程的主要目的是维持充填和冷却的均匀温度。
相应地, 当考虑冷却系统和建立冷却过程条件时至少有二个重要的准则供设计师参考：1、达到均匀温度；2、缩小循环时间。要实现这两个目标，设计师可能需要一个最佳的计算机辅助设计系统来完成一个快速和均匀的冷却体系。在充填和冷却过程期间，最优系统设计需要进行热传递分析。这个热分析工具将预测压铸件的温度梯度和变形。
一般而言，传统的压模设计仍然依靠经验，由于缺乏铸造流动和热传递的有利分析，设计师不能评价和控制由于压铸材料、膨胀和收缩引起的变形。不同冷却系统参数可以引起大的温度梯度和不同的变形。虽然有限元法软件能够分析一个在不同的冷却系统的压铸模具的注射金属压力和热应力、热膨胀和温度分布情况的填充流动和冷却条件，分析模型的建立是很难的，特别是三维自由形态的几
何学。除了了解多腔模、金属流动和固化过程非常必要，设计师还应该完全地掌握基本的有限元软件。只要完全的了解压出板制造是能有效避免人员移动麻烦的过程，引用软件就可以达到和节省大量金钱和时间。
首先，对冷室压模铸件注射和压铸型腔填充排气孔和溢流口进行设计。当金属铸件使用一个活塞进入到一个腔内，他会考虑金属发生的变化和型腔内的空气被熔化的金属置换。随后Garber 将会显示太大的或太小的活塞速度可能影响铸件的质量Groenevelt 和Kaiser 研讨了注射入型腔内熔融金属的速度的影响、流经距离和腔内产品铸件上表面的温度。根据压铸件不同的浇注初始温度实验可得太低的预先加热温度可能引起铸塑料液堵塞流道，从而发生故障。但较高的温度可能增加冷却时间和减少生产能力。Truelove 使用一个冷却系统控制压铸过程的整个温度，目的是获得一最佳的传热特征，减少压铸件的热节问题的发生，从而改善铸件的质量。
Jong 和一些人发明了一个用于熔融金属在高气压压铸期间流动和凝固数学方程，以便分析型腔内压铸元件的温度情况和冷却应力。kenichiro 和一些人使用有限元法分析和设计压铸模；结果不仅改善精度，但被考虑的因素还有许多，如压模铸件的压力、浇铸的液体的流动速度、粘性和材料随温度和相变化的机械特性。使用CAD\CAE故障软件对压出板的系统设计过程的研究，目的是减少压模设计过程中的人为误差。它使用CAD 软件创造一个形式自由的模型、使用有限元软件分析压铸过程的情况。它模拟压铸件和在不同参数（冷却线长度R 、开槽中心距L 、孔道直径D ）下的铸件变形的温度分布，如图1所示。它使用一个推断系统建立了关系图1，冷却通道和自由形态压出板之间的关系，变形和冷却系统参数模型之间的关系。根据推断模拟方法，它能描绘输入和输出变量之间的复杂的和不确定的关系。
一旦推断系统构造出输入和输出压力铸造参数的关系，一个合理的带有性能指标的优选法能探索出最佳的铸造参数。在这里，一个模拟退火的测深优化方法被采用。这个模拟退火算法是通过模拟退火过程来减少性能指标。它已经被成功地应用到压铸模具设计中等。这个基础理论可以被广泛地应用。
2. 压铸流动理论
在压铸过程中大约80%的时间花费在冷却过程中。压模铸件的变形是由于浇铸过程中不均匀的温度分布引起的，它影响铸件的质量。冷却系统的设计者不得不考虑整体循环和计算压铸过程中不同阶段的变形。铸造过程分析包括三主要阶段：第一，浇铸过程必须保证浇铸充满型腔。主要的压模铸件流动方程被分成五阶段。在填充阶段，模槽在高压下充满浇铸的塑性流体。
3. 建立冷却系统和压铸模具变形之间的关系
高气压注射铝合金压铸的铸造压力大约是30–150 Mpa；通常注射压力随时间而变。为了研究铸造过程压力的影响，Dochler 和Borton 使用阴极射线示波器和照相机分析铸造过程中的气压变化，那就是说高压充填、冷却和顶出。压铸模具的设计包括流道、均匀的型腔布置、分析压铸模具的寿命（残余应力）、冷却系统等等。
这个研究结果的目的是找到适合铸造任何工件的压铸模具的最佳冷却系统。假定铸造条件是：压铸压力120 Mpa、浇注速度2.8 m / s、压铸循环时间20s 每次、预先加热温度150oC 、注射温度700oC 。对流入型腔的液体的基本假定：1、三维流动；2、牛顿流体；3、层流；4、不可压缩流体；5、流体在垂直的和水平方向无流速差别。根据在零件面的闭合截面不同的冷却参数，有15个设计数据用于模拟压铸过程。根据三维流动模型的模型流动分析，基本布局是一个自由形态的表面。压铸模具的表面温度被预先加热到一定温度(150度) ，熔融金属的温度被控制在700度。注射口的温度特别需要维持在700度。模具的温度是150度、冷却水温度是40度、其它的温度在填充时需要即时使用有限元分析控制，如图2和3所示。
因为获得其临界温度条件需进行分析，变形分析使用三维流动和非线性条件对实体模型进行分析。各节点的配置温度作为初始条件被输入。使注射口的边界约束。条件充当三维热应变条件。机械性能随温度变化而变。它是从非线性稳定阶段分析中获得。上面讨论的型腔流动分析结果用应变分析阶段执行显示在表格1上。铸造过程中的参数是很复杂的和难以控制的。在各参数和指标函数之间的关系很难明确决定。用于实际压铸条件的实验方法和统计法是不同的。在实际运用中有很多地限制。研究使用一个神经网络去学习和培养一个系统，它用于压铸件的变形和铸造过程中的变形，使用这个神经网络完成各参数的进一步地分析。
图2、温度梯度图3 变形分布
同样地，输入参数关系的建立（冷却系统参数： R, 冷却线距离: D,孔道直径: L,开槽中心距）和在铸造过程期间输出参数（变形）被显示在附录上。建设一个完整的推断系统，第一个必要条件是建立数据库。由输入和输出产生的信息必须足够的多。因而推断网络训练的导流因素（冷却系统参数）应该完美和制造没有缺点的产品。表格1阐明了从三维模型流动分析获得的压铸件的冷却系统参数和极限变形。
根据压铸模型的发展，三层推断系统能自动地综合处理，它由冷却系统参数和铸件结果（变形）组成。不同的控制参数被用于这个系统，它能够预先模拟压铸模型在不同的控制参数下面的变形。全部的多项式方程被登记在附录（PSE =
5.43 X 10_7）。表格2比较这些出错预测的模型和模拟情况。这模拟情况是从因为建立这个模型进行压铸模拟试验而设置的20个装置中得到的这个数据集被用来检定这模型建立的合理性。我们看得见来源于表2的故障大约2% ，则可以得到建立这模型的目的。