模具外文翻译-关于注塑模有效冷却系统设计的方法 【中文3400字】【PDF+中文WORD】

模具外文翻译-关于注塑模有效冷却系统设计的方法 【中文3400字】【PDF+中文WORD】,中文3400字,PDF+中文WORD,模具,外文,翻译,关于,注塑,有效,冷却系统,设计,方法,中文,3400,PDF,WORD 【中文3400字】 关于注塑模有效冷却系统设计的方法 摘要：在热塑性注塑模设计中，配件的质量和生产周期很大程度上取决于冷却阶段。已经进行了大量的研究，目的是确定能减少像翘曲变形和不均匀性收缩等的不必要影响的冷却条件。在本文中，我们提出了一种能优化设计冷却系统的方法。基于几何分析，使用形冷却概念来定义冷却管路。它定义了冷却管路的位置。我们只是沿着已经确定好了的冷却水路来分析强度的分布特征和流体的温度。我们制定了温度分布作为最小化的目标函数，该函数由两部分组成。它表明了两个对抗性的因素是如何调解以达到最佳的状态。预期的效果是改善零件质量方面的收缩和翘曲变形。 关键词：逆问题 热传递 注射模 冷却设计 1 简介 在塑料工业领域，热塑性注射模应用非常广泛。这个过程包括四项基本阶段：加料、塑化、冷却和脱模。大约整个过程的70%的时间都在进行产品的冷却。此外，这一阶段直接影响产品的质量。因此，产品必须尽可能统一冷却达到最小化凹痕、翘曲变形、收缩和热残余应力等不必要影响的目的。为了达到这个目标需要的最有影响力的参数有冷却时间、冷却管路的数量、位置和大小、冷却液的温度以及流体和管道内表面的热传递系数。 冷却系统的设计主要基于设计师的经验，但是新的快速成型工艺的发展使非常复杂的管路形状制造成为可能，这是先前的经验理论达不到的。所以冷却系统的设计必须制定为一个优化问题。 1.1 热传递分析 由于参数随温度的变化，在注射工具方面热传递的研究是一个非线性问题。然而，像热导率和热容量这些模具的热物理参数在温度变化范围内都恒为定值。除了聚合物结晶的影响被忽视外，模具及产品之间的热接触阻力也常常被认为是常数。 温度场的分布是在周期边值条件下求解傅里叶方程得到的。这个演化过程可以分成两个部分：一个循环部分和一个平均瞬时的部分。循环部分常常被忽略，因为热渗透的深度对温度场的影响不显著。许多做着所使用的平均循环分析简化了微积分学，但平均波动范围在15%到40%之间。越接近水路的部分，平均波动范围越高。因此，即使在静止状态，模拟瞬态热传递也变的非常重要。在这项研究中，温度的周期瞬态分析优于平均周期时间的分析。 应该注意的是，在实际操作中，冷却系统的设计应作为工具设计的最后一步。不过冷却影响零件质量的最重要的因素，热设计应该是工具设计的第一阶段之一。 1.2 成型技术的优化 在文献中,各种优化程序被使用,但都关注于相同的目标。唐孙俐使用了一种优化程序,获取了零件的均匀温度分布，得到了最小坡度和最少冷却时间。黄试着获得均匀的温度分布于零件和高生产效率下的最小的冷却时间。林总结了模具设计在3个事实方面的目标。零件的冷却均匀,就能达到预期的模具温度，所以,接下来就可注射和减小周期时间。 冷却系统的最优配置是均匀时间和周期时间的折衷。实际上，模具型腔表面和冷却通道之间的距离越远，则温度分布的均匀性越高。相反,距离越短,聚合物的散热速度越快。然而模具表面不均匀的温度会导致零件的缺陷。达到这些目标的控制参数有管路的位置和大小,冷却液流量和流体的温度。 可以采用两种方法。第一个是寻找管路的最优位置以此尽量减小目标函数。这第二种方法是建立在一种形冷却管路。林在冷却通道的位置设计了一个冷却管路。最佳冷却条件(冷却位置和管路大小)都是对冷却线路的研究得到的。徐孙俐进行了更深一步的研究,把冷却水路分成一个个单元并对每个冷却单元进行优化。 1.3 计算法则 方案的计算，数值方法是非常必要的。进行传热分析,可以通过边界元素法或有限元素法。第一种方法的好处就是未知数量的计算要低于有限元素法。边界元素法的唯一问题是网格划分所花费的计算解决方案的时间短于有限元素法。然而这种方法只提供边界问题的结果。在本研究中有限元法是首选，原因是零件的内部温度需要制定为优化问题。 为了计算能最小化目标函数的最优参数，Tang et al.使用鲍威尔共轭方向搜索方法。Mathey et al使用了序列二次规划算法,它是一基于梯度的方法。它不仅可以找到传统的确定方法也可以找到进化方法。Huang et al用遗传算法实现解决方案。这最后一种算法是非常耗时的因为它的计算范围很广。在实际操作中，模具设计的时间必须最小化，于是一个可以更快达到预期解决方案的确定性方法(共轭梯度)应优先选择。 2 方法论 2.1 目标 本文所描述的方法应用于一个T形零件的冷却系统的优化设计 (图1)。这种形状在很多论文中都出现过，因此能比较容易做到。 Part: 零件 Mould: 模具 图 1 基于零件的形态分析, Γ1和Γ3两个表面分别介绍了零件的侵蚀和扩张(冷却线) (图1)。沿着冷却水路Γ3边界条件的导热问题是第三类在无限的温度条件下流体温度的影响。优化就是寻找这些流体的温度。在优化前使用冷却线路阻止冷却管路的数量和大小的选择。这对于那些冷却管路不直观的复杂零件很有效。零件侵蚀线的位置对应于凝固聚合物的最小厚度,以便冷却结束阶段可以消除部分汽压铸模的损害。 2.2 目标函数 在冷却系统优化时，产品的质量应该是最重要的。因为最低冷却时间被零件的厚度和材料性能所影响,因此在特定的时间达到最优的质量是很重要的。 流体温度直接影响模具及配件的温度，且对湍流流体流量唯一的控制参数是冷却液温度。接下来, 优化的参数就是流体温度，且零件最优分布的制定是在冷却时期的最后阶段由最小化的目标函数S确定的(方程(1))。S1时期的目标是要达到零件侵蚀部分的温度水平。S2时期运用于许多工作中，旨在均匀零件表面的温度分布,从而减少沿Γ2表面和零件厚度方向的热梯度。这两个步骤都是为了引入变量△Tfref。必须指出的是当ΔTfref→∞时参考标准会减少到第一时期。相反, 当ΔTfref→0第二个时期的比重会增加。 3 数值计算结果 数值计算结果是与Tang et al的理论结果比较而来的，他们认为T形零件的最佳冷却是通过7个冷却管道和冷却剂的最佳流体流量的最佳位置的确定得到的。第一步是复制他们的结果(图2的左部，)获得下列条件(W= 0.75):T = 303K、流体流动速率Q= 364cm3 / s每个冷却通道,t= 23.5 s。 图 2 例1:冷却管路与有限数目的渠道使流体温度恒定。 冷却系统中的7条管道和模具表面的平均距离(d = 1.5cm)是为了确定冷却线Γ3 的位置。此外,Tang所提出的流体温度传热系数是加给Γ3的扩张部分。 在插图3中沿零件表面Γ2的温度曲线是与脱模时间比较得来的。所有表面的温度曲线都是沿逆时针方向绘制的,只是从A到B的部分。我们观察到采用冷却线的温度值比采用7条管路更不均匀。因此用有限数目的通道计算出来的最佳冷却配置计比冷却线更好，这将作为一种参考。 图3 例2: 在变流体温度下的冷却管路和ΔTfref→∞下的比重因子。 流体温度T在方程1的最小目标函数下计算得到的，这里忽略了第二时期。结果如图4和5所示。 图 4 图 5 在图4中，侵蚀部分的温度曲线很不均匀，比较接近我们脱模温度。 然而在这两种情况下最高值都保持在0.12m和0.14m之间，对应于的筋的顶部位置（图1中的B1）。这些热点是由于零件的几何形状产生的，很难冷却。 然而在图5中,我们注意到零件表面的温度曲线比第一种情况更不均匀。总之,第一部分对于零件表面的均与性还不够完善，但达到预期的温度水平是足够 的。 例3： 图 6 图 7 S2阶段的影响如图6所示。这个阶段使得零件的表面温度均匀。实际上,在ΔT = 10 K的情况下，整个Γ2表面上的温度都类似恒定的，除了之前解释的热点之外。然而对于ΔT的值,侵蚀时的温度是不被接受的，因为平均气温过高(340K相对于理想水平 336 K)。接着第二阶段提高分界面的均匀性,但对解决方案不利。使分界面的温度均匀化，同时提取需要的所有热通量,来获得零件的理想温度，如果这水平太低，将会成为对抗性的问题。最好的解决方案是质量和效率的统一。例如ΔT = 100K时零件的温度比ΔT = 10 K时更不均匀。然而这种方案还是比Tang提出的方案更好。零件的最佳流体温度曲线如图8所示。 图 8 4 结论 本文提出了一种确定冷却线温度分布优化方法来获得零件的均匀温度场，从而得到最小的梯度和最短的冷却时间。与参考文献相比,显示出了它的效率和效益。特别是它不需要指定冷却通道的数量。对于确定管路的最少数量需要进一步比较已提出的最佳流体温度曲线的解决方案。 参考文献 [1] Pichon J. F. Injection des matières plastiques.Dunod, 2001. [2] Plastic Business Group Bayer. Optimised mould temperature control. ATI 1104, 1997. [3] S. Y. Hu, N. T. Cheng, S. C. Chen. Effect of cooling system design and process parameters on cyclic variation of mold temperatures simulation by DRBEM, Plastics, rubber and composites proc. And appl., 23:221-232, 1995 [4] L. Q Tang, K. Pochiraju, C. Chassapis, S. Manoochehri. A computer-aided optimization approach fort he design of injection mold cooling systems. J. of Mech. Design, 120:165-174, 1998. [5] J. Huang, G. M. Fadel. Bi-objective optimization design of heterogeneous injection mold cooling systems. ASME, 123:226-239, 2001. [6] J. C. Lin. Optimum cooling system design of a freeform injection mold using an abductive network. J. of Mat. Proc. Tech., 120:226-236, 2002. [7] E. Mathey, L. Penazzi, F.M. Schmidt, F. Rondé- Oustau. Automatic optimization of the cooling of injection mold base don the boundary element method. Materials Proc. and Design, NUMIFORM, pages 222-227, 2004. [8] X. Xu, E. Sachs, S. Allen. The design of conformal cooling channels in injection molding tooling. Polymer engineering and science, 41:1265-1279, 2001. Int J Mater Form (2010) Vol. 3 Suppl 1:13–16 DOI 10.1007/s12289-010-0695-2 © Springer-Verlag France 2010 A METHODOLOGY FOR THE DESIGN OF EFFECTIVE COOLING SYSTEM IN INJECTION MOULDING A.Agazzi1*, V.Sobotka1, R. Le Goff2, D.Garcia2, Y.Jarny1 1 Université de Nantes, Nantes Atlantique Universités, Laboratoire de Thermocinétique de Nantes, UMR CNRS 6607, rue Christian Pauc, BP 50609, F-44306 NANTES cedex 3, France 2 Pôle Européen de Plasturgie, 2 rue Pierre et Marie Curie, F- 01100 BELLIGNAT, France ABSTRACT: In thermoplastic injection moulding, part quality and cycle time depend strongly on the cooling stage. Numerous strategies have been investigated in order to determine the cooling conditions which minimize undesired defects such as warpage and differential shrinkage. In this paper we propose a methodology for the optimal design of the cooling system. Based on geometrical analysis, the cooling line is defined by using conformal cooling concept. It defines the locations of the cooling channels. We only focus on the distribution and intensity of the fluid temperature along the cooling line which is here fixed. We formulate the determination of this temperature distribution, as the minimization of an objective function composed of two terms. It is shown how this two antagonist terms have to be weighted to make the best compromise. The expected result is an improvement of the part quality in terms of shrinkage and warpage. KEYWORDS: Inverse problem, heat transfer, injection moulding, cooling design 1 INTRODUCTION In the field of plastic industry, thermoplastic injection moulding is widely used. The process is composed of four essential stages: mould cavity filling, melt packing, solidification of the part and ejection. Around seventy per cent of the total time of the process is dedicated to the cooling of the part. Moreover this phase impacts directly on the quality of the part [1][2]. As a consequence, the part must be cooled as uniformly as possible so that undesired defects such as sink marks, warpage, shrinkage, thermal residual stresses are minimized. The most influent parameters to achieve these objectives are the cooling time, the number, the location and the size of the channels, the temperature of the coolant fluid and the heat transfer coefficient between the fluid and the inner surface of the channels. The cooling system design was primarily based on the experience of the designer but the development of new rapid prototyping process makes possible to manufacture very complex channel shapes what makes this empirical former method inadequate. So the design of the cooling system must be formulated as an optimization problem. 1.1 HEAT TRANSFER ANALYSIS The study of heat transfer conduction in injection tools is a non linear problem due to the dependence of parameters to the temperature. However thermophysical parameters of the mould such as thermal conductivity and heat capacity remain constant in the considered temperature range. In addition the effect of polymer crystallisation is often neglected and thermal contact resistance between the mould and the part is considered more often as constant. The evolution of the temperature field is obtained by solving the Fourier’s equation with periodic boundary conditions. This evolution can be split in two parts: a cyclic part and an average transitory part. The cyclic part is often ignored because the depth of thermal penetration does not affect significantly the temperature field [3]. Many authors used an average cyclic analysis which simplifies the calculus, but the fluctuations around the average can be comprised between 15% and 40% [3]. The closer of the part the channels are, the higher the fluctuations around the average are. Hence in that configuration it becomes very important to model the transient heat transfer even in stationary periodic state. In this study, the periodic transient analysis of temperature will be preferred to the average cycle time analysis. It should be noticed that in practice the design of the cooling system is the last step for the tool design. Nevertheless cooling being of primary importance for the quality of the part, the thermal design should be one of the first stages of the design of the tools. · Corresponding author: Alban Agazzi, Université de Nantes-Laboratoire de thermocinétique de Nantes, La Chantrerie, rue Christian Pauc, BP 50609, 44306 Nantes cedex 3-France, phone : +332 40 68 31 71, fax :+332 40 68 31 41 · email : alban.agazzi@univ-nantes.fr 1.2 OPTIMIZATION TECHNIQUES IN MOULDING In the literature, various optimization procedures have been used but all focused on the same objectives. Tang et al. [4] used an optimization process to obtain a uniform temperature distribution in the part which gives the smallest gradient and the minimal cooling time. Huang [5] tried to obtain uniform temperature distribution in the part and high production efficiency i.e a minimal cooling time. Lin [6] summarized the objectives of the mould designer in 3 facts. Cool the part the most uniformly, achieve a desired mould temperature so that the next part can be injected and minimize the cycle time. The optimal cooling system configuration is a compromise between uniformity and cycle time. Indeed the longer the distance between the mould surface cavity and the cooling channels is, the higher the uniformity of the temperature distribution will be [6]. Inversely, the shorter the distance is, the faster the heat is removed from the polymer. However non uniform temperatures at the mould surface can lead to defects in the part. The control parameters to get these objectives are then the location and the size of the channels, the coolant fluid reaches an acceptable local solution more rapidly is preferred. 2 METHODOLOGY 2.1 GOALS The methodology described in this paper is applied to optimize the cooling system design of a T-shaped part (Figure 1). This shape is encountered in many papers so comparison can easily be done in particularly with Tang et al. [4]. Figure 1 : Half T-shaped geometry G G 1 3 Based on a morphological analysis of the part, two flow rate and the fluid temperature. surfaces and are introduced respectively as the Two kinds of methodology are employed. The first one consists in finding the optimal location of the channels in erosion and the dilation (cooling line) of the part (Figure 3 1). The boundary condition of the heat conduction order to minimize an objective function [4][7]. The problem along the cooling line G is a third kind second approach is based on a conformal cooling line. Lin [6] defines a cooling line representing the envelop of the part where the cooling channels are located. Optimal conditions (location on the cooling and size of the channels) are searched on this cooling line. Xu et al. [8] go further and cut the part in cooling cells and perform the optimization on each cooling cell. 1.3 COMPUTATIONAL ALGORITHMS To compute the solution, numerical methods are needed. The heat transfer analysis is performed either by boundary elements [7] or finite elements method [4]. The main advantage of the first one is that the number of unknowns to be computed is lower than with finite elements. Only the boundaries of the problem are meshed hence the time spent to compute the solution is shorter than with finite elements. However this method only provides results on the boundaries of the problem. In this study a finite element method is preferred because temperatures history inside the part is needed to formulate the optimal problem. To compute optimal parameters which minimize the objective function Tang et al. [4] use the Powell’s conjugate direction search method. Mathey et al. [7] use the Sequential Quadratic Programming which is a method based on gradients. It can be found not only deterministic methods but also evolutionary methods. Huang et al. [5] use a genetic algorithm to reach the solution. This last kind of algorithm is very time consuming because it tries a lot of range of solution. In practice time spent for mould design must be minimized hence a deterministic method (conjugate gradient) which condition with infinite temperatures fixed as fluid temperatures. The optimization consists in finding these fluid temperatures. Using a cooling line prevents to choose the number and size of cooling channels before optimization is carried out. This represents an important advantage in case of complex parts where the location of channels is not intuitive. The location of the erosion line in the part corresponds to the minimum solidified thickness of polymer at the end of cooling stage so that ejectors can remove the part from the mould without damages. 2.2 OBJECTIVE FUNCTION In cooling system optimization, the part quality should be of primarily importance. Because the minimum cooling time of the process is imposed by the thickness and the material properties of the part, it is important to reach the optimal quality in the given time. The fluid temperature impacts directly the temperature of the mould and the part, and for turbulent fluid flow the only control parameter is the cooling fluid temperature. In the following, the parameter to be optimized is the fluid temperature and the determination of the optimal distribution around the part is formulated as the minimization of an objective function S composed of two terms computed at the end of the cooling period (Equation (1)). The goal of the first term S1 is to reach a temperature level along the erosion of the part. The second term S2 used in many works [4][7] aims to homogenize the temperature distribution at the surface of the part and therefore to reduce the components of 15 thermal gradient both along the surface G and through the cooling line and it will be then considered as a 2 the thickness of the part. These two terms are weighted reference. ref by introducing the variable ΔT . It must be noted that ref when ΔT ® ¥ the criterion is reduced to the first term. On the contrary the weight of the second term is ref increased when ΔT ® 0 . V T - T  2 2 1 f I I V T - T I S (Tfluid ) = f I G1 T ejec - T I .dG . + I u I G ΔT I .dG2 u (1) inj ejec 2 réf ejec inj T : Ejection temperature, T : Injection temperature, ΔT ref : Reference temperature, T : Fluid temperature, inf 2 T : Temperature field computed with the periodic Figure 3: Temperature profiles along the part surface G f conditions T (0, X ) = T (0 + t , X ) X Î Ω È Ω 1 2 1 , and  Case 2: Cooling line with a variable fluid temperature [0, t f ] is the cooling period,  G 2 ref T = f T.dG : Average G2  ( T fluid (s) ) and the weighting factor ΔT ® ¥ . f surface temperature of the part at the ejection time t . The fluid temperatures  T (s) fluid are computed by 3 NUMERICAL RESULTS Numerical results are compared with those of Tang et al [4] who consider the optimal cooling of the T-shaped part by determining the optimal location of 7 cooling channels and the optimal fluid flow rate of the coolant. The first step was to reproduce their results (left part of Figure 2) obtained with the following conditions (case minimizing the objective function of Equation 1 where the second term is ignored. The results are plotted in Figures 4 and 5. w=0.75 in [4]):  T fluid = 303K , fluid flow rate f Q = 364cm3 / s in each cooling channels, t = 23.5 s . Figure 2: Geometry Tang (left) and cooling line (right) fluid Case 1: Cooling line versus finite number of channels for a constant fluid temperature ( T ). 3 The average distance ( d = 1.5cm ) between the 7 channels and the part surface in the cooling system determined by Tang is adopted in our system for locating the cooling line G . Moreover, the fluid temperature and 3 the heat transfer coefficient values issued from Tang are imposed on the dilation of the part G . In Figure 3 the temperature profiles along the part surface G are compared at the ejection time t . All the  Figure 4: Temperature profiles along the erosion Figure 5: Temperature profiles along the part surface 2 temperature profiles along the surfaces f i G i = 1,2,3 are In Figure 4 the temperature profile on the erosion is 1 much uniform and close to the ejection temperature with A i plotted counter-clockwise only on the half part from our method ( S = 1.79.10-5 ) than with Tang’s method i to B (Figure 1) and at the ejection time. We observe that ( S = 2.32.10-5 ). However in both cases a peak remains 1 the magnitude of the temperature is less uniform with the cooling line than with the 7 channels (15K instead of 5K). Hence the optimal cooling configuration computed with a finite number of channels is better than this with between 0.12m and 0.14m which corresponds to the top of the rib (B1 in Figure 1). This hotspot is due to the geometry of the part and is very difficult to cool. Nevertheless in Figure 5 we notice that the profile of temperature at the part surface is less uniform than in case 1 (20K instead of 15K). In conclusion, the first term is not sufficient to improve the homogeneity at the part surface but it is adequate for achieving a desired level of temperature in the part. uniform than the solution given by Tang. The optimal fluid temperature profile along the dilation of the half part is plotted (Figure 8). Case 3: Cooling line with ( T  fluid (s) ) and the weighting ref factors ΔT = 10K and ΔT = 100K . ref The fluid temperatures  T fluid (s) are now computed by minimizing the objective function of Equation 1 with ΔT ref = 10K and  ΔT ref = 100K . Results are plotted in Figures 6 and 7. Figure 6: Temperature profiles along the part surface Figure 7: Temperature profiles along the erosion The influence of the term S2 is shown in Figure 6. This term makes the surface temperature of the part uniform.  Figure 8: Optimal fluid temperature profile 4 CONCLUSIONS In this paper, an optimization method was developed to determine the temperature distribution on a cooling line to obtain a uniform temperature field in the part which leads to the smallest gradient and the minimal cooling time. The methodology was compared with those found in the literature and showed its efficiency and benefits. Notably it does not require specifying a priori the number of cooling channels. Further work will consist in deciding a posteriori the minimal number of channels needed to match the solution given by the optimal fluid temperature profile REFERENCES [1] Pichon J. F. Injection des matières plastiques. Dunod, 2001. [2] Plastic Business Group Bayer. Optimised mould temperature control. ATI 1104, 1997. [3] S. Y. Hu, N. T. Cheng, S. C. Chen. Effect of cooling system design and process parameters on cyclic variation of mold temperatures simulation by DRBEM, Plastics, rubber and composites proc. and appl., 23:221-232, 1995 [4] L. Q Tang, K. Pochiraju, C. Chassapis, S. ref Indeed in case ΔT = 10K temperature is quasi-constant Manoochehri. A computer-aided optimization approach fort he design of injection mold cooling all over the surface G except for the hotspot as systems. J. of Mech. Design, 120:165-174, 1998. 2 explained previously. However for this value of  ΔT , ref [5] J. Huang, G. M. Fadel. Bi-objective optimization the temperature on the erosion is not acceptable, the mean temperature being too high (340K for a desired level of 336 K). Then the second term improves the homogeneity at the interface but hedges the solution. Making uniform the temperature at the interface meanwhile extracting the total heat flux needed to obtain a desired level of temperature in the part, become antagonistic problems if this level is too low. The best solution will be a compromise between quality and design of heterogeneous injection mold cooling systems. ASME, 123:226-239, 2001. [6] J. C. Lin. Optimum cooling system design of a free- form injection mold using an abductive network. J. of Mat. Proc. Tech., 120:226-236, 2002. [7] E. Mathey, L. Penazzi, F.M. Schmidt, F. Rondé- Oustau. Automatic optimization of the cooling of injection mold base don the boundary element method. Materials Proc. and Design, NUMIFORM, efficiency. For example, by setting  ΔT ref = 100K the pages 222-227, 2004. [8] X. Xu, E. Sachs, S. Allen. The design of conformal ejec level of temperature ( T ) in the part is reached whereas the solution becomes less uniform than with the value of cooling channels in injection molding tooling. Polymer engineering and science, 41:1265-1279, ΔT ref = 10K . Nonetheless this solution remains more 2001.