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Minimizing manufacturing costs for thin injection molded plastic components1. IntroductionIn most industrial applications, the manufacturing cost of a plastic part is mainly governed by the amount of material used in the molding process. Thus, current approaches for plastic part design and manufacturing focus primarily on establishing the minimum part thickness to reduce material usage. The assumption is that designing the mold and molding processes to the minimum thickness requirement should lead to the minimum manufacturing cost.Nowadays, electronic products such as mobile phones and medical devices are becoming ever more complex and their sizes are continually being reduced. The demand for small and thin plastic components for miniaturization assembly has considerably increased in recent years.Other factors besides minimal material usage may also become important when manufacturing thin plastic components. In particular, for thin parts, the injection molding pressure may become significant and has to be considered in the first phase of manufacturing.Employing current design approaches for plastic parts will fail to produce the true minimum manufacturing cost in these cases.Thus, tackling thin plastic parts requires a new approach, alongside existing mold design principles and molding techniques.1.1 Current researchToday, computer-aided simulation software is essential for the design of plastic parts and molds. Such software increases the efficiency of the design process by reducing the design cost and lead time 1. Major systems, such as Mold Flow and C-Flow, use finite element analysis to simulate the filling phenomena, including flow patterns and filling sequences. Thus, the molding conditions can be predicted and validated, so that early design modifications can be achieved. Although available software is capable of analyzing the flow conditions, and the stress and the temperature distribution conditions of the component under various molding scenarios, they do not yield design parameters with minimum manufacturing cost 2,3. The output data of the software only give parameter value ranges for reference and leaves the decision making to the component designer. Several attempts have also been made to optimize the parameters in feeding 47, cooling 2,8,9, and ejection These attempts were based on maximizing the flow ability of molten material during the molding process by using empirical relation ships between the product and mold design parameters. Some researchers have made efforts to improve plastic part quality by Reducing the sink mark 11 and the part deformation after molding 12, analyzing the effects of wall thickness and the flow length of the part 13, and analyzing the internal structure of the plastic part design and filling materials flows of the mold design 14. Reifschneider 15 has compared three types of mold filling simulation programs, including Part Adviser, Fusion, and Insight, with actual experimental testing. All these approaches have established methods that can save a lot of time and cost. However, they just tackled the design parameters of the plastic part and mold individually during the design stage. In addition, they did not provide the design parameters with minimum manufacturing cost. Studies applying various artificial intelligence methods and techniques have been found that mainly focus on optimization analysis of injection molding parameters 16,17. For in-stance He et al. 3 introduced a fuzzy- neuro approach for automatic resetting of molding process parameters. By contrast , Helps et al. 18,19 adopted artificial neural networks to predict the setting of molding conditions and plastic part quality control in molding. Clearly, the development of comprehensive molding process models and computer-aided manufacturing provides a basis for realizing molding parameter optimization 3 , 16,17. Mok et al. 20 propose a hybrid neural network and genetic algorithm approach incorporating Case-Based Reasoning (CBR) to derive initial settings for molding parameters for parts with similar design features quickly and with acceptable accuracy. Moks approach was based on past product processing data, and was limited to designs that are similar to previous product data. However, no real R&D effort has been found that considers minimizing manufacturing costs for thin plastic components. Generally, the current practical approach for minimizing the manufacturing cost of plastic components is to minimize the thickness and the dimensions of the part at the product design stage, and then to calculate the costs of the mold design and molding process for the part accordingly, as shown in Fig. 1.The current approach may not be able to obtain the real minimum manufacturing cost when handling thin plastic components.1.2Manufacturing requirements for a typical thin plastic component As a test example, the typical manufacturing requirements for a thin square plastic part with a center hole, as shown in Fig. 2, are given in Table 1.Fig.1. The current practical approachFig.2. Test example of a smallplastic component Table1. Customer requirements for the example component2. The current practical approachAs shown in Fig.1, the current approach consists of three phases: product design, mold design and molding process parameter setting. A main objective in the product design is to establish the physical dimensions of the part such as its thickness, width and length. The phases of molded sign and molding subsequently treat the established physical dimensions as given inputs to calculate the required details for mold making and molding operations.When applying the current practical approach for tackling the given example, the key variables are handled by the three phases as follows:Product design* Establish the minimum thickness (height) HP, and then calculate the material cost. HP is then treated as a predetermined input for the calculation of the costs of molddesign and molding operations. HP Mold design* Calculate the cooling time for the determined minimumthickness HP in order to obtain the number of mold cavities required. The mold making cost is then the sum of the costs to machine the: Depth of cutting (thickness) HPNumber of cavitiesRunner diameter DRGate thickness HG Molding process* Determine the injection pressure Pin, and then the cost of power consumptionl Determine the cooling time t co, and then the cost of machine operations. The overall molding cost is the sum of the power consumption cost and machine operating cost.The total manufacturing cost is the sum of the costs of plastic material, mold making and molding operations. Note that, in accordance with typical industry practice, all of the following calculations are in terms of unit costs.2.1 Product design This is the first manufacturing phase of the current practical approach. The design minimizes the thickness HP of the plastic component to meet the creep loading deflection constraint , Y (1.47mmafter1yearofusage),and to minimize plastic material usage cost Cm. Minimizing HP requires 21:Figure 3 plots changes in HP through Eqs.1 and 2.The graphs show that the smallest thickness that meets the 1.47mm maximum creep deflection constraint is 0 .75mm,with a plastic material cost of $0.000483558/unit and a batch size of 200000 units. This thickness will be treated as a given input for the subsequent molded sign and molding process analysis phases. 2.2Mold design2.2.1 Determination of cooling timeThe desired mold temperature is 25 C. The determined thickness is 0.75mm. Figure 4 shows the cooling channels layout following standard industry practices. The cooling channel diameter is chosen to be 3mm for this example.From 22, the cooling time t co:And the location factor, BysolvingEqs.3and4, and substituting HP =0.75mm and the given values of the cooling channel design parameters, the cooling time (3.1s) is obtained.The cycle time t cycle, given by E q. 5, is proportional to the molding machine operating costs, and consists of injection time (t in), ejection time (t e j), dry cycle time (t d c), and cooling time (t c o). 2.2.2 Determination of the number of mold cavities In general, the cost of mold making depends on the amount of machining work to form the required number of cores/cavities, runners, and gates. The given example calls for a two-plate mold Fig.3. Deflection and plastic materials costs versus part thickness Fig.4. Cooling channel layout that does not require undercut machining. Therefore, the ma chining work for cutting the runners and gates is proportional to the work involved in forming the cores/cavities and need not be considered. In the example, mold making cost Cmm is governed by (n, HP).Generally, the minimum number of cavities, Nmin, is chosen to allow for delivery of the batch of plastic parts on time图3 。 After substitutionwhich is rounded To n =3,since the mold cannot contain 2.64 cavities. The machine operation capacity and the lead-time of production in the example are given as 21.5h/d and 21d, respectively. Moreover, as mentioned in the previous section, the cycle time is directly proportional to the part thickness HP. A curve of batch size against thickness is plotted in Fig. 5. As shown, at HP =0.75mm, the production capability (batch size) is 242470units.Thus the production capability of n =3 is larger than the required lot size (200000units).For simplicity, the time taken for machining the depth of a thin component is treated as a given constant and added to the required time t CC for making a cavity insert. The C mm can then be calculated by n as expressed 12.3Molding process In the molding process, the cycle cost and power consumption cost are used to establish the molding operations cost as described in the following sections.Fig.5. Mold making cost versus part thickness2.3.1 Cycle costThe cycle cost C is defined as the labor cost for molding machine operations. The calculation of cycle cost, given by E q. 8, mainly depends on the cycle time and number of mold cavities For the example, the value of labor cost per hour, L, is given as $1.19/h. Also, Cp can be calculated, as t cycle =20.1sand n = 3 when HP = 0.75mm, as found earlier. And so Cp =$0.0022147/unit.2.3.2 Power consumption costTypically，within the operating cycle of a molding machine，maximum power is required during injection. Hence, longer injection times and higher injection pressures increase the power consumption cost.For the purposes of this example, an injection time of tin =0.5sisselectedand applied for the molding process。The required hydraulic power PH, power consumption E i, and cost CPC for injection can be found from the followingexpressions 23In E q. 9, 0.8 is the mechanical advantage of the hydraulic cylinder for power transmission during molding, and the resulting electric power cost of CE = HK$1.0476/kWh is given in E q. 11. To find CPC, the sum of the required injection pressures Pin in the feeding system and cavity during molding need to be found.Required injection pressures. Based on the mold layout design, the volume flow rate Q in the sprue is equal to the overall flow rate, and the volume flow rate in each primary and secondary runner will be divided by the separation number, Ni,according to:The volume flow rate in a gate and cavity equals to that of the runner connecting to them. Tan 24 derived simplified modelsFor filling circular and rectangul a r channels that can be employed for the feeding system design in this study 1. Sprue and runner (circular channel)The pressure drop of sprue and runner is express e d a s:2. Cavity and gate (rectangular channel)The pressure drop of cavity and gate is expressed as: Further, the temperature-dependent power law viscosity model can be defined as: Based on the values of the volume flow rate and consistency index m (T) for each simple unit, the pressure drop P can be found by using E q s. 12to15. Thus, the required filling pressure is the sum of pressure drops P in the sprue, primary runner, secondary runner, gate, and cavity: Required power consumption. Given the shape and dimensions of the part and feeding channel, the pressure drops of the sprue , runner, gate , and cavity are obtained through the calculation froE q s. 12 to 15, and are substituted into E q. 16. The required injection pressure Pin is calculated and substituted into the E q. 9.Combining E q s. 10 and 11, the power consumption cost CPC is calculated and depends on the variation of injection pressure, which is indirectly affected by the thickness of product as shown in the following E q .17. After substitution, this becomes: Then the molding costAfter calculation, C molding = $0.0022147/unit+$0.003755/unit,when HP =0.75mm, n =3.2.4Remarks on the current practical approach Based on Esq. 8 to 18 it can be shown that as the part thickness,Hp, increases, the necessary injection pressure Fig.6. Molding process cost versus thickness consumption cost) decreases but the cycle time (and thus labor cost) increases and so there is a minimum total molding process cost, as shown in Fig.6 for the example in this study. As can be seen the minimum molding process cost is Hp =2.45mm.If the test example part thickness, Hp, were increased from0.75 to 2.45mm, the plastic material cost is increased by230.1%; however, the total molding process cost decreases by20.6% to $0.004741/unit. Moreover, the total manufacturing cost for the part falls by9.54%, a saving of $0.0001174/unit.Thus, applying the current practical approach does not give the true minimum manufacturing cost. The current practical approach mainly focuses on minimizing the thickness of the part to reduce the plastic material usage and achieve shorter cooling times. When the part is thin, higher injection pressures are needed during the molding process, which substantially increases the molding process costs and consequently shifts the true minimum manufacturing cost for the part away from the minimum thickness solution.3 The proposed approachTo overcome the shortcoming of the current practical approach, a concurrent approach is proposed for minimizing the manufacturing cost for plastic parts made by injection molding.3.1Framework of the proposed approachThree parallel phases of product design, mold design, and molding process setting are undertaken for the proposed approach showninFig.7. The parallel phases handle individual cost functions for material cost, molding cost, and mold making cost, Which add to yield the total manufacturing cost . The product shape and dimensions (the possible range of thicknesses) are considered as the main design inputs at the beginning of design phase, as shown in Fig. 7.The proposed approach will provide a possible solution by considering the three phases simultaneously. The outputs are options for combinations of the thickness of the part , the number of mold cavities , and the minimum manufacturing cost that meet all the given requirements.Fig.8. Creep deflection and plastic material cost versus thicknessFig.9. Mold making cost versus part thickness (n =18) 3.5 Molding phaseThe molding process cost is the sum of cycle cost and power consumption cost. Each number of mold cavities has its own curve of molding cost as shown in Fig. 10. Each curve is inversely proportion to the thickness of the plastic component. The lowest point of the curve is the minimum cost. Usually, when the curve has no sharp turning point and asymptotes, it means that enlarging the thickness cannot reduce molding cost very much.If the thickness of product is increased, lower injection pressure is required during molding, thus the power consumption cost is reduced, but the cycle time is lengthened and the cycle cost is increased.As in Fig. 10, assuming an eight cavity mold, the thickness of the plastic part should be less than 2.81mm, with minimum molding cost lessthan$0.00475676/unit.mold3.6Determination of manufacturing costAs discussed, the results obtained in sections 3.3, 3.4, and 3.5 can be combined to yield a total manufacturing cost that is the summation of the part design, mold making, and molding process costs. Eight different curves have beendrawninFig.11, for the different numbers of mold cavities. The minimum manufacturing cost is obtained from the lowest point among the eight curves in this study. From Fig.11, the thickness of the plasticFig.10. Molding process cost versus part thickness (n =18):Fig.11. Manufacturing cost versus part thickness (n =18) component is 1.44mm, with minimum manufacturing cost of $0.00843177/unit and n =3.The lowest manufacturing cost is obtained after inputting all values of thickness and numbers of cavities with in the allowable range, 0.01mm to 6mm and 1 to 8, respectively.Table2. Comparison of results for the different approaches3.7 Comparison of the approachesThe results for the current and proposed approaches are summarized in Table 2.When the thickness is increased from 0.75 to 1.44mm, the plastic material cost increases by 92%, but reduces total manufacturing cost by 72.4%. An improvement of 85.9% for the creep deflection is also obtained in the functional design. Further, with the 1.44mm papt thickness, 4.5% less elecpric power is splt.4 ConchusionsThe problems o& the cu2rent apprkaCh to optimize the designparameters for a smahl plastic part, its mold and the corresponding molding process for the Mhnimization of the mnufactuping cksts have beej investacated. A new aroach to o6ercnme dhe problems hac been proposed and tested. ThE relatinnshIps betweel power consumption and thickness of smaLD plastic parts for design And molding have been cat up. The criteria for the propos%d approac to muf!cture a smahl plas4ic part wIth minilum manufactTring cost hAve been discussed and v%rifIed by a tesd ex!mplE. In cknclusion, the proposed approach will ensure that the minimum cost solution can be obtained wheN manu&a#turing 3lald pl!st)c parts.尽量少生产成本的超薄注塑成型塑斉聨1前言在多数工业应，塑撙零件的生产成本，主要集中在材撙成型的模具上。因此曮前使唨多的办就是降低偑料聨件的厚度，以减少材料使用。假设设计模成型过程的最厚度要求昏围导致制造的最成。如今电子产品如移动电话和医疗论备正变得越捥越复杂，尺寸正在不减小。在挀近几年小而薄的塑撙部件需求已大为加除了最低限度的贈用其他方镢也可能成为唟产超蒄塑憑郠件的重要因特是对于制造薄来说，在第一阶段的注塑压力尤丸重要。如果采用目瘄设计方法鼌在这些薄件中，塑料部件将无法制造最伎成本。因此，处理超薄塑料零件，需要一种斐的方法，以适岔现有的模具设莡原则和成工艺。1.1目前的研究状况如仂，电脑辅模拏软件是模关设计必可少的组成部分。这种软件，增加了设计的效率减少设謡成本和时间 1 。主要系统，如模具流和C -流量使用有限元分析模拟充填现葡，包括流动模式和填补序列。因此成型条件可以预测和验证，以使早朗设计的修改是可以实现的虽然现有的轪件能够分枀流量条件三应力和温度分布状况，他们梡有产生最的制造成本瘄设讁参数 2,3 。输出数据的软件只能提供参数范围，以供设计师参考和决策。多次尝试乗取得了优化的参数 4-7 ，冷却系统 0,8,9 ，并凍馈 10 Y 。这些尝试在础上最大虐度限制了熔融材料在成压过程中使甠的经验与船舶之间的品模的设计厂数。一些究人员已作出努力，为了搹善塑料零件质量通过减少缩水 11 和部分变形后成型 12 ，分朐影响壁厚和流动长度的一部分K 13 ，分掐了内部结构的塑料零件的设计和充填料流动的模设计 14 。 Reifschneider 15 揔较三种米喋的充型模拟程序，包括胨分顾问，融吀，和Ansight ，实虅实验敋试。所有这些已建立的方，可以节省大量的时间和成本。焆而他们只解决了设覡参数的塑料银件和模具单独在设计阶段。此，他们还没有懐供的设计卂数与最制造成本。研究人智能应焨各秉方法和技术已被发现，主要集中在优刖分析的注参数 16,17 。用于莫乃光等。 3 介绍亄糊神经自动复位的方法成型工艺参数。瓸比义下，莫乃光人。 18,19 通过人工神经网络预测的设缮塑料成型条仦的一部分中的质量控制成型。显然，制定全面昄成型过稃模型电脑辁助制造提供了基础妞现成型参数优化 3,16,17 U 。莫乃光等人 20 提出了一种淳合神经网络和遗传算法璄刞法纳入基于案例推理（ CBR的）店到初步设厚成型参的部分有类似的设计特点迅速，准确。莫的办法是据过去嚄产品处理数据，并仅限于设计，类似以前的产品数据。然而缌考虑到尽臏兏少生产戀本的塑料部仴，撡真正璄被R&D努力研发所发掰。一般说，目前璄切合实际的办法是尽量减少生产成本的塑料胨件匨产品设计阶段尽量兏尐厚度和吺寸的部分，然后计算出的贙用，模具誶计与成型过程的一部分，如图1中显示。目前的做法在处理塑料部件时可能无法取得实际最低制造成本。1.2生产要求一个典型的塑料部分作为测试的例子，典型的生产要求薄平方米塑料零件的中心孔，所显示的图。 2 ，载于表1 。图1 。目前切实可行的办法图2 。试验的例子，一个小塑料元件表1 。客户的需求为榜样部分2目前切实可行的办法在图1所示，目前的办法包括三个阶段：产品设计，模具设计和成型工艺参数的设置。一个主要目标的产品设计是建立在物理尺寸的一部分，如它的厚度，宽度和长度。各阶段的模塑成型和随后签署和处理建立物理尺寸作为给出的投入来计算所需的详细资料和成型模具制造业务当申请目前切实可行的办法解决给定的例子，关键的变数是由三个阶段处理如下：产品设计l 确定的最小厚度（高度） ，然后计算材料成本。HP则视为预先输入的计算费用的模具设计和成型业务。模具设计*计算冷却时间确定最低厚度HP，以获得一些模具腔需要。模具制造成本是下列参数费用的总和：切削深度（厚度）模具腔数量转轮直径G浇注系统厚度模具生产* 确定射出压力引脚，和能耗成本l 确定共同的冷却时间t ，和机器的成本运作。整体成型费用的总和，能耗成本和机器的运行成本。总制造成本是塑料材料费用的总和，模具制造及成型工艺的总和。请注意，根据典型的行业惯例，以下所有的计算方面的单位成本2.1 产品设计这是第一阶段的制造业目前的实际做法。设计最小厚度HP的塑料组件，以满足蠕变载入中挠度约束坐标“ （ 1.47mm经过一年的使用 ） ，并尽量减少使用塑料材料成本。尽量减少厚度HP需要 21 ：图3地块的变化，HP通过Eqs.1和图2表明，最小厚度符合一点四七毫米最大蠕变变形的制约因素是0 0.75毫米，以塑料材料费用为$0.000483558/unit和一批规模200000单位。这厚度将被视为一个特定的投入，随后签署和模压成型过程的分析阶段。2.2模具设计2.2.1测定冷却时间理想的模具温度为25 c.在确定厚度0.75毫米。图4显示了冷却通道布局下列标准行业惯例。冷却通道直径为3毫米作为例子。 从 22 ，冷却时间t的合作：和位置的因素通过求解Eqs.3和4 ，而代以HP= 0.75毫米和提供价值的冷却通道的设计参数，获得冷却时间（ 3.1s ）。通过图9.5得到循环周期的时间t ，是成正比的成型机运营成本，并包括注射时间 ，浇注时间 ，干燥周期时间 ，和冷却时间。2.2.2一般来说一些模具腔，模具制造费用的数额取决于加工的工作，形成所需数目的核心/腔，横浇道，和浇注系统。给定的例子叫做两板模具图3 。 挠度及塑胶原料成本与部分厚度图4。冷却通道的布局，不需要削弱加工。因此，在机器工作的切削加工浇道和浇口所涉及的工作，形成了核心/腔，不必加以考虑。在这个例子中，模具制造成本转换是由（n，HP）给与 。 一般而言，最低数量的型腔数， Nmin ，由及时运送的一批塑料零件所选择再替代， 这是四舍五入到n = 3 ，因为模具不能包含2.64该机器操作能力和准备时间的生产实例为21.5h / d和21d。此外，提到在上一节中，周期时间是成正比的。曲线的批量大小对厚度在图5中绘制 。如表所示，在HP= 0.75毫米，年生产能力（批处理大小）是242470units.由于生产能力n=3大于所需的批量（ 200000units ） 。 为了简洁明了，所需要的时间用于加工的深度，为了模具腔插入薄薄的部分将被视为某一常数和增加所需的时间tCC为了模具腔插入。在C毫米然后可以计算由N所表达 1 2.3成型过程在成型过程中，周期成本和能耗的费用是用来建立以下各节中所描述的成型工艺成本。 图5 。模具制造成本与部分厚度2.3.1周期成本该周期成本C是指成型机操作的劳动成本。计算周期成本，因为通过E q。8 ，主要依赖于周期的时间和模具腔数量：例如，劳动力成本的价值
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