外文翻译--一种使注射成型冷却更有效的系统设计方法 英文版

桂林电子科技大学毕业设计（论文）说明书用纸 第 1 页 共 18 页 A METHODOLOGY FOR THE DESIGN OF EFFECTIVE COOLING SYSTEM IN INJECTION MOULDING Int J Mater Form (2010) Vol. 3 Suppl 1:13 16 DOI10.1007/s12289-010-0695-2 Springer-VerlagFrance2010 ABSTRACT In thermoplastic injection molding, 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 war page 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 war page. KEYWORDS: Inverse problem； heat transfer； injection molding； Cooling design 1. INTRODUCTION In the field of plastic industry, thermoplastic injection molding 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 桂林电子科技大学毕业设计（论文）说明书用纸 第 2 页 共 18 页 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 thermo physical parameters of the mould such as thermal conductivity and heat capacity remain constant in the considered temperature range. In addition the effect of polymer crystallization 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 Fouriers 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. 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 桂林电子科技大学毕业设计（论文）说明书用纸 第 3 页 共 18 页 these objectives are then the location and the size of the channels, the coolant fluid flow rate and the fluid temperature. Two kinds of methodology are employed. The first one consists in finding the optimal location of the channels in order to minimize an objective function 4 7. The 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 Powells 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 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. Based on a morphological analysis of the part, two surfaces 1 and 3 are introduced respectively as the erosion and the dilation (cooling line) of the part (Figure 1). The boundary condition of the heat conduction problem along the cooling line 3 is a third kind condition 桂林电子科技大学毕业设计（论文）说明书用纸 第 4 页 共 18 页 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. Figure 1 : Half T-shaped geometry 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. 3 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. 桂林电子科技大学毕业设计（论文）说明书用纸 第 5 页 共 18 页 An integrated framework for die and mold cost estimation using design features and tooling parameters Received: 5 August 2003 / Accepted: 6 January 2004 / Published online: 2 February 2005 Springer-Vela London Limited 2005 Abstract Tooling is an essential element of near net shape manufacturing processes such as injection molding and die casting, where it may account for over 25% of the total product cost and development time, especially when order quantity is small. Development of rapid and low cost tooling, combined with a scientist approach to mold cost estimation and control, has therefore become essential. This paper presents an integrated methodology for die and mold cost estimation, based on the concept of cost drivers and cost moodier. Cost drivers include the geometric features of cavity and core, handled by analytical cost estimation approach to estimate the basic mold cost. Cost moodier include tooling parameters such as parting line, presence of side core(s), surface texture, ejector mechanism and die material, contributing to the total mold cost. The methodology has been implemented and tested using 13 industrial examples. The average deviation was 0.40%. The model is edible and can be easily implemented for estimating the cost of a variety of molds and dies by customizing the cost moodier using quality function deployment approach, which is also described in this paper. Keywords： Cost estimation； Die casting； Injection molding； Quality function deployment。 1 Introduction Product life cycles today are typically less than half of those in the 1980s, owing to the frequent entry of new products with more features into the market. Manufacturing competitiveness is measured in terms of shorter lead-time to market, without scribing quality and cost. One way to reduce the lead-time is by employing near net shape (NNS) manufacturing processes, such as injection molding and die casting, which involve fewer steps to obtain the desired shape. However, the tooling (die or mold), which is an essential element of NNS manufacturing, consumes considerable resources in terms of cost, time and expertise. A typical die casting die or plastic injection mold is made in two halves: moving and axed which butt together during mold ling and move apart during part ejection. The 桂林电子科技大学毕业设计（论文）说明书用纸 第 6 页 共 18 页 construction of a typical cold chamber pressure die casting die is shown in Fig. 1. The main functional elements of the die and mold include the core and cavity, which impart the desired geometry to the incoming melt. These may be manufactured as single blocks or built-up with a number of inserts. The secondary elements include the feeding system, ejection system, side core actuators and fasteners. The feeding system comprising of spree bush, runner, gate and overawe enables the town of melt from machine nozzle to mold cavity. The ejector mechanism is used for ejecting the molded part from the core or cavity. All the above elements are housed in a mold base set, comprising of support blocks, guides and other elements. Part-specie elements, including core and cavity and feeding system are manufactured in a tool room. Other elements are available as standard accessories from vendors. Mold assembly and functional trials are conducted by experienced toolmakers in consultation with tool designers. Fig. 1. Construction of a typical pressure diecasting die The tooling industry is presently dominated by Japan, Germany, USA, Canada, Korea, Taiwan, China, Malaysia, Singapore and India. The major users of tooling include automobiles, electronics, consumer goods and electrical equipment sectors. Plastic molds account for the major share of tooling industry. About 60% of tool rooms belong to small and medium scale industries worldwide 1. The tooling requirement is over US$ 600 million per year in India alone, with an annual growth rate of over 10% during the last decade. In India, the share of different types of molds and dies is: plastic molds 33%, sheet metal punches and 桂林电子科技大学毕业设计（论文）说明书用纸 第 7 页 共 18 页 dies 31%, die casting dies 13%, jigs & stores 13%, and gauges 10% 2. The tooling industry is increasingly facing the pressure to reduce the time and cost of die and mold development, offer better accuracy and surface knish, provide edibility to accommodate future design changes and meet the requirements of shorter production runs. To meet these requirements, new technologies like high speed machining, hardened steel machining, process modeling, tooling design automation, concurrent engineering, rapid prototyping and rapid tooling have been applied. For successful operations and to maintain the competitive edge, it is necessary to establish quantitative methods for cost estimation. Our current research aims at developing a systematic and integrated framework for development of rapid hard tooling (dies and molds) for injection molding and pressure die-casting applications. The necessity of a systematic cost estimation model for comparative evaluation of different routes to tooling development motivated us to review the existing models, presented in the next section, followed by our proposed methodology. 2 Previous works There is considerable similarity in cost estimation approaches used for product and tooling as reported in technical literature. These approaches can be classed into vet group s: intuitive, analogical, analytical, geometric feature based and parametric based methods, briery reviewed here. In the intuitive method, the accuracy of cost estimation depends on the cost appraisers experience and interpretations. The estimation is usually performed in consultation with the tool designer. The estimator acquires the wisdom and intuition concerning the costs through long association with dies and mold development. This method is still in practice in small workshops and tool rooms. In the analogical method, the cost of die and mold is estimated based on similarity coefficients of previous dies and molds manufactured by the rm. In this technique, dies are coded considering factors such as die size, die material, complexity, ejector and gating mechanism. The appraiser starts by comparing the new die design with the closest match among all previous designs. The basic hypotheses are: similar problems have similar solutions, and reuse is more practical than problem solving from scratch 3. However, this approach, also referred to as case based reasoning, requires a complete case base and an appropriate retrieval system, which has not been reported for die and mold cost estimation so far. In the analytical cost estimation, the entire manufacturing activity is decomposed into 桂林电子科技大学毕业设计（论文）说明书用纸 第 8 页 共 18 页 elementary tasks, and each task is associated with an empirical equation to calculate the Manufacturing cost. For example, a common equation for machining cost is： Machining cost = (cutting length / feed per minute) Machine operation cost. Wilson (quoted in 4, Chap. 6, p. 121) suggested a mathematical model for incorporating a geometric complexity factor in turning and milling operations, given by: di = i th dimension of feature ti = corresponding dimensional tolerance N = total number of dimensions. This is explained with the help of an example later. Another method called activity based costing (ABC) involves applying the analytical method to all steps in manufacturing a given product, to estimate the resources (material, labor and energy) involved in each step. Such a detailed approach for various processes, including casting has been developed by Crease 5. In tool rooms, this approach is used in the case of dies with complex cavity geometry. The sources of mold cost can be divided into three categories: mold base cost, functional elements (core, cavity inserts) cost and secondary elements cost. In each category, the time needed to obtain the desired geometry by machining is considered as a reference for costing 4. As can be expected, establishing and validating the costing equation, as well as using it in practice, are cumbersome tasks. In the feature based method, mold geometric features (cylinder, slot, hole, rib, etc.) are used as the cost drivers. The die manufacturing cost is then estimated using either empirical equations or tools such as knowledge-based systems and arterial neural networks. Chen and Liu 6 used the feature recognition method to evaluate a new injection molded product design for its cost effectiveness. They assumed that a product is an aggregation of a set of features and feature relationships. These feature relationships were mapped to convert a part feature into mold related cost evaluations. Chin and Wong 7 used decision tables linked to a knowledge base to estimate injection mold cost. In the parametric cost estimation, technical, physical or functional parameters are used as basis for cost evaluation. This method allows one to proceed from technical values characterizing the product (available with design engineers) to economic data. Sandarac and Maslekar 8 used regression model approach in injection mold cost estimation. Lowe and Walshe 9 used labor involvement in injection mold making as a reference； mold cost was estimated using linear regression analysis. 桂林电子科技大学毕业设计（论文）说明书用纸 第 9 页 共 18 页 To summarize, cost similarity and cost functions (cost factors) are the two sets of methods for estimating the mold cost. In the rest set, similarity between a new mold and a previous mold developed in the tool rooms is used as a reference. Intuitive and analogical methods fall under this category. In the widely used intuitive method, the cost appraiser may not be in a position to identify all the risk factors and to quantify many of them. The analogical method can be successfully used for estimating the cost of die bases and other secondary elements where grouping is much easier. However, in the case of functional elements (core and cavity), grouping becomes a difficult task as their geometry, machining sequence and tolerance greatly vary with product design. In the second set of methods, the dependency between the mold cost and its drivers are expressed in mathematical functions. Analytical method, activity based costing, feature based method and parametric costing methods falls under this category. While analytical methods are well established for estimating the machining cost of simple parts, they are difficult to apply in die and mold manufacturing because of their geometric complexity. Similarly, feature based cost estimation is difficult to apply because the current feature recognition and classification algorithms cannot handle freeform surfaces present in most of the dies and molds, and other computational techniques like knowledge-based systems, fuzzy logic and arterial neural networks may be required to establish the cost relations. Further, these techniques may not be able to consider the impact of assembly restrictions, surface knish requirements, mold trials and other factors. The parametric costing method functions like a black box, by correlating the total cost of mold with a limited number of design parameters, and it is difficult to justify or explain the results. Menges and Mohren 10 developed an integrated approach for injection mold cost estimation, in which similar injection molds and structural components of the same kind are grouped together and a cost function for each group is determined. The cost components are grouped into cavity, mold base, basic functional elements and special functional elements. Machining cost for cavity and EDM electrodes is driven by machining time and hourly charges adjusted by factors like machining procedure, cavity surface, parting line, surface quality, axed cores, tolerances, degree of difficulty and number of cavities. The mold bases are assumed to be standard components. Cost of basic functional elements like sprue, runner systems, cooling systems and ejector systems are estimated on a case to case basis. The cost of special functional elements like side cores, three-plate mold, side cams and unscrewing devices is determined based on actual expenses. One of the limitations is that the machining time estimate based on mean cavity depth may not give accurate results in case of complex shaped molds that require different modes of machining like roughing, noshing and leftover 桂林电子科技大学毕业设计（论文）说明书用纸 第 10 页 共 18 页 material machining, due to cutting tool size and geometry constraints, orientations and settings. Secondly, the work does not appear to consider machining cost for secondary surfaces (particularly in case of built-in type cavities or cores), cost implications of mold material (which directly affects cutting tool selection and machining time), secondary operations on standard mold bases (to accommodate cavities, side cores and accessories, special ejector mechanisms and hot runners etc.), and some cushion in cost estimation to take care of additional work during nal machining of mating parts. This approach uses more than 1520 analytical models with average 58 variables, which need to be statistically established, and offers research opportunities. In general, all of above approaches give relatively accurate estimates only when tool rooms are involved in developing a single type of mold (such as injection molds or pressure die casting dies). Die and mold manufacturing is still regarded as skill and experience oriented manufacturing, and moreover it is not repetitive in nature. Thus there is a need to develop a generic die and mold cost estimation model that can be easily implemented for different types of molds and complexity, and is also edible to accommodate the decisions of the cost appraiser. We propose a cost model to meet the above requirements, based on the notion of cost drivers and cost modiers.Cost drivers depend on geometry and machining time. Cost moodier depend on complexity, and can be customized using a quality function deployment approach, which is also discussed in this paper. 3 Framework for die and mold cost estimation The cost components of a typical injection molded automotive part (assuming a die life of 250,000 parts) are given in Fig. 2 11. It shows that mold cost (41%) has a much larger share of total cost and therefore must be estimated accurately. Molds for other applications (pressure die casting, forging, sheet metal tools, etc.) also react a similar breakup. The mold cost comprises mold material, mold design and manufacturing. Among these mold-manufacturing costs represents the largest share and is the focus of our work. The structure of the proposed mold cost estimation model is shown in Fig. 3. In this approach, all geometric features are mapped to machining features, which are used as cost drivers and their cost is obtained by the analytical costing method. Other factors affecting the complexity of the die and mold are considered as cost moodier. Hereafter, the term mold will be used to represent both die and mold. 桂林电子科技大学毕业设计（论文）说明书用纸 第 11 页 共 18 页 3.1 Cost drivers: core and cavity features In feature based design, a part is constructed, edited and manipulated in terms of geometric features (such as whole, slot, rib and boss) with certain spatial and functional relationships. The part features are used for generating mold cavity features； Table 1 shows the feature mapping between part and mold. The mold features are analyzed to identify the geometric dimensions, manufacturing processes and relative manufacturing cost. Essentially, the size and shape complexity of mold cavity features, which in turn nuance the selection of the manufacturing method, act as cost drivers. The manufacturing methods 1D,2D, etc., represent the simultaneous movement of tool or work piece with respect to axis X, Y , Z, a, b and c, to get the desired geometry. The relative cost for feature manufacturing (basic mold cost) is proposed based on our experience. This is useful when sufficient mold design and cost data are not available. More precise cost estimation can be assured by integrating analytical costing methods with machined features in later stages. The manufacturing cost of mold geometry can be calculated by Eq. 1 using predetermined machining parameters like feed per minute (S) and machine hour rate. The summation of machining cost of all features gives the basic mold cost: L f = Total cutting length of feature ( f = 1 to n) S = Corresponding feed (mm/min) M f = Corresponding machine minute rate (hour rate /60) I f = Machining complexity factor I n = number of features . While calculating the machining complexity factor for cost estimation purposes, it is not necessary to consider all dimensions of a feature (the process engineer will select the manufacturing process and corresponding machine considering the geometry as well as tolerance of primary dimension). The machine hour rate already considers these effects. There are other factors like the number of settings, number of tooling and their sequence, which are again dependent on geometric complexity (number of surfaces and their orientation and special relationships). We therefore muddied Eq. 1 by introducing a machining process constant “K”. The value of K varies from 0.05 for plain turning to 0.5 for EDM and machine polishing processes. Thus machining complexity factor of a feature is given by: 桂林电子科技大学毕业设计（论文）说明书用纸 第 12 页 共 18 页 For example, consider a circular whole feature with diameter 20+0.018 mm and depth 160.010 mm. In this case, diameter 20 is a primary dimension and tolerance 18 m can be achieved by the reaming operation. Therefore, it becomes necessary to consider only the depth that is, 160.010. Reaming operation is normally performed in either CNC vertical machining center or a jig-boring machine. The number of settings is one, and the number of tooling is four (center drill, pilot drill, nal drill and machine reamer). Therefore, the machining process constant is considered as 0.2. Hence the machining complexity of the above feature is given by: 3.2 Cost moodier: Die complexity factors In die and mold manufacturing, there are many die complexity factors that have a sign cant impact on the total cost and are considered as cost moodier. These include parting surface complexity, presence of side cores, surface nish and texture, ejector mechanism and die material. Their values, established from our experience, are given in Tables 24, as a percentage of the basic mold cost (derived from Eq. 3). These are explained in detail here. 3.2.1 Parting surface complexity Selection of the most appropriate parting surface is an important activity in die and mold design. Many researchers have reported different algorithms to identify a parting surface considering the ejection of part from die cavity, ease of manufacturability and aesthetic issues. A complex parting signicantly increases the manufacturing cost due to increase in machining complexity (because of cutting tool geometry constraints) and die assembly time. A non-planar parting surface makes it difficult to match the two halves. Often it results in re-machining, which is not quant able by feature based approach. To consider these uncertainties, die parting surface complexity is divided into three levels: straight, stepped and freeform parting surfaces. Straight parting surface will not impose any additional cost； however the cost implications of steeped and freeform parting surface will 1020% and 2040%, respectively. This can also be customized as discussed in a later section. 桂林电子科技大学毕业设计（论文）说明书用纸 第 13 页 共 18 页 3.2.2 Presence of side cores The product geometry may comprise a number of undercuts to the line of draw, hindering its removal from the die and mold. This is overcome by the use of side cores, which slide in such a way that they get disengaged from the molded part before its ejection. Side cores need secondary elements like guide ways, cams and hydraulic-pneumatic actuators, which impose an additional cost. If product geometry calls for a number of side cores that are actuated in different directions, then die size and cost will increase signicantly. Aggravated by additional die cooling arrangements, increased mold assembly time and nish machining during assembly, which may not be easily quant able. While the cost of side cores machining is already considered in cost drivers, their inuence on over all die complexity due to additional accessories, and secondary machining is considered here. The corresponding values for this cost moodier (c ) are given in Table 2 based on our experience. 3.2.3 Surface nish and texture The die surface is usually polished to obtain surface roughness Ra from 0.2 to 0.8 m. Some surface textures may be added to injection-molded parts to increase the aesthetic look or some functional requirement. This requires specialized processes like EDM texturing, photo etching and surface treatment, increasing the toolmakers job. Therefore, polishing and texturing impose additional cost, and the values for this cost moodier ( p ) are listed in Table 3 based on our experience. 3.2.4 Ejection mechanism The mechanism for ejecting a part from its mold or die may comprise a simple ejector pin or cam operated mechanism, or a complex hydraulic-pneumatic actuator. Construction of the ejector mechanism depends on the part geometry and the desired rate of production. In addition, ejector design may lead to a larger die size to accommodate the sliders, cams, actuators, etc. The ejector materials are usually of special grade, requiring hardening and nit riding treatments. Therefore, the ejector mechanism adds to the total cost depending on its type. The values for this cost moodier (e ) are given in Table 4. 3.2.5 Die and mold material The die and mold material should have good mechanical properties like high hardness, low thermal distortion, high compressive strength and manufacturability. Commonly used tool steels for injection molds and pressure die casting dies include P20, P18, EN-24, A3, D1, D2, H11 and H13, which are more expensive than general steels. The die material cost is directly 桂林电子科技大学毕业设计（论文）说明书用纸 第 14 页 共 18 页 based on the Volume of die inserts (considered in the total cost model). The die material also affects the feature manufacturing cost, because of its impact on cutting tool life. A recent development is high speed machining of hardened die steel, which shows sign cant improvement in accuracy and surface nish. Based on an average of ten case studies carried out at our center, the die material factor (m ) can increase the basic mold cost by 210%, for die materials ranging from carbon steel to hot die steel. 4 Establishing the cost moodier As seen from Tables 24, the impact of various factors on the total cost of a die or mold cost is sign cant. While the values given in the above tables are based on our experience, they cannot be jostled in other tool rooms, unless they have a large case base to verify the same. The cost moodier must therefore be customized for an individual tool room. One way to customize the cost moodier is by using multiple regression analysis. This involves collecting historical data and establishing the regression coefficient or cost estimating relationships (CERs). However, the CERs established in commercial tool rooms may not simulate the real situation, since such tool rooms manufacture a large variety of dies and molds, and a huge amount of historical data would be required for computation. We propose another approach, based on quality function deployment (QFD) for establishing the cost moodier, to overcome the above limitation. This QFD-based cost model is project specie, and establishes the cost factors by considering the different tooling parameters. The user has to assess the impact of tooling parameters (parting surface complexity, surface nish, etc.) by considering basic mold cost as a reference. This improves the accuracy of total cost estimation. Table 5 explains the tooling parameters and their Associated cost factors considered in developing the QFD-based cost model. The steps involved in the methodology are as follows: 1.Identify major tooling parameters other than basic die and mold feature manufacturing. 2. Categorize the tooling parameters into different complexity levels (columns of QFD). 3. Identify cost elements other than basic mold manufacturing cost (rows of QFD). 4. Represent the importance of these cost elements in percent age of basic mold cost. For example, parting surface machining cost is about 10% of basic mold cost, and hence 0.1 is used as cost appraisers preference. 5. Develop the relationship matrix considering the complexity, using 19 scale (1 = weak, 3 = medium, 9 = strong) 桂林电子科技大学毕业设计（论文）说明书用纸 第 15 页 共 18 页 6. Construct the correlation matrix using 0.11.0 scale (0.1 =weak, 0.3 = medium, 0.9 = strong) 7. Normalize the relationship matrix using the Wasserman method. The coefficient of the normalized matrix is given by the following equation 12: 8. Calculate the technical importance of each tooling parameter. 9. The technical importance values can be used as respective cost moodier. The entire methodology for die and mold cost estimation is illustrated with an industrial example in Sect. 5. Fig. 4. Pressure die cast component and die inserts 5 Industrial examples Figure 4 shows an aluminum part used in ceiling fans, along with the corresponding die inserts. The fan component is produced using cold chamber pressure die casting process. The die design and development was relatively difficult as the part consists of a number of small geometric features and split parting surface. A combination of CNC and EDM processes are used to manufacture core and cavity die inserts in H13 material. Mold bases, ejectors and screws are purchased from standard vendors. 5.1 Basic mold manufacturing cost A CAD model of the casting was used as input to design the die. To estimate the basic mold cost, the mold machining features and the corresponding processes were rest indented. Then the feature machining cost was estimated using Eq. 3. The feature and its critical dimensions did (I the dimension of feature) and corresponding dimensional tolerance it (dimensional tolerance of i th dimension) were considered in calculating the complexity factor. The results are shown in Table 6. The following rates were used (in Indian Rupees； 1 INR US$ 0.02): 5.2 Cost moodier The main complexity characteristics of the die considered in this example are as follows: 桂林电子科技大学毕业设计（论文）说明书用纸 第 16 页 共 18 页 1.Straight parting surface (simple) 2.Circular cavity split on both sides (chances of mismatching) 3.12 ejector pins (diameter minimum 3 mm, maximum 8 mm) 4.Die material H13 (needs hardening and tempering, hard to machine) 5.Surface nish Ra 0.4 m (needs polishing) 6.Number of side cores: Nil 7.Number of core pins: 12 + 1 (alignment is critical). The QFD model was developed as discussed in Sect. 4. The eight cost