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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 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 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.
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 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 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 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 Γ1 and Γ3 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 Γ3 is a third kind 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.
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.
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 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 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 groups: 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 appraiser’s 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 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.
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