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Design optimization of an injection mold for minimizing temperature deviation Abstract The quality of an injection molded part is largely affected by the mold cooling Consequently this makes it necessary to optimize the mold cooling circuit when designing the part but prior to designing the mold Various approaches of optimizing the mold cooling circuit have been proposed previously In this work optimization of the mold cooling circuit was automated by a commercial process integration and design optimization tool called Process Integration Automation and Optimization PIAnO which is often used for large automotive parts such as bumpers and instrument panels The cooling channels and baffle tubes were located on the offset profile equidistant from the part surface The locations of the cooling channels and the baffle tubes were automatically generated and input into the mold cooling computer aided engineering program Autodesk Moldflow Insight 2010 The objective function was the deviation of the mold surface temperature from a given design temperature Design variables in the optimization were the depths distances and diameters of the cooling channels and the baffle tubes For a more practical analysis the pressure drop and temperature drop were considered the limited values Optimization was performed using the progressive quadratic response surface method The optimization resulted in a more uniform temperature distribution when compared to the initial design and utilizing the proposed optimization method a satisfactory solution could be made at a lower cost Key words Injection molding Cooling channel Cooling analysis PQRSM Design optimization 1 Introduction The cooling stage is the longest stage during the cycle time of the injection molding process Therefore the most effective method to reduce the cycle time is to reduce the cooling time The cooling time is fundamentally determined by the part thickness and mold temperature which creates a cooling time limitation If the mold temperature and part thickness are uniform over a whole part the cooling time is not a concern however non uniform part thickness and mold temperature distribution lengthen the overall cooling time A longer cooling time means poor temperature uniformity which can cause the part to warp This is especially true for large products such as automotive bumpers and instrument panels It is for these types of parts that temperature uniformity becomes the most important factor in mold design We developed an automated optimization of the cooling circuit for an early part design in order to check the design validity Usually the early part design is checked by the filing packing and warpage analyses without a cooling analysis This is because the assumption is that the mold temperature is uniform which is not actually true Providing a rapidly optimized cooling circuit for the designed part would help part designers correct their design The optimization was designed to minimize the part temperature deviation using design variables such as the diameters and distances of the cooling channels and baffle tubes and the depths of the part from the mold surface of the cooling channels and baffle tubes A commercial computeraided engineering CAE tool Autodesk Moldflow Insight was used for the cooling analysis We successfully obtained an optimized cooling circuit in a time much shorter than can be achieved in a manual design In order to develop the automated optimization of the cooling circuit for the practical mold design practical design parameters such as the pressure drop limit and the coolant temperature rise were considered in the optimization The performance of the optimization technique can be affected by numerical noise in the responses To find an optimum solution effectively when numerical noise exists we performed an optimization by applying a regressionbased sequential approximate optimizer known as the Progressive Quadratic Response Surface Method PQRSM Hong et al 2000 which was part of a commercial process integration and design optimization PIDO tool known as the Process Integration Automation and Optimization PIAnO FRAMAX 2009 Figure 1 Finite element model of the product used for the optimization 2 MODEL AND CHANNEL CONFIGURATION 2 1 Model Configuration The model used for the optimization and CAE analysis was an automotive front bumper FB The size of the part was1 800 600 mm the element type was triangular and then umber of elements in the model was approximately 26 000 with an average aspect ratio of 1 5 The model is shown in Figure 1 2 2 Cooling Channel Configuration The cooling circuit for the automotive bumper mold is typically designed to have a horizontal plane of lin e cooling channels and to install baffle tubes from the line cooling channels However in this design unnecessarily long baffle tubes attached at a line cooling channel may cause a high pressure drop in the cooling channel The line cooling channels may not contribute to mold cooling due to their large distance from the part surface In order to improve the design the line cooling channels were located along the offset profile of the part surface as shown in Figure 2 The end points of the baffle tubes were also located on the offset profile along a line cooling channel Either the line cooling channels or baffle tubes were located on the offset profiles with equal arc distances between them 3 FORMULATION 3 1 Design Constraints The limitation of the pressure drop and the temperature rise between the inlet and outlet of cooling channel should also be considered in the design of the mold cooling circuit A high pressure drop usually occurs in a needlessly long cooling circuit In a long cooling circuit the flow rate of coolant is low which results in a high mold temperature and a high temperature rise at the outlet The design defect could eventually be found in the cooling analysis however the optimization is already time consuming so it is better to instead apply the limits as constraints in the optimization In this work we assumed that 4 line cooling channels were connected in series as a cluster as shown in Figure 3 Clusters are connected in parallel by a manifold Usually the maximum pressure drop in a cluster is limited to 200kPa and the maximum temperature rise at the outlet is 5oC Menges et al 2001 In the cooling analysis each line cooling channel is regarded as a separate independent circuit for convenience Because there were 4 line cooling channels in a circuit the limits on the pressure drop and the temperature rise in each line cooling channel were 50kPa and 1 25oC respectively We also have an additional constraint due to the fact that the diameter of the baffle tube must be greater than or equal to the diameter of the cooling channel because the baffle tube has lower heat removal efficiency than the cooling channel where G1 is the constraint on pressure drop G2 is the constraint on temperature rise and G3 represents the subtraction of the diameter of the baffle tube from the diameter of the cooling channel Figure 2 Configuration of cooling channels located along the offset profiles 3 2 Design Variables In this work the diameters distances and depths of the line cooling channels and baffle tubes were chosen as design variables for optimization The total number of design variables was 6 as shown in Table 1 Typically the diameters of the cooling channels and baffle tubes are determined by the mold designer according to their rule of thumb Rhee et al 2010 However it has been examined in great detail among the mold designers Table 1 shows the design variables with their ranges and initial values The minimum values for the cooling channel distance baffle distance and baffle depth were determined by the constraints of the machining requirement The maximum values of cooling channel distance and baffle distance were determined by the empirical maximum obtained from the mold designers The baffle distance was a discrete variable due to a restriction in the automated use of the CAE software In this work the baffle distances for optimization were 60 90 and 120 mm Figure 3 Clusters consisting of 4 cooling channels with baffle tubes Figure 4 Scheme of the temperature field by the cooling channels 3 3 Objective Function A principal purpose of the mold cooling circuit optimization is to achieve uniform temperature distribution over the part The uniform temperature distribution means that the temperature deviation caused by the cooling channels is minimized as shown in Figure 4 The objective function in the optimization was the standard deviation of part temperature as shown in Equation 4 The part temperature was an arithmetic average of the upper and the lower surfaces of the mold halves The mold surface temperature was calculated from the finite element of the part where is the standard deviation of the part temperature E i is the temperature of i th element Ew is the average temperature of the entire triangular elements and N is the number of elements 4 OPTIMIZATION 4 1 Parametric Study In order to examine the effects of the design variables on the objective function pressure drop and temperature rise parametric studies were carried out A parametric study was performed by changing a variable in a certain range while keeping all other variables fixed Figures 5 7 show the results of parametric studies for the objective function pressure drop temperature rise respectively In each figure the x axis indicates the levels of design variables Every design variable was divided into 11 levels from its lower bound to its upper bound 5 and 5 mean the lower and upper bounds respectively When examining the temperature deviation the diameter of the cooling channels shows little influence to the objective function see Figure 5 This result was predictable because the cooling channel affects the part temperature to a lesser degree than the baffle tubes in the automotive bumper mold The automotive bumper mold has a deep core so that the mold cooling depends upon the baffle tubes rather than the cooling channels Another reason of the lack of influence can be that the flow state in the cooling channel remains turbulent in the range of the parametric study The cooling channel usually has a smaller diameter than the baffle tube When the flow in the baffle tube is kept in the turbulent state the flow in the cooling channel will be in the turbulent state The diameters of the baffle tubes show a tangible influence when it increases above a certain value Increasing of the diameter changes the flow in the tube to a laminar flow state This is the cause for the lower heat transfer coefficient when compared to the turbulent flow state This is why the temperature deviation becomes larger when the baffle tube diameter increases Among all parameters the baffle depth shows the largest influence on the objective function as shown in Figure 5 As the baffle depth increases the objective function increases This means that the deeper location of the baffle tubes causes the temperature deviation to increase Also it confirms that the cooling of the automotive bumper mold depends upon the baffle tubes The diameters of the cooling channels and the baffle tubes have the highest influence on the pressure drop in the cooling circuit while the other variables show little influence see Figure 6 As the diameters increase the pressure drop decreases after a certain value This is also a predictable result as a larger diameter decreases the pressure drop The influences of the temperature rise at the outlet are shown in Figure 7 The most influential parameters are the baffle diameter and the channel distance The influence of the baffle diameter shows the highest values in the range from 1 to 3 In the case of the smaller baffle diameter the reduced surface area for the heat transfer may cause a smaller temperature rise while the larger baffle diameter may cause the lower heat transfer coefficient due to the lower flow rate The increased channel distance means that each cooling channel takes up a larger area of the part surface with a larger amount of heat removal This may give a physical explanation to why the increase of the temperature rise increases with channel distance The fluctuations shown in Figure 7 are supposed to be numerical noise Figure 5 Parametric study result of temperature deviation objective function 5 CONCLUSION In this study we carried out the optimization of the cooling circuit for an automotive front bumper The design objective was to minimize the temperature deviation while satisfying all constraints There were three design constraints that included the pressure drop temperature rise and aspect ratio in addition to side constraints on six design variables Among the six design variables the baffle distance was the discrete design variable Thus we carried out optimizations for the three cases of baffle distances being60 90 and 120 mm The lowest temperature deviation was obtained in the case of a baffle distance of 60 mm In this case the temperature deviation was reduced by 19 2 compared to the baseline design while satisfying all design requirements It is believed that the design optimization approach of employing CAE and PIDO tools adopted in this study can be applied for the design of many industrial manufacturing processes REFERENCES FRAMAX Inc 2009 PIAnO Tutorial FRAMAX Inc 2009 PIAnO User s Manual Hong K J Choi D H and Kim M S 2000 Progressive quadratic approximation method for effective constructing the second order response surface models in the large scaled system design The Korean Society of Mechanical Engineers A 24 12 12 3040 3052 Koresawa H and Suzuki H 1999 Autonomous arrangement of cooling channels layout in injection molding Proc 1999 Annual Technological Conf Society of Plastics Engineers 1073 1077 Menges G Michaeli W and Mohren P 2001 How to Make Injection Molds 3rd Edn Hanser Gardner Publications Inc Ohio 298 302 Rhee B O Park C S Chang H K Jung H W and Lee Y J 2010 Automatic generation of optimum cooling circuit for large injection molded parts Int J Precision Eng and Manufacturing 11 439 444