INVERSED COOLING CHANNEL DESIGN FOR INJECTION MOULDS BASED ON LOCAL COOLING DEMAND AND MATERIAL PROPERTIES

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1 INVERSED COOLING CHANNEL DESIGN OR INJECTION MOULDS BASED ON LOCAL COOLING DEMAND AND MATERIAL PROPERTIES Prof. Dr.-Ing. Christian Hopmann and Dipl.-Wirt.-Ing. Philipp Nikoleizig Institute of Plastics Processing (IKV) at RWTH Aachen University Seffenter Weg 01, 5074 Aachen, Germany Abstract Due to the high influence of the cooling phase in injection molding, the thermal mold design is a crucial element for high precision injection molded parts. Thus, a method for an automated cooling channel design phase o the local cooling demand of the part is introduced. A hybrid simulation chain is used to calculate this demand and derive cooling channels afterwards. Also an outlook how to influence and control the local cooling supply of the derived cooling channel system is given and implemented as an extension to the methodology. irst results show a promising perspective to combine local cooling demand and supply for an improved and suitable thermal mould design. Introduction The cooling phase of the part from processing temperatures to ejection temperatures mainly characterizes the injection molding process. In this phase also cycle time and the part quality are determined to a high level [1]. Especially the dimensional accuracy of the part is crucial for high precision parts. Plastics tend to a comparatively high change in density within the production relevant temperatures and pressures. This shrinkage potential is illustrated in igure 1 in the pνt-diagram for a Polyamide 6 (Durethan B 30 S, Lanxess Deutschland GmbH, Cologne, Germany). The pνt-diagram features the specific volume (reciprocal of density) ν of the plastics in relation to the temperature T and pressure p. The green line demonstrates the course along an exemplary injection molding cycle at a local point of a part. igure 1. pνt-data of a Polyamide 6 []. The part warpage is caused by a different shrinkage potential in different areas of the part, as proven for example by Jürgens [3]. Regarding the pνt- diagram it can be described as different local solidification curves, so that the 1 bar line (0 bar line for measurement and fitting) is locally hit at different specific volumes. If different shrinkage potential occurs, inner stresses inside the part are the result, which can only be balanced through the warpage of the part. So, the avoidance of different shrinkage potentials is elementary for a dimensional accurate part. Because the local solidification is significantly influenced by the molds cooling channel system, the importance of a proper thermal mold design phase becomes immanent. State of the Art Besides the wish for a fast and efficient injection molding cycle, the aforementioned challenges lead to investigations to describe and simplify the thermal mold design phase. The efforts reach from a transfer of analytical approaches into the computer aided design to full mathematical and computational descriptions of the solidification process. Those efforts have a forward looking character and need an intense interpretation after the solution is calculated. An automated thermal mold design phase is still not available. Nowadays, this issue is progressively addressed through different research activities into user independent optimization strategies for a proper cooling channel design [4, 5, 6]. Mehnen et al. rely on the use of evolutionary algorithms and model a system based on light exchanging surfaces, which are simulated by a ray tracing method [4]. As the first step only spheres are used of the system, as parts to be analyzed. Maag and Küfer, in contrast, study a cluster algorithm which is combined with a branch and bound search algorithm to find the ideal cooling channel position [5]. Contrarily, aßnacht et al. approach an automated cooling channel positioning by an artificial neural network, which covers numerous problems concerning temperature control [6]. This also means that solutions may only come from the space of simulated training problems respectively from the possible interpolations in between. Common to all of these approaches is the forward headed nature which emphasizes the temperature control, SPE ANTEC Indianapolis 016 / 1115

2 but the evaluation of the cooling quality is only possible after the simulation [4, 5, 6]. Though also for those computer-aided optimizations a precise definition of the cooling channel design is necessary in advance and essential for the quality of the result. Without knowledge regarding the local cooling demand for minimal part warpage and control of the polymer a targeted use of an optimization is not possible. inally Agazzi et al. show a promising approach which is based on an inverse heat conduction problem [7]. Thus, in this case a part is defined as polymer with homogeneous starting temperature. Along a given cooling area, surrounding the part, an optimized temperature distribution is calculated with a conjugate gradient algorithm in respect to a given objective function, which is based on fast heat removal as well as a homogeneous temperature distribution inside the part. Indeed, an inverse cooling channel design is performed, but also along the analytical approach of thermal homogeneity of the part. Especially the approach of Agazzi et al. seems promising to implement the initial premise to reduce and, in the best case, avoid different shrinkage potential completely. The following is an attempt to adapt this premise to his methodology. Design Approach and Setup The general setup of the inversed thermal mold design phase is based on the optimization of Agazzi et al. But there are already several significant extensions made to their original model [8, 9]. This hybrid simulation chain enables the use of more accurate process and material data as well as a better description of the shrinkage and warpage process. The complete process of the hybrid design approach is shown in igure. temperature, density and other material properties like viscosities etc. of the part material. This information is exported and mapped to the optimization step. To identify the local cooling demand, a modified quality function is introduced, which is minimized by altering the temperatures on the surrounding mold domain. The quality function Q, shown in equation 1, is based on two basic elements. Q T C = m i1 k i1 1 T Ej - Tloc (x i, ;t;tc ) d 1 wm - (x wk i, ;t;tc ) d The first term addresses the differences to the required ejection temperatures T Ej on the parts surface and the local differences T to it. The second term loc addresses the part quality with the aimed homogeneous density and their local differences inside the part. Both terms can be weighted with w m / and are integrated k over their respective domains. Here, a gradient based algorithm is used, which can identify the minimum in an efficient way. After the optimization is converged, the local cooling demand of the part is available and cooling channels can be derived. To validate the current approach, an additional injection molding simulation is carried out. Exemplary Investigation To validate the functionality of the modified approach, a test case was setup for a simple plate specimen with three rips as illustrated in igure 3. The thickness of the plate is 1.5 mm and 1 mm for the rips. (1) igure. Hybrid approach and flow chart of the proposed inversed thermal mold design phase. irst, the necessary cooling time according to the thickest area of the part is calculated. urthermore, a surrounding area around the part is defined as the optimization space and mold domain. Here, the local cooling demand of the part is later calculated. or the next step a conventional injection molding simulation delivers input data at different time steps regarding local pressure, igure 3. Exemplary part and dimensions. SPE ANTEC Indianapolis 016 / 1116

3 The modelled material is the Polyamide 6 shown in igure 1 of Lanxess Deutschland GmbH, Cologne, Germany. And the simulation boundary conditions can be found in Table 1. Table 1. Settings for the injection molding simulation of part cooling, shrinkage and warpage. Parameters Melt temperature 80 C Ejection temperature 140 C Cooling fluid temperature 80 C Injection pressure 1,000 bar Holding pressure 800 bar Cooling time 8 s Results and Discussion The first result of the hybrid design phase is the solution to the quality function and the temperature distribution inside the mold around the part as shown in igure 4. more manual driven one, so a fully automated design is not jet implemented. But still, this approach is close to solutions most commonly available for injection molds in comparison to generic 3D conformal cooling channels. Implementation to local cooling supply Next step of the cooling channel design methodology is the derivation of a useful cooling channel system. Within the test case this was done along the isothermal line of 80 C and conventional rounded shapes. Here, also alternative ways to proceed are possible, which will be investigated in the future. Besides some good results, as discussed below in igure 8 (left side), it is also obvious, that the derived cooling channels are a simplification and that the local cooling supply of this cooling channel system is not yet fully connected to the local cooling demand of the part. A new and innovative possibility to influence the heat transfer between mold and coolant locally is the use of so called turbulators or rips at certain areas of the cooling channel. In an additional research project founded by the Ai, it was investigated, to what extend the heat transfer can be increased and what the relevant geometric aspects of turbulators were. In igure 5 an example of a ripped cooling channel in comparison to a plain channel is given [11]. igure 4. Result of the optimization and derived cooling channels. The solution reflects the local cooling demand of the part. Here, careful design of the optimization affects the results, which can be seen by the comparable low range of temperatures, which are needed to reach the minimum of the quality function. Based on this solution, isothermal lines of 80 C, which is the initial mold temperature, are identified and used according to Agazzi et al.. His approach is modified in a way, that on the position of the isothermal lines conventional round channels are to be placed. This procedure was chosen based on investigations, where an analysis of different cooling channel shapes showed that round shapes delivered good heat transfer rates and comparatively low pressure drops [10]. This approach is a simplification compared to the original solution and other methods of cooling channel derivation as described e.g. by Aggazi et al.. urthermore, it is a igure 5. Effect of turbulators on the HTC inside a cooling channel. It is significant, that the heat transfer of the shown cooling channel can be homogenized along the flow path and therefore, the heat transfer at the end of the path is significantly higher in the case of the ripped channel. Besides the rising of the heat transfer, also the resulting rise in the pressure drop of the complete system has to be covered within the design phase. Within this example solely the theoretical point of view of the problem to SPE ANTEC Indianapolis 016 / 1117

4 adjust the local heat transfer is in the center of the investigation, so pressure drop is not considered any further here. In view of the Ai funded research project and a possible influence on the local cooling supply of the cooling channel system and the simplification of the derived cooling channel of the first result, a possible combination of both researches can be realized in a modified flow chart of the inversed thermal mold design phase as given in igure 6. improvement through local variable heat transfer is clearly visible. The level of HTC was set to a level, which can be reached though turbulators and set between 9,000 and 15,000 W/m²K. Because those boundaries are met, the approach can be stated as possible in principle. igure 8. Result of the mold temperatures and part warpage of the hybrid approach with fixed HTCs. igure 6. Extended Hybrid approach and flow chart of the proposed inversed thermal mold design phase. After the determination of the local cooling demand and the derivation of cooling channels a fourth step is integrated in the design phase. Here, the heat transfer coefficient (HTC) between mold and coolant is optimized with the same quality function. While the heat transfer coefficient for the first design was set to a constant level of 10,000 W/m²K and the position of the cooling channels were identified, here the positions remain fixed and the necessary varying local HTC is determined. The result of the local HTCs and the variations from the original setup of 10,000 W/m²K are shown in igure 7. inally, a comparison between the design with constant HTC and the extended design with variable HTC and the effect of the design is shown in igure 8 and igure 9. Both igures show the mold temperatures at the ejection point. Here, there are only slight differences visible between the two setups, but still existing, as for example shown in magnifications. In the right side of the igures the resulting warpage of the part is visualized. igure 9. Result of the mold temperatures and part warpage of the extended approach with variable HTCs. igure 7. Results of local HTCs for each cooling channel. The level of HTC for the second version is significantly different compared to the constant version. Also some channels need to have lower HTC in the area at the end of the rips, while most of the channels need to have higher HTC. Here, the simplification as well as the or a better comparison, the differences between the two results are also illustrated on three exemplary points, which are summarized in Table. The already good results of the first design can further be improved with the second design at all three measurement points of the part. Table. Total displacement of the part for the two setups at three points [mm]. Constant HTC Various HTC P [mm] [mm] P [mm] [mm] P3.449 [mm].344 [mm] SPE ANTEC Indianapolis 016 / 1118

5 Thus the effectiveness of the enhanced inverse cooling channel design can be shown. However, as a perspective for a further reduction of part warpage, there are additional aspects, which should be integrated into the inverse thermal mold design methodology. irst, a threedimensional design has to be considered and realized. However, to do so, the challenge is the minimization of the required computing power. Secondly, the possibilities for the derivation of the cooling channels system must be qualified and validated. Concerning the realization of a local controllable cooling supply, different options arise to extend the actual design methodology. Besides the consideration of controlling the local heat transfer in the cooling channel system with rip turbulators, also different mold materials and coating, which support or insulate heat conduction, should be covered. Also the possibility for local heating of the mold, respectively the regulation of heat supply, should be introduced. inally, it is also necessary, to consider and realize a mold compensation for the unavoidable volume shrinkage induced by the thermal contraction of the material. These topics will be addressed in currently running research projects at the IKV and other partners of the collaborative research centre. Conclusions A method of an inversed automated thermal mold design phase is introduced. The fundamental principle of this method is a hybrid simulation approach beginning with a quality function which avoids warpage by minimizing the local shrinkage potential. By introducing an exemplary part the basic functionality of the method could be shown. In the next step a sensible derivation of the cooling channels has to be developed. A possible approach can be a stacked design beginning with the identification of the local cooling demand of the part and followed by the determination of the local cooling supply of the cooling channel system. An innovative possibility to control heat transfer locally between mold and coolant, can be the use of rip turbulators, which are applied in certain section of the cooling channels. Acknowledgement The research project 1871 N of the orschungsvereinigung Kunststoffverarbeitung has been sponsored as part of the "Industrielle Gemeinschaftsforschung und -entwicklung (IG)" by the German Bundesministerium für Wirtschaft und Energie (BMWi) due to an enactment of the German Bundestag through the Ai. We would like to extend our thanks to all organizations mentioned. The depicted research has been funded by the Deutschen orschungsgemeinschaft (DG) as part of the Collaborative Research Centre 110, as part of the research group B1 Algorithms for Interpreting a Temperature Layout for Injection molding Tools While Considering Local Cooling Demands. We would like to extend our thanks to the DG. References 1. G. Menges, W. Michaeli, P. Mohren: Spritzgießwerkzeuge. Auslegung, Bau, Anwendung. München, Wien: Carl Hanser Verlag, (007). N.N.: Datenblatt Durethan B 30 S Datenblatt, Lanxess Deutschland GmbH, Köln, (015) 3. Jürgens, W.: Untersuchungen zur Verbesserung der ormteilqualität beim Spritzgießen teilkristalliner und amorpher Kunststoffe. RWTH Aachen, PhD Thesis, (1969) 4. J. Mehnen, T. Michelitsch, T. Beielstein, K. Schmitt: Evolutionary Optimization of Mold Temperature Control Strategies. Journal of Engineering Manufacture (JEM) B6 657 (004) 5. V. Maag, K.-H. Küfer: Optimal cooling in injection molding and die casting. Proceedings of the International Conference on Engineering Optimization. Rio de Janeiro, Brazil, (008) 6. P. aßnacht, J. Kerkeling, R. Nickel: Keep it cool mit KI. kunststoff-magazin 9 18 (011) 7. A. Agazzi, V. Sobotka, R.L. Goff, Y. Jarny: Uniform Cooling and Part Warpage Reduction in Injection Molding Thanks to the Design of an Effective Cooling System. Key Engineering Materials (013) 8. K. Meschede: Simulative Untersuchung der Verzugsminimierung von Spritzgießbauteilen anhand numerisch optimierter Kühlkanallayouts unter Berücksichtigung des spezifischen Volumens. RWTH Aachen, unpublished master thesis, (015) 9. C. Hopmann, P. Nikoleizig: Minimisation of warpage for injection moulded parts with reversed thermal mould design. Conference Proceedings of the 4th ECCOMAS GACM Young Investigators Conference (YIC). Aachen, (015) 10. L. Gesenhues: Simulative Analyse der Charakteristika eines verrippten Temperierkanals für Spritzgießwerkzeuge. RWTH Aachen, unpublished bachelor thesis, (014) 11. J.-M. Werner: Konstruktion eines Werkzeugeinsatzes zur Validierung der simulativen Untersuchung des Einflusses von ließhindernissen auf die lokale Wärmeübertragung im Spritzgießwerkzeug. RWTH Aachen, unpublished bachelor thesis, (015) SPE ANTEC Indianapolis 016 / 1119