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Int J Mater FormDOI 10.1007/s12289-016-1334-3ORIGINAL RESEARCHInverse thermal mold design for injection moldsAdressing the local cooling demand as quality function for an inverse heat transferproblemCh. Hopmann1 P. Nikoleizig1Received: 26 September 2016 / Accepted: 7 December 2016 Springer-Verlag France 2016Abstract The thermal mold design and the identificationof a proper cooling channel design for injection moldsbecomes more and more complex. To find a suitable cool-ing channel system with objective rules based on the localcooling demand of the part a new methodology for thethermal mold design based on an inverse heat transfer prob-lem was introduced. Based on a quality function regardingproduction efficiency as well as part quality, additionalaspects to model the injection molding process are dis-cussed. Aim of those extensions is the improvement of theinverse optimization of the problem.Keywords Injection molding Thermal mold design Inverse heat transfer problem pvT-data Heat transferIntroductionWith injection molding, increasingly complex componentscan be produced, but at the same time the requirements ofthe necessary injection mold rise. Concurrently due to theeconomic pressure, e.g. by global competition, strives forhigh efficiency and short production cycles are essential.Since the injection molding cycle is primarily characterizedthrough the cooling of the melt into a dimensionally stablestate, it is contiguous to focus on the cooling channel systemenvelopeback P. Nikoleizigphilipp.nikoleizigikv.rwth-aachen.de1Institute of Plastics Processing (IKV), RWTH AachenUniversity, Seffenter Weg 201, 52074 Aachen, Germanyof the injection mold for additional improvement in effi-ciency (Fig. 1b). Usually, the cooling channels are realizedthrough bores in the injection mold, which are connected byfittings to a complete channel system. Innovative technolo-gies such as the selective laser melting (SLM) now enablethe layered structured buildup of molds from metal pow-der. With this approach, the cooling channel system can begenerated almost in any desired shape and course. The cre-ation of a proper cooling channel system is a challengingtask, also hindered by these opportunities and at the sametime more complex parts. Additionally thermal mold designphase is impeded due to particular thermoplastic materi-als, which are often used in technical parts and tend to acomparatively large shrinkage (Dependent on temperatureand pressure) as a result of the crystallization process (asillustrated in Fig. 1a between points 3 to 5). This shrink-age causes stresses inside the part, if local differences inthe shrinkage potential occur. Furthermore, the stresses canonly be compensated through a deformation of the part. Thisso-called warpage may prevent the correct usage of the partand therefore must be avoided 1, 2.State of the artBesides the wish for a fast and efficient injection moldingcycle, the aforementioned challenges lead to investigationsto describe and simplify the thermal mold design phase. Theefforts reach from a transfer of analytical approaches intothe computer aided design to full mathematical and com-putational descriptions of the solidification process. Thoseefforts have a forward looking character and need an intenseinterpretation after the solution is calculated. A fully auto-mated thermal mold design phase is still not available.Int J Mater FormFig. 1 Visualisation of theinjection molding cycle withprocess variables (a)andapiechart (b)3Pressurepg1 p1= 1 bar 300100 2002.5Total deformation mm1.250MP2MP1MP3MP2MP1MP3Int J Mater FormTable 3 Warpage of the cooling channel systems Z01 and Z15Total deformation Measuringpoint 1 mmMeasuringpoint 2 mmMeasuringpoint 3 mmZ01 1.890 1.247 2.848Z15 1.616 1.007 1.807Since the change of the quality function is less than 1 %when viewing 15 cycles against 25 cycles, thus 15 cyclescan be seen as a useful optimization range. Figure 6ashowsthe temperature distribution at the point of optimization ofthe setups Z01 and Z15. The local cooling demand is esti-mated on the basis of the reference temperatures. In bothcases temperature distribution alternates between high andlow values compared to the calculated reference temper-atures. The reference temperatures, which are determinedin optimizing Z01, vary much more than those which aredetermined in the optimization of Z15. Because in the innerside of the corners the cooling demand is greater thanin the plate-shaped sections, very low reference tempera-tures are intended here. Figure 6b also shows the 80Cisothermal lines of the temperature for three different cyclenumbers (1 cycle, 15 cycles and 50 cycles). The isother-mal lines optained by Z15 do not differ significantly fromthose obtained by the optimization at 50 cycles. However,the difference to the isothermal lines of Z01 is considerable.This is evident, for example, in the lower areas of the ribs,where more isothermal lines lines emerge for the multicycleoptimization Z15.The cooling channel systems are analysed in conven-tional injection molding simulations to investigate theeffects of the differences between the systems on the valueof the quality function and the part warpage. For the cool-ing channel system a heat transfer coefficient of =10000 W/m2K and a fluid temperature of T = 80Cis chosen. The setup is given in Fig. 7a, which shows thetemperature distribution at the end of the cooling phase ofthe 15thcycle. All the other parameters of the simulationremain unchanged compared to the values used prior. Thefluctuations of the temperature on the surface of the cavityand especially in the corners are lower with the temperingsystem Z15.The calculated total deformation is visualized in Fig. 7band the values of three measuring points which are locatedat the ends of the ribs, are shown in Table 3. The result-ing warpage, which is achieved with the tempering systemZ15, is overall lower than the one, which is determined withthe tempering system Z01. At the measuring points the totaldeformation, resulting from use of the cooling channel sys-tem Z15, is between 14.50 % at MP1 and 36.55 % at MP3lower compared to the system Z01. Therefore, the accuracyof the methodology can be increased by the extension of themodel by using multiple cycles.Implementation of handling timesInitially, only the cooling phase of the injection mold-ing process was modeled. To further enhance the accuracyof the model, a view on the influence of mold openingand closing as well as part ejection is made. These pro-cess phases are generally much shorter than the coolingphase. Still, heat is transferred during these phases, so theimplementation can make a difference for the optimiza-tion. Modeling of the opening and closing process elongatesthe optimization duration of each cycle to the durationof these processes. During these times (hereafter sum-marized called handling times) the cooling channel fluid(usually water) will continue to remove heat out of themold.Fig. 8 Optimization results (a)and derived isothermal lines (b)without and with handling timesTemperaturedistribution at the end of coolingphase of cycle 15200Temperature C1002.5Total deformation mm1.250Temperature C95 11080b)a) Deformation of the partMP2MP1MP3Int J Mater FormTable 5 Warpage for simulations without and with handling timesTotal deformation Measuringpoint 1 mmMeasuringpoint 2 mmMeasuringpoint 3 mmWithout handling times 2.168 1.465 2.883With handling times 2.048 1.165 2.775of 65C. In comparison the simulation covering the han-dling times results in lower warpage. This indicates, that theimplementation of handling times is useful. However, thetwocoolingchannelsystems derivedfromthe65Cisother-mal lines, result in higher warpage compared to the coolingchannel system derived from the 80C isothermal line andwithout covering handling times (see Table 5). This showsthat the quality of the generated cooling channel systemdepends on the set of isothermal lines, which are selected toderive the cooling channels. It can be stated, that the resultis affected by the handling times, but no universal claimcan be made. From the perspective of calculation time, itseems useful to disregard the handling times in order to savecomputation time.Implementation of injection phaseSimilar to the handling times, the filling phase, also calledinjection phase, takes only a short part of the injection mold-ing cycle. Sincethe melt is heavily sheared and still transfersheat to the mold, a variation of the melt temperature differ-ent from the initial melt temperature is obvious. In expandedmethodology, the melt is injected into a cavity which issurrounded by a mold without cooling channels. The tem-peratures which are established immediately at the end ofthe injection phase in the molded part are used as initial tem-peratures in the optimization. With this method, the shearheating as well as the simultaneous cooling is taken intoaccount in the optimization largely. Use of this initial tem-perature field is based on the assumption that the coolingchannel system has little effect on the heat transfer in themelt during the (short) injection process. In the following,this assumption will be examined. The aim of the investi-gation is to determine whether the injection phase needs tobe considered directly in the optimization or whether thiscan be avoided by the use of appropriate initial temperaturedistribution.The direct modeling of the injection process inside theoptimization would require considerable additional compu-tation time, since it requires the solution of fluid dynamicprocesses in the cavity. Also this approach needs a muchmore accurate discretization of space and time.Here, three different optimizations are performed. In thefirst optimization a uniform initial temperature through-out the melt is used. The hereby generated temperaturesystem is characterized in the following with T1. For thesecond optimization, the injection process is simulated ina mold having a uniform temperature of 80C. The tem-perature and pressure distribution of the part at the endof the injection phase is then used as the initial temper-ature of the melt in the optimization (T2). The derivedcooling channel system from T2 is then used in a third injec-tion molding simulation, to determine the temperatures atthe end of the injection phase again. These recursive gen-erated temperatures are used as initial temperatures for athird optimization named T3. In Fig. 10, the differencesin the assumed initial temperatures are shown. The dif-ference between the temperature field of T2 compared tothe uniform optimization T1 is shown in Fig. 10a. Num-bers indicate, that the temperatures differ more than 5 K.The difference between the second simulation T2 and thethird simulation T3 is visualized in Fig. 10b and here theFig. 10 Influence of shearstress warming and cooling onthe temperature distribution ofthe part for setup T2T1 (a)andT3T2 (b)Warming of the melt through shear stressduring injection phase5Temperature difference K02.5Total deformation mm1.250MP2MP1MP3MP2MP1MP3Int J Mater FormTable 6 Warpage of the cooling channel systems T1, T2 and T3Deformation Measuringpoint 1 mmMeasuringpoint 2 mmMeasuringpoint 3 mmSystem T1 1.952 1.223 2.601System T2 1.616 1.007 1.807System T3 1.677 1.181 1.87617.21 %, 17.66 % and 30.53 %, which is a more noteableimprovement.As we consider the setup of T2 as the basic setup forfurther design investigations, we compared this setup witha setup, which uses the quality function as proposed byAgazzi et al. and is also covering a homogeneous tem-perature distribution. Analysing the warpage of this cor-rensponding setup results in higher warpage for all threemeasuring points (+21.10 %, +39.52 % and +12.01 %)when compared to T2. Based on this result, the modifiedquality function and the implementation of additional injec-tion molding phases turn out to be better suitable in regardof quality.Conclusion and outlookOverall, the outlined investigations show the increase inaccuracy of the methodology through an alternatively pro-posed quality function and a enhanced detailed modelingof the injection molding process. Here, the quality func-tion is based on the local cooling demand of the part andthe prevention of local density variations inside the part. Asteady state is achieved with the simulation of several cool-ing cycles at the time of optimization. This will derive acooling channel system much better forming local coolingrequirements, which are required for an economic and qual-ity driven cooling phase, what is specified by the extensionof the model to other phases of the injection molding cycle.First, the extension of the model to multicycle optimizationdelivers much better results. Second the implementation ofthe handling times may improve the results, but may forcethe selection of new isothermal lines. No explicit recom-mendation can be given here, but future work will need tofocus on deriving a proper cooling channel system from theresult of the optimization. Also computation time for han-dling times, should be considered to decide if a modellingof the handling times is worth the effort. Thirdly the injec-tion phase was considered within the optimization. Here, theimplementation of the share of the shear stress warming isundoubtly an improvement for the methodology. The shareof the influence of the cooling channel system on the otherhand, does not lead to a further improvement, but requiresmore calculation time. As a conclusion an implementationhere is not clear without ambiguity.Further investigation will first focus on a more accu-rate modeling of the holding pressure phase. Currently, thisphase is simplified, due to numerical reasons. Second, mate-rial properties of pvT-data and modeling of shrinkage andwarpage come to the fore in respect to the proposed qual-ity function covering part density. Also, in the future, morecomplex, three-dimensional geometries should be includedin continuing investigations. In total, the proposed method-ology with the presented extensions already offers a promis-ing approach to the automated thermal mold design forinjection molds.Acknowledgments The depicted research was funded by theDeutschen Forschungsgemeinschaft (DFG) as part of the Collabora-tive Research Centres 1120 “Precision Manufacturing by ControllingMelt Dynamics and Solidification in Production Processes”, as partof the research group B1 “Algorithms for Interpreting a TemperatureLayout for Injection molding Tools While Considering Local CoolingDemands”. We would like to extend our thanks to the DFG.Compliance with Ethical StandardsConflictofinterests The authors declare that they have no conflictof interest.References1. Menges G, Michaeli W, Mohren P (2007) Spritzgiewerkzeuge.Carl Hanser Verlag, Munchen2. Michaeli W (2010) Einfuhrung in die Kunststoffverarbeitung. CarlHanser Verlag, Munchen3. 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