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EP2323050A1 - Computer-implemented method for optimizing an injection molding process for the production of thick-walled components - Google Patents
Computer-implemented method for optimizing an injection molding process for the production of thick-walled components Download PDF
Application number EP09013073A Other languages English (en) French (fr) Inventor Florian Dorin Christoph Klinkenberg Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.) Covestro Germany AG Original assignee Covestro Germany AG Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.) Filing date Publication date Application filed by Covestro Deutschland AGfiledCriticalCovestro Deutschland AG Priority to EP09013073ApriorityCriticalpatent / EP2323050A1 / de Publication of EP2323050A1publicationCriticalpatent / EP2323050A1 / de Withdrawnlegal-statusCriticalCurrent
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- The invention relates to a computer-implemented method for optimizing an injection molding process for the production of thick-walled components on the basis of a model parameterized on the basis of parameters to be specified. The present invention also relates to a corresponding computer program which, when executed on a computing unit, executes the proposed method. The method according to the invention is used in particular to increase the productivity of thermoplastic injection molding processes for the production of thick-walled components, such as, for example, optical components
- Optical lenses made of thermoplastics or other organic and inorganic plastics, for example for imaging or light-shaping (non-imaging) purposes, are currently being manufactured or developed using the injection molding process, including various special injection molding processes such as injection compression molding or dynamic temperature control of the corresponding shape.
- The optical performance of imaging and non-imaging lenses depends, among other things, on the wall thickness, the refractive index of the material used and the design of the lens surfaces. Often, depending on the application, lens wall thicknesses greater than 5, 10 or 15 mm are required, which is referred to as "thick-walled" in plastic injection molding.
- Plastic injection molded parts with wall thicknesses of more than 4 - 5 mm are considered "thick-walled". On the one hand, large wall thicknesses extend the cycle time considerably, since the wall thickness is included in the cooling time as a square. On the other hand, care must be taken to ensure that the holding pressure can be maintained for a sufficiently long time even in thick-walled areas without the connection between the gate and the thick-walled area (molten core) freezing. Furthermore, it is important that thick and thin-walled areas in the component are filled evenly, i.e. that the melt does not stagnate and begin to freeze in thin-walled areas due to the higher flow resistance.
- Injection molding is the basis for all other injection molding processes and is the most commonly used plastic processing method. Today it is common to use a so-called screw-piston injection molding machine as the injection molding machine, which usually pulls plastic in the form of granules from a funnel into the screw flights of the machine, breaks it up and shears it. The resulting frictional heat, in conjunction with the heat supplied by a heated cylinder, ensures a relatively homogeneous melt. This melt collects in front of a tip of the receding screw. In what is known as an injection phase, the screw of the screw-piston injection molding machine is pressurized on the rear side hydraulically or by mechanical force. The melt is pressed under high pressure, usually between 500 and 2000 bar, through a non-return valve, the nozzle pressed against the injection molding tool, possibly a hot runner system and a sprue channel into a shaping cavity, a so-called cavity of the temperature-controlled injection molding tool. A reduced pressure acts as what is known as holding pressure on the melt until the connection, also known as the sprue, has solidified or frozen. This ensures that any volume shrinkage that occurs during cooling can be largely compensated for. This is important for dimensional accuracy and the desired surface quality. Then the screw begins to rotate. In this way, the shot compound is prepared for the following molded part. During this time, the molded part can still cool down in the tool until the material in the core has solidified. The tool then opens and ejects the finished component.
- The locking force is the force that locks the corresponding tool against injection and re-pressing.
- The cavity, the cavity, of the tool determines the shape and the surface structure of the component to be manufactured. The screw profile also plays a role in the injection molding parameters, whereby a screw can be a single-flight three-zone screw with feed, compression and discharge zone or a barrier screw, usually for increased performance, or a core progressive PVC screw.
- So-called computer-aided engineering programs, or CAE programs for short, are often used today to simulate an injection molding process. However, these are focused on corresponding filling processes and not on minimizing cycle times or predicting component quality. In addition to these CAE programs, there are programs that are able to parameterize simulation calculations. Parameterization here means, on the one hand, a change in boundary conditions, such as melting temperature, mold temperature, holding pressure, etc. and, on the other hand, a change in geometries. In a multi-layer injection molding process, for example, a corresponding component can be divided into several layers that are injected one after the other or in parallel. For more information, see the publication by Döbler, Protte, Klinkenberg "Free Ride for White Light - LED Optics", published in Kunststoffe 04/2009, pages 83 to 86. The text by Stricker, Pillwein, Giessauf "Precision in focus - injection molding of optical molded parts", published in Kunststoffe 04/2009, pages 30 to 34, can also be used. With the possibility of parameterization, influences of individual parameters, for example on cooling time and component quality, can be examined and optimized. Rheological simulations and commercial optimizers cannot be combined sufficiently at the moment. Other CAE programs that can be combined with optimizers can depict a temperature behavior, but only to a limited extent, taking the respective injection molding process into account.
- Furthermore, various technologies for the injection molding of optical lenses are known, which can also be found in the above-mentioned publication by Stricker, Pillwein and Giessauf. Up to now, however, an injection molding process has always been optimized using a complex so-called “trial and error” process, which is usually expensive and lengthy.
- Multi-layer injection molding is the ideal production technology for thick-walled lenses. The component to be manufactured is injection molded step by step in several layers. Depending, among other things, on the wall thickness distribution, the arrangement of the respective layers, the order of the "partial shots" and different mold temperatures in the individual cavities, improvements in component quality and significant reductions can be achieved with multi-layer injection molding compared to single-layer injection molding of the cycle times. A reduction in cycle times is due, among other things, to the fact that the wall thickness of the component to be manufactured is included in the cooling time formula as a square. Of course, it must be taken into account here that the total potential of a reduction in wall thickness cannot be fully exploited, since optimal heat dissipation is only given for a second layer in the direction of the tool.
- The cycle times necessary to achieve the high quality often required for optical components are usually very long and are in the range of 5 to 20 minutes, in some cases even longer, in the case of thick-walled lenses in particular. This currently makes the use of such standard produced lenses in mass production, such as in the automotive industry or for other lighting purposes using LEDs, uneconomical.
- There is therefore a need for a method with the help of which corresponding cycle times in the production of optical components, in particular according to the multi-layer injection molding process, can be reduced even further, so that rational production is also possible for mass markets, as in the case of LED lighting becomes. At the same time, however, the highest possible quality of the respective lens should be achieved.
- One object of the present invention is therefore to provide a method to optimize a method for the production of thick-walled components, in particular thick-walled optical lenses, and to provide an injection molding method for optical precision components which is significantly shorter than the prior art Cycle times.
- A computer-implemented method is proposed for optimizing an injection molding process for the production of thick-walled components on the basis of a model parameterized on the basis of parameters to be specified. A thick-walled component with a component geometry is mapped in the model. The proposed method has at least the following steps:
- a) Definition of a group of parameters as main parameters on the basis of a relative influence of the parameters on a given model response,
- b) definition of parameter values for the main parameters as starting values for a subsequent optimization of the model and of respective tolerance ranges for the main parameters,
- c) Optimizing the parameter values of the individual main parameters with regard to a desired value of the model response in the respective tolerance ranges based on the starting values from step b),
- d) Setting the optimized parameter values of the individual main parameters from step c) as corresponding starting parameter values on an injection molding machine.
In the context of the present invention, a model response is to be understood as a result variable that results from the simulation or the corresponding model present here. Depending on the objective, a desired model response can be specified here, the value of which is then determined with the aid of the proposed method for respective values of the individual parameters and is ultimately optimized with regard to a desired value using the proposed method.
In the context of the present invention, a main characteristic is referred to as a parameter which is one of those parameters which, compared to other parameters, has a great effect on the corresponding model response or on its value. The number of main parameters to be determined depends on an optional determination or definition of the term “greatest influence” on the respective value of a desired model response.
According to one possible embodiment, the method further comprises that before step a) is carried out in a step al) for the individual parameters in each case a value for the predefined model response at different parameter values of the respective parameter and a resulting relative influence of the individual parameters on the value is determined for the model response, wherein in step a) the setting of the group of parameters as main parameters takes place on the basis of the relative influence of the individual parameters determined in this way, and that in a step b1) a correlation of the main parameters with respect to the value for the Model response is determined for different parameter values of the individual main parameters, the parameter values for the main parameters then being set as starting values for the subsequent optimization of the model and the respective tolerance ranges for the main parameters on the basis of the correlation determined in this way.
Before performing step a), in step al) when calculating the value for the model response for one of the various parameter values of a first parameter, this parameter value is entered into the model in each case in combination with all the different parameter values of the other parameters and from the respective resulting values for the model response is a mean value, which is then assigned to the parameter value of the first parameter as the value for the model response. This procedure is carried out for all further parameters with regard to their respective different parameter values. A joint consideration of the respective values thus obtained for the model response allows conclusions to be drawn about the relative influence of the individual parameters on the value of the model response. Such a consideration or evaluation takes place, for example, graphically.
As described above, the respective relative influence of the individual parameters can be determined by simulation, but with regard to the relative influence, empirical values for the individual parameters can also be used. The same applies to the definition of the parameter values of the main characteristics as starting values for the subsequent optimization. Here too, empirical values can be used.
In one possible embodiment of the proposed method, the component geometry includes, in addition to an overall shape, a variable number of layers and a respective thickness of these layers. The geometric shape of these layers in the component is also variable. Such a structure is relevant, for example, in the multi-layer injection molding process mentioned at the outset, or a component produced using this process generally has such a structure. Components to be produced in this way can, as already mentioned at the beginning, be optical lenses.
In a further possible embodiment of the proposed method, the desired value of the model response corresponds to an extreme value, in particular a maximum or minimum of the model response.
Furthermore, it is conceivable that suitable starting values for optimizing the model are determined not only for the main parameters but also for the remaining parameters. For this purpose, the proposed method, while retaining the starting values for the main parameters determined in step b), also provides the following step:
- b2) determining a correlation of the remaining parameters in relation to the value for the model response for various parameter values of the individual remaining parameters and from this determining parameter values for the remaining parameters as starting values for the subsequent optimization of the model and of respective tolerance ranges for the remaining parameters,
- c1) Optimizing the parameter values of the remaining parameters with regard to the desired value of the model response in the respective tolerance ranges based on the starting values from step b) and b2),
It can be provided that the method also has the following step:
- c2) determining the value for the model response for the optimized parameter values.
In a possible embodiment of the method according to the invention, the parameters to be specified are selected from a group consisting of component geometry parameters and injection molding parameters.
The component geometry parameters can be a layer thickness and a number of layers of the component to be produced.
The injection molding parameters are generally settings on a corresponding injection molding machine. This can be, for example, tool temperatures, melting temperatures, pressures, cooling times, injection profile, switchover point and holding pressure profile. Further parameters can be: cooling rates on the mold wall and other thermal properties of the mold.
It is possible that the respective parameters to be specified are specified as a function of a further variable such as temperature, time or another freely selectable field size.
When determining the relative influence of the parameters (with their different parameter values) on the model response, when determining the value for the model response for a respective parameter according to an embodiment of the method, 1 to 5 parameter values, in particular 2 parameter values, for example a minimum - and a maximum value is given. For these different parameter values of a respective parameter, the value for the predefined model response is then determined and a relative influence of the respective parameter on the value for the model response in comparison to the other parameters is specified therefrom. When determining the value for the model response for a parameter value of a first parameter, the parameter values of the remaining parameters are varied in such a way that one parameter value of the first parameter is combined with all parameter values of the other parameters, a respective value of the model response is calculated for all combinations and from the totality a mean value is formed of the values of the model response, which is then assigned to the one parameter value of the first parameter as the value of the model response. The same is carried out for the other specified parameter values of the first parameter and in each case for the different parameter values of the other parameters. For example, if you have only two parameters A and B and two different parameter values 1 and 2 for parameter A and two different parameter values 1 'and 2' for parameter B, then in a first calculation parameter A is given with parameter value 1 and parameter B with parameter value 1 ', in a second calculation parameter A with parameter value 1 and parameter B with parameter value 2' and to determine the relative influence of parameter A on the value of the model response, the mean value of the values obtained for the model response from the first and the second bill determined. The same is done for parameter value 2. The same procedure is used for parameter B and the corresponding parameter values 1 'and 2'. A comparison is then made of how the change in parameter A, parameter value 1 and parameter value 2, affects the model response or its value in comparison to a change in parameter B, parameter value 1 'and 2'. Using an example, this means: In the case of 2 parameter values each for parameters A and B, there are two values for the model response for each parameter, consequently, entered in an xy diagram, corresponding to two points each, namely for parameter A (1 , Model answer (1)) and (2, model answer (2)) and for parameters B (1`, model answer (1`)) and (2`, model answer (2`)). If you connect the respective two points for the respective parameters, a straight line results for each of the two parameters. The slope of the respective straight line shows the influence of the respective parameter on the value for the model response. The greater the amount of slope, the greater the influence.
The respective resulting relative influences of the individual parameters on the value for the model response are compared and a group of parameters can then be defined as main parameters from this. This means that, as a rule, those parameters are specified as the main parameters which, compared to the remaining parameters, have a high relative influence on the value of the model response.
A correlation with respect to the value for the model response can then be determined for these main parameters then determined on the basis of various parameter values of the individual main parameters. This means that the main parameters in this step are not considered independently of one another, but rather in combination and interrelationship with one another. It is possible to determine the interdependencies of 2 main parameters. In the case of a graphical evaluation in an xy diagram, the model response, such as the cycle time, as the dependent variable y, and a first main characteristic, such as a parameter A, as the independent variable x, are plotted, the model response then for various parameter values , such as parameter value 1 and parameter value 2, is calculated by parameter A and the resulting points are plotted accordingly in the xy diagram. Such a plot is carried out for different parameter values, for example parameter values 1 'and 2', of a second main characteristic such as a parameter B, whereby a corresponding number of plots or graphs results depending on the number of parameter values for the second main characteristic results whose behavior to one another provides information about the correlation of the first and second main parameters. If the plots run essentially parallel to one another, this indicates a low correlation; if the plots do not run parallel, a recognizable correlation is present. On the basis of a thus determined correlation of the main parameters in relation to the value for the model response, parameter values for the main parameters can then be established, which are used as starting values for a subsequent optimization of the model. Furthermore, on the basis of this determination of the correlation between the main parameters, respective tolerance ranges for the main parameters can be derived. When determining the correlation, the parameter values for the remaining, i.e. H. parameters not included in the correlation analysis are kept constant. In each case, a value that is relevant for practice is assumed. If, for example, the reprint is not a main parameter, ie if a fixed value is to be assumed for it, then this parameter value will be chosen as low as possible both in practice and then in the model in order to save material and energy, ie one Parameter value that is favorable for material and processing technology.
The correlation of the main parameters can be determined, for example, by introducing a covariance, which establishes a connection between main parameters in relation to the value for the model response.
In one possible embodiment of the method, 1 to 5 parameters are defined as main parameters, starting with the parameter with the greatest relative influence and, in the case of more than one parameter, continuing with the parameters immediately following with regard to the relative influence. This means that the five parameters with the greatest relative influence on the value of the predefined model response are generally used as main parameters, and their correlation with one another is determined in relation to the value for the model response. It is possible that when determining a correlation of the main parameters in relation to the value for the model response for different parameter values of the individual main parameters, 3 to 10 different parameter values are used for the individual main parameters. It can be provided that a total of 5 different parameter values are used for the individual main parameters.
On the basis of the determination of the correlation, parameter values are then established for the main parameters, which are used as starting values for a subsequent optimization. Furthermore, for the respective main parameters and the specified parameter values, respective tolerance ranges are determined for the main parameters, which are also included in the subsequent optimization. Those parameter values for the main parameters that lead to a value that is as close as possible to the desired value for the predefined model response can be used as starting values. While maintaining the starting values for the main parameters, additional starting values for these parameters can optionally also be defined for the remaining parameters by determining their correlation with one another in relation to the value for the model response, which then also flow into a subsequent optimization.
The specified starting values are now used to optimize the parameters with regard to a desired value of the model response in the respective tolerance ranges and to determine the value of the model response that results in this way. Such an optimization is usually carried out using a commercial optimizer such as "HyperStudy®"carried out, the parameters, in particular the main parameters, being varied in the specified tolerance ranges and an optimal combination of parameters for the individual main parameters being determined from this. The resulting optimized parameter values then serve as corresponding starting parameter values on a corresponding injection molding machine for manufacturing a corresponding component, in particular an optical component.
After determining or setting the start parameter values on a real injection molding machine, these can be further adjusted and optimized in practical tests.
With the help of the method according to the invention, it is therefore possible to quickly and automatically determine the relative influences of parameters on the value of a given model response of a parameterized model depicting an injection molding process and to optimize the parameterized model with the help of a targeted variation of the respective parameter values, so that in contrast With the prior art, no trial and error process is now necessary in order to ultimately obtain an optimization of the corresponding injection molding process.
In one possible embodiment of the proposed method, the model response is specified from the group consisting of the maximum temperature in the component to be produced, the total duration of the injection molding process, and the duration up to the earliest possible point in time for demolding. This means that, for example, if the model response is specified as a duration up to the earliest possible point in time for demolding, in step al) of the proposed method a value for the duration up to the earliest possible point in time for demoulding is determined for various parameter values of the respective parameter , which is carried out separately for all parameters to be specified, resulting in a resulting relative influence on the value for the individual parameters for the duration up to the earliest possible point in time for demoulding. This means that it can be deduced from this which parameters have a relatively high or low influence on the duration up to the earliest possible point in time for demoulding, when viewed independently of one another.
In the event that it is desired to reduce the cycle times in the manufacturing process of an optical component using an injection molding process, it is desirable to minimize the earliest possible point in time for demolding or the time it takes to reach the earliest possible point in time for demolding. The actual optimization step c) then takes place with this specification, so that specific parameter values for the main parameters can be defined as starting parameter values for a real injection molding machine.
As already mentioned, the parameters to be specified can on the one hand be injection molding parameters, i. H. about parameters that are related to the actual injection molding process. These are, for example, the melting temperature of the material that is used to manufacture the respective component, the mold temperature of the mold used for injection molding, the cooling time, d. H. how long the tool, including the molded component located in it, is cooled and the cooling rate. The injection molding parameters also include the so-called switchover point, which is defined by the injection time, injection pressure, screw position, locking force and volume. Furthermore, an injection molding parameter is the holding pressure profile, which is determined by the duration and level of the required holding pressure, and an injection profile which is obtained from the injection time, volume flow, screw position and screw advance speed.
Material properties must also be observed as boundary conditions, although these are essentially to be assumed as fixed values and are generally not varied. Material properties are the properties of the material which is used to manufacture the component, for example the optical component, and which is accordingly injected into the injection molding tool. Material properties include, in particular, heat capacity, thermal conductivity, thermal expansion and the so-called no-flow temperature. This no-flow temperature is a flow limit temperature for which it is assumed that the respective material, such as a plastic used, no longer flows when it cools below this temperature.This yield point temperature is an empirically determined variable. The material properties also include the transition temperature as well as the glass transition temperature or the glass point, the solidification temperature, the melting temperature, the so-called D3 coefficient, which indicates a pressure-dependent viscosity, and a so-called C1 / C2 coefficient, which is a so-called junction loss, i.e. H. an inlet pressure loss. Viscosity, creep behavior, modulus of elasticity, density and PVT data of the material to be used must also be taken into account. These material properties must be included in the modeling at least partially, ideally completely. Although the material properties can also be parameterized and optimized, the material would then have to be adapted accordingly, which would usually result in a material development that certainly does not necessarily mean 100% implementation in the direction of the desired parameters, i.e. H. which will enable optimized parameter values. Such adjustments could only be made within the framework of what is chemically and physically possible.
Other influences are gravitation, mass inertia and the transition temperature of component material / tool. The transition temperature of component material / tool cannot currently be measured with sufficient accuracy, but can only be determined using what is known as reverse engineering. In general, the component material is, i. H. in the case of the material that is used to manufacture the component, a plastic.
In addition to the parameters mentioned above, the geometry of the component to be manufactured also flows into the parameterized model. A specific geometry is required for the component to be produced, which in turn flows as such into the model in the form of parameters. In addition to the overall shape, which is usually fixed, the component geometry can, for example, comprise several layers or be subdivided into several layers and have variable parting planes, ie. H. variable layer thicknesses. The number of layers can vary.
Another special feature is the fact that certain parameters cannot be specified as specific values, but must be specified as a function of, for example, the temperature or time or another freely selectable variable.
On the basis of the specified parameters, the model is first parameterized accordingly, on the basis of which the underlying injection molding process is ultimately to be optimized. After parameterizing the model, this model is first validated, i. H. checked its validity with real values. This is usually only done once.
Furthermore, a test calculation is carried out for each geometry (in the event that different numbers of layers exist for different geometries) and then a type of macro is recorded with a postprocessor, with which all further calculations are evaluated in the same way in the further course can. The post processor is a program for evaluating simulation results. Is the model validated, i. H. If the model reflects real behavior, the now parameterized model is included in the proposed computer-implemented method, so that the proposed method steps can be carried out accordingly on the basis of the parameterized model. For the method to be carried out, the parameters that are to be varied in the underlying parameterized model are first specified. This can be both the component geometry and the parameters mentioned above, which include the injection molding parameters, possibly also the material properties and other physical parameters.
Furthermore, before starting the implementation of the proposed method, a model response is specified, with regard to which the injection molding process is to be optimized. Examples of model responses are:
- Maximum temperature in the component to be produced;
- Total injection molding process time;
- Duration until a respective demolding temperature is reached.
The time it takes to reach the demolding temperature directly determines the cycle rates prevailing in the injection molding process, which are to be minimized or kept as low as possible, for example when optimizing the injection molding process. This means that it can be a goal, for example, to minimize the earliest possible point in time for demoulding or the time it takes to reach this point in time.
However, when it comes to determining demolding times, it is usually not that easy, since, for example, with a multi-layer injection molding process, the component to be manufactured is not injected in one go and with an associated demolding time, but rather a first layer, a so-called one Pre-molded part, injected and cooled until its demolding temperature is reached. Only then or precisely then is the tool opened and the pre-molded part is brought into a next cavity of the same tool, for example with the aid of a rotary plate, an index plate, a sliding table or a robot. There a second layer is injected over the pre-molded part. The use of two or more injection molding machines and tools that are independent of one another is also conceivable. Each machine can be responsible for the injection of a layer, the transfer of the injection molded parts between the machines is carried out using suitable means. In the proposed computer-implemented method, however, it is not known in advance how long it will take for a component to be produced to reach a demolding temperature. This must first be determined in a first invoice. To do this, set a significantly longer cooling time than necessary and check the point in time at which the respective cooling temperature or demolding temperature has been reached. However, this can also be set automatically in simulations using a termination criterion, i. H. it is simulated until the demoulding temperature has been fallen below everywhere. The determined value is then used again to determine the first layer, i.e. H. to calculate the pre-molded part, namely exactly up to the time of the previously determined demolding temperature. When calculating the simulation of the pre-molded part, a corresponding temperature profile is also determined. The second layer is then simulated. When calculating the second layer, the time it takes to reach the demolding temperature for the now two layers in combination is also first calculated. The specific temperature profile of the pre-molded part can be used to support this. Furthermore, the cooling behavior between the individual steps can also be simulated, e.g. if the pre-molded part is temporarily stored for a long time, or it takes a few minutes before the pre-molded part is overmolded, or it only takes a few seconds before the pre-molded part is back-molded. The procedure described can run automatically with the help of scripts and macros, in which case only a single entry is necessary. There is a script that executes the following: 1. Start the invoice, after the invoice has been completed, start a second script to evaluate the demolding time of the pre-molded part and enter it into another computing deck, 2. Start the invoice and a second one again after the invoice has been completed Start script that evaluates the results and outputs the demolding time. The second script (to determine demolding time 1) loads a macro in which the calculation is evaluated and the temperature profile over time is output as a tabular value pair. An additional script is used to extract from the table when the temperature fell below the demolding temperature. Here, between the two points (immediately before the demolding temperature and immediately after the demolding temperature), the demoulding temperature is interpolated so that the time is determined even more precisely (because the calculation only reaches the demolding temperature by chance, here there are deviations of 1- 2 ° C is the rule.) The time gained from this is output in a new file, which is then integrated in a further subscript in the second model (in which the post-injection part is also calculated). Analog scripts then run for the calculation and scripting of the post-injection part (except that the end time is then not reintegrated into a calculation model).
This means that in the case, as described here, it is necessary to provide for a successive determination of the demolding time, ie the duration until the demolding temperature is reached, accompanied by a repeated implementation of the proposed method for each of the two layers by a minimum To determine the value for a total duration of the required cooling time.
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