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optimization of preform temperature distribution for the stretch-blow molding of pet bottles: infrared heating and blowing modeling.
by：Labelong Packaging Machinery
2020-04-05
The technology used in the manufacture of polyethylene ester (PET)
Bottle, doublestage stretch-blow molding (SBM)
Processes are probably the most popular.
This process involves a semi-amorphous structure.
Products made by injection molding of PET Resin, called pre-forming.
In contrast to that
StageSBM, these pre-tables are stored and fed later (after cooling)into theblow-Forming Machine.
A re-heating step is then required to apply the pre-forming to the appropriate temperature distribution (
Slightly higher than typical ~ 75 [Glass transition]degrees]C).
Infrared is usually used at this stage (IR)
Heaters using solar energy
The transparent behavior of PET in infrared radiation.
In the second stage, the pre-formed body is stretched vertically through the cylinder rod, and the pre-formed body is blown using two-stage air pressure.
The bottle is then cooled down by the mold and the temperature of the mold is adjusted through the cooling channel.
Finally, perform the exhaust before the pop-up.
In order to meet the performance specifications defined by the manufacturer, the bottle must meet a large number of tests used to measure its functional properties (
Such as top load resistance, Thickness Boundary, transparency, barrier performance, etc. ).
The performance of the container depends not only on its thickness distribution, but also on its mechanical, structural and optical properties.
The parameters affecting the final performance of the bottle can be summarized as three main families related to pre-forming and mold design, PET performance and flow behavior under two-way stretching, and process conditions.
In particular, the heating conditions that control the temperature distribution of the preforming strongly affect the blowing motion (
Stretch and inflation)
So the thickness of the bottle is distributed.
Temperature also affects orientation caused by bi-directional stretching, which in turn affects the mechanical, optical, and barrier properties of the bottle (1).
Venkateswaran and others. (1)
The effects of uneven temperature distribution through prefabricated side walls on the functional properties of PETcontainers were studied.
This study shows that when the inner surface temperature is higher than the outer surface, the optical asymmetry through the wall thickness of the bottle is minimal.
Therefore, temperature is one of the most important variables in SBM.
However, its measurement is still a delicate task, especially in the direction of thickness.
Some experimental methods, such as infrared thermal images, are able to measure the surface temperature during the heating phase (2).
This type of measurement has the advantage of being non-invasive and therefore does not affect the process.
However, these methods may not be able to provide a temperature distribution measurement of the thickness of the entire pre-made rod.
Recent work has studied the use of a thermocouple inserted into the thickness of a premade Rod (3).
Nevertheless, this approach is still very subtle.
On the other hand, the numerical methods used to simulate the SBM re-heating stage have grown rapidly over the past decade.
The researchers applied the model to the commercial finite element (FE)packages (4), (5)
Or develop your own software (6-9)
To predict the temperature distribution of the premade rod.
Pet behavior is like
Transparent objects in the spectral range corresponding to irradiation, resulting in significant challenges in modeling radiation heat transfer.
Different methods are proposed to calculate the radiation absorption inside the premade rod.
Most of them think pets are a non-scattered half
Transparent media, except for the works of Lebaudy and Grenet (10).
In this work, the author is particularly dedicated to the heating simulation of multi-layer premix, taking into account the relationship between the crystal rate and the PET scattering coefficient.
Therefore, without a precise understanding of the heat transfer properties, the simulation of re-heating of the preformed body cannot be fully carried out.
The simulation of forming stage is also an important research topic in the past 20 years.
Few studies focus on the feasibility of 3D temperature
Displacement simulation (5), (11),(12);
But in general, the researchers proposed 2D. 9),(13-20).
As we all know, modeling PET behavior is still the key to achieving accurate simulation of forming process.
Yang et al submitted an excellent literature review on the Law of materials developed for PET. (18).
Therefore, this issue will not be discussed further here.
Interestingly, the focus of recent work is on integrating fluids-
Structure Interaction model to sbmsimulation (21-24).
These models are usually based on the thermodynamic equation to automatically calculate the air pressure inside the preformed body, rather than directly applying the pressure as a boundary condition.
The recent development of thermodynamic models can be explained by two main reasons.
First, it is observed that the air pressure inside the pre-made rod is very different from the nominal pressure applied upstream of the blowing device (23).
Obviously, the internal pressure and the closed volume of the preformed body are completely coupled.
Second, the results show that the direct use of air pressure as a boundary condition will lead to untrue results (24).
Only a few studies have been reported on this specific issue, and the subject is still open.
Finally, the numerical optimization method of SBM has received more and more attention in the past decade.
They tried to replace it with time-consuming experiments. and-
Wrong method, which is usually valid. Thibault et al. (12)
A work review on numerical optimization strategies for the blow molding process was reported, including extrusion-blow molding.
About SBM, Lee andSoh (25)
A fe optimization method for determining the best thickness profile of the preformed body is proposed, and the wall thickness distribution required for blow is given. molded part.
Recently, Thibault and others. (12)
The automatic optimization of the geometry of the preformed body is proposed (
Initial shape and thickness)
Using Nonlinear constraint algorithm sequence quadratic programming (SQP).
The stability of the method is discussed by comparing with the experiments under industrial conditions.
To optimize the parameters of the heating system, SQP is also used (26).
The aim is to homogenize the temperature along the length of the premade rod by modifying the process parameters associated with the IR oven.
Interestingly, the authors question the relevance of the goals chosen for optimization.
The models presented in the literature are properly simulated for the deformation process and can usually accurately predict the thickness distribution of the bottle mouth.
However, it is worth noting that there is very little inspection of blasting motion, although blasting motion may be a wise criterion for measuring the accuracy of the results.
The lack of heat transfer models is also evident.
In fact, although the temperature distribution of the wall thickness of the preformed body has a significant effect, it is usually omitted.
In addition, the heat transfer coefficient (
For example, between the polymer and the mold)
Usually not related to experimental measurements.
Finally, only a few studies have proposed modeling of re-heating and blowing steps.
In this work, we perform numerical simulations of the entire sbm process.
The model is mainly based on limited-
Infrared heating and finite element simulation in forming stage using finite element softwareR].
At each increment of the FE simulation, we use a thermodynamic model to calculate the air pressure applied inside the preformed body.
Therefore, we do not consider air pressure as an input variable.
This method allows to consider the relationship between the internal air pressure and the closed volume of the preformed body, I . E. e. , the fluid-
Structure Interaction.
To verify our method, we compare the distribution of numerical and experimental pressures over time.
In the second step, we propose a numerical optimization strategy for SBM.
To this end, we have developed an interactive program that allows the automatic calculation of the optimal temperature distribution along the pre-formed length to provide a uniform thickness for the bottle.
We simulated FE with Nelder-
Meadoptimization algorithm
Nonlinear simple shape.
The results were verified by careful in-situ testing and measurement of 18. 5 g--
Month cl PETbottles.
For this purpose, special attention is paid to the measurement of the boundary conditions required in the IR heating stage and the blowing stage.
In the SBM process, the heating device consists of a set of halogen lamps that usually have aluminum reflector.
Preform is converted through the oven and animated by rotating motion to provide an even temperature along its perimeter.
Before heat conduction, the radiation part emitted by the IR lamp is absorbed by the thickness of the premade rod.
In addition, the exterior of the pre-Blank is affected by the high radiation heat flow, which is usually cooled by ventilation to prevent hot crystals.
Reheating is a highly coupled phase, produced by a combination of conduction, convection, and radiation heat transfer.
Heat transfer simulation the temperature T of the prefabrication Rod evolves over time and space is controlled by the following heat balance equation :[rho][c. sub. p]
= DT/It is also called the radiation source term.
Without a precise understanding of the heat transfer properties of radiation, including the spectral and directional dependence of radiation, this source term cannot be fully calculated.
The researchers propose different numerical methods to calculate radiation sources, such as thermal tracing (5)
Or partition method (6).
In this work, we have adopted a two-step approach.
First, we calculate the radiation heat flow reaching the surface of the premade rod.
To this end, the IR lamp is divided into surface elements by grid, and the contribution of these elements is taken into account by visual factor calculation.
In addition, it is assumed that the behavior of IR lamps is similar to that of constant temperature Gray-bodies.
Their emissions are then defined by planck\'s law (27).
Finally, the radiation flux of the event [q [lambda]
O re-calculate [q. sub. [lambda]0]= (1 -[[rho]. sub. [lambda]])[Overi sum]([F. sub. ip][S. sub. i])[[epsilon]. sub. t[lambda]][pi][L. sub. [lambda]]([T. sub. ti])(5)where [[rho]. sub. [lambda]
Spectral reflection coefficient of PET ,[F. sub. ip]
Represents the view factor between the lamp element I and the premade bar ,[S. sub. i]
Is the surface area of the lamp element ,【[epsilon]. sub. t[lambda]]
Specific radiation rate of tungsten spectrum and [L. sub. [lambda]]
At the filament temperature, the strength of the Planck lamp I is [T. sub. ti].
The second time, radiation absorption is calculated according to Beer
Lambert\'s law under the assumption of non-scattered cold medium (27).
Then, the heat flow density is given by the following formula :[q. sub. [lambda]](x)= [q. sub. [lambda]0]exp(-[[kappa]. sub. [lambda]]x)(6)where [q. sub. [lambda]](x)
Represents the spectral radiation heat flux density of position x, [q. sub. [lambda]0]
Spectral radiation heat flux, and [k. sub. [lambda]]
Spectral absorption coefficient of PET ([inm. sup. 1]).
Finally, the radiation source termis is calculated according to the following equation :[
Mathematical expressions that cannot be reproduced in ASCII]
PET radiation properties are measured according to the protocol defined by Monte IX et al. (2).
PET t74 f9 samples were measured on Range 2 using the Perkin Elmer infrared spectrometer. 5-2. 5[micro]m.
The thermal performance of PET is assumed to be temperature-
This is especially true for the heat capacity that has increased dramatically above the glass transition temperature.
Application and experimental verification this section aims to evaluate the ability of the model to simulate the re-heating of a rotating preformed body under the process conditions used by the laboratory bottle blowing machine.
For this purpose, the oven consists of six halogen lamps (
Nominal power 1 KW)
With ceramic and rear aluminum reflector (see Fig. 1).
After heating 50 s, within 10 s, the pear-like muscle cools down by natural convection.
The empirical correlation of Chruchilland Chu is used to calculate the natural convection coefficient (28).
Its value is estimated to be 7 W [m. sup. -2][K. sup. -1].
The nominal power percentage for each lamp is reported in Table 1.
Preform speed is equal to 1. 2 rps.
The pre-made rods used are 18. 5 gweight, 2. Thickness 58mm.
The polymer grade is PET TF9 (IV = 0. 74).
Both the diagram and the chart are shown in the diagram. 2. [
Figure 1 slightly][
Figure 2:
Numerical verification was performed using temperature measurements.
Previous studies have shown that pets behave like 8-12 [micro]
M band (2).
So we chose the anAGEMA 880 IR camera to work in the long wavelength spectrum range12 [micro]m.
This option makes it possible to confirm that the camera measures the surface temperature.
According to the protocol defined by Monte IX et al, the average radiation rate of PET was also measured. (2).
Its value is equal to 0. 93.
Figure 3 shows the external temperature distribution calculated with infrared heating software and the measured temperature map.
To achieve a more accurate comparison, the temperature distribution along the length of the premade bar at the end of the cooling step is shown in the figure4.
Since the maximum relative error is less than 5%, we can observe good consistency between simulation and measurement.
Figure 5 shows the change of single point temperature over time located 47mm from the neck of the premade rod.
This point is selected because it corresponds to a node located at the middle height of the grid division.
This curve clearly shows the effect of this stage.
In fact, it is worth noting that after cooling 3 s (
Also called reverse time)
The temperature on the inside is higher than the temperature on the outside.
This phenomenon is easy to explain,
Natural convection tends to cool the outside, while the inside is cooled by heat conduction.
This is critical to the SBM process.
In fact, there may be significant differences between the medial and lateral ring tensile ratios.
In order to provide a good uniformity of stress distribution through the thickness of the bottle, it is necessary to deliberately form an uneven temperature distribution throughout the prefabrication bar before stretching and blowing (10). Finally, Fig.
6 it is clearly shown that the temperature distribution through the thickness is not linear, but exponential.
At the end of the thermal adjustment step, the temperature difference is about 4 [degrees]C.
However, this value is closely related to cooling conditions. [
Figure 3 slightly]
Therefore, the model is able to properly predict the temperature distribution of the pre-made rod at the end of the re-heating phase.
It allows to check the effect of the process parameters on the temperature distribution, especially through the thickness of the pre-made rod. [
Figure 4 slightly]BLOW-
Finite element analysis of molding simulation (FEA)
The SBM process is to package ABA using commercial FE-QUS.
In this section, we evaluate the ability of the above model to simulate the deformation process of asimple 18. 5 g-
PET bottle 50 cl
Special attention was paid to the measurement of the initial and boundary conditions, namely the temperature, air pressure and heat transfer coefficient between the premade Rod and the mold.
Boundary conditions calculate the initial temperature distribution of the premade rods using the previously proposed finite volume software.
The heat transfer of the interface between the mold and the inflatable preforming body is considered by heat transfer coefficient h.
For this study, a sensor was developed to measure the heat transfer coefficient.
The sensor and the method used for measurement are described in a previous article (29).
The peak of H is related to the nominal air pressure applied by the blowing device.
As shown in the figure.
7. The heat transfer coefficient increases exponentially with the air pressure, reaching the gradient value of [285 W]m. sup. -2][K. sup. -1]
Apressure in 10 bars.
This coefficient is very important because it will greatly affect the cooling time of the bottle. [
Figure 5 Slightly]
Measuring the air pressure inside the preformed body using the Kulite sensor is a function of time (see Fig. 2).
The typical air pressure profile shown in Figure 1. 8.
Before deformation, we can observe a sharp increase in air pressure.
Once the pre-made Rod starts to expand, its closed volume increases rapidly, resulting in a drop in pressure.
Then, the pressure increases steadily due to strain hardening and mold
Surface contact of premade rods.
After the pre-forming body is completely blown, the pressure gradually reaches the nominal value.
This typical evolution of air pressure gives a good representation of blowing motion. Menary et al. (24)
It has been shown that applying pressure directly as a fundamental condition may result in unrealistic results.
In fact, a drop in pressure can lead to deflation of the pre-made rods, which is inconsistent with the rapid expansion observed in the experiment.
In fact, the pressure applied by the air flow interacts with the premade Rod, resulting in structural deformation, which in turn changes the air flow itself by changing the pressure.
Therefore, it is clear from the above discussion that it is essential to simulate the fluid
The structural interaction between the preformed body and the airflow, rather than treating the pressure as an input variable.
In this work, we propose to consider the fluid-
Structural interaction using a \"fluid static hydraulic element\"
At each increment of FEsimulation, the thermodynamic model automatically calculates the air pressure inside the preformed body.
For this purpose, the closed volume of the preformed body is simulated by the fluid
The filling cavity should be uniform in temperature and pressure.
In addition hypothesis fluid of behavior similar to ideal gas.
Then, the volume of the cavity is calculated at each increment using the coordinates of the boundary node.
By assuming that the cavity is a closed system and the fluid inertia, volume-
The ideal gas law gives pressure compliance under static and hydraulic conditions.
During each small time interval, the amount of air contained in the cavity is considered constant, but at the end of the time increment, updates are made using the value of the mass flow rate (MFR). [
Figure 6 slightly]
To estimate MFR, Schmidt and others. (16)
A thermodynamic model has been developed, which establishes a clear relationship between MFR and air pressure.
In the case of equal volume transformation (
For example, this conversion can be performed by applying air pressure inside a rigid container)
, The manufacturer can work with the initial slopeof pressureversus-time curve.
However, this method is limited to blow freely.
In contrast, in the case of strikes
Molding, MFR may be a strong time-dependent.
In fact, as shown in the figure.
8, the pressure inside the pre-blank reaches a gradient value, which clearly shows that MFR gradually decreases and becomes zero at the end of the blowing sequence.
In this work, we measured MFR as a function of time using the Bronkhorst hotline sensor EL-FLOW[R].
The experimental results are shown in the figure. 8. [
Figure 7 Slightly][
Figure 8:
PET Flow behavior using the following viscous plastic G\' sell-simulated material behavior
WLF material model (30): [bar. [sigma]]= [k. sub. 0][a. sub. t](1 -exp(-A[bar. [epsilon]]))exp[(B[[bar. [epsilon]]. sup. C]). sub. [epsilon]. sup. -m]with [a. sub. t]= exp([c. sub. 1](T -[T. sub. ref])/[c. sub. 2]T -[T. sub. ref])(8)
Here, the equivalent stress [bar. [sigma]]
Dependent on the equivalent strain rate [bar. [epsilon]]
Cumulative strain [bar. [epsilon]]
Temperature T.
The sensitivity to strain rate is considered by parameter m, while (B, C)
Hardening modulus. Finally, [k. sub. 0]
Represents consistency.
The model takes into account the dependence of temperature and strain rate, as well as the strain hardening that occurs during large deformation.
Its advantage is that the value is stable and relatively easy to implement.
However, the law of this elephant-like behavior is kept within a very small range of temperature and strain rate.
In addition, it does not take into account the viscosity and elasticity of the material, nor does it take into account the orientation of the material.
We use an inverse method to determine the constituent parameters (
Nonlinear constraint algorithm called sequence quadratic programmingfrom equi-
Two-way tensile test Chavalier andMarco. (31). The thermo-
Dependencies were previously found in the shear test on PET t74 f9 (32).
We have implemented this model into finite element software that we call user creep.
Using the characteristic of bottle type, we use the asymmetric model to reduce the computing time.
In our application environment, this method is feasible because both the pre-forming and the mold design are symmetrical and the load applied to the structure.
Previous studies examined the effect of the preformed body mesh on the thickness distribution calculated using FE simulation (33).
These studies show that shell elements can save a lot of CPU time compared to solid elements while providing accurate results.
In this work, however, to provide an accurate calculation of the closed volume of the preformed body, we have adopted solid elements.
In fact, the node coordinates used to mesh the inner surface of the premade rod are used to calculate the closed volume.
Therefore, the use of shell elements to mesh the median surface of the pre-made rod will result in an overestimate of 30% of the closed volume of the pre-made rod, and therefore, non-
The error in calculating the pressure is negligible, which is unacceptable.
The pre-made rod is divided into a secondary solid of 100-elements (405 nodes)
As shown in the figure. 9. [
Figure 9 omitted
The mold used is a prototype developed in CROMeP.
It produces 50 clbottles.
We assume that this is rigid and constant temperature.
In fact, for the oneSBM cycle, its temperature rise is about 1 [degrees]C (29).
Figure 9 illustrates the mold geometry and boundary conditions.
In order to calculate the heat transfer between the polymer and the mold, we chose the coupling temperature-
Displacement model in standard (
Implicit time integration scheme.
Although it has a potential effect on blasting motion, the viscosity dissipation is not calculated.
Consistent with the blowing prototype, there is no simulated stretch rod.
Finally, it is assumed that the friction contact between the premade Rod and the mold is adhesive. [
Figure 10 slightly][
Figure 11 omitted]
Results and Experiments verify that one of the main objectives of this section is to evaluate the consistency of the model with the blow motion.
One way to do this is to compare the pressure measured in the bottle with the pressure calculated by the model.
Two pressuresversus-
The time distribution is shown in the figure. 10.
There is a fair agreement on the trend between the two curves.
The relative error between the measured pressure and the predicted pressure is about 16% at the end of the process.
It is worth noting that the model was successfully captured in (ii)the die-
The surface contact of the preformed body is considered sticky: This prevents any sliding along the side wall of the mold, which tends to reduce the thickness of the bottom of the bottle; and (iii)
The injection point located at the top of the premade rod may be partially hot crystalline.
This may make the deformation of the corner difficult.
Nevertheless, the model was able to properly predict the deformation process and accurately predict the thickness distribution of the bottle while observing the movement of the blowing bottle. [
Figure 12:
Optimization of pre-forming temperature the performance of bottles manufactured by SBM is seriously affected by its thickness distribution.
In order to achieve the bottle with the appropriate thickness distribution, it is more desirable to adjust the process conditions and make bottles of different shapes using the same pre-forming design.
This method is designed to minimize the cost associated with the design of the new premade bar (
Especially the manufacture of a new injection mold).
However, it is still expensive and time consuming to determine the appropriate operating conditions.
Different methods are possible, such as trial. and-
The wrong method, or the design of the experiment.
Both require a lot of experiments (or simulations)
, Especially when the parameters are interdependent.
As a sequence, they become inadequate and not feasible for complex problems.
In contrast, the optimization algorithm makes the optimization process completely automated, and from this point of view, it has produced significant help in the development cycle.
In this section, we propose to combine the optimization algorithm with the fe simulation to optimize the temperature distribution of the length of the premade rod.
The goal is to provide a uniform thickness for the bottle.
To describe the temperature distribution along the length of the premade bar, we consider three optimization variables.
They correspond to three temperatures at different heights of the premade bar, as shown in the figure13.
The entire temperature distribution is then derived using the workpiece
3-order Hermite interpolation polynomial (PCHIP)method (34).
In order to provide accurate interpolation, an additional temperature is attached to the neck of the premade rod.
The fourth temperature is not optimized, but fixed at 80 [degrees]
C, approximately corresponds to the glass transmission of PET.
In fact, during the whole re-heating phase, the premade rod neck is usually protected by infrared radiation to prevent its temperature from changing over PET glass.
This method is designed to prevent any deformation of the bottleneck during the molding process.
Finally, to simplify the problem, it is assumed that the temperature is uniform by the thickness of the premade rod. [
Figure 13:
The lower limit and upper limit constraint optimization variables are used, corresponding to the penetration temperature of PET glass and PET crystal temperature, respectively.
Naturally these two physical limits were chosen to prevent the occurrence of severe hardening of the structure, in which case any deformation during the formation phase would be prohibited.
Let\'s note that there is neither a linear constraint nor a nonlinear constraint.
In this application, we try to provide a uniform thickness for the bottle.
This goal must be set by a mathematical approach to the appropriate cost. function.
An easy way is to define the target function F as the standard deviation for calculating the thickness as follows: F (X)= [(1/n -1[
Sum on N (NMP-PRIORITY 3. www. apt-pack. com.
Special thanks to the Logoplaste technology for the production of premix and the cooperation of QUB.
The author also thanks N. Billon, L. Chevalier, Y. Marco, G. Menary, V. Lucin, and C.
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Bottle, doublestage stretch-blow molding (SBM)
Processes are probably the most popular.
This process involves a semi-amorphous structure.
Products made by injection molding of PET Resin, called pre-forming.
In contrast to that
StageSBM, these pre-tables are stored and fed later (after cooling)into theblow-Forming Machine.
A re-heating step is then required to apply the pre-forming to the appropriate temperature distribution (
Slightly higher than typical ~ 75 [Glass transition]degrees]C).
Infrared is usually used at this stage (IR)
Heaters using solar energy
The transparent behavior of PET in infrared radiation.
In the second stage, the pre-formed body is stretched vertically through the cylinder rod, and the pre-formed body is blown using two-stage air pressure.
The bottle is then cooled down by the mold and the temperature of the mold is adjusted through the cooling channel.
Finally, perform the exhaust before the pop-up.
In order to meet the performance specifications defined by the manufacturer, the bottle must meet a large number of tests used to measure its functional properties (
Such as top load resistance, Thickness Boundary, transparency, barrier performance, etc. ).
The performance of the container depends not only on its thickness distribution, but also on its mechanical, structural and optical properties.
The parameters affecting the final performance of the bottle can be summarized as three main families related to pre-forming and mold design, PET performance and flow behavior under two-way stretching, and process conditions.
In particular, the heating conditions that control the temperature distribution of the preforming strongly affect the blowing motion (
Stretch and inflation)
So the thickness of the bottle is distributed.
Temperature also affects orientation caused by bi-directional stretching, which in turn affects the mechanical, optical, and barrier properties of the bottle (1).
Venkateswaran and others. (1)
The effects of uneven temperature distribution through prefabricated side walls on the functional properties of PETcontainers were studied.
This study shows that when the inner surface temperature is higher than the outer surface, the optical asymmetry through the wall thickness of the bottle is minimal.
Therefore, temperature is one of the most important variables in SBM.
However, its measurement is still a delicate task, especially in the direction of thickness.
Some experimental methods, such as infrared thermal images, are able to measure the surface temperature during the heating phase (2).
This type of measurement has the advantage of being non-invasive and therefore does not affect the process.
However, these methods may not be able to provide a temperature distribution measurement of the thickness of the entire pre-made rod.
Recent work has studied the use of a thermocouple inserted into the thickness of a premade Rod (3).
Nevertheless, this approach is still very subtle.
On the other hand, the numerical methods used to simulate the SBM re-heating stage have grown rapidly over the past decade.
The researchers applied the model to the commercial finite element (FE)packages (4), (5)
Or develop your own software (6-9)
To predict the temperature distribution of the premade rod.
Pet behavior is like
Transparent objects in the spectral range corresponding to irradiation, resulting in significant challenges in modeling radiation heat transfer.
Different methods are proposed to calculate the radiation absorption inside the premade rod.
Most of them think pets are a non-scattered half
Transparent media, except for the works of Lebaudy and Grenet (10).
In this work, the author is particularly dedicated to the heating simulation of multi-layer premix, taking into account the relationship between the crystal rate and the PET scattering coefficient.
Therefore, without a precise understanding of the heat transfer properties, the simulation of re-heating of the preformed body cannot be fully carried out.
The simulation of forming stage is also an important research topic in the past 20 years.
Few studies focus on the feasibility of 3D temperature
Displacement simulation (5), (11),(12);
But in general, the researchers proposed 2D. 9),(13-20).
As we all know, modeling PET behavior is still the key to achieving accurate simulation of forming process.
Yang et al submitted an excellent literature review on the Law of materials developed for PET. (18).
Therefore, this issue will not be discussed further here.
Interestingly, the focus of recent work is on integrating fluids-
Structure Interaction model to sbmsimulation (21-24).
These models are usually based on the thermodynamic equation to automatically calculate the air pressure inside the preformed body, rather than directly applying the pressure as a boundary condition.
The recent development of thermodynamic models can be explained by two main reasons.
First, it is observed that the air pressure inside the pre-made rod is very different from the nominal pressure applied upstream of the blowing device (23).
Obviously, the internal pressure and the closed volume of the preformed body are completely coupled.
Second, the results show that the direct use of air pressure as a boundary condition will lead to untrue results (24).
Only a few studies have been reported on this specific issue, and the subject is still open.
Finally, the numerical optimization method of SBM has received more and more attention in the past decade.
They tried to replace it with time-consuming experiments. and-
Wrong method, which is usually valid. Thibault et al. (12)
A work review on numerical optimization strategies for the blow molding process was reported, including extrusion-blow molding.
About SBM, Lee andSoh (25)
A fe optimization method for determining the best thickness profile of the preformed body is proposed, and the wall thickness distribution required for blow is given. molded part.
Recently, Thibault and others. (12)
The automatic optimization of the geometry of the preformed body is proposed (
Initial shape and thickness)
Using Nonlinear constraint algorithm sequence quadratic programming (SQP).
The stability of the method is discussed by comparing with the experiments under industrial conditions.
To optimize the parameters of the heating system, SQP is also used (26).
The aim is to homogenize the temperature along the length of the premade rod by modifying the process parameters associated with the IR oven.
Interestingly, the authors question the relevance of the goals chosen for optimization.
The models presented in the literature are properly simulated for the deformation process and can usually accurately predict the thickness distribution of the bottle mouth.
However, it is worth noting that there is very little inspection of blasting motion, although blasting motion may be a wise criterion for measuring the accuracy of the results.
The lack of heat transfer models is also evident.
In fact, although the temperature distribution of the wall thickness of the preformed body has a significant effect, it is usually omitted.
In addition, the heat transfer coefficient (
For example, between the polymer and the mold)
Usually not related to experimental measurements.
Finally, only a few studies have proposed modeling of re-heating and blowing steps.
In this work, we perform numerical simulations of the entire sbm process.
The model is mainly based on limited-
Infrared heating and finite element simulation in forming stage using finite element softwareR].
At each increment of the FE simulation, we use a thermodynamic model to calculate the air pressure applied inside the preformed body.
Therefore, we do not consider air pressure as an input variable.
This method allows to consider the relationship between the internal air pressure and the closed volume of the preformed body, I . E. e. , the fluid-
Structure Interaction.
To verify our method, we compare the distribution of numerical and experimental pressures over time.
In the second step, we propose a numerical optimization strategy for SBM.
To this end, we have developed an interactive program that allows the automatic calculation of the optimal temperature distribution along the pre-formed length to provide a uniform thickness for the bottle.
We simulated FE with Nelder-
Meadoptimization algorithm
Nonlinear simple shape.
The results were verified by careful in-situ testing and measurement of 18. 5 g--
Month cl PETbottles.
For this purpose, special attention is paid to the measurement of the boundary conditions required in the IR heating stage and the blowing stage.
In the SBM process, the heating device consists of a set of halogen lamps that usually have aluminum reflector.
Preform is converted through the oven and animated by rotating motion to provide an even temperature along its perimeter.
Before heat conduction, the radiation part emitted by the IR lamp is absorbed by the thickness of the premade rod.
In addition, the exterior of the pre-Blank is affected by the high radiation heat flow, which is usually cooled by ventilation to prevent hot crystals.
Reheating is a highly coupled phase, produced by a combination of conduction, convection, and radiation heat transfer.
Heat transfer simulation the temperature T of the prefabrication Rod evolves over time and space is controlled by the following heat balance equation :[rho][c. sub. p]
= DT/It is also called the radiation source term.
Without a precise understanding of the heat transfer properties of radiation, including the spectral and directional dependence of radiation, this source term cannot be fully calculated.
The researchers propose different numerical methods to calculate radiation sources, such as thermal tracing (5)
Or partition method (6).
In this work, we have adopted a two-step approach.
First, we calculate the radiation heat flow reaching the surface of the premade rod.
To this end, the IR lamp is divided into surface elements by grid, and the contribution of these elements is taken into account by visual factor calculation.
In addition, it is assumed that the behavior of IR lamps is similar to that of constant temperature Gray-bodies.
Their emissions are then defined by planck\'s law (27).
Finally, the radiation flux of the event [q [lambda]
O re-calculate [q. sub. [lambda]0]= (1 -[[rho]. sub. [lambda]])[Overi sum]([F. sub. ip][S. sub. i])[[epsilon]. sub. t[lambda]][pi][L. sub. [lambda]]([T. sub. ti])(5)where [[rho]. sub. [lambda]
Spectral reflection coefficient of PET ,[F. sub. ip]
Represents the view factor between the lamp element I and the premade bar ,[S. sub. i]
Is the surface area of the lamp element ,【[epsilon]. sub. t[lambda]]
Specific radiation rate of tungsten spectrum and [L. sub. [lambda]]
At the filament temperature, the strength of the Planck lamp I is [T. sub. ti].
The second time, radiation absorption is calculated according to Beer
Lambert\'s law under the assumption of non-scattered cold medium (27).
Then, the heat flow density is given by the following formula :[q. sub. [lambda]](x)= [q. sub. [lambda]0]exp(-[[kappa]. sub. [lambda]]x)(6)where [q. sub. [lambda]](x)
Represents the spectral radiation heat flux density of position x, [q. sub. [lambda]0]
Spectral radiation heat flux, and [k. sub. [lambda]]
Spectral absorption coefficient of PET ([inm. sup. 1]).
Finally, the radiation source termis is calculated according to the following equation :[
Mathematical expressions that cannot be reproduced in ASCII]
PET radiation properties are measured according to the protocol defined by Monte IX et al. (2).
PET t74 f9 samples were measured on Range 2 using the Perkin Elmer infrared spectrometer. 5-2. 5[micro]m.
The thermal performance of PET is assumed to be temperature-
This is especially true for the heat capacity that has increased dramatically above the glass transition temperature.
Application and experimental verification this section aims to evaluate the ability of the model to simulate the re-heating of a rotating preformed body under the process conditions used by the laboratory bottle blowing machine.
For this purpose, the oven consists of six halogen lamps (
Nominal power 1 KW)
With ceramic and rear aluminum reflector (see Fig. 1).
After heating 50 s, within 10 s, the pear-like muscle cools down by natural convection.
The empirical correlation of Chruchilland Chu is used to calculate the natural convection coefficient (28).
Its value is estimated to be 7 W [m. sup. -2][K. sup. -1].
The nominal power percentage for each lamp is reported in Table 1.
Preform speed is equal to 1. 2 rps.
The pre-made rods used are 18. 5 gweight, 2. Thickness 58mm.
The polymer grade is PET TF9 (IV = 0. 74).
Both the diagram and the chart are shown in the diagram. 2. [
Figure 1 slightly][
Figure 2:
Numerical verification was performed using temperature measurements.
Previous studies have shown that pets behave like 8-12 [micro]
M band (2).
So we chose the anAGEMA 880 IR camera to work in the long wavelength spectrum range12 [micro]m.
This option makes it possible to confirm that the camera measures the surface temperature.
According to the protocol defined by Monte IX et al, the average radiation rate of PET was also measured. (2).
Its value is equal to 0. 93.
Figure 3 shows the external temperature distribution calculated with infrared heating software and the measured temperature map.
To achieve a more accurate comparison, the temperature distribution along the length of the premade bar at the end of the cooling step is shown in the figure4.
Since the maximum relative error is less than 5%, we can observe good consistency between simulation and measurement.
Figure 5 shows the change of single point temperature over time located 47mm from the neck of the premade rod.
This point is selected because it corresponds to a node located at the middle height of the grid division.
This curve clearly shows the effect of this stage.
In fact, it is worth noting that after cooling 3 s (
Also called reverse time)
The temperature on the inside is higher than the temperature on the outside.
This phenomenon is easy to explain,
Natural convection tends to cool the outside, while the inside is cooled by heat conduction.
This is critical to the SBM process.
In fact, there may be significant differences between the medial and lateral ring tensile ratios.
In order to provide a good uniformity of stress distribution through the thickness of the bottle, it is necessary to deliberately form an uneven temperature distribution throughout the prefabrication bar before stretching and blowing (10). Finally, Fig.
6 it is clearly shown that the temperature distribution through the thickness is not linear, but exponential.
At the end of the thermal adjustment step, the temperature difference is about 4 [degrees]C.
However, this value is closely related to cooling conditions. [
Figure 3 slightly]
Therefore, the model is able to properly predict the temperature distribution of the pre-made rod at the end of the re-heating phase.
It allows to check the effect of the process parameters on the temperature distribution, especially through the thickness of the pre-made rod. [
Figure 4 slightly]BLOW-
Finite element analysis of molding simulation (FEA)
The SBM process is to package ABA using commercial FE-QUS.
In this section, we evaluate the ability of the above model to simulate the deformation process of asimple 18. 5 g-
PET bottle 50 cl
Special attention was paid to the measurement of the initial and boundary conditions, namely the temperature, air pressure and heat transfer coefficient between the premade Rod and the mold.
Boundary conditions calculate the initial temperature distribution of the premade rods using the previously proposed finite volume software.
The heat transfer of the interface between the mold and the inflatable preforming body is considered by heat transfer coefficient h.
For this study, a sensor was developed to measure the heat transfer coefficient.
The sensor and the method used for measurement are described in a previous article (29).
The peak of H is related to the nominal air pressure applied by the blowing device.
As shown in the figure.
7. The heat transfer coefficient increases exponentially with the air pressure, reaching the gradient value of [285 W]m. sup. -2][K. sup. -1]
Apressure in 10 bars.
This coefficient is very important because it will greatly affect the cooling time of the bottle. [
Figure 5 Slightly]
Measuring the air pressure inside the preformed body using the Kulite sensor is a function of time (see Fig. 2).
The typical air pressure profile shown in Figure 1. 8.
Before deformation, we can observe a sharp increase in air pressure.
Once the pre-made Rod starts to expand, its closed volume increases rapidly, resulting in a drop in pressure.
Then, the pressure increases steadily due to strain hardening and mold
Surface contact of premade rods.
After the pre-forming body is completely blown, the pressure gradually reaches the nominal value.
This typical evolution of air pressure gives a good representation of blowing motion. Menary et al. (24)
It has been shown that applying pressure directly as a fundamental condition may result in unrealistic results.
In fact, a drop in pressure can lead to deflation of the pre-made rods, which is inconsistent with the rapid expansion observed in the experiment.
In fact, the pressure applied by the air flow interacts with the premade Rod, resulting in structural deformation, which in turn changes the air flow itself by changing the pressure.
Therefore, it is clear from the above discussion that it is essential to simulate the fluid
The structural interaction between the preformed body and the airflow, rather than treating the pressure as an input variable.
In this work, we propose to consider the fluid-
Structural interaction using a \"fluid static hydraulic element\"
At each increment of FEsimulation, the thermodynamic model automatically calculates the air pressure inside the preformed body.
For this purpose, the closed volume of the preformed body is simulated by the fluid
The filling cavity should be uniform in temperature and pressure.
In addition hypothesis fluid of behavior similar to ideal gas.
Then, the volume of the cavity is calculated at each increment using the coordinates of the boundary node.
By assuming that the cavity is a closed system and the fluid inertia, volume-
The ideal gas law gives pressure compliance under static and hydraulic conditions.
During each small time interval, the amount of air contained in the cavity is considered constant, but at the end of the time increment, updates are made using the value of the mass flow rate (MFR). [
Figure 6 slightly]
To estimate MFR, Schmidt and others. (16)
A thermodynamic model has been developed, which establishes a clear relationship between MFR and air pressure.
In the case of equal volume transformation (
For example, this conversion can be performed by applying air pressure inside a rigid container)
, The manufacturer can work with the initial slopeof pressureversus-time curve.
However, this method is limited to blow freely.
In contrast, in the case of strikes
Molding, MFR may be a strong time-dependent.
In fact, as shown in the figure.
8, the pressure inside the pre-blank reaches a gradient value, which clearly shows that MFR gradually decreases and becomes zero at the end of the blowing sequence.
In this work, we measured MFR as a function of time using the Bronkhorst hotline sensor EL-FLOW[R].
The experimental results are shown in the figure. 8. [
Figure 7 Slightly][
Figure 8:
PET Flow behavior using the following viscous plastic G\' sell-simulated material behavior
WLF material model (30): [bar. [sigma]]= [k. sub. 0][a. sub. t](1 -exp(-A[bar. [epsilon]]))exp[(B[[bar. [epsilon]]. sup. C]). sub. [epsilon]. sup. -m]with [a. sub. t]= exp([c. sub. 1](T -[T. sub. ref])/[c. sub. 2]T -[T. sub. ref])(8)
Here, the equivalent stress [bar. [sigma]]
Dependent on the equivalent strain rate [bar. [epsilon]]
Cumulative strain [bar. [epsilon]]
Temperature T.
The sensitivity to strain rate is considered by parameter m, while (B, C)
Hardening modulus. Finally, [k. sub. 0]
Represents consistency.
The model takes into account the dependence of temperature and strain rate, as well as the strain hardening that occurs during large deformation.
Its advantage is that the value is stable and relatively easy to implement.
However, the law of this elephant-like behavior is kept within a very small range of temperature and strain rate.
In addition, it does not take into account the viscosity and elasticity of the material, nor does it take into account the orientation of the material.
We use an inverse method to determine the constituent parameters (
Nonlinear constraint algorithm called sequence quadratic programmingfrom equi-
Two-way tensile test Chavalier andMarco. (31). The thermo-
Dependencies were previously found in the shear test on PET t74 f9 (32).
We have implemented this model into finite element software that we call user creep.
Using the characteristic of bottle type, we use the asymmetric model to reduce the computing time.
In our application environment, this method is feasible because both the pre-forming and the mold design are symmetrical and the load applied to the structure.
Previous studies examined the effect of the preformed body mesh on the thickness distribution calculated using FE simulation (33).
These studies show that shell elements can save a lot of CPU time compared to solid elements while providing accurate results.
In this work, however, to provide an accurate calculation of the closed volume of the preformed body, we have adopted solid elements.
In fact, the node coordinates used to mesh the inner surface of the premade rod are used to calculate the closed volume.
Therefore, the use of shell elements to mesh the median surface of the pre-made rod will result in an overestimate of 30% of the closed volume of the pre-made rod, and therefore, non-
The error in calculating the pressure is negligible, which is unacceptable.
The pre-made rod is divided into a secondary solid of 100-elements (405 nodes)
As shown in the figure. 9. [
Figure 9 omitted
The mold used is a prototype developed in CROMeP.
It produces 50 clbottles.
We assume that this is rigid and constant temperature.
In fact, for the oneSBM cycle, its temperature rise is about 1 [degrees]C (29).
Figure 9 illustrates the mold geometry and boundary conditions.
In order to calculate the heat transfer between the polymer and the mold, we chose the coupling temperature-
Displacement model in standard (
Implicit time integration scheme.
Although it has a potential effect on blasting motion, the viscosity dissipation is not calculated.
Consistent with the blowing prototype, there is no simulated stretch rod.
Finally, it is assumed that the friction contact between the premade Rod and the mold is adhesive. [
Figure 10 slightly][
Figure 11 omitted]
Results and Experiments verify that one of the main objectives of this section is to evaluate the consistency of the model with the blow motion.
One way to do this is to compare the pressure measured in the bottle with the pressure calculated by the model.
Two pressuresversus-
The time distribution is shown in the figure. 10.
There is a fair agreement on the trend between the two curves.
The relative error between the measured pressure and the predicted pressure is about 16% at the end of the process.
It is worth noting that the model was successfully captured in (ii)the die-
The surface contact of the preformed body is considered sticky: This prevents any sliding along the side wall of the mold, which tends to reduce the thickness of the bottom of the bottle; and (iii)
The injection point located at the top of the premade rod may be partially hot crystalline.
This may make the deformation of the corner difficult.
Nevertheless, the model was able to properly predict the deformation process and accurately predict the thickness distribution of the bottle while observing the movement of the blowing bottle. [
Figure 12:
Optimization of pre-forming temperature the performance of bottles manufactured by SBM is seriously affected by its thickness distribution.
In order to achieve the bottle with the appropriate thickness distribution, it is more desirable to adjust the process conditions and make bottles of different shapes using the same pre-forming design.
This method is designed to minimize the cost associated with the design of the new premade bar (
Especially the manufacture of a new injection mold).
However, it is still expensive and time consuming to determine the appropriate operating conditions.
Different methods are possible, such as trial. and-
The wrong method, or the design of the experiment.
Both require a lot of experiments (or simulations)
, Especially when the parameters are interdependent.
As a sequence, they become inadequate and not feasible for complex problems.
In contrast, the optimization algorithm makes the optimization process completely automated, and from this point of view, it has produced significant help in the development cycle.
In this section, we propose to combine the optimization algorithm with the fe simulation to optimize the temperature distribution of the length of the premade rod.
The goal is to provide a uniform thickness for the bottle.
To describe the temperature distribution along the length of the premade bar, we consider three optimization variables.
They correspond to three temperatures at different heights of the premade bar, as shown in the figure13.
The entire temperature distribution is then derived using the workpiece
3-order Hermite interpolation polynomial (PCHIP)method (34).
In order to provide accurate interpolation, an additional temperature is attached to the neck of the premade rod.
The fourth temperature is not optimized, but fixed at 80 [degrees]
C, approximately corresponds to the glass transmission of PET.
In fact, during the whole re-heating phase, the premade rod neck is usually protected by infrared radiation to prevent its temperature from changing over PET glass.
This method is designed to prevent any deformation of the bottleneck during the molding process.
Finally, to simplify the problem, it is assumed that the temperature is uniform by the thickness of the premade rod. [
Figure 13:
The lower limit and upper limit constraint optimization variables are used, corresponding to the penetration temperature of PET glass and PET crystal temperature, respectively.
Naturally these two physical limits were chosen to prevent the occurrence of severe hardening of the structure, in which case any deformation during the formation phase would be prohibited.
Let\'s note that there is neither a linear constraint nor a nonlinear constraint.
In this application, we try to provide a uniform thickness for the bottle.
This goal must be set by a mathematical approach to the appropriate cost. function.
An easy way is to define the target function F as the standard deviation for calculating the thickness as follows: F (X)= [(1/n -1[
Sum on N (NMP-PRIORITY 3. www. apt-pack. com.
Special thanks to the Logoplaste technology for the production of premix and the cooperation of QUB.
The author also thanks N. Billon, L. Chevalier, Y. Marco, G. Menary, V. Lucin, and C.
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2008 Society of Plastic EngineersBordival, F. M. Schmidt, Y. Le Maoult, V.
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