SBM Simulation of PET Bottles Using Newtonian Fluid Method in ANSYS Polyflow
Seong-Gyu Cho1, Joon-Seong Lee*2
1Dept. of Mechanical Engineering, Graduate School, Kyonggi University,154-42, Gwanggyosan-ro, Yeongtong-gu, Suwon-si, Gyeonggi-do,16227, Korea
*2Dept. of Mechanical System Engineering, Kyonggi University, 154-42, Gwanggyosan- ro, Yeongtong-gu, Suwon-si, Gyeonggi-do, 16227,Korea
1[email protected], *2[email protected]
Abstract
Background/Objectives: The rational assumption of the viscosity of the preform, which is difficult to obtain an accurate value, and the simulation using a Newtonian fluid model rather than a visco-elasto-plasticity, make it easy to check the molding behavior of PET bottles in the field.
Methods/Statistical analysis: Except for the viscosity coefficient, the variables are configured as if they were actual. Viscosity coefficients are performed at 50,000 intervals from 50,000 cps to 250,000 cps. At this time, SBM is divided into stretch and blowing phases, and each process operates in order of 0.1 second. The lateral thickness of the bottle obtained by this simulation is compared with the distribution of the lateral thickness of the actual bottle.
Findings: In the SBM process, the viscosity of the preform was confirmed to be less than 50,000 cps. In addition, when focusing on the lateral thickness of the bottle, the thickness distribution of the simulation and the actual thickness distribution of the bottle does not show a big difference. Therefore, the simulation using the Newtonian fluid method used in this study is expected to be suitable for field application. As the computing power evolves, more simulations can be performed in a shorter time, so it is expected that a variety of variables can be set in the field to understand molding behavior.
Improvements/Applications: By simulating the viscosity coefficients of the preforms in the field, it is possible to find suitable assumptions and to perform simulations in the production of other shaped products.
Keywords: Ansys Polyflow, Molding Behavior, Newtonian fluid, SBM, Viscosity.
1. Introduction
PET bottles are the most widely used containers in the world[1]. The bottle is characterized by being cheap, sturdy and light in weight. In addition, since the transparent material in general, there is an advantage that the beverage state inside the bottle can be easily checked. There are various methods for producing this bottle, such as simple blowingor stretch blowing method[2].If the bottle is long in the longitudinal direction, the stretch blowing method is used a lot[3]. These various production methods have common drawbacks[4]. It is difficult to visually observe the molding process because the molding process of the bottle is made in an opaque moldand most field producing PET bottles go through trial and error to catch product failure rates[5,6]. Also, since the PET bottle is made of a high molecular compound, it is very difficult to find the viscosity coefficient commonly used in mechanical engineering. This increases the difficulty of performing simulations for PET bottle molding.
Simulation of PET bottle forming is a more necessary task for those who manufacture bottles in thefield[7].This is because the process pressure should be optimized to minimize the occurrence of defective products depending on the shape of the bottle[8].In
particular, in order to perform the simulation in the field, the viscosity coefficient of the preform of the bottle is inevitably required, but since the preform manufacturer provides only the intrinsic viscosity value indicating the viscosity of the polymer compound, it is difficult to apply the value to the simulation in the field. This necessitates the derivation of rational assumptions of the viscosity coefficients rather than the intrinsic viscosity of the preform.
In this study, the simulation of ISBM process is performed to confirm the molding behavior of preform and finally to find a suitable viscosity coefficient. In addition, to make the analysis easier in the field, we will make sure that reasonable results can be obtained if the material is assumed to be a typical Newtonian fluid.
2. Theory and Simulation
2.1. Theoretical background
The most effective model for predicting the plasticity behavior of PET bottles is known as the visco-elasto-plasticity model[9]. This model has the advantage of being more accurate in complex mathematical models. On the other hand, there are disadvantages in that the difficulty of analysis and the number of material tests are increased. Therefore, there is a need to simplify the theory of analysis to favor field application. PET bottles often come with a thin side for labeling. Or, unlike the upper end or the lower part of the bottle, the shape of the side part is often complicated. In order to verify the molding behavior of the bottle's side to simplify the analysis, it is necessary to look at the Newtonian fluid model that is simpler than the visco-elasto-plasticity model and proceed with the analysis.
2.1.1. Newtonian Fluid Method
Viscosity determines the shear rate of a fluid generated by a given shear stress. This may predict that the upper surface of the fluid will move at a higher speed than the lower surface while the stress is maintained. Therefore, it can be seen as a linear relationship between the shear stress and the resulting strain. This is represented by Equation (1).
τ∝δθδt (1)
If Equation 1 is expressed geometrically, it can be expressed as Equation (2).
tan δθ =δuδtδy (2)
If Equation 2 is expressed as the relationship between velocity gradient and shear strain, Equation (3) is obtained.
dθ dt =du
dy (3)
Summarizing all the above equations, the shear stress is proportional to the velocity gradient in a general linear fluid, where the proportionality constant is the viscosity coefficient.
τ= μdθ
dt = μdu
dy (4)
PET bottle molding maintains a high temperature except the surface of the preform in contact with the mold. At this time, since the preforms of the remaining parts except the surface temporarily maintain the liquid state, it is assumed that a general Newtonian fluid
is used to determine the molding behavior until the molding is completed.
2.1.2. Ramp Function in Ansys Polyflow
The ramp function applicable to ANSYS polyflow has the shape shown in Figure 1.
Figure 1. Ramp function form in ANSYS polyflow
Where variables a and c have the x-axis and variables b and d have the y-axis. The x- axis represents time and the y-axis represents intensity. In this study, stretch rod motion and blowing pressure were used.
2.2.Simulation process description
Figure 2 shows a typical SBM process for PET bottles[10]. Since visual observation is not possible from 2) to 4) during this process, it is necessary to infer the numerical value necessary for simulation based on the dimensions of the finished product after molding.
Figure 2. SBM Process Diagram
In this study, the heated preform was assumed to be Newtonian fluid, and Finite element analysis was performed using ANSYS polyflow.
2.2.1. Meshes and Properties Used in Simulation
Figure 3 shows the mesh of mold, preform, and stretch rod used in the FEA simulation.
Table 1 and Table 2 summarize the values applied to the simulation.
Figure 3. Mesh geometry of mold, preform, and stretch rod used in the simulation Table 1. Properties of preforms applied to simulation
Item Preform Note
Density 1.4 g/cm3
Fixed Thickness 2.5 mm
Table 2. Variables for ramp function entered in an Ansys Polyflow
Item Variable of Ramp Function Note
a b c d
See Figure 1
To Stretch Rod 0.1 1 0.1 0
To Pressure 0.1 0 0.1 1
Since the value to be found as a reasonable assumption in this study is the viscous coefficient, the analysis was conducted by applying various viscous coefficients.
3. Results and Discussion
The velocity of the stretch rod was applied at 0.3 m/s, and the viscosity coefficient was simulated at 50,000 cps from 50,000 cps to 250,000 cps. Figure 4 shows only stretch results assuming a viscosity of 50,000 cps, and Figure 5 shows only stretch results assuming a viscosity of 250,000 cps.
Figure 4. Only Stretch result at 50,000cp
Figure 5. Only Stretch result at 250,000cp
Figure 6 shows the result of Stretch Blowing assuming a viscosity of 50,000 cp. Figure 7 shows the result of Stretch Blowing assuming a viscosity of 250,000 cp.
Figure 6. Stretch Blowing result at 50,000cp
Figure 7. Stretch Blowing result at 250,000cp
When visually comparing only the results at both ends of the assumed viscosity coefficient values, it was confirmed that it is difficult to find a numerically significant difference. The shapes of the mold, stretch rod and preform used in the simulations are actually 3D models of the PET bottles being manufactured. The bottle side thickness of
the actual product has an average thickness distribution of 0.35 to 0.55mm from the bottom to 100mm height. In view of the simulation results, it can be seen that the viscosity coefficient of the preform during the molding process can have a value of 50,000 cps or less.
4. Conclusion
In this study, the ISBM molding behavior of PET bottles was verified by assuming a Newtonian fluid model rather than a mathematically complicated viscoplastic or visco- elasto-plasticity model. In addition, the simulations were performed assuming a viscosity coefficient that could not be observed in the field and could not be obtained from the preform manufacturer.
As a result of the simulation, it was confirmed that the simplified simulation using the Newtonian fluid model, rather than the complicated mathematical model, could obtain results similar to those of the actual product. It is possible to easily predict the molding behavior of PET bottles in the field by using 3D FEM analysis of many cases based on daily computing power. In addition, in this study, the simulation was focused on the distribution of the lateral thickness of the bottle, but more accurate thickness distribution can be obtained by functionalizing the thickness distribution of the actual preform and applying it in polyflow.
Finally, further studies on how to function the preform thickness distribution and how to obtain more reasonable viscosity coefficients are needed to obtain more accurate simulation results in the field.
5. Acknowledgment
This work was supported by GRRC program of Gyeonggi province. [GRRC 2018- 0261, Research on Innovative Intelligent ManufacturingSystem].
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