KR101068072B1 - Sensitivity Analysis in Polymer Film Process - Google Patents

Abstract

The present invention discloses a method for sensitivity analysis of polymer wheel processing. The present invention maintains a two-dimensional governing equation derived for a polymer wheel processing process, the two-dimensional governing equation comprising boundary conditions defined as a function of the periodic disturbances that may occur during the process; Calculating a transient solution for at least one of wheel thickness, width, and cross-sectional area while varying the frequency of the sine function using the governing equation; and calculating the amplitude ratio at each frequency using the calculated transient solution. Analyzing. According to the present invention, there is an advantage that accurate sensitivity analysis applicable to an actual process is possible through the introduction of a two-dimensional governing equation and a sign function that simulates periodic disturbance.

Polymer, wheel casting, sensitivity, amplitude ratio, viscoelasticity, governing equation, sine wave disturbance

Description

Sensitivity Analysis Method in Polymer Wheel Process {Sensitivity Analysis in Polymer Film Process}

The present invention relates to a method for analyzing the sensitivity of the polymer wheel processing process, and more particularly, to a method for analyzing the sensitivity to control the product non-uniformity caused by the periodic disturbance generated in the polymer wheel processing process, in particular the wheel casting process. .

Wheel casting, a typical extensional deformation process, shows a chill roll or winding of polymer melt continuously discharged from a die 100 in the flow axis direction, as shown in FIG. A pull-up roll is pulled to produce a thin polymer wheel.

The pulling force at the take-up 102 extends the wheel in the axial direction, thereby promoting molecular orientation in the wheel, thereby improving the properties of the product. Adjust the drawdown ratio, r, which is the ratio of the speed at the winding point 102 and the speed at the die exit, and the aspect ratio, which is the ratio of the axial length and the die width, or the viscoelastic properties of the material (Deborah number). Depending on the deborah number, the product properties of the wheel casting process can be controlled as desired.

Draw resonance in which the cross sectional area and width of the wheel change periodically, edge thickness of the wheel is larger than the thickness of the center (edge beads), and the width of the wheel decreases from the die exit to the winding point Since the instability of the wheel casting process such as (neck in) has been discovered, many research groups have conducted theoretical and experimental studies on the instability of the wheel casting process.

However, the linear stability of such instability, derivation of transients and analysis of one-dimensional models have been advanced.However, sensitivity analysis using transient response analysis of sine wave disturbances is used for multi-dimensional models that reflect actual processes. It is not established.

In the actual process, disturbances such as pulsation of the pump supplying the polymer melt, unevenness of the roll speed such as the cooling roll or the winding roll at the winding point are inevitably introduced and thus the product non-uniformity It is important to understand the impact on your business.

The analytical method using the one-dimensional model assumes that the thickness of the wheels is constant along the width, so that the actual process cannot be simulated properly. Therefore, the analysis results cannot be applied to the actual site.

That is, in the actual process, it is common that the thickness of the wheels varies depending on the width. However, the conventional one-dimensional model-based analysis method has a problem in that accurate sensitivity analysis is difficult because the sensitivity is analyzed in a state where these points are ignored.

In order to solve the problems of the prior art as described above, the present invention is a polymer wheel processing process that can analyze the sensitivity closer to the actual process by predicting the phenomenon that the thickness varies in the direction of the wheel width using a two-dimensional model applicable in the field We propose a method for analyzing sensitivity.

Another object of the present invention is to provide a method for sensitivity analysis of a polymer wheel processing process, which allows a more rigorous theoretical analysis by defining periodic disturbances as a sign function.

According to a preferred embodiment of the present invention to achieve the above object, a method for analyzing the sensitivity of the polymer wheel processing process, (a) maintaining the two-dimensional governing equations induced for the polymer wheel processing process- The two-dimensional governing equations include boundary conditions defined as a function of the periodic disturbances that may occur during the process; (b) calculating a transient solution for at least one of wheel thickness, width and cross-sectional area while varying the frequency of the sine function using the governing equation; And (c) analyzing the sensitivity by calculating the amplitude ratio at each frequency using the calculated transient solution.

According to another aspect of the present invention, a program of instructions that can be executed by a digital processing apparatus for the purpose of analyzing the sensitivity of a polymer wheel processing process is tangibly implemented and can be read by a digital processing apparatus. a) maintaining a two-dimensional governing equation derived for the polymer wheel processing process, the two-dimensional governing equation comprising a boundary condition defined as a function of a periodic disturbance that may occur during the process; (b) calculating a transient solution for at least one of wheel thickness, width and cross-sectional area while varying the frequency of the sine function using the governing equation; And (c) using the calculated transient solution to calculate the amplitude ratio at each frequency.

According to the present invention, since the sensitivity of the polymer wheel processing process is analyzed in consideration of the point that the thickness varies in the width direction of the wheel, there is an advantage that the analysis result can be applied to the actual process.

In addition, according to the present invention, since a function wrapped in the speed of the cooling roll or the winding roll is introduced to simulate periodic disturbance, there is an advantage that accurate sensitivity analysis of the polymer wheel processing process can be accurately reflected by reflecting the actual process more accurately.

Furthermore, according to the present invention, there is an advantage that can be easily applied when analyzing the instability generated in the processing of other polymer wheels precisely the result of sensitivity analysis.

As the invention allows for various changes and numerous embodiments, particular embodiments will be illustrated in the drawings and described in detail in the written description. However, this is not intended to limit the present invention to specific embodiments, it should be understood to include all modifications, equivalents, and substitutes included in the spirit and scope of the present invention. Like reference numerals are used for like elements in describing each drawing.

When a component is said to be "connected" or "connected" to another component, it may be directly connected to or connected to that other component, but it may be understood that another component may exist in between. Should be. On the other hand, when a component is said to be "directly connected" or "directly connected" to another component, it should be understood that there is no other component in between.

The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to be limiting of the present invention. Singular expressions include plural expressions unless the context clearly indicates otherwise. In this application, the terms "comprise" or "have" are intended to indicate that there is a feature, number, step, operation, component, part, or combination thereof described in the specification, and one or more other features. It is to be understood that the present invention does not exclude the possibility of the presence or the addition of numbers, steps, operations, components, components, or a combination thereof.

Unless defined otherwise, all terms used herein, including technical or scientific terms, have the same meaning as commonly understood by one of ordinary skill in the art. Terms such as those defined in the commonly used dictionaries should be construed as having meanings consistent with the meanings in the context of the related art and shall not be construed in ideal or excessively formal meanings unless expressly defined in this application. Do not.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. In order to facilitate a thorough understanding of the present invention, the same reference numerals are used for the same means regardless of the number of the drawings.

The present invention analyzes the sensitivity in consideration of the occurrence of periodic disturbance in the polymer wheel processing process, and proposes a method for analyzing the sensitivity according to the viscoelastic properties of each process condition or material in a wide frequency range. Here, the process according to the present invention may be performed through a program according to a preset algorithm.

In the following, the sensitivity analysis according to the present invention will be described based on the process performed in the wheel casting process, which is the stretch deformation process of the polymer, but is not limited thereto. A roll is used and other polymer wheel processing processes in which periodic disturbance is applied. Those skilled in the art will appreciate that they can be applied.

2 is a flowchart illustrating a process of analyzing a sensitivity of a wheel casting process according to an exemplary embodiment of the present invention.

Referring to FIG. 2, first, a governing equation in consideration of viscoelastic fluid properties is derived (step 200).

The two-dimensional governing equations of the wheel casting process used in the present invention are as follows.

To derive the governing equation, an isothermal condition is assumed that ignores crystallization, and the velocity and stress changes in the thickness direction are ignored. The governing equations derived from these assumptions include continuous equations (Equation 1), kinetic equations (Equation 2), and constitutive equations (Equation 3) to simulate the rheological behavior of polymer fluids.

In the case of exercise, it is assumed that the rheological forces are very dominant for high viscosity polymers and other secondary forces do not affect the analytical methodology to be obtained in the present invention.

연속식:

Continuous:

here,

운동식:

Exercise:

here,

구성방정식:

Constitutive Equation:

here,

The boundary conditions for calculating the transient solution of the process variable are set as follows.

경계조건:

Boundary conditions:

는 영점 전단 점도,

는 진동수를 각각 뜻한다. 또한, 하첨자 0은 원점, x, y는 각각 축 방향과 폭 방향을 각각 나타낸다. 또한 중심(center)에서의 경계조건은 대칭 조건을 의미한다.In Equations 1 to 4, e is a dimensionless wheel thickness, w is a dimensionless wheel width, v is a dimensionless wheel speed, and s is Dimensionless total stress tensor, τ is dimensionless extra stress tensor, t is dimensionless time, D is dimensionless strain tensor, De is Deborah number, λ is release time, ε and ξ is PTT (Phan Thien-Tanner) model variable, where D _r is the draw ratio, d is the amplitude of the disturbance, n is the vertical vector,

Is the zero shear viscosity,

Is the frequency. Subscript 0 indicates the origin, x and y indicate the axial direction and the width direction, respectively. In addition, the boundary condition at the center means a symmetry condition.

According to the present invention, as shown in the boundary condition (iii) of Equation 4, a roll speed (curling speed) such as a cooling roll or a winding roll is defined as a sign function having a specific frequency (step 202). A sine function is used to mathematically simulate periodic disturbances that can occur during a process. The sine function according to the invention responds with transient changes in wheel thickness, width and cross-sectional area.

Here, the transient solution is a solution derived through the above Equations 1 to 3 when the process variables change with time.

According to the present invention, the amplitude ratio of the transient response (transient solution) to the sine wave disturbance is calculated through Equation 5 below (step 204).

Here, e _max means the maximum value of the wheel thickness, width or cross-sectional area, and e _min means the minimum value.

3 is a view showing a change in the wheel take-up area at the winding point for the sine wave disturbance in the wheel casting process, and FIGS. 3 (a) to 3 (c) show the frequency of the sine wave disturbance. This is a result showing the change in amplitude ratio of the wheel cross-sectional area calculated as it increases.

According to the present invention, step 204 may be performed over a wide range of frequency domains, as shown in FIG.

The sensitivity of the wheel casting process is then analyzed via the amplitude ratio at each frequency (step 206).

3 to 4 show the change in the cross-sectional area of the wheel at the winding point for the sine wave disturbance, but according to the present invention, the center thickness, edge thickness, and width of the wheel at the winding point are shown. The amplitude ratio of (width) can be calculated for the sine wave disturbance of each frequency.

FIG. 5 shows the sensitivity of a system in which a viscoelastic fluid (Phan-Thien and Tanner (PTT model)) is introduced, and FIG. 5 (a) is a sign for an extension thickening fluid such as LDPE (Low Density PolyEthylene). It is a figure which shows the amplitude ratio of the center thickness, edge thickness, and wheel width of a wheel in a wave disturbance.

Meanwhile, FIG. 5 (b) shows the center thickness, edge thickness, and wheel width of wheels in sine wave disturbances for extension thinning fluids such as HDPE (High Density PolyEthylene). It is a figure which shows the amplitude ratio of width.

5 (a) to 5 (b), it can be seen that the thickness of the center portion of the wheel is more sensitive than the change of the corner portion or the width of the wheel in the wide frequency range regardless of the physical properties of the fluid. have.

Meanwhile, according to the present invention, the sensitivity analysis according to the change of the process conditions and the material variables as well as the frequency change of the sine wave disturbance is performed (step 208).

Herein, the process conditions may include an elongation ratio D _r or a distance ratio A _r , and the material variable may be a Deborah number De representing the viscoelastic properties of the material.

FIG. 6 is a diagram illustrating sensitivity according to process conditions in a system incorporating a viscoelastic fluid.

Figure 6 (a) is a view showing the change in the cross-sectional area of the wheel at the winding point according to the draw ratio, as shown in Figure 6 (a), as the draw ratio increases, the amplitude ratio of the wheel cross-sectional area is greatly changed, through which the draw ratio As it increases, the sensitivity of the wheel casting process increases.

On the other hand, Figure 6 (b) is a diagram showing the change in the cross-sectional area of the wheel at the winding point according to the distance ratio, as shown in Figure 6 (b), the amplitude ratio of the wheel cross-sectional area changes as the distance ratio is smaller, this As a result, as the distance ratio decreases, the sensitivity of the wheel casting process increases.

FIG. 7 shows the effect of Deborah number on sensitivity in a system in which an extension thinning fluid is introduced.

Here, Figure 7 (a) is the amplitude ratio to the thickness of the wheel edge portion according to the Deborah number of HDPE fluid, Figure 7 (b) is the amplitude ratio of the thickness of the wheel center portion according to the Deborah number, Figure 7 (c) is according to the Deborah number It is a figure which shows the width | variety of a wheel thickness direction, ie, the amplitude ratio of a cross-sectional area.

As shown in Figure 7 (a) to 7 (c), it can be seen that in the case of extension thinning fluid such as HDPE, the sensitivity of the process increases as the number of Deborah increases, that is, the viscoelastic properties increase.

In the wheel casting process using HDPE, the draw ratio in the process is set to be small in order to reduce the sensitivity of the process, the distance ratio is set high, and the extrusion speed in the die is reduced in order to reduce the viscoelastic properties. It is found that it is desirable to carry out the wheel casting process by reducing or adding the desired additives.

Meanwhile, FIG. 8 illustrates the effect of Deborah number on sensitivity in a system in which an extension thickening fluid is introduced.

Here, Figure 8 (a) is the amplitude ratio of the thickness of the wheel edge portion according to the Deborah number of LDPE fluid, Figure 8 (b) is the amplitude ratio of the thickness of the center portion of the wheel according to the Deborah number, Figure 8 (c) according to the Deborah number It is a figure which shows the width of the wheel thickness direction, ie, the amplitude ratio of a cross-sectional area.

As shown in FIGS. 8 (a) to 8 (c), in the case of an extension thicking fluid such as LDPE, the sensitivity of the process decreases as the number of Deborah increases, that is, the viscoelastic properties increase. .

 6 and 8, in the wheel casting process using LDPE, in order to reduce the sensitivity of the process, the draw ratio in the process is small, the distance ratio is set high, and the extrusion speed in the die is increased to increase the viscoelastic properties. It is found that it is desirable to increase the wheel casting process.

According to the present invention, as shown in Figs. 6 to 8, the sensitivity of the wheel casting process may have a dichotomous behavior and the opposite effect on the sensitivity of the process depending on what kind of fluid is used in the process. We can see that

This can lead to process conditions and material variables that can minimize sensitivity.

According to the present invention, first, the influence of each process condition or material variable in the actual process can be theoretically analyzed by simulating disturbance by using the sine function, and secondly, as shown in the results of FIGS. 7 and 8. Therefore, the opposite effect on the sensitivity can be predicted. Third, the sensitivity of the thickness difference can be distinguished in the direction of the wheel width, which cannot be determined by the conventional one-dimensional model analysis method.

On the other hand, in the above described the sensitivity analysis only for the wheel casting process, the sensitivity analysis according to the present invention will be generally applicable to the polymer wheel processing process is applied to the sine wave disturbance.

Preferred embodiments of the present invention described above are disclosed for purposes of illustration, and those skilled in the art will be able to make various modifications, changes, and additions within the spirit and scope of the present invention. Additions should be considered to be within the scope of the following claims.

1 is a schematic diagram of a typical wheel casting process.

Figure 2 is a flow chart of the sensitivity analysis process of the polymer wheel processing process according to the present invention.

3 shows a change in the wheel take-up area at the winding point for sine wave disturbance in the wheel casting process.

Fig. 4 is a diagram showing the results of introducing the frequency of the sine wave disturbance over a wide range and calculating the amplitude ratio.

5 shows the sensitivity of a system incorporating a viscoelastic fluid (Phan-Thien and Tanner (PTT model)).

FIG. 6 shows the sensitivity to process conditions in a system incorporating a viscoelastic fluid.

FIG. 7 shows the effect of Deborah number on sensitivity in a system in which an extension thinning fluid is introduced. FIG.

FIG. 8 shows the effect of Deborah number on sensitivity in a system in which an extension thickening fluid is introduced. FIG.

Claims (10)

As a method of analyzing the sensitivity of the polymer wheel processing process, (a) maintaining a two-dimensional governing equation derived for the polymer wheel processing process, the two-dimensional governing equation comprising a boundary condition defined as a function of a periodic disturbance that may occur during the process; (b) calculating a transient solution for at least one of wheel thickness, width and cross-sectional area while varying the frequency of the sine function using the governing equation; And (c) analyzing the sensitivity by calculating the amplitude ratio at each frequency using the calculated transient solution. The method of claim 1, The two-dimensional governing equation,

Where e is the dimensionless wheel thickness, w is the dimensionless wheel width, v is the dimensionless wheel speed,

Is Dimensionless total stress tensor, τ is dimensionless extra stress tensor, t is dimensionless time, D is dimensionless strain tensor, De is the Deborah number, λ is the release time, ε and ξ are PTT (Phan Thien-Tanner) model variables, D _r is the draw ratio,

Is the amplitude of disturbance, n is the vertical vector,

Is the zero shear viscosity,

Is the frequency (frequency), subscript 0 is the origin, x and y are the axial and width directions. Sensitivity analysis method of polymer wheel processing process consisting of. The method of claim 2, Sensitivity analysis method of a polymer wheel processing process, wherein the speed of the roll used in the polymer wheel processing process is defined by the sign function. The method of claim 2, The amplitude ratio is

Wherein A is an amplitude ratio, e _max is a maximum value for at least one of wheel thickness, width and cross-sectional area, and e _min is a minimum value. The method of claim 1, And repeatedly performing the amplitude ratio calculation while changing process conditions and material parameters. The method of claim 5, Wherein said process conditions comprise at least one of an elongation ratio and a distance ratio, and said material variable comprises a deborah number. The method of claim 6, A method of analyzing the sensitivity of a polymer wheel processing process comprising determining one of an optimal draw ratio, a distance ratio, and a deborah number by comparing an amplitude ratio according to each process condition and a material variable. The method of claim 1, The polymer wheel processing process is a sensitivity analysis method of a polymer wheel processing process, which is a wheel casting process that is a stretch deformation process using a roll. The method of claim 1, Wherein said amplitude ratio exhibits opposite trends for extension thickening fluids and extension thinning fluids. In order to analyze the sensitivity of the polymer wheel processing process, a program of instructions that can be executed by a digital processing device is tangibly embodied and can be read by the digital processing device. (a) maintaining a two-dimensional governing equation derived for the polymer wheel processing process, the two-dimensional governing equation including a boundary condition defined as a function of a periodic disturbance that may occur during the process; (b) calculating a transient solution for at least one of wheel thickness, width and cross-sectional area while varying the frequency of the sine function using the governing equation; And (c) using the calculated transient solution to calculate the amplitude ratio at each frequency to analyze sensitivity.

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