Method for estimating gas concentration in molten resin in injection device for foam molding

Abstract

To provide a method for estimating the concentration of gas dissolved in a molten resin.SOLUTION: During the rotation of the screw (18), a gas concentration speed dC / dt that changes by being dissolved in the molten resin (29) from the gas-liquid interface between the gas and the molten resin (29) in the non-filled section (27) is given by the following equation. The gas concentration in the molten plastic (29) is estimated from the c1 equation and a passage time T which is a time required for the molten plastic (29) to pass through the unfilled section (27).SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a gas concentration estimation method for estimating the concentration of gas dissolved in molten resin in an injection device used in foam molding, in which a gas is injected into molten resin and injected into a mold to obtain a foam-molded product. [Background technology]

[0002] Molded products containing many fine bubbles inside, i.e., foam molded products, are not only lightweight but also strong, and have a wide range of applications. To obtain foam molded products by injection molding, a foaming agent must be mixed into the resin. When a physical foaming agent is selected, gases such as nitrogen and carbon dioxide are used. When a gas is used as the foaming agent, the gas is injected into molten resin in a heated cylinder, kneaded, and dissolved. When this is injected into a mold, the pressure is released within the resin, causing the gas to turn into bubbles. When the resin cools and solidifies, the foam molded product is obtained.

[0003] When forming a foam-molded product using gas, one method involves injecting the gas in a supercritical state at high pressure and high temperature. Another method, as used in the injection molding machine described in Patent Document 1, involves injecting a relatively low-pressure gas to obtain a foam-molded product. When using this method, the screw groove depth is increased in a predetermined section of the screw, thereby reducing the pressure of the molten resin in the heating cylinder. This creates a starvation section. A gas injection port is provided in the heating cylinder corresponding to this starvation section, and the gas is injected through this section. The gas penetrates the molten resin in the starvation section. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Publication No. 2019-177696 Summary of the Invention [Problem to be solved by the invention]

[0005] The starvation zone allows for the injection of gas into the molten resin, which is advantageous because it allows for a simple gas injection device and is inexpensive to implement. However, the gas concentration in the molten resin affects the quality of the resulting foam-molded product. However, there is a problem in that it is unclear what the concentration of gas dissolved in the molten resin will be.

[0006] The present disclosure aims to provide a method for estimating the concentration of gas dissolved in molten resin.

[0007] Other objects and novel features will become apparent from the description of this specification and the accompanying drawings. [Means for solving the problem]

[0008] This disclosure relates to an injection device for foam molding in which, when the screw is rotated to melt the resin and send it downstream, the molten resin is decompressed by the shape of the flight, forming a non-filled section in the heating cylinder, and gas is supplied to this non-filled section to dissolve the gas in the molten resin.This disclosure describes the rate of gas concentration dC / dt in the solution resin that changes as it dissolves into the dissolved resin from the gas-liquid interface between the gas and the molten resin in the non-filled section during screw rotation, and is given by the following equation: JPEG2026013227000002.jpg50135The gas concentration in the molten resin is estimated from this formula (c1) and the passage time T, which is the time required for the resin to pass through the non-filled section. [Effects of the Invention]

[0009] According to the present disclosure, it is possible to estimate the concentration of gas dissolved in molten resin. [Brief explanation of the drawings]

[0010] [Figure 1] 1 is a front view showing an injection molding machine according to an embodiment of the present invention; [Figure 2] 1 is a front cross-sectional view showing an injection device according to an embodiment of the present invention. [Figure 3A] FIG. 2 is a front cross-sectional view showing a part of the injection device according to the present embodiment. [Figure 3B] FIG. 2 is a front cross-sectional view showing a part of the injection device according to the present embodiment. [Figure 4] This figure shows a cross section of a portion of an injection device according to this embodiment, the inside of a heating cylinder expanded along the direction of the flight, and a cross section of the inside of the heating cylinder cut in a direction perpendicular to the flight. [Figure 5A] FIG. 2 is a front cross-sectional view showing a part of the injection device according to the present embodiment. [Figure 5B] FIG. 2 is a front cross-sectional view showing a part of the injection device according to the present embodiment. [Figure 6] 1 is a front cross-sectional view showing an injection device according to an embodiment of the present invention. [Figure 7] 10 is a flowchart showing a gas concentration estimation method according to a second embodiment. [Figure 8A] FIG. 2 is a front cross-sectional view showing a part of the injection device according to the present embodiment. [Figure 8B] FIG. 2 is a front cross-sectional view showing a part of the injection device according to the present embodiment. [Figure 8C] FIG. 2 is a front cross-sectional view showing a part of the injection device according to the present embodiment. [Figure 9] 10 is a flowchart showing a gas concentration estimation method according to a third embodiment. [Figure 10] FIG. 2 is a front cross-sectional view showing a portion of a flight-extruded molten resin. [Figure 11] FIG. 2 is a front cross-sectional view showing a part of the injection device according to the present embodiment. [Figure 12] 10 is a flowchart showing a gas concentration estimation method according to a fourth embodiment. [Figure 13A] 1 is a graph showing gas concentrations in molten resin obtained by an experiment. [Figure 13B] 1 is a graph of gas concentration in molten resin obtained by simulation 1. [Figure 13C] 10 is a graph of gas concentration in molten resin obtained by simulation 2. [Figure 13D]10 is a graph of gas concentration in molten resin obtained by simulation 3. DETAILED DESCRIPTION OF THE INVENTION

[0011] Specific embodiments will be described in detail below with reference to the drawings. However, the present invention is not limited to the following embodiments. For clarity of explanation, the following description and drawings have been simplified as appropriate. In each drawing, the same elements are given the same reference numerals, and duplicate explanations are omitted as necessary. Furthermore, hatching has been omitted in some areas to avoid cluttering the drawings.

[0012] <Injection molding machine> The present embodiment will be described below. The gas concentration estimation method according to the present embodiment is a method for estimating the concentration of gas dissolved in molten resin in an injection molding machine for so-called foam molding. The configuration of the injection molding machine to be used is not particularly limited, but as an example, an injection molding machine 1 according to the present embodiment will be described with reference to FIG. 1. The injection molding machine 1 according to the present embodiment includes a mold clamping unit 2 and an injection unit 3.

[0013] <Mold clamping device> The mold clamping unit 2 includes a fixed platen 7 fixed to bed B, a movable platen 8 slidably provided on bed B, and a mold clamping housing 9 similarly slidably provided on bed B. The fixed platen 7 and the mold clamping housing 9 are connected by a plurality of tie bars 10, 10, ..., and the movable platen 8 is slidable between the fixed platen 7 and the mold clamping housing 9. A mold clamping mechanism, i.e., a toggle mechanism 11 in this embodiment, is provided between the movable platen 8 and the mold clamping housing 9. A fixed-side mold 13 is provided on the fixed platen 7, and a movable-side mold 14 is provided on the movable platen 8. When the toggle mechanism 11 is driven, the fixed-side mold 13 and the movable-side mold 14 are opened and closed.

[0014] <Injection device> As shown in FIGS. 1 and 2, the injection device 3 according to this embodiment includes a heating cylinder 17, a screw 18 housed within the heating cylinder 17, a screw driver 19, and a gas supply device 21. The screw 18 and the gas supply device 21 will be described in detail below. A hopper 23 is provided at the rear end, i.e., upstream side, of the heating cylinder 17, through which pellets of resin material are supplied. An injection nozzle 24 is provided at the tip of the heating cylinder 17. Although not shown in FIGS. 1 and 2, the injection nozzle 24 is equipped with a shutoff valve. The injection device 3 according to this embodiment injects a gas dissolved in the molten resin, and this shutoff valve closes the resin flow path to prevent foaming or dripping of the molten resin in the injection nozzle 24 when the injection nozzle 24 is separated from the fixed mold 13.

[0015] The injection device 3 according to this embodiment is characterized by the shape of the screw 18, which supplies gas into the heating cylinder 17 to dissolve the gas in the molten resin. Specifically, as shown in Fig. 2, the screw 18 has a groove depth between the flights 25 that varies from the rear end, i.e., the upstream side, to the tip end, i.e., the downstream side. The depth of the groove between the flights 25 gradually becomes shallower from the upstream side to the midstream side, and then becomes deeper in the midstream portion. Then, it gradually becomes shallower again toward the downstream side.

[0016] Because the screw 18 is configured in this manner, the interior of the heating cylinder 17 is divided into three sections 26, 27, and 28: a first filled section 26 on the upstream side, a non-filled section 27 in the midstream, and a second filled section 28 on the downstream side. The resin melts in the first filled section 26 to become molten resin, which fills the heating cylinder 17. FIG. 3A shows a state in which the heating cylinder 17 is filled with molten resin 29. The molten resin is then depressurized in the non-filled section 27. As shown in FIG. 3B, the molten resin 29 becomes non-filled in the heating cylinder 17. As will be described next, gas is supplied in this non-filled section 27, and the molten resin dissolves in the molten resin. The molten resin again fills the heating cylinder 17 in the second filled section 28 and is compressed.

[0017] 2, the gas supply device 21 includes a gas cylinder 30 filled with a gas such as carbon dioxide or nitrogen, a regulator 32 that reduces the gas pressure to a predetermined constant pressure, and gas pressure gauges 31 and 34 that measure the gas pressure. A gas injection section 36 is provided in the heating cylinder 17 at a location corresponding to the non-filled section 27. Gas from the gas supply device 21 is supplied into the heating cylinder 17 at the gas injection section 36. The supplied gas dissolves in the molten resin 29 in the non-filled section 27, as shown in FIG. 3B.

[0018] <Gas concentration estimation method according to the first embodiment> A gas concentration estimation method according to the first embodiment will now be described. Gas dissolves in molten resin 29 (see FIG. 3B) in non-filled section 27 (see FIG. 2). More specifically, gas dissolves into molten resin 29 from the interface with molten resin 29, i.e., the gas-liquid interface. The amount of change per time in gas concentration C in molten resin 29 due to dissolution, i.e., the rate of change dC / dt, can be given by the following equation (1). Note that equation (1) is derived from equation (3-1) which will be described later. JPEG2026013227000003.jpg50139

[0019] The gas concentration can be calculated using equation (1). For example, if the gas is carbon dioxide and the resin is polypropylene, the gas solubility C* is 2.72 x 10 at 207°C and 4 MPa. -2 [g / m 3 ]. The constant k can be derived from a model of the behavior of the molten resin 29 in the non-filled section 27, as will be explained later, or can be obtained from experiments. Methods for deriving it from a model and methods for obtaining it from experiments will be explained later. Here, the explanation will be given assuming that the value of the constant k is given.

[0020] Transforming the above equation (1) gives equation (2-1). Calculating equation (2-1) gives equation (2-2). JPEG2026013227000004.jpg105139

[0021] By the way, when t = 0, that is, immediately after the molten resin begins to come into contact with the gas, the gas concentration C is 0. Substituting this into equation (2-2) gives us (2-3). This allows us to rearrange equation (2-2) to obtain equation (2-4). By rearranging equation (2-2) while keeping in mind that the gas solubility C* is always greater than the gas concentration C in the molten resin, and C* - C is positive, we obtain equations (2-5) and (2-6).

[0022] The gas concentration estimation method according to the first embodiment calculates the gas concentration of the molten resin using equation (2-6). Specifically, the transit time T that the molten resin takes to pass through the non-filled section 27 (see FIG. 2) is substituted for time t in equation (2-6). This gives the gas concentration C of the molten resin after the transit time T seconds.

[0023] Incidentally, in the explanation of equation (1), it was explained that the constant k can be obtained by experiment. Specifically, this can be done as follows. The injection device 3 according to this embodiment (see Figure 2) is used. The transit time T for the molten resin to pass through the non-filled section 27 is measured. This transit time T is substituted into equation (2-6). Then, the gas concentration C in the molten resin is given by a formula including the constant k. The gas concentration is measured for the molten resin injected from the injection nozzle 24 of the injection device 3. The constant k is determined so that the calculated gas concentration C matches the measured gas concentration value. In other words, the constant k can be obtained by experiment.

[0024] Incidentally, any measuring device can be used to measure the gas concentration in the molten resin. For example, a transmission-type near-infrared spectroscopic probe can be used. The transmission-type near-infrared spectroscopic probe is attached to the injection nozzle 24 to obtain the near-infrared light absorption spectrum of the molten resin. Each type of gas absorbs infrared light at a specific wavelength. Measuring the degree of infrared absorption at that wavelength makes it possible to calculate the gas concentration. For example, if carbon dioxide is used as the gas, it is sufficient to examine the absorption at a wavenumber of 4950 / cm (wavelength 2.02 nm). The constant k is determined by such an experiment. Then, the gas concentration C in the molten resin can be calculated using equation (2-6).

[0025] The constant k in equation (1) can be derived from a model of the behavior of the molten resin 29 in the non-filled section 27. This will be explained below. The upper part of Figure 4 shows how the molten resin 29 is extruded to a predetermined thickness by the flight 25 of the screw 18 in the non-filled section 27 of the heating cylinder 17. Of the pair of wall surfaces of the flight 25, the surface extruding the molten resin 29 will be called the push side 41, and the other will be called the pull side 42.

[0026] When the molten resin 29 in the non-filled section 27 is examined in detail, the molten resin 29a having a large volume is poured into the non-filled section 27 to a predetermined thickness w by the flight 25. p A very small amount of molten resin 29b is extruded to the inner circumferential surface of the heating cylinder 17 with a thickness of δ f The adhering molten resin 29b is molten resin leaking from the gap between the top of the flight 25 and the heating cylinder 17. The molten resin 29a extruded by the flight 25 is extruded at a height h' of the flight 25. For convenience, hereinafter, the extruded molten resin 29a will be referred to as flight-extruded molten resin 29a, and the molten resin 29b that leaks from the gap in the heating cylinder 17 and adheres to the inner surface of the heating cylinder 17 will be referred to as cylinder-adhered molten resin 29b.

[0027] The height h' of the flights 25, the distance h between the grooves 44 between the flights 25 and the inner circumferential surface of the heating cylinder 17, and the thickness δ of the molten resin 29b adhering to the cylinder are fis related by the following equation: h' = h-δ f The thickness δ of the molten resin 29b attached to the cylinder f is sufficiently small compared to the flight height h, so it can be treated as follows: h' ≒ h

[0028] The middle part of Figure 4 shows a diagram in which the spirally formed flight 25 is linearly expanded. The flight extruded molten resin 29a is also expanded in the same manner. The length of one circumference of the inner circumferential surface of the heating cylinder 17, i.e., the circumference length 45, is the inner diameter D of the heating cylinder 17. b From [m], πD b For this circumference 45, the component in the direction perpendicular to the flight 25, i.e., the x-direction component 46, and the component in the direction parallel to the flight 25, i.e., the z-direction component 47, are given by πD b sinθ, πD b cosθ. The screw 18 rotates at a speed of N [s -1 ], the speed of a given point at the apex of the flight 25 is given by the product of the length of one revolution 45 and the number of revolutions N, so πD b N. Then, the velocity component perpendicular to Flight 25 is πD b N sinθ, and the velocity component parallel to flight 25 is πD b It is given by N cosθ.

[0029] The bottom part of Figure 4 shows a cross section perpendicular to the direction of the flight 25. The direction perpendicular to the flight 25 is the x direction, and the height direction of the flight 25 is the y direction. Below, we will derive the constant k in equation (1) based on this model.

[0030] When gas and molten resin are in contact, the gas dissolves into the molten resin from the gas-liquid interface. The average dissolution rate of gas per unit time at the gas-liquid interface, i.e., the surface of the molten resin, is N gs is given by the following equation (3-1). JPEG2026013227000005.jpg142137

[0031] While various formulas for the mass transfer coefficient K are given based on various theories, such as the double-layer boundary film hypothesis, we consider a surface renewal model based on the so-called penetration theory. In other words, assuming that the gas-liquid interface is renewed by the flow of the flight-extruded molten resin 29a, the renewal time of the gas-liquid interface, i.e., the time τ during which the resin is exposed to the gas, is used as a parameter and is given by equation (3-2). Then, equation (3-3) can be derived from equations (3-1) and (3-2). Incidentally, when the screw 18 rotates within the heating cylinder 17, the spiral-shaped flight 25 appears to move relatively forward within the heating cylinder 17, i.e., to the left in Figure 5A. If the x and y coordinates are shifted along with the flight 25, which appears to move leftward, the heating cylinder 17 will actually move relatively to the right, as indicated by the reference symbol 50 in Figure 5A. The speed of this rightward movement of the heating cylinder 17 is determined by the rotation speed N [s -1 When rotating by ], πD b N sinθ(D b : inner diameter of the heating cylinder 17, θ: flight angle). From the consideration of FIG. 4, the velocity component perpendicular to the flight 25 when the screw 18 rotates is b This is because it becomes N sin θ.

[0032] At this time, the flight-extruded molten resin 29a extruded by the pushing surface 41 of the flight 25 flows as shown by the arrows 51, 51, .... Due to this flow, the surface of the flight-extruded molten resin 29a, i.e., the gas-liquid interface, moves at a speed πD, which is the same as the speed of the heating cylinder 17 moving rightward. b The flight extruded molten resin 29a has a gas-liquid interface that is curved convexly near the center as shown in Figure 5A, but it is considered that the gas-liquid interface is a vertical plane as shown in Figure 5B.

[0033] Then, the renewal time of the gas-liquid interface in the flight extruded molten resin 29a, i.e., the exposure time τ during which the resin is in contact with the gas, is the time it takes for the gas-liquid interface to pass through the flight height h', and is given by the following equation (4). JPEG2026013227000006.jpg62137

[0034] If the flight-extruded molten resin 29a is treated as a single mass, the gas that penetrates from the gas-liquid interface penetrates the entire flight-extruded molten resin 29a, changing the gas concentration. Therefore, the rate of change dC / dt of the gas concentration C in the flight-extruded molten resin 29a is given by the following equation (5-1): JPEG2026013227000007.jpg212137

[0035] Substituting the above equation (5-2) into equation (5-1) and solving it using equations (3-3) and (4) gives equation (5-3). Comparing equation (5-3) with equation (1), the constant k is given by the following equation (6-1). To reiterate the explanation already given, the constant k given in equation (6-1) was obtained by assuming that the flight extruded molten resin 29a is a single mass as a whole and that the gas permeates the entire flight extruded molten resin 29a evenly. JPEG2026013227000008.jpg83137

[0036] where the gas diffusion coefficient D m Although it varies depending on the type of resin and gas, and the temperature, for example, when carbon dioxide is dissolved and diffused into polypropylene at a temperature of 190°C, it is 8.0 x 10 -9 [m 2 / s]. Other constants, such as the thickness of the molten resin, p The value of the constant k can be obtained by substituting appropriate values ​​for the inner diameter N of the heating cylinder, etc. into equation (6-1). This concludes the explanation of how to derive the constant k using a model of the behavior of the molten resin 29.

[0037] <Gas concentration estimation method according to the second embodiment> A gas concentration estimation method according to the second embodiment will be described. In the gas concentration estimation method according to the second embodiment, calculations are made taking into consideration not only the dissolution of gas into the molten resin from the gas-liquid interface, but also the change in gas concentration due to the flow of the molten resin. A model for implementing the gas concentration estimation method according to the second embodiment is shown in FIG. 6. Of the molten resin 29, the flight-extruded molten resin 29a is divided into a plurality of meshes in a lattice pattern. In FIG. 6, the mesh is divided into a plurality of meshes in the x and y directions, but it is also considered to be divided into a plurality of short, predetermined widths in the z direction. The gas concentration of this flight-extruded molten resin 29a is estimated by calculation using the mesh. Note that in the second embodiment, the cylinder-adhered molten resin 29b is excluded from the calculation of the gas concentration. The reason for this is that the thickness δ f The molten resin 29b adhering to the cylinder has a smaller volume than the molten resin 29a extruded from the flight, and therefore has a relatively small effect on the gas concentration of the entire molten resin 29.

[0038] The gas concentration estimation method according to the second embodiment is carried out as shown in FIG. 7. A predetermined width of molten resin in the z direction is the object of calculation. Calculation begins immediately after this predetermined width of molten resin enters the non-filled section 27. First, step S1 is carried out. That is, among the multiple meshes of the flight-extruded molten resin 29a (see FIG. 6), the gas dissolution rate over a short time Δt is calculated for the mesh at the gas-liquid interface, i.e., the mesh indicated by reference numeral 53. The calculation is carried out using equation (1), but the constant k is determined using the following equation (6-2). Note that equation (6-2) is derived by assuming, similar to the derivation of equation (6-1), that gas permeates evenly within the mesh in contact with the gas, i.e., the mesh at the gas-liquid interface. JPEG2026013227000009.jpg83137

[0039] For example, the calculation is as follows. Transforming equation (1) gives equation (7-1). If the gas concentration in the melted gas at a given time is C, then the gas concentration C after a short time Δt seconds is newis given by equation (7-2). Since the gas concentration is 0 immediately after the start of contact with the gas, the boundary condition is set to the initial gas concentration C = 0. JPEG2026013227000010.jpg63139

[0040] For the meshes corresponding to the reference numeral 53 in FIG. 6, the calculation in step S1 is performed to obtain the gas concentration C new Once this is calculated, the process moves to step S2 as shown in Figure 7. In step S2, the gas concentration in each mesh is calculated, taking into account the flow of each mesh in the flight extruded molten resin 29a. The change in gas concentration in each mesh due to flow can be calculated using the following equation (8-1). This equation (8-1) is the so-called advection-diffusion equation (8-3), which is a general equation for gas concentration change, and is obtained by setting the left side to 0, assuming that the change in concentration due to diffusion is small compared to the magnitude of the change in concentration due to flow. However, here we will further simplify equation (8-1). In other words, we will treat the resin as flowing only in the xy direction, and calculate the flow velocity v in the z direction. z is set to 0, we obtain equation (8-2). The calculation is performed using this. Note that the flow velocity in the z direction, v z Naturally, this is not 0, and will be taken into consideration in the next steps S3 and S4. JPEG2026013227000011.jpg131139

[0041] For example, the flow velocity can be calculated using commercially available flow analysis software. For example, for any one mesh, the flow velocity flowing out to one or more adjacent meshes after Δt seconds and the flow velocity flowing into that mesh from one or more adjacent meshes are calculated using the flow analysis software. Then, the gas concentration after Δt seconds is calculated from the respective gas concentrations in these meshes, the outflow amount from that mesh, and the inflow amount to that mesh. This calculation is performed for all meshes.

[0042] After the calculation in step S2 is completed, step S3 is executed as shown in Fig. 7. That is, it is checked whether or not the width of the mesh in the z direction has been passed. This will be explained in detail. First, the flight extruded molten resin 29a moves at an average speed πD in the z direction. b N cosθ / 2(D b : inner diameter of the heating cylinder 17, N: rotation speed of the screw 18, θ: flight angle). The reason for giving the average velocity in the z direction is that the velocity component in the z direction at the top of the flight 25, obtained from the consideration in FIG. 4, is πD b N cosθ, the assumption that the z-direction velocity component of the resin at the bottom of the flight 25 is 0, and the z-direction velocity component increases linearly in the height direction of the flight 25. Hereinafter, the flight extruded molten resin 29a moves at an average z-direction velocity πD b It is assumed that the flow is uniform at N cosθ / 2. In other words, the entire mesh has an average flow velocity v in the z direction. z =πD b It is assumed that the flow proceeds in the z direction at a rate of N cosθ / 2. This average flow velocity v z In the first calculation, the first Δt seconds, that is, πD b Move forward in the z direction by N cos θΔt / 2. Check whether this distance traveled passes through the width of the mesh in the z direction. If it does not pass, the determination is NO and return to step S1.

[0043] In step S1, the calculation for the next Δt seconds is performed, that is, the dissolution of gas from the gas-liquid interface for the mesh indicated by reference numeral 53 in FIG. 6 is calculated using equation (7-2), and C new Next, in step S2, the change in gas concentration due to flow is calculated. Then, step S3 is carried out again. The average flow velocity v z If the distance traveled in the z direction by the distance does not pass through the width of the mesh in the z direction (NO), the process returns to step S1 again, but if it does pass through (YES), the process proceeds to step S4. In step S4, the gas concentration in each mesh is passed on to the next mesh group in the z direction, that is, the downstream mesh group. In other words, the average flow velocity in the z direction vz This is treated as if the gas concentration has moved from the upstream mesh group to the adjacent downstream mesh group.

[0044] After step S4 is executed, step S5 is executed. That is, it is determined whether the flight extruded molten resin 29a being calculated has passed through the non-filled section, that is, whether the passing time has been completed. If the passing time has not been completed (NO), the process returns to step S1. If the time has been completed (YES), the calculation ends. Note that in step S5, it is determined whether the flight extruded molten resin 29a has passed through the non-filled section, but it may also be determined whether the metering time has been completed, and the calculation may end when the metering time has been completed. This concludes the description of the gas concentration estimation method according to the second embodiment.

[0045] <Gas concentration estimation method according to the third embodiment> A gas concentration estimation method according to the third embodiment will be described below. In the gas concentration estimation method according to the third embodiment, calculations are performed taking into consideration dissolution of gas into the molten resin from the gas-liquid interface, mixing of the molten resin 29b adhering to the cylinder (see FIG. 5B) with the molten resin 29a extruded by the flight, and changes in gas concentration due to the flow of the molten resin.

[0046] In the gas concentration estimation method according to the third embodiment, a method is proposed for calculating changes in gas concentration due to the flow of molten resin, so that calculations can be performed even on a personal computer or the like with relatively insufficient computing power, without using commercially available flow analysis software. Therefore, the number of meshes of the flight extruded molten resin 29a is reduced so that calculations of the flow can be performed relatively simply. When determining the mesh size, etc., the flow of the flight extruded molten resin 29a is considered.

[0047] As shown in Figure 8A, the flight extruded molten resin 29a in a cross section perpendicular to the flight 25 is divided into two in the x direction. p / 2, and consider a virtual boundary 55. The flow velocity of the molten resin in the x direction at the boundary 55 is v xThe magnitude of πD changes depending on the y position and is a function of y. The groove 44 between the flights 25 is fixed, and the inner circumferential surface of the heating cylinder 17 moves at a speed of πD b N sinθ(D b : inner diameter of heating cylinder 17, N: rotation speed of screw 18, θ: flight angle). The boundary 55 located at half the thickness of the flight-extruded molten resin 29a is a symmetrical plane of the molten resin, so the flow velocity v of the molten resin at boundary 55 x It can be considered that the flow velocity of the molten resin in the x direction at the boundary 55 is v x can be expressed as a superposition of the so-called Couette flow and two-dimensional Poiseuille flow by equation (9-1).

[0048] JPEG2026013227000012.jpg156139

[0049] The width in the z direction (see FIG. 4) is dz, and the volume flow velocity Qv of the molten resin in the x direction over the entire surface of the boundary 55 is x Considering this, we can integrate equation (9-1) in the y direction to obtain the volumetric flow rate Qv x By the way, in the flight extrusion molten resin 29a, the thickness of the molten resin w p is treated as being constant in the z direction (see Figure 4). p does not change with time. In this case, the volumetric flow rate Qv x must be 0. If we set equation (9-2) to 0, we get equation (10-1). Substituting this into equation (9-1), we get equation (10-2).

[0050] JPEG2026013227000013.jpg127141

[0051] Next, in the flight extrusion molten resin 29a, the right half side in FIG. 8A, that is, 0≦x≦w p / 2 range and the left half side, i.e., w p / 2≦x≦w pIn the range of , the flow velocity of the molten resin in the y direction v y Regarding the right half side, the amount of molten resin flowing from the left half side to the right half side at the boundary 55 in the width dy is -v x The amount of molten resin that flows in this way is v x dy, the flow velocity v y The amount by which -v x dy×2 / w p On the left half side, the amount of molten resin flowing from the right half side to the left half side at the boundary 55 in the width dy is v x The amount of molten resin that flows in this way is v x dy, the flow velocity v y The amount by which v increases x dy×2 / w p At y=0, the flow velocity of the molten resin on both the right and left halves is v y = 0, the flow velocity of the molten resin on the left and right half sides at any y position y* is v y is given by equation (11).

[0052] JPEG2026013227000014.jpg108140

[0053] Here, we consider the division of the mesh in the x and y directions of the flight-extruded molten resin 29a. As shown in FIG. 8B, in the x direction, the boundary 55, that is, x=w p The gas concentration is divided by 2h / 3 from the groove 44 between the flights 25, 25, that is, at the boundary 57 at y=2h / 3, from equation (10-2), v x = 0. In other words, the flow velocity of the molten resin in the x direction is v x becomes zero at the boundary 57. The velocity v in the x direction x is positive in magnitude below boundary 57 and negative in magnitude above boundary 57.

[0054] In the gas concentration estimation method according to the third embodiment, the change in gas concentration due to the incorporation of the molten resin 29b adhered to the cylinder into the molten resin 29a extruded by the flight is also calculated. f is generally thin, about 0.1 to 0.2 mm. Therefore, it is considered that the gas penetrates quickly and quickly reaches the gas solubility C*. In this way, the molten resin 29b attached to the cylinder that has reached the gas solubility C* is b The flight moves at an angle N sin θ and comes into contact with the extruded molten resin 29a. That is, as shown in Fig. 8C, the molten resin 29b adhering to the cylinder comes into contact with the meshes 60, 61 at the top of the extruded molten resin 29a. As a result, some of the molten resin in the meshes 60, 61 mixes with the molten resin 29b adhering to the cylinder.

[0055] In the gas concentration estimation method according to the third embodiment, these uppermost meshes 60 and 61 have a thickness δ 63 shown in FIG. 8C. f The molten resin in the range of thickness δ f The molten resin 29b attached to the cylinder with a solubility of gas C* flows at a speed of πD b The gas penetrates by Nsinθ and the gas concentration is C and the thickness is w p Since the thickness δ indicated by the reference numeral 63 is mixed with the molten resin of the meshes 60 and 61, the change in gas concentration in the molten resin indicated by the reference numeral 63 is given by equation (12). By using this equation (12), the gas concentration of the molten resin of the meshes 60 and 61 due to mixing with the molten resin 29b adhering to the cylinder can be calculated. f It is assumed that the molten resin is uniformly mixed in the molten resin within the meshes 60 and 61 having a thickness indicated by the reference numeral 64.

[0056] JPEG2026013227000015.jpg65141

[0057] When the gas concentration estimation method according to the third embodiment is carried out, the thickness w of the flight-extruded molten resin 29a is p This thickness w p can be obtained by experiment or calculation. A method for obtaining it by calculation will be explained. First, the flow velocity v of the molten resin in the z direction of the flight extruded molten resin 29a is z Consider the flow velocity of the molten resin in the z direction, v z The magnitude of changes depending on the y position and is a function of y. The groove 44 between the flights 25, 25 is fixed, and the inner circumferential surface of the heating cylinder 17 moves at a velocity πD in the z direction, referring to the consideration in FIG. b N cosθ(D b : inner diameter of the heating cylinder 17, N: rotation speed of the screw 18, θ: flight angle). Then, the flow velocity of the molten resin in the z direction v z is given as equation (13-1) in the same way as equation (9-1), as a superposition of the so-called Couette flow and two-dimensional Poiseuille flow.

[0058] JPEG2026013227000016.jpg173141

[0059] In the non-filled section 27, the pressure gradient ΔP / Δz of the molten resin in the z direction is considered to be 0, so equation (13-2) can be obtained from equation (13-1). Then, the volumetric flow rate Qv in the z direction in the non-filled section 27 is z is the number of flights n f and the thickness of the flight extruded molten resin 29a w p and the flow velocity v shown in (13-2) z is multiplied by the integral of the y-axis, and the result is given by equation (13-3).

[0060] On the other hand, in the injection device 3 (see FIG. 2), when the screw 18 is rotated to deliver the molten resin, the molten resin is metered to the tip of the heating cylinder 17. Then, the volume flow rate Q of the molten resin in the axial direction of the heating cylinder 17 during metering is m is the length of the molten resin to be measured, L st and measurement time t rTherefore, it is given by equation (14). JPEG2026013227000017.jpg50139

[0061] Here, the volumetric flow rate Qv of the molten resin in the z direction is given by equation (13-3). z and the axial volumetric flow rate Q given by Eq. (14) m Assuming that and are equal, Qv z =Q m Solving this, the thickness of the flight extruded molten resin 29a w p is obtained.

[0062] The gas concentration estimation method according to the third embodiment will be described with reference to the flowchart in Fig. 9. The calculation starts immediately after a predetermined width of molten resin enters the non-filled section 27 (see Fig. 4). First, step S11 is carried out. That is, among the multiple meshes of the flight-extruded molten resin 29a (see Fig. 8B), the gas dissolution in the shortest time Δt is calculated for the mesh at the gas-liquid interface, i.e., the mesh on the left side. The calculation is carried out using equation (1), and the constant k is the value obtained from equation (6-2) explained in the second embodiment, that is, the mesh thickness d in this equation. x The thickness of the flight extruded molten resin is 29a p Assuming that it is 1 / 2 of (d x =w p / 2), and use the calculated values.

[0063] Next, step S12 is performed. That is, the change in gas concentration due to the incorporation of the cylinder-adhered molten resin 29b into the flight-extruded molten resin 29a is calculated. That is, the gas concentration is calculated for meshes 60 and 61 shown in FIG. 8C based on equation (12).

[0064] Next, step S13 is performed. That is, the change in gas concentration due to the flow of the flight extrusion molten resin 29a is calculated. In FIG. 10, a part of the mesh of the flight extrusion molten resin 29a is shown enlarged. Each mesh is represented as mesh m(0,k), m(1,k), m(0,k+1), etc. Then, the flow velocity v in the x direction in mesh m(0,k) or mesh m(1,k) is calculated. x v x (k), the velocity v in the y direction at mesh m(0,k) y v y These are written as (0, k), respectively. As already explained, the change in gas concentration due to flow is given by equation (8). Integrating this gives equation (15-1).

[0065] JPEG2026013227000018.jpg169144

[0066] Here, dx is the width of the mesh in the x direction, w p If we set k / 2 as dy and the width f in the y direction, we obtain equations (15-2) and (15-3) based on the notations in Figure 10. These equations hold for any k. Based on equations (15-2) and (15-3), we can calculate the gas concentration C after Δt seconds due to flow for each mesh. new When k=0, that is, when calculating for the bottom mesh m(0,0) and m(1,0), in equations (15-2) and (15-3), C(0,-1) and C(1,-1) can be replaced with C(0,0) and C(1,0). Similarly, when k is the maximum k in the range, max When the mesh m(0,k max ), m(1,k max ) can be calculated in the same way.

[0067] In FIG. 9, after step S13 is performed, step S14 is performed. That is, it is checked whether or not the flight extruded molten resin 29a has passed through the width of the mesh in the z direction. That is, the flight extruded molten resin 29a has an average velocity component πD in the z direction. b N cosθ / 2(D b: inner diameter of the heating cylinder 17, N: rotation speed of the screw 18, θ: flight angle) in the z direction. Then, the entire mesh flows at an average flow velocity v in the z direction. z =πD b It is assumed that the flow proceeds in the z direction at a velocity of N cosθ / 2. z In the first calculation, the first Δt seconds, that is, πD b Move forward in the z direction by N cos θΔt / 2. Check whether this distance traveled passes through the width of the mesh in the z direction. If it does not pass, the determination is NO and return to step S11.

[0068] In step S11, the calculation is performed for the next Δt seconds, that is, for the mesh at the gas-liquid interface, that is, the mesh on the left side, among the multiple meshes of the flight extrusion molten resin 29a (see FIG. 8B), the gas dissolution is calculated for the short time Δt. Next, in step S12, the change in gas concentration due to flow is calculated. Then, step S13 is performed again. The average flow velocity v z If the distance traveled in the z direction by the distance does not pass through the width of the mesh in the z direction (NO), the process returns to step S11 again, but if it does pass through (YES), the process proceeds to step S15. In step S15, the gas concentration in each mesh is passed on to the next mesh group in the z direction, that is, the downstream mesh group. In other words, the average flow velocity in the z direction v z This is treated as if the gas concentration has moved from the upstream mesh group to the adjacent downstream mesh group.

[0069] After step S15 is executed, the process proceeds to step S16. That is, it is determined whether or not the flight extruded molten resin 29a of a predetermined width in the z direction, which is the subject of the calculation, has passed through the non-filled section 27 (see FIG. 2). If it has not passed through, the process returns to step S11 and the calculation is repeated. On the other hand, if it is determined that it has passed through (YES), the calculation is terminated. Alternatively, instead of step S15, the end of the calculation may be determined based on whether or not the measurement time has elapsed. This concludes the explanation of the gas concentration estimation method according to the third embodiment.

[0070] <Gas concentration estimation method according to the fourth embodiment> In the gas concentration estimation method according to the fourth embodiment, the change in gas concentration in the flight extruded molten resin 29a is calculated while the screw 18 is not rotating. When the screw 18 is not rotating, as shown in FIG. 11, the inner wall of the heating cylinder 17 is stationary relative to the screw 18, and the flow rate of the molten resin in the flight extruded molten resin 29a is zero. At this time, the change in gas concentration in the flight extruded molten resin 29a is due only to the dissolution of gas from the gas-liquid interface and the penetration of the dissolved gas into the interior of the molten resin. When the screw 18 is not rotating, the mesh is finely divided in both the x and y directions as shown in FIG. 11 for calculations. When there is no flow of molten resin, the penetration of gas into the molten resin is given by Equation (16-1), which is a modification of Equation (8-3).

[0071] JPEG2026013227000019.jpg52141

[0072] In the gas concentration estimation method according to the fourth embodiment, the gas concentration of the mesh corresponding to the gas-liquid interface is given by the gas solubility C*. Then, calculations are performed as shown in FIG. 12. That is, step S21 is executed. The change in gas concentration due to gas penetration between meshes in the x, y, and z directions is calculated using equation (16-1). Next, step S22 is executed. That is, it is determined whether the calculation for the screw stop time is complete. If not completed (NO), return to step S21 and repeat the calculation. On the other hand, if completed (YES), end the calculation. Note that in actual gas concentration changes due to penetration, the magnitude of changes in the y and z directions is sufficiently small compared to the change in the x direction. Therefore, in step S21, equation (16-2), which is a modification of equation (16-1), can be used. Performing calculations using equation (16-2) can reduce the amount of calculations. This concludes the explanation of the gas concentration estimation method according to the fourth embodiment.

[0073] <Modification> The gas concentration estimation method according to this embodiment can be modified in various ways. For example, the gas concentration estimation method according to the second embodiment and the gas concentration estimation method according to the third embodiment can be modified. In these gas concentration estimation methods, as described in step S3 of FIG. 7 and step S14 of FIG. 9, calculations are performed until the molten resin to be calculated passes through the non-filled section 27. In other words, once the resin enters the non-filled section 27, calculations are continued until the resin passes through the non-filled section 27.

[0074] However, when actual foam molding is performed, the rotation of the screw 18 is stopped once the required amount of resin has been measured. As a result, some resin passes through the non-filled section 27 and is sent out, while other resin stops midway through the non-filled section 27. The resin that stops midway through the non-filled section 27 is held in that state for a predetermined period, that is, until the injection operation in the injection device 3 (see FIG. 2) is completed, and is then sent forward once the screw 18 rotates again. Therefore, the gas concentration estimation method according to the second embodiment and the gas concentration estimation method according to the third embodiment can be modified to suit such actual foam molding conditions.

[0075] That is, while the screw 18 is rotating, the gas concentration in the molten resin is calculated using the gas concentration estimation method according to the second or third embodiment, and the completion of the metering time is also determined in step S3 of Fig. 7 or step S14 of Fig. 9. When the metering time is completed, for the resin stopped in the non-filled section 27, the change in gas concentration while the screw 18 was stopped is calculated using the gas concentration estimation method according to the fourth embodiment. Then, when the rotation of the screw 18 resumes, the gas concentration in each mesh at that time is used as the initial condition, and the gas concentration in the molten resin is calculated using the gas concentration estimation method according to the second or third embodiment. [Example]

[0076] <Experiments and Simulations> In order to investigate the accuracy with which the gas concentration estimation method according to this embodiment can estimate the gas concentration in molten resin, experiments were conducted using the actual injection unit 3 and computer simulations were carried out, and the experimental results were compared with the simulation results.

[0077] <Experiment using actual equipment> An experiment was conducted using the actual injection device 3 to measure the gas concentration in the molten resin by allowing the gas to penetrate and measuring the resin. The conditions for the experiment were as follows. "Injection device 3" Inner diameter D of heating cylinder 17 b 2.2×10 -2 [m] Flight 25 height of screw 18 h' (≒h) 4.6 x 10 -3 [m] The gap δ between the top of the flight 25 and the inner surface of the heating cylinder 17 f 7.5×10 -5 [m] Flight 25 pitch 2.2 x 10 -2 [m] Flight angle of flight 25: 0.308[rad] Groove width between flights 1.88×10- 2 [m] Flight number 1[-] Length of unfilled section 27: 4.95×10 -1 [m] Gas concentration measuring device A heat-resistant and pressure-resistant transmission near-infrared spectroscopic probe was attached to the injection nozzle 24 (see Figure 2) of the injection device 3 and connected to a Fourier transform spectrophotometer via an optical fiber, allowing the gas concentration in the molten resin to be measured.

[0078] "Resin, gas" Resin type: Polypropylene ·Resin specific gravity ρ 740[kg / m3] (210℃) Gas type: carbon dioxide Gas diffusion coefficient D m 8.0×10 -9 [m 2 / s] Gas solubility C* 2.72×10 -2 [g / m 3 ] "Molding conditions" Metering stroke 4.5 x 10 -2 [m] Molding cycle time: 40 seconds Molding cycle count: 5 [-]

[0079] A feeder was installed in the hopper 23 to allow the material supply rate to be adjusted, and experiments were conducted. First, the material supply rate from the feeder was set to 2.6 kg / h, and the screw rotation speed was set to 80 rpm. Five molding cycles were conducted under the above conditions. The gas concentration, i.e., the average CO2 concentration, was measured using a gas concentration measurement device and the average value was obtained. Similarly, the material supply rate was set to 2.6 kg / h, and 100, 120, and 140 rpm screw rotation speeds were used to conduct 10 to 50 molding cycles, respectively, and the average CO2 concentration was obtained. Next, similar experiments were conducted with different material supply rates. That is, the material supply rate was set to 4.0 kg / h, and 10 to 50 molding cycles were conducted with 80, 100, 120, and 140 rpm screw rotation speeds, respectively, and the average CO2 concentration was obtained. The results are shown in Figure 13A.

[0080] Even if the material supply speed by the feeder is controlled, when the screw rotation speed is low, the volume flow rate Q m does not reach the material supply speed. Also, even when the screw rotation speed is sufficiently high, the volume flow rate Q m does not necessarily coincide with the material supply speed. Therefore, when the above experiment was carried out, the volume flow rate Q that actually flowed in the heating cylinder 17 was calculated for each combination of the set material supply speed and screw rotation speed. m The recorded volumetric flow rate Q mwill be used in the simulations described below. Furthermore, if the material supply speed or screw rotation speed changes, the metering time will inevitably change, and therefore the stop time of the screw 18 will also change. The stop time of the screw 18 is the molding cycle time of 40 seconds minus the metering time. Therefore, the actual metering time and stop time were measured and recorded for each combination of the set material supply speed and screw rotation speed. These will also be used in the simulations described below.

[0081] <Simulation 1> The gas concentration of the molten resin was calculated using the gas concentration estimation method according to the first embodiment. Specifically, a simulation was performed using equations (2-6) and (6-1) under the same conditions as the experimental conditions. Note that the simulation using the gas concentration estimation method according to the first embodiment did not take into account the state when the screw 18 was stopped, and calculations were performed only when the screw 18 was rotating. The results of the simulation are shown in Figure 13B.

[0082] <Simulation 2> The gas concentration of the molten resin was calculated using the gas concentration estimation method according to the third embodiment. That is, the calculation was performed according to the flowchart in Fig. 9. The mesh division of the flight-extruded molten resin 29a was as follows: the number of divisions in the x direction of the mesh was 2, the number of divisions in the y direction was 200, and the length of the mesh in the z direction was 3.63 × 10 -3 In this simulation 2, the calculation was performed only when the screw 18 was rotating, without taking into consideration the state when the screw 18 was stopped. The results of the simulation are shown in Fig. 13C.

[0083] <Simulation 3> The gas concentration of the molten resin was calculated by combining the gas concentration estimation method according to the third embodiment with the gas concentration estimation method according to the fourth embodiment. That is, when the screw 18 was rotating, calculation was performed using the gas concentration estimation method according to the third embodiment, and when the screw 18 was stopped, calculation was performed by switching to the gas concentration estimation method according to the fourth embodiment. The mesh division of the flight extruded molten resin 29a was changed depending on whether the screw 18 was rotating or stopped. That is, when the screw 18 was rotating, the number of divisions in the mesh in the x direction was 2, the number of divisions in the y direction was 200, and the length of the mesh in the z direction was 3.63 × 10 -3 On the other hand, when the screw 18 is stopped, the number of divisions in the x direction of the mesh is 200, the number of divisions in the y direction is 200, and the length of the mesh in the z direction is 3.63 × 10 -3 The number of divisions in the x direction was changed to [m]. The simulation results are shown in Figure 13D.

[0084] <Consideration> It was confirmed that simulations 1, 2, and 3 all yielded gas concentrations close to those obtained experimentally. It was also found that the gas concentration estimation method according to the third embodiment can calculate gas concentrations closer to the results obtained experimentally than the gas concentration estimation method according to the first embodiment. In other words, it was confirmed that gas concentration estimation can be performed with higher accuracy by taking into account not only the dissolution of gas from the gas-liquid interface but also the flow of molten resin.

[0085] In contrast, Simulation 3, which took into account gas diffusion while the screw 18 was stopped, calculated a value higher than the gas concentration obtained in the experiment. In Simulations 1, 2, and 3, the length of the non-filled section 27 was assumed to be fixed, but in reality the length of the non-filled section 27 changes. It is presumed that the calculated gas concentration was higher as a result of performing a simulation without considering the change in length. Therefore, to estimate the gas concentration with even higher accuracy, it is preferable to perform a simulation using a model in which the length of the non-filled section 27 changes. The change in the length of the non-filled section 27 may be obtained by actual experiment or by calculation using flow analysis software.

[0086] The invention made by the inventor has been specifically described above based on the embodiments, but it goes without saying that the present invention is not limited to the above-described embodiments and various modifications are possible without departing from the spirit of the invention. The multiple examples described above can also be implemented in appropriate combinations. [Explanation of symbols]

[0087] 1 Injection molding machine 2 Mold clamping device 3 Injection device 7 Fixed plate 8 Movable platen 9 Clamping housing 10 Tie bar 11 Toggle mechanism 13 Fixed side mold 14 Movable side mold 17 Heating cylinder 18 Screw 19 Screw drive device 21 Gas supply device 24 Injection nozzle 25 Flight 26 First filling section 27 Non-filling section 28 Second filling section 29 Molten resin 29a Flight extrusion molten resin 29b Cylinder-adhered molten resin 30 Gas cylinder 32 Regulator 31 Gas pressure gauge 34 Gas pressure gauge 36 Gas injection section 41 Push side 42 Pull side 44 Groove 55 Boundary 57 Boundary

Claims

1. A heating cylinder; a screw that is placed in the heating cylinder and has flights formed thereon; a gas supply means; In an injection device for foam molding, when the screw is rotated in the heating cylinder to melt the resin and send it downstream, the shape of the flight reduces the pressure of the molten resin to form a non-filled section in the heating cylinder, and gas is supplied from the gas supply means to the non-filled section, so that the gas dissolves in the molten resin. During rotation of the screw, the gas concentration rate dC / dt in the solution resin that changes as it dissolves into the dissolved resin from the gas-liquid interface between the gas and the molten resin in the non-filled section is given by the following equation: A gas concentration estimation method for estimating the gas concentration in molten resin from the formula (c1) and a passage time T that is the time required for the resin to pass through the non-filled section.

2. The following formula obtained based on the formula (c1): The gas concentration estimation method according to claim 1, wherein the gas concentration in the molten resin is estimated by:

3. In the non-filled section, the gas-liquid interface is renewed by the flow of the molten resin extruded by the flight. The amount of gas dissolved into the molten resin from the gas-liquid interface per unit time is N gs is given by the following formula, 3. The gas concentration estimation method according to claim 1, wherein k in the formula (c1) is obtained to estimate the gas concentration in the molten resin.

4. When one of the pair of wall surfaces of the flight is the push surface that extrudes the molten resin as the screw rotates and the other is the pull surface, the molten resin comes into contact with the push surface and is extruded in the non-filling section, and the thickness w of the extruded molten resin in the direction perpendicular to the flight is p Assuming that is constant, k is expressed by the following equation 3. The gas concentration estimation method according to claim 1, wherein the gas concentration in the molten resin is estimated by giving the following equation:

5. 2. The gas concentration estimation method according to claim 1, wherein the gas concentration C in the solution resin, which increases based on the amount of dissolved gas, is calculated for a predetermined time interval based on the formula (c1) for the molten resin extruded in the non-filled section, and the calculation is repeated until the passing time T is reached to estimate the gas concentration in the molten resin.

6. When one of the pair of wall surfaces of the flight is a push surface that extrudes the molten resin as the screw rotates and the other is a pull surface, the molten resin comes into contact with the push surface in the non-filling section. The thickness of the extruded molten resin in the direction perpendicular to the flight is w p Assuming that is constant, k is expressed by the following equation 6. The gas concentration estimation method according to claim 5, wherein the gas concentration in the molten resin is estimated by giving the following equation:

7. When one of the pair of wall surfaces of the flight is a push surface that extrudes the molten resin as the screw rotates and the other is a pull surface, the molten resin is extruded by the push surface to a predetermined thickness in the non-filling section, and a gas is filled between the push surface and the pull surface, so that a gas-liquid interface is formed, the molten resin of a predetermined thickness extruded by the pushing surface is considered to be composed of a plurality of elemental resins divided into a plurality of parts in the direction along the spiral of the flight, in the thickness direction of the molten resin, and in the height direction of the flight, and the gas concentration inside each of the elemental resins is considered to be uniform at any given moment; 2. The gas concentration estimation method according to claim 1, wherein the dissolution of gas into the molten resin from the gas-liquid interface is calculated using the formula (c1) only for the element resins among the plurality of element resins that are in contact with the gas, and the gas concentration in the molten resin is estimated by treating the plurality of element resins as moving and mixing as the screw rotates.

8. When one of the pair of wall surfaces of the flight is the push surface that extrudes the molten resin as the screw rotates and the other is the pull surface, the molten resin comes into contact with the push surface and is extruded in the non-filling section, and the thickness w of the extruded molten resin in the direction perpendicular to the flight is p Assuming that is constant, the thickness d x Divide so that k is constant, and use the following formula The gas concentration estimation method according to claim 7, wherein the gas concentration in the molten resin is estimated by giving the following equation:

9. 9. A gas concentration estimation method according to claim 7 or 8, wherein in the non-filled section, a film of molten resin adhering to the inner surface of the heating cylinder and in contact with the gas is treated as being taken up by the molten resin extruded by the flight as the screw rotates, and the gas concentration in the molten resin is estimated.

10. 10. The gas concentration estimation method according to claim 9, wherein the gas concentration in the film-like molten resin is treated as being equal to the gas solubility C*, and the gas concentration in the molten resin is estimated.

11. When the screw rotation is stopped, the change in gas concentration in the molten resin due to the gas permeating into the molten resin in the non-filled section is expressed by the following formula:

9. The gas concentration estimation method according to claim 7, wherein the gas concentration in the molten resin is estimated as given by:

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