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

Abstract

Provided is a method for estimating the concentration of a gas in a molten resin in an injection device for foam molding, said method being capable of estimating the concentration of the gas dissolved in the molten resin. During the rotation of the screw (18), the rate of change (dC / dt) of the gas concentration, which changes by dissolving into the molten resin (29) from the gas-liquid interface between the gas and the molten resin (29) in the non-filled section (27), is provided by the following formula. Wherein the rate of change of the gas concentration in the molten resin [g / (m3s)] k: constant [ / s] C *: solubility of the gas [g / m3] C: gas concentration in the molten resin [g / m3] is estimated from the equation (c1) and the passage time T, which is the time required for the molten resin (29) to pass through the non-filled section (27).

Description

TECHNICAL FIELD

[0001] The present application relates to a gas concentration estimation method for estimating the concentration of a gas dissolved in molten resin in an injection device used in a foaming molding in which a gas is injected into a molten resin and injected into a mold to obtain a foamed molded product. BACKGROUND

[0002] A molded product containing a large number of fine gas bubbles in the interior, that is, a foamed molded product, is not only lightweight but also excellent in strength, and is widely used in various fields. For a foamed molded product obtained by injection molding, a foaming agent is mixed in a resin, and in the case where a physical foaming agent is selected as the foaming agent, a gas such as nitrogen, carbon dioxide, or the like is used. In the case where a gas is used as a foaming agent, the gas is injected into a resin molten in a heating cylinder, and is mixed and dissolved. If this is injected into a mold, the pressure in the resin is released and the gas is gasified. If the resin is cooled and solidified, a foamed molded product is obtained.

[0003] There is also a method in which a gas is injected in a supercritical state of high pressure and high temperature when a foamed molded product is molded by a gas, but there is also a method in which a foamed molded product is obtained by injecting a gas at a relatively low pressure using an injection molding machine as described in Patent Literature 1. In the case where such a method is implemented, the groove depth of the screw is deepened in a prescribed section of the screw, and thus the pressure of the molten resin in the heating cylinder is reduced. That is, a starvation section is formed. An injection portion of the gas is provided in the heating cylinder corresponding to the starvation section to inject the gas. In the starvation section, the gas permeates into the molten resin.

[0004] PRIOR ART DOCUMENTS

[0005] PATENT LITERATURE

[0006] Patent Literature 1: Japanese Patent Application Laid-Open No. 2019-177696 SUMMARY

[0007] In the case where a starvation section is provided and a gas is injected to dissolve the gas into a molten resin, the gas injection device can be constituted to be simple, and can be implemented inexpensively and thus is excellent. In addition, the concentration of the gas in the molten resin can have an influence on the quality of a foamed molded product to be molded. However, there is a problem that it is not clear to what extent the concentration of the gas dissolved in the molten resin is.

[0008] An object of the present disclosure is to provide a method capable of estimating the concentration of a gas dissolved in a molten resin.

[0009] Other problems and new features will be clear from the description of the present specification and the added drawings.

[0010] This disclosure focuses on an injection molding apparatus for foam molding. In this apparatus, as the screw rotates to melt resin and convey it downstream, the molten resin is depressurized due to the shape of the screw thread, creating a non-filled zone within a heating cylinder. Gas is supplied to this non-filled zone, causing the gas to dissolve in the molten resin. During screw rotation, this disclosure provides the rate of change dC / dt of the gas concentration in the molten resin, which varies due to the gas dissolving into the molten resin from the gas-liquid interface in the non-filled zone, using the following formula.

[0011]

[0012] in The rate of change of gas concentration in the molten resin [g / (m 3 s)]

[0013] k: constant

[0014] C * Solubility of gas [g / m³] 3 ]

[0015] C: Gas concentration in molten resin [g / m³] 3 ]

[0016] The gas concentration in the molten resin is estimated based on the formula (c1) and the time required for the resin to pass through the non-filled section, i.e., the passage time T.

[0017] Invention Effects

[0018] According to this disclosure, the concentration of dissolved gases in the molten resin can be estimated. Attached Figure Description

[0019] Figure 1 This is a front view of the injection molding machine according to this embodiment.

[0020] Figure 2 This is a front sectional view of the injection device according to this embodiment.

[0021] Figure 3A This is a front sectional view showing a portion of the injection device according to this embodiment.

[0022] Figure 3B This is a front sectional view showing a portion of the injection device according to this embodiment.

[0023] Figure 4 This is a diagram showing a cross-section of a portion of the injection device of this embodiment, the state of the heating cylinder being unfolded along the direction of the thread, and a cross-section obtained by cutting the heating cylinder in a direction orthogonal to the thread.

[0024] Figure 5Ais a front sectional view showing a part of the injection device of the embodiment.

[0025] Figure 5B is a front sectional view showing a part of the injection device of the embodiment.

[0026] Figure 6 is a front sectional view showing the injection device of the embodiment.

[0027] Figure 7 is a flowchart showing the gas concentration estimation method of the 2nd embodiment.

[0028] Figure 8A is a front sectional view showing a part of the injection device of the embodiment.

[0029] Figure 8B is a front sectional view showing a part of the injection device of the embodiment.

[0030] Figure 8C is a front sectional view showing a part of the injection device of the embodiment.

[0031] Figure 9 is a flowchart showing the gas concentration estimation method of the 3rd embodiment.

[0032] Figure 10 is a front sectional view showing a part of the screw extrusion of the molten resin.

[0033] Figure 11 is a front sectional view showing a part of the injection device of the embodiment.

[0034] Figure 12 is a flowchart showing the gas concentration estimation method of the 4th embodiment.

[0035] Figure 13A is a graph of the gas concentration in the molten resin obtained through the experiment.

[0036] Figure 13B is a graph of the gas concentration in the molten resin obtained through simulation 1.

[0037] Figure 13C is a graph of the gas concentration in the molten resin obtained through simulation 2.

[0038] Figure 13D is a graph of the gas concentration in the molten resin obtained through simulation 3.

[0039] BRIEF DESCRIPTION OF DRAWINGS

[0040] 1: injection molding machine, 2: mold clamping device, 3: injection device, 7: fixed platen, 8: movable platen, 9: mold clamping housing, 10: tie bar, 11: toggle mechanism, 13: fixed side mold, 14: movable side mold, 17: heating cylinder, 18: screw, 19: screw drive, 21: gas supply device, 24: injection nozzle, 25: thread, 26: 1st full-filling section, 27: non-full-filling section, 28: 2nd full-filling section, 29: molten resin, 29a: thread pushed-out molten resin, 29b: cylinder-attached molten resin, 30: gas cylinder, 32: regulator, 31: gas pressure gauge, 34: gas pressure gauge, 36: gas injection portion, 41: push side, 42: pull side, 44: groove, 55: boundary, 57: boundary DETAILED DESCRIPTION

[0041] Hereinafter, a specific embodiment will be described in detail with reference to the drawings. However, the embodiment is not limited to the following. In order to make the description clear, the following description and drawings are appropriately simplified. In each drawing, the same reference numeral is assigned to the same element, and redundant description is omitted as necessary. In addition, in order to avoid the drawings from becoming complicated, there are portions in which hatching is omitted.

[0042] <Injection molding machine>

[0043] Hereinafter, the present embodiment will be described. The gas concentration estimation method of the present embodiment is a method of estimating the concentration of a gas dissolved in a molten resin using a so-called injection molding machine for foam molding as an object. The structure of the injection molding machine to be the object is not particularly limited, and as an example, an injection molding machine 1 according to the present embodiment is used. Figure 1 An injection molding machine 1 according to the present embodiment will be described. The injection molding machine 1 according to the present embodiment includes a mold clamping device 2 and an injection device 3.

[0044] <Mold clamping device>

[0045] The mold clamping device 2 includes a fixed platen 7 fixed to a base B, a movable platen 8 provided on the base B so as to be slidable, and a mold clamping housing 9 also provided on the base B so as to be slidable. The fixed platen 7 and the mold clamping housing 9 are linked by a plurality of tie bars 10, 10,.... 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 the present 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. If the toggle mechanism 11 is driven, the fixed side mold 13 and the movable side mold 14 are opened and closed.

[0046] <Injection device>

[0047] As shown in FIG. 1, the injection device 3 includes a heating cylinder 17, a screw 18, a screw drive 19, a gas supply device 21, and an injection nozzle 24. The screw 18 is provided in the heating cylinder 17, and the screw drive 19 is provided in the heating cylinder 17 so as to be rotatable. The gas supply device 21 is provided in the heating cylinder 17. The injection nozzle 24 is provided in the heating cylinder 17 so as to be movable. Figure 1 , Figure 2As shown, the injection device 3 of the present embodiment is provided with a heating cylinder 17, a screw 18 which is inserted into the heating cylinder 17, a screw driving device 19, and a gas supply device 21. The screw 18 and the gas supply device 21 will be described in detail later. A hopper 23 is provided at the rear end of the heating cylinder 17, i.e. the upstream side, for supplying resin pellets as a material. An injection nozzle 24 is provided at the front end of the heating cylinder 17. Although not shown in FIG. 1, the injection nozzle 24 is provided with a shut-off valve. The injection device 3 of the present embodiment injects the gas dissolved in the molten resin, in order to close the resin flow path at the time of separation of the injection nozzle 24 from the stationary side mold 13, to prevent the molten resin in the injection nozzle 24 from foaming or dripping. Figure 1 、 Figure 2

[0048] The injection device 3 of the present embodiment has a feature in the shape of the screw 18 in order to supply the gas into the heating cylinder 17 and dissolve the gas in the molten resin. Specifically, as shown in FIG. 2, the depth of the groove between the flights 25 changes from the rear end, i.e. the upstream side, to the front end, i.e. the downstream side, of the screw 18. From the upstream side to the middle upstream side, the depth of the groove between the flights 25 gradually becomes shallower, and becomes deeper at the middle upstream portion. Further, it gradually becomes shallower toward the downstream side. Figure 2

[0049] Since the screw 18 is formed as described above, the heating cylinder 17 is divided into three sections 26, 27, 28. That is, the first full section 26 at the upstream side, the non-full section 27 at the middle upstream portion, and the second full section 28 at the downstream side. The resin is melted in the first full section 26 to become a molten resin, and is filled in the heating cylinder 17. Figure 3A FIG. 3 shows a state in which the molten resin 29 is filled in the heating cylinder 17. Next, the molten resin is depressurized in the non-full section 27. As a result, as shown in FIG. 4, the molten resin 29 becomes a non-full state in the heating cylinder 17. The gas is supplied in the non-full section 27 as described later, and the gas is dissolved in the molten resin. The molten resin is again filled in the heating cylinder 17 and is compressed in the second full section 28. Figure 3B

[0050] As shown in FIG. 5, the gas supply device 21 is provided with a gas cylinder 30 in which carbon dioxide, nitrogen, or the like is stored, a regulator 32 which depressurizes the gas pressure to a predetermined certain pressure, and gas pressure gauges 31, 34 which measure the gas pressure. In the heating cylinder 17, a gas injection portion 36 is provided at a portion corresponding to the non-full section 27. The gas from the gas supply device 21 is supplied into the heating cylinder 17 at the gas injection portion 36. The supplied gas is dissolved in the molten resin 29 in the non-full section 27 as shown in FIG. 6. Figure 2 Figure 3B

[0051] <Gas Concentration Estimation Method of the First Embodiment>​​​​​

[0052] The gas concentration estimation method of the first embodiment will be described. The gas dissolves in the molten resin 29 (refer to FIG. 2) in the non-full section 27 (refer to FIG. 2). If described in more detail, the gas dissolves in the molten resin 29 from the interface with the molten resin 29, that is, the gas-liquid interface. The amount of change per unit time of the gas concentration C in the molten resin 29, that is, the change rate dC / dt, which changes due to the dissolution, can be provided by the following equation (1). Further, the equation (1) is an equation derived from the equation (3-1) to be described later. Figure 2 ) in the non-full section 27 (refer to FIG. 2). If described in more detail, the gas dissolves in the molten resin 29 from the interface with the molten resin 29, that is, the gas-liquid interface. The amount of change per unit time of the gas concentration C in the molten resin 29, that is, the change rate dC / dt, which changes due to the dissolution, can be provided by the following equation (1). Further, the equation (1) is an equation derived from the equation (3-1) to be described later. Figure 3B

[0053]

[0054] where change rate of the gas concentration in the molten resin [g / (m 3 s)]

[0055] k: constant [s]

[0056] C * : solubility of the gas [g / m 3 ]

[0057] C: gas concentration in the molten resin [g / m 3 ]

[0058] According to the equation (1), the gas concentration can be calculated. For example, it is assumed that the gas is carbon dioxide, the resin is polypropylene, and the solubility C* of the gas is 2.72 x 10 -2 [g / m 3 ] at 207°C and 4 MPa. Further, the constant k can be derived from a model of the behavior of the molten resin 29 in the non-full section 27 or can be obtained from experiments, as will be described later. The method of derivation from the model and the method of obtaining by experiments will be described later. It is assumed here that the value of the constant k is a given value.

[0059] The equation (1) above is modified to become the equation (2-1). If the equation (2-1) is calculated, the equation (2-2) is obtained.

[0060]

[0061] ln |C - C * | = -kt + A (2-2)

[0062] where A: integration constant

[0063] A = ln C * (2-3)

[0064] ​

[0065] c = (1 - exp(-kt))C * (2-6)

[0066] In addition, at t = 0, that is, immediately after the molten resin comes into contact with the gas, the gas concentration C is 0. If this is substituted into (2-2), (2-3) is obtained. From this, (2-4) is obtained by modifying (2-2). If modification is made with the understanding that the solubility C* of the gas is always greater than the gas concentration C in the molten resin and C* - C is positive, (2-5) and (2-6) are obtained.

[0067] The gas concentration estimation method of the first embodiment calculates the gas concentration of the molten resin using (2-6). Specifically, the passage time T of the molten resin passing through the non-saturation section 27 (refer to Figure 2 ) is substituted into the time t in (2-6). Thus, the gas concentration C of the molten resin after the passage time T seconds is obtained.

[0068] In addition, in the explanation of (1), it is explained that the constant k can be obtained by experiment. Specifically, the following can be done. The injection device 3 of the present embodiment (refer to Figure 2 ) is used. The passage time T of the molten resin passing through the non-saturation section 27 is measured. This passage time T is substituted into (2-6). Thus, the gas concentration C in the molten resin is provided by a numerical expression including the constant k. The gas concentration is measured with respect to the molten resin injected from the injection nozzle 24 of the injection device 3. The constant k is determined in such a way that the calculated gas concentration C coincides with the numerical value of the measured gas concentration. That is, the constant k can be obtained by experiment.

[0069] In addition, the measurement of the gas concentration in the molten resin can be done using any measuring device. For example, a method using a transmission-type near-infrared spectroscopy probe is used. The transmission-type near-infrared spectroscopy probe is attached to the injection nozzle 24, and the near-infrared light absorption spectrum of the molten resin is obtained. The gas absorbs infrared rays of a specific wavelength depending on the kind. As long as the degree of absorption of the infrared rays of this wavelength is measured, the gas concentration can be calculated. For example, in the case where carbon dioxide is used as the gas, it is sufficient to investigate the absorption at a wave number of 4950 / cm (wavelength 2.02 nm). The constant k is determined by such an experiment. Thus, thereafter, the gas concentration C in the molten resin can be calculated using (2-6).

[0070] With respect to the constant k in (1), it can be derived from a model of the behavior of the molten resin 29 in the non-saturation section 27. The following is explained. In Figure 4The upper layer shows the condition where molten resin 29 is pushed out to a specified thickness through the thread 25 of screw 18 in the unfilled section 27 of heating cylinder 17. The side of the thread 25 that pushes out the molten resin 29 is called the pushing side 41, and the other side is called the pulling side 42.

[0071] If we discuss the molten resin 29 in the non-filled section 27 in detail, the large-capacity molten resin 29a is passed through the thread 25 to a specified thickness w. p Launched, a very small amount of molten resin 29b with a thickness δ f The molten resin 29b adheres to the inner circumferential surface of the heating cylinder 17. The adhered molten resin 29b is the molten resin leaking from the gap between the top of the thread 25 and the heating cylinder 17. The molten resin 29a pushed out by the thread 25 is pushed out by the height h' of the thread 25. For ease of explanation, the pushed-out molten resin 29a will be referred to as thread-pushed molten resin 29a, and the molten resin 29b leaking from the gap in the heating cylinder 17 and adhering to the inner circumferential surface of the heating cylinder 17 will be referred to as cylinder-attached molten resin 29b.

[0072] The height h' of thread 25, the distance h between the groove 44 between threads 25 and the inner circumferential surface of heating cylinder 17, and the thickness δ of the molten resin 29b attached to the cylinder. f The relationship is as follows.

[0073] h' = h - δ f

[0074] Furthermore, the thickness δ of the molten resin 29b attached to the cylinder f It is very small compared to the thread height h, so it can be processed as follows.

[0075] h'≒h

[0076] exist Figure 4 The middle layer shows a diagram of the spiral thread 25 unfolded into a straight line. The thread ejecting the molten resin 29a is also unfolded in the same way. The length of one revolution of the inner circumference of the heating cylinder 17, i.e., the revolution length 45, is determined according to the inner diameter D of the heating cylinder 17. b [m] as πD b And provided. Regarding the length of one revolution 45, the components in the direction orthogonal to the thread 25, i.e., the x-direction component 46, and the components in the direction parallel to the thread 25, i.e., the z-direction component 47, pass through the thread angle θ [rad] of the thread 25, respectively, as πD. b sinθ, πD b cosθ is provided. At screw 18, the rotational speed N[s- 1 During rotation, the speed of a specified portion at the apex of thread 25 is provided by the product of the revolution length 45 and the rotational speed N, thus becoming πD. bN. Thus, the component of the velocity normal to the thread 25 provides a velocity component parallel to the thread 25 of πD b Nsinθ. b Ncosθ.

[0077] In Figure 4 The lower layer shows a cross section perpendicular to the direction of the thread 25. The direction normal to the thread 25 is set as the x direction, and the height direction of the thread 25 is set as the y direction. Hereinafter, the constant k in the equation (1) is derived based on such a model.

[0078] When a gas contacts with a molten resin, the gas dissolves from the gas-liquid interface into the molten resin. With respect to the gas-liquid interface, i.e., the surface of the molten resin, the average dissolving speed N gs is provided as in the following equation (3-1).

[0079] N gs = K(C * -C) (3-1)

[0080] where N gs : average dissolving speed of the gas [g / (m 2 s)]

[0081] K: mass transfer coefficient [m / s]

[0082] C * : solubility of the gas [g / m 3 ]

[0083] C: gas concentration in the molten resin [g / m 3 ]

[0084]

[0085] where D m : diffusion coefficient of the gas [m 2 / s]

[0086] τ: exposure time to the gas [s]

[0087]

[0088] where N gs : average dissolving speed of the gas [g / (m 2 s)]

[0089] D m : diffusion coefficient of the gas [m 2 / s]

[0090] τ: exposure time to the gas [s]

[0091] C* Solubility of gas [g / m³] 3 ]

[0092] C: Gas concentration in molten resin [g / m³] 3 ]

[0093] Furthermore, regarding the mass transfer coefficient K, various formulas are provided based on various theories such as the interfacial double-film hypothesis. Here, we consider a surface renewal model based on the so-called permeation theory. That is, let the molten resin 29a be pushed out by the screw and the gas-liquid interface be renewed by the flow. Let the renewal time of the gas-liquid interface, i.e., the time when the resin is exposed to the gas, τ, be set as a parameter and provided by equation (3-2). Thus, equation (3-3) can be derived from equations (3-1) and (3-2). In addition, when the screw 18 rotates in the heating cylinder 17, the helical thread 25 appears to advance relatively in the heating cylinder 17, i.e., in Figure 5A The cylinder moves to the left. If the xy coordinates are moved together with the thread 25, which appears to move to the left, then the heating cylinder 17... Figure 5A In the middle, as indicated by reference numeral 50 in the attached figure, it moves relatively to the right. The screw 18 rotates at a speed of N [s]. -1 When rotating, the moving speed of the heating cylinder 17 in the right direction is πD. b Nsinθ(D b θ: Inner diameter of heating cylinder 17; θ: Thread angle. This is because, according to... Figure 4 In the study, the velocity component orthogonal to the thread 25 when the screw 18 rotates is called πD. b Nsinθ.

[0094] At this time, the molten resin 29a pushed out by the pusher side 41 of the thread 25 flows as shown by arrows 51, 51, ... Through this flow, the surface of the molten resin 29a pushed out by the thread, i.e., the gas-liquid interface, moves at the same speed πD as the heating cylinder 17 moving to the right. b Nsinθ moves upwards. The thread ejects molten resin 29a as shown. Figure 5A That is, the gas-liquid interface has a convex and curved shape near the center, but it is set as follows: Figure 5B Therefore, the gas-liquid interface is considered as a vertical plane.

[0095] Therefore, the renewal time of the gas-liquid interface in the molten resin 29a pushed out by the thread, that is, the exposure time τ of the resin and gas contact, becomes the time for the gas-liquid interface to pass through the thread height h', and is thus provided by the following equation (4).

[0096]

[0097] Where τ: exposure time to the gas [s]

[0098] h' : height of thread [m]

[0099] D b : inner diameter of heating cylinder [m]

[0100] N : rotation speed of screw [1 / s]

[0101] θ : thread angle [rad]

[0102] h : distance between thread and inner circumferential surface of heating cylinder [m]

[0103] If the thread is pushed out of the molten resin 29a as a whole and treated, the gas permeating from the gas-liquid interface permeates to the whole of the thread pushed out of the molten resin 29a and the gas concentration changes, and therefore, the change speed dC / dt of the gas concentration C in the thread pushed out of the molten resin 29a is provided by the following (5-1).

[0104]

[0105] wherein change speed of gas concentration in molten resin [g / (m 3 s)]

[0106] N gs : average dissolution speed of gas [g / (m 2 s)]

[0107] S p : surface area of molten resin in non- filled section [m 2 ]

[0108] V p : volume of molten resin in non- filled section [m 3 ]

[0109]

[0110] wherein L : length of molten resin in non- filled section [m]

[0111] h' : height of thread [m]

[0112] h : distance between thread and inner circumferential surface of heating cylinder [m]

[0113] w p : thickness of molten resin in push side surface of thread [m]

[0114]

[0115] wherein w p : thickness of molten resin in push side surface of thread [m]

[0116] D m : Diffusion coefficient of gas [m 2 / s]

[0117] D b : Inner diameter of heating cylinder [m]

[0118] N: Rotational speed of screw [ / s]

[0119] θ: Thread angle [rad]

[0120] h': Height of thread [m]

[0121] C * : Solubility of gas [g / m 3 ]

[0122] c: Gas concentration in molten resin [g / m 3 ]

[0123] h: Distance between thread groove and inner periphery of heating cylinder [m]

[0124] If the above (5-2) is substituted into (5-1), and solved by (3-3) and (4), (5-3) is obtained. If this (5-3) is compared with (1), the constant k is provided by the following (6-1). Further, if the already explained is repeated, the constant k provided by (6-1) is obtained assuming that the thread pushes out the molten resin 29a as a whole and the gas uniformly penetrates the thread pushed out molten resin 29a as a whole.

[0125]

[0126] where k: Constant [ / s]

[0127] w p : Thickness of molten resin in push side of thread [m]

[0128] D m : Diffusion coefficient of gas [m 2 / s]

[0129] D b : Inner diameter of heating cylinder [m]

[0130] N: Rotational speed of screw [ / s]

[0131] θ: Thread angle [rad]

[0132] h': Height of thread [m]

[0133] h: Distance between thread groove and inner periphery of heating cylinder [m]

[0134] Here, the gas diffusion coefficient D m varies depending on the kind of resin, the kind of gas, and the temperature, and is, for example, 8.0 x 10 -9 [m 2 / s] when carbon dioxide is dissolved and diffused in polypropylene at a temperature of 190°C. As for other constants, such as the thickness w p of the molten resin, the inner diameter D b of the heating cylinder, and the like, the value of the constant k can be obtained by appropriately using suitable values and substituting them into (6-1). The description of the derivation method of the constant k based on the model of the behavior of the molten resin 29 is complete.

[0135] <Gas concentration estimation method of the 2nd embodiment>

[0136] The gas concentration estimation method of the 2nd embodiment will be described. In the gas concentration estimation method of the 2nd embodiment, not only the dissolution of the gas from the gas-liquid interface into the molten resin is considered, but also the change in the gas concentration due to the flow of the molten resin is calculated. Figure 6 A model in which the gas concentration estimation method of the 2nd embodiment is implemented is shown in FIG. 12. The screw extruded molten resin 29a in the molten resin 29 is divided into a plurality of meshes in a lattice shape. In the model, the screw extruded molten resin 29a is divided into a plurality of meshes in the x direction and the y direction. Figure 6 In the model, the meshes are divided into a plurality in the x direction and the y direction, but it is considered that the z direction is also divided in a short prescribed width. As for the screw extruded molten resin 29a, the gas concentration is estimated based on mesh-based calculation. Further, in the 2nd embodiment, the cylinder-attached molten resin 29b is excluded from the calculation of the gas concentration. The reason is that the thickness δ f is very thin, the cylinder-attached molten resin 29b is small in volume compared to the screw extruded molten resin 29a, and has a relatively small influence on the gas concentration of the entire molten resin 29.

[0137] The gas concentration estimation method of the 2nd embodiment is implemented as shown in FIG. 13. The molten resin of the prescribed width in the z direction is set as the calculation target. At the start of the calculation, the calculation is started just after the molten resin of the prescribed width enters the non-full section 27. Step S1 is first implemented. That is, as for the mesh that becomes the gas-liquid interface among the plurality of meshes of the screw extruded molten resin 29a (refer to FIG. 12), that is, the mesh shown by reference numeral 53, the dissolution of the gas in a short time Δt is calculated. The calculation is implemented by (1), and the constant k is calculated using the following (6-2). Further, (6-2) is obtained by considering the same as the derivation of (6-1), and is a formula obtained by assuming that the gas uniformly permeates within the mesh that contacts the gas, that is, the mesh belonging to the gas-liquid interface. Figure 7 Figure 6

[0138] ​​

[0139] where k: constant [ / s]

[0140] d x : thickness of the grid (depth in the x direction from the gas-liquid interface) [m]

[0141] D m : diffusion coefficient of the gas [m 2 / s]

[0142] D b : inner diameter of the heating cylinder [m]

[0143] N: rotational speed of the screw [ / s]

[0144] θ: thread angle [rad]

[0145] h': height of the thread [m]

[0146] h: distance between the thread and the inner periphery of the heating cylinder [m]

[0147] The calculation is performed, for example, as follows. If the equation (1) is modified, the equation (7-1) is obtained. Then, if the gas concentration in the molten resin at a prescribed time is set as C, the gas concentration C new is provided by the equation (7-2). The gas concentration is 0 immediately after the contact with the gas, and thus, as a boundary condition, it is set as the initial gas concentration C = 0.

[0148] ΔC = k (C * - C) x Δt (7-1)

[0149] where ΔC: change amount of the gas concentration in the molten resin [g / m 3 ]

[0150] k: constant [ / s]

[0151] C * : solubility of the gas [g / m 3 ]

[0152] C: gas concentration in the molten resin [g / m 3 ]

[0153] C new = c + k (C * - C) x Δt (7-2)

[0154] where C new : gas concentration in the molten resin after Δt seconds [g / m 3 ]

[0155] Regarding the gas concentration in the molten resin at the time of the start of the heating, the equation (6) is used. Figure 6In the grid corresponding to reference numeral 53 in the attached figure, the calculation of step S1 is performed to calculate the gas concentration C for each grid. new After that, as Figure 7 The process proceeds to step S2. In step S2, for each grid of the threaded molten resin 29a, considering the flow, the gas concentration in each grid is calculated. The change in gas concentration in each grid due to the flow can be calculated using the following equation (8-1). Equation (8-1) is derived by setting the left side to 0 in the general equation concerning the change in gas concentration, namely the so-called flow-diffusion equation (8-3), assuming that the change in concentration due to diffusion is smaller than the change due to flow. However, equation (8-1) is further simplified here. That is, it is assumed that the resin is processed only in the xy direction, and the flow velocity v in the z direction is assumed to be... z Equation (8-2) is obtained by setting the value to 0. Calculations are then performed based on this. Furthermore, the flow velocity v in the z-direction... z It is not zero, and will be considered in the following steps S3 and S4.

[0156]

[0157] Where C: gas concentration in the molten resin [g / m³] 3 ]

[0158] v: Resin flow rate [m / s]

[0159] v x The x-component of the resin flow velocity [m / s]

[0160] v y : The y-component of the resin flow velocity [m / s]

[0161] v z The z-axis component of the resin flow velocity [m / s]

[0162]

[0163] in The rate of change of gas concentration in the molten resin [g / (m 3 s)]

[0164] v: Flow rate of molten resin [m / s]

[0165] D m : Diffusion coefficient of gas [m 2 / s]

[0166] C: Gas concentration in molten resin [g / m³] 3 ]

[0167] For example, the flow velocity can be calculated using a commercially available flow analysis software. For example, with respect to any one grid, the flow velocity flowing out to the adjoining one or more grids and the flow velocity flowing in from the adjoining one or more grids to the one grid after Δt seconds is calculated using the flow analysis software. Then, the gas concentration after Δt seconds is calculated from the respective gas concentrations in these grids, the outflow amount from the one grid, and the inflow amount to the one grid. This calculation is performed with respect to all the grids.

[0168] After the calculation in step S2 is completed, step S3 is executed as shown in Figure 7 . That is, it is checked whether the width in the z direction of the grid is passed. Detailed explanation will be given. First, the thread pushes out the molten resin 29a at the average velocity πD b Ncosθ / 2 (D b : the inner diameter of the heating cylinder 17, N: the rotational speed of the screw 18, θ: the thread angle) in the z direction. The average velocity in the z direction is provided on the basis of the point that the velocity component in the z direction at the top of the thread 25 is πD b Ncosθ, the assumption that the velocity component in the z direction of the resin at the bottom of the thread 25 is 0, and the assumption that the velocity component in the z direction linearly increases in the height direction of the thread 25, which are obtained in the study in Figure 4 . Hereinafter, it is considered that the thread pushes out the molten resin 29a to flow at the average velocity πD b Ncosθ / 2 in the z direction regardless of the height of the thread 25. That is, it is considered that the entire grid advances in the z direction at the average flow velocity v z = πD b Ncosθ / 2. According to this average flow velocity v z , in the first calculation, the distance advanced in the z direction is πD b NcosθΔt / 2, which corresponds to the amount of the initial Δt seconds. It is checked whether this advanced distance passes the width in the z direction of the grid. If not, it is determined as No, and the process returns to step S1.

[0169] In step S1 with respect to the calculation after the next Δt seconds, that is, the grid shown by the reference numeral 53 in Figure 6 , the dissolution of the gas from the gas-liquid interface is calculated using the formula (7-2), and C new after the next Δt seconds is calculated, respectively. Next, the change in the gas concentration due to the flow is calculated by step S2. Step S3 is executed again. If the average flow velocity v zIf the distance traveled in the z-direction does not cross the width of the grid in the z-direction (No), return to step S1; otherwise, proceed to step S4. In step S4, the gas concentration in each grid is transferred to the next grid group in the z-direction, i.e., the downstream grid group. That is, the gas concentration is set according to the average flow velocity v in the z-direction. z The processing is performed by moving the grid group from the upstream side to the adjacent downstream side.

[0170] After executing step S4, step S5 is executed. That is, it is determined whether the threaded ejection of molten resin 29a, which is the object of calculation, has passed the non-filling interval, that is, whether the passing time has elapsed. If the passing time has not elapsed (No), the process returns to step S1. If the passing time has elapsed (Yes), the calculation ends. In addition, in step S5, it is determined whether the threaded ejection of molten resin 29a has passed the non-filling interval, but it can also be determined based on whether the metering time has elapsed, and the calculation ends when the metering time has elapsed. The description of the gas concentration estimation method of the second embodiment is completed.

[0171] <Method for estimating gas concentration in the third embodiment>

[0172] The gas concentration estimation method of the third embodiment will be described. In the gas concentration estimation method of the third embodiment, the dissolution of gas from the gas-liquid interface to the molten resin and the adsorption of molten resin 29b (see reference) are taken into account. Figure 5B The calculations are performed based on the mixing of molten resin 29a pushed into the thread and the change in gas concentration caused by the flow of molten resin.

[0173] In the gas concentration estimation method of this third embodiment, when calculating the change in gas concentration caused by the flow of molten resin, a method is proposed that allows calculations to be performed using a personal computer or similar device with relatively limited computing power, without the need for commercially available flow analysis software. Therefore, reducing the number of grids for the threaded ejection of molten resin 29a makes flow calculations simpler. The flow of the threaded ejection of molten resin 29a is discussed when determining the grid size, etc.

[0174] like Figure 8A As shown, the thread ejecting molten resin 29a from the section perpendicular to thread 25 is considered to be divided into two parts in the x-direction. That is, with x = w p / 2 Consider a hypothetical boundary 55. The flow velocity v of the molten resin in the x-direction at boundary 55. x Its magnitude changes according to the y-position, becoming a function of y. The groove 44 between threads 25 and 25 is fixed, and the inner circumferential surface of the heating cylinder 17 moves at a speed of πD. b Nsinθ(D b: inner diameter of the heating cylinder 17, N: rotational speed of the screw 18, θ: thread angle) slides. The boundary 55 located at a thickness of 1 / 2 of the molten resin 29a pushed out by the thread is a symmetric plane of the molten resin left and right, and therefore, the flow velocity v x of the molten resin at the boundary 55 can be considered as a stable flow of a so-called viscous fluid flowing between parallel plates. Thus, the flow velocity v x of the molten resin in the x direction at the boundary 55 becomes a so-called Couette flow and a two-dimensional Poiseuille flow, and can be expressed by the formula (9-1).

[0175]

[0176] where v x : x-direction component of flow velocity of the resin [m / s]

[0177] h: distance between the thread and the inner circumferential surface of the heating cylinder [m]

[0178] D b : inner diameter of the heating cylinder [m]

[0179] N: rotational speed of the screw [ / s]

[0180] θ: thread angle [rad]

[0181] η: viscosity of the molten resin [Pa-s]

[0182] P: pressure of the molten resin [Pa]

[0183]

[0184] where Qv x : x-direction component of volume flow rate of the resin [m 3 / s]

[0185] v x : x-direction component of flow velocity of the resin [m / s]

[0186] h: distance between the thread and the inner circumferential surface of the heating cylinder [m]

[0187] D b : inner diameter of the heating cylinder [m]

[0188] N: rotational speed of the screw [ / s]

[0189] θ: thread angle [rad]

[0190] η: viscosity of the molten resin [Pa-s]

[0191] P: pressure of the molten resin [Pa]

[0192] And, if the width in the z direction (refer to Figure 4 ) is set as dz and the volume flow rate Qv x of the molten resin at the entire surface of the boundary 55 in the x direction is considered x , then this (9-1) is integrated in the y direction to obtain the volume flow rate Qv p as (9-2). In addition, in the threaded pushing-out of the molten resin 29a, the thickness w p of the molten resin is set as a constant in the range of the z direction (refer to Figure 4 ). Thus, the thickness w x of the molten resin does not change according to time. In this case, the volume flow rate Qv b must be 0. If the (9-2) is set as 0, then (10-1) is obtained. If this is substituted into (9-1), then (10-2) is obtained.

[0193]

[0194] where η: viscosity of the molten resin [Pa-s]

[0195] P: pressure of the molten resin [Pa]

[0196] h: distance of the groove between threads from the inner circumferential surface of the heating cylinder [m]

[0197] D x : inner diameter of the heating cylinder [m]

[0198] N: rotational speed of the screw [1 / s]

[0199] θ: thread angle [rad]

[0200]

[0201] where v b : x-direction component of the flow velocity of the resin [m / s]

[0202] h: distance of the groove between threads from the inner circumferential surface of the heating cylinder [m]

[0203] D p : inner diameter of the heating cylinder [m]

[0204] N: rotational speed of the screw [1 / s]

[0205] θ: thread angle [rad]

[0206] Next, regarding the threaded pushing-out of the molten resin 29a, Figure 8A the range of the right half side, i.e., 0 ≤ x ≤ w p / 2, and the left half side, i.e., w p / 2 ≤ x ≤ wThe range, considering the flow rate v of the molten resin in the y direction. v Regarding the right half, at boundary 55, the amount of molten resin flowing from the left half to the right half in width dy is -v per unit width in the z-direction. x dy. Based on the amount of molten resin flowing in like this -v x dy and flow rate v y The increase becomes -v x dy×2 / w p Regarding the left half, at boundary 55, the amount of molten resin flowing from the right half into the left half in width dy is v per unit width in the z-direction. x dy. Based on the amount of molten resin flowing in like this, v x dy and flow rate v y The increase becomes v x dy×2 / w p When y = 0, the flow rate v of the molten resin is the same on both the right and left halves. v =0, therefore, the flow rate v of the molten resin on the left and right halves at any y position y* is 0. v Provided in formula (11).

[0207] Time (11)

[0208]

[0209] hour

[0210]

[0211] Where v x The x-component of the resin flow velocity [m / s]

[0212] h: Distance between the grooves in the threads and the inner circumference of the heating cylinder [m]

[0213] D b The inner diameter of the heating cylinder [m]

[0214] N: Screw rotational speed[ / s]

[0215] θ: Thread angle [rad]

[0216] y*: Any y-coordinate

[0217] Here, the mesh segmentation in the x and y directions of the threaded ejection of molten resin 29a is discussed. For example... Figure 8B As shown, regarding the x-direction, with boundary 55, i.e., x = w pis divided. Also with respect to the y direction, the division is into a plurality of meshes of low height. In the gas concentration estimation method of the third embodiment, when calculating the change in gas concentration due to the flow of the molten resin, the gas concentration of the molten resin 29a pushed out by the thread is calculated based on the meshes thus divided. Also, at the boundary 57 at the height of 2h / 3 from the groove 44 between the threads 25, 25, i.e., at y = 2h / 3, v = 0 according to equation (10-2). That is, the flow velocity vxof the molten resin in the x direction becomes 0 at the boundary 57. The flow velocity vxin the x direction becomes a positive magnitude on the lower side of the boundary 57 and a negative magnitude on the upper side thereof. x x The flow velocity vxin the x direction becomes 0 at the boundary 57. The flow velocity vxin the x direction becomes a positive magnitude on the lower side of the boundary 57 and a negative magnitude on the upper side thereof.

[0218] In the gas concentration estimation method of the third embodiment, the change in gas concentration due to the entrainment of the molten resin 29a pushed out by the thread by the molten resin 29b adhering to the cylinder is also calculated. The thickness δ f of the molten resin 29b adhering to the cylinder is very thin, generally about 0.1 to 0.2 mm. Therefore, it is considered that the gas rapidly permeates and rapidly reaches the solubility C* of the gas. The molten resin 29b having reached the solubility C* of the gas moves with the velocity πD b Nsinθ and comes into contact with the molten resin 29a pushed out by the thread. That is, as shown in FIG. 6, the molten resin 29b adhering to the cylinder comes into contact with the uppermost meshes 60, 61 of the molten resin 29a pushed out by the thread. Then, a portion of the molten resin within these meshes 60, 61 mixes with the molten resin 29b adhering to the cylinder. Figure 8C

[0219] In the gas concentration estimation method of the third embodiment, it is assumed that these uppermost meshes 60, 61 are Figure 8C meshes in which the thickness δ f of the molten resin is in the range of the thickness δ f of the molten resin 29b adhering to the cylinder. Then the molten resin 29b having the solubility C* of the gas invades with the velocity πD b Nsinθ and mixes with the molten resin of the meshes 60, 61 having the gas concentration C and the thickness w p Therefore, the amount of change in the gas concentration in the molten resin shown by the reference numeral 63 is provided by equation (12). By this equation (12), the gas concentration of the molten resin of the meshes 60, 61 due to the mixing with the molten resin 29b adhering to the cylinder can be calculated. Further, it is assumed that the molten resin having the thickness δ f shown by the reference numeral 63 also mixes with the molten resin within the meshes 60, 61 having the thickness shown by the reference numeral 64.

[0220] ​​

[0221] Where C: gas concentration in the molten resin [g / m³] 3 ]

[0222] D b The inner diameter of the heating cylinder [m]

[0223] N: Screw rotational speed[ / s]

[0224] θ: Thread angle [rad]

[0225] C * Solubility of gas [g / m³] 3 ]

[0226] w p The thickness of the molten resin ejected by the thread [m]

[0227] When implementing the gas concentration estimation method of the third embodiment, it is necessary to thread out the thickness w of the molten resin 29a. p The thickness w p It can be obtained through calculation or experimentation. The method for obtaining it through calculation will be explained. First, consider the flow velocity v of the molten resin in the z-direction as the molten resin 29a is ejected by the thread. z The flow rate v of the molten resin in the z-direction z Its size changes according to the y-position, becoming a function of y. The slot 44 between threads 25 and 25 is fixed. (Refer to...) Figure 4 The study in the middle showed that the inner circumferential surface of the heating cylinder 17 moves at a velocity πD in the z-direction. b Ncosθ(D b (where N is the inner diameter of heating cylinder 17, N is the rotational speed of screw 18, and θ is the thread angle) Therefore, the flow velocity v of the molten resin in the z-direction... z As a superposition of the so-called Cueter flow and the two-dimensional Poiseuille flow, it is provided as (13-1) in the same way as (9-1).

[0228]

[0229] Where v z The z-axis component of the resin flow velocity [m / s]

[0230] h: Distance between the grooves in the threads and the inner circumference of the heating cylinder [m]

[0231] D b The inner diameter of the heating cylinder [m]

[0232] N: Screw rotational speed[ / s]

[0233] θ: Thread angle [rad]

[0234] η: Viscosity of molten resin [Pa·s]

[0235] P: pressure of the molten resin [Pa]

[0236]

[0237] where Qv z : volume flow rate in the z direction of the molten resin [m 3 / s]

[0238] n f : number of threads [-]

[0239] w p : thickness of the molten resin pushed out by the thread [m]

[0240] v z : z direction component of the flow velocity of the resin [m / s]

[0241] h: distance between the groove and the inner circumferential surface of the heating cylinder [m]

[0242] D b : inner diameter of the heating cylinder [m]

[0243] N: rotational speed of the screw [1 / s]

[0244] θ: thread angle [rad]

[0245] In the non-full section 27, the pressure gradient δP / δz in the z direction of the molten resin can be considered to be 0, and thus (13-2) is obtained from (13-1). Then, the number of threads n f , the thickness w p of the molten resin 29a pushed out by the thread, and the flow velocity v z indicated by (13-2) are multiplied, and the volume flow rate Qv z in the z direction in the non-full section 27 is obtained as indicated by (13-3).

[0246] On the other hand, in the injection device 3 (refer to Figure 2 ), if the screw 18 is rotated to send out the molten resin, the molten resin is metered at the front end of the heating cylinder 17. Then, the volume flow rate Q m of the molten resin in the axial direction of the heating cylinder 17 at the time of metering is provided from the length L st of the molten resin to be metered and the metering time t r as indicated by (14).

[0247]

[0248] where Q m : volume flow rate of the molten resin in the axial direction of the heating cylinder [m3 / s]

[0249] D b The inner diameter of the heating cylinder [m]

[0250] L st The length of the molten resin measured at the front end of the heating cylinder [m].

[0251] t r : Measurement time [s]

[0252] Here, let Qv be the volumetric flow rate in the z-direction of the molten resin provided by equation (13-3). z The axial volumetric flow rate Q provided by equation (14) m If they are equal, then solving for Qv z =Q m Then the thickness w of the molten resin 29a ejected by the thread is obtained. p .

[0253] according to Figure 9 The flowchart illustrates the gas concentration estimation method of the third embodiment. The molten resin of a specified width just enters the non-filled region 27 (see...). Figure 4 Then the calculation begins. First, step S11 is performed. That is, regarding the thread ejection of molten resin 29a (refer to...). Figure 8B The dissolution of gas over a short time Δt is calculated using the grid on the left, which forms the gas-liquid interface among multiple grids. The calculation is performed using equation (1), where the constant k is set to the value obtained using equation (6-2) as described in the second embodiment, i.e., the grid thickness d in that equation. x For the thread, the thickness w of the molten resin 29a is pushed out. p 1 / 2 (d) x =w p / 2), using the calculated values.

[0254] Next, step S12 is performed. That is, the change in gas concentration caused by the introduction of molten resin 29a from the threaded part of the molten resin 29b adhering to the cylinder is calculated. Specifically, regarding... Figure 8C The grids 60 and 61 shown are used to calculate the gas concentration based on equation (12).

[0255] Next, step S13 is performed. That is, the change in gas concentration caused by the flow of molten resin 29a ejected by the thread is calculated. Figure 10 Regarding the threaded ejection of molten resin 29a, a portion of the mesh is shown in enlarged view. Each mesh is labeled as m(0,k), m(1,k), m(0,k+1). Furthermore, the flow velocity v in the x-direction within mesh m(0,k) or mesh m(1,k) is also shown. x Marked as vx (k), the flow velocity v in the y direction in the grid m(0,k) y Marked as v v (0, k). As already explained, the change in gas concentration due to flow is given by equation (8). Integrating it gives equation (15-1).

[0256]

[0257] Where C: gas concentration in the molten resin [g / m³] 3 ]

[0258] v x The x-component of the resin flow velocity [m / s]

[0259] v y : The y-component of the resin flow velocity [m / s]

[0260]

[0261] Where C new (0, k): Gas concentration in the molten resin after Δt seconds at grid m(0, k) [g / m] 3 ]

[0262] C(0,k): Gas concentration in the molten resin of grid m(0,k) [g / m] 3 ]

[0263] v x (k): The x-direction component of the resin flow velocity in grid m(0,k) or m(1,k) [m / s]

[0264] v v (0, k): The y-component of the resin flow velocity in grid m(0, k) [m / s]

[0265] w p The thickness [m] of the molten resin ejected by the thread (twice the width of the mesh in the x-direction)

[0266] f: Width of the grid in the y-direction [m]

[0267] Here, if the width w in the x-direction of the grid is provided as dx p / 2, as dy, provides the width f in the y direction, then based on Figure 10 Equations (15-2) and (15-3) are obtained by considering the various labels. These equations hold for any k. Based on equations (15-2) and (15-3), the gas concentration C after Δt seconds due to the flow can be calculated for each grid. newFurthermore, when k = 0, i.e., when calculating with respect to the lowest-level grid m(0,0) and m(1,0), in equations (15-2) and (15-3), C(0,-1) and C(1,-1) are replaced by C(0,0) and C(1,0) respectively, and so on. Similarly, when k is the maximum k in its range... max At that time, that is, regarding the topmost grid m(0, k) max m(1, k) max When performing calculations, set it to the same value.

[0268] exist Figure 9 In step S14, after step S13, it is performed. That is, it is checked whether the width of the grid in the z-direction has been reached. In other words, the threaded molten resin 29a is ejected with an average velocity component πD in the z-direction. b Ncosθ / 2(D b (where N is the inner diameter of heating cylinder 17, N is the rotational speed of screw 18, and θ is the thread angle) moves in the z-direction. Therefore, the entire mesh is assumed to move at an average flow velocity v in the z-direction. z =πD b Ncosθ / 2 moves in the z-direction. Based on this flow velocity v z In the first calculation, the quantity corresponding to the initial Δt seconds is πD. b NcosθΔt / 2 moves forward in the z-direction. Check if the distance traveled exceeds the width of the grid in the z-direction. If not, determine no and return to step S11.

[0269] Regarding the calculation of the next Δt seconds after step S11, that is, the thread ejects the molten resin 29a (refer to...). Figure 8B The grid representing the gas-liquid interface (the left-hand grid) is used to calculate the gas dissolution within a short time interval Δt. Next, step S12 calculates the change in gas concentration due to flow. Step S13 is then executed again. If the average flow velocity v... z If the distance traveled in the z-direction does not cross the width of the grid in the z-direction (No), return to step S11; if it does cross (Yes), proceed to step S15. In step S15, the gas concentration in each grid is transferred to the next grid group in the z-direction, i.e., the downstream grid group. That is, the gas concentration is set according to the average flow velocity v in the z-direction. z The process involves moving from the upstream grid group to the adjacent downstream grid group.

[0270] After performing step S15, proceed to step S16. Specifically, regarding the thread of a specified width in the z-direction that is the object of calculation, which ejects molten resin 29a, it is determined whether it has passed through the non-filled region 27 (see reference). Figure 2If the calculation fails, return to step S11 and repeat the calculation. On the other hand, if the calculation is successful, the calculation ends. Alternatively, step S15 can be substituted to determine the end of the calculation based on whether the measurement time has elapsed. This concludes the description of the gas concentration estimation method of the third embodiment.

[0271] <The Gas Concentration Estimation Method of Embodiment 4>

[0272] In the gas concentration estimation method of the fourth embodiment, the change in gas concentration of the threaded molten resin 29a during the period when the screw 18 stops rotating is calculated. When the screw 18 stops rotating, as... Figure 11 As shown, the inner wall of the heating cylinder 17 is stopped relative to the screw 18, and the flow rate of the molten resin in the screw-out molten resin 29a becomes 0. At this time, the change in gas concentration in the screw-out molten resin 29a depends only on the dissolution of gas from the gas-liquid interface and the penetration of dissolved gas into the interior of the molten resin. When the screw 18 stops rotating, as... Figure 11 As shown, the calculation is performed by dividing the mesh into finer sections in both the x and y directions. When the molten resin is not flowing, equation (8-3) is modified to provide gas permeation within the molten resin using equation (16-1).

[0273]

[0274] Where C: gas concentration in the molten resin [g / m³] 3 ]

[0275] D m : Diffusion coefficient of gas [m 2 / s]

[0276]

[0277] In the gas concentration estimation method of the fourth embodiment, the gas concentration is provided as a grid corresponding to the gas-liquid interface, using the gas solubility C*. And as... Figure 12 The calculation is performed as shown. That is, step S21 is executed. The change in gas concentration caused by gas permeation between the grids in the x, y, and z directions is calculated using equation (16-1). Then, step S22 is executed. That is, the calculation is determined based on the screw stop time. If it is not completed (no), the calculation is repeated in step S21. On the other hand, if it is completed (yes), the calculation ends. In addition, in fact, in the gas concentration change caused by permeation, the changes in the y and z directions are sufficiently small compared to the changes in the x direction. Therefore, equation (16-2), which is obtained by transforming equation (16-1), can be used in step S21. If the calculation is performed based on equation (16-2), the amount of calculation can be reduced. The description of the gas concentration estimation method of the fourth embodiment is completed.

[0278] <Variation Example>

[0279] The gas concentration estimation method of this embodiment can be modified in various ways. For example, the gas concentration estimation method of the second embodiment and the gas concentration estimation method of the third embodiment can be modified. In these gas concentration estimation methods, as regarding... Figure 7 Step S3 and Figure 9 As described in step S14, calculations are performed until the molten resin of the object being calculated passes through the unfilled region 27. That is, calculations continue until the resin enters and passes through the unfilled region 27.

[0280] However, in actual foam molding, the screw 18 stops rotating once the necessary amount of resin has been measured. Thus, there is both resin passing through and being delivered from the non-filled section 27, and resin stopping midway through the non-filled section 27. Resin stopping midway through the non-filled section 27 in this way is stored in the injection unit 3 (see reference 3) for a specified period. Figure 2 The gas concentration estimation method of the second embodiment and the gas concentration estimation method of the third embodiment can be modified accordingly to the actual state of foaming molding.

[0281] In other words, when the screw 18 is rotated, the gas concentration in the molten resin is calculated using the gas concentration estimation method of the second or third embodiment. Figure 7 Step S3 and Figure 9 In step S14, the elapsed metering time is also determined. When the metering time has elapsed, the change in gas concentration during the stopping process of the screw 18 is calculated for the resin that has stopped in the non-filled interval 27 using the gas concentration estimation method of the fourth embodiment. Furthermore, if the rotation of the screw 18 resumes, the gas concentration in each grid at that time point is simply set as the initial condition, and the gas concentration in the molten resin is calculated using the gas concentration estimation method of the second or third embodiment.

[0282]

Example 1

[0283] <Experiments and Simulations>

[0284] To investigate the degree of accuracy with which the gas concentration estimation method of this embodiment can estimate the gas concentration in molten resin, experiments were conducted using the injection device 3 as the actual machine, as well as computer-based simulations, and the experimental results and simulation results were compared.

[0285] <Experiments Based on Real Machines>

[0286] An experiment was conducted using injection device 3 as the actual instrument, in which gas was permeated and metered in the resin, and the gas concentration in the molten resin was measured. The experimental conditions are as follows.

[0287] "Injection Device 3"

[0288] • The inner diameter D of heating cylinder 17 b 2.2×10 -2 [m]

[0289] • The thread height h'(≒h) of screw 18 is 4.6×10 -3 [m]

[0290] • The gap δf between the top of thread 25 and the inner circumferential surface of heating cylinder 17 is 7.5×10. -5 [m]

[0291] • Thread 25 has a pitch of 2.2 × 10 -2 [m]

[0292] • The thread angle of thread 25 is 0.308 [rad]

[0293] • The groove width between threads is 1.88 × 10 -2 [m]

[0294] • Number of threads: 1 [-]

[0295] The length of the non-filled interval 27 is 4.95 × 10. -1 [m]

[0296] • Gas concentration measuring device

[0297] In the injection nozzle 24 of the injection device 3 (refer to) Figure 2 A heat- and pressure-resistant transmission-type near-infrared spectroscopy probe was installed and connected to a Fourier transform spectrophotometer via optical fiber to measure the gas concentration in the molten resin.

[0298] "resin, gas"

[0299] • Resin type: Polypropylene

[0300] • Resin specific gravity ρ 740 [kg / m³] 3 (210℃)

[0301] • Gas type: carbon dioxide

[0302] • Gas diffusion coefficient D m 8.0×10 -9 [m 2 / s]

[0303] • Gas solubility C*2.72×10 -2 [g / m3 ]

[0304] "forming conditions"

[0305] • metering stroke 4.5 x 10 -2 [m]

[0306] • forming cycle time 40 [s]

[0307] • number of forming cycles 5 [-]

[0308] A hopper 23 was provided with a feeder to enable the material supply speed to be set. First, the material supply speed from the feeder was set to 2.6 kg / h and the screw rotation speed was set to 80 rpm, and five forming cycles were implemented under the above conditions. The average value of the gas concentration, i.e., the CO2 concentration, measured by the gas concentration measuring device was obtained. Similarly, with respect to the case where the material supply speed was set to 2.6 kg / h and the screw rotation speed was set to 100 rpm, 120 rpm, and 140 rpm, 10 to 50 forming cycles were each implemented, and the average value of the CO2 concentration was obtained. Next, experiments were similarly performed by changing the material supply speed. That is, with respect to the case where the material supply speed was set to 4.0 kg / h and the screw rotation speed was set to 80 rpm, 100 rpm, 120 rpm, and 140 rpm, 10 to 50 forming cycles were each implemented, and the average value of the CO2 concentration was obtained. Figure 13A The results obtained are shown in Table 1.

[0309] In addition, even if the material supply speed based on the feeder is controlled, the volumetric flow rate Q m flowing in the heating cylinder 17 does not reach the material supply speed when the screw rotation speed is low. In addition, even if the screw rotation speed is sufficiently large, the volumetric flow rate Q m does not necessarily coincide with the material supply speed. Therefore, in the above experiments, the volumetric flow rate Q m flowing in the heating cylinder 17 was actually measured and recorded for each combination of the set material supply speed and screw rotation speed. The recorded volumetric flow rate Q m was used in the simulation described below. In addition, if the material supply speed and the screw rotation speed change, the metering time necessarily changes, and therefore the stop time of the screw 18 also changes. The stop time of the screw 18 becomes the time obtained by subtracting the metering time from the forming cycle time of 40 seconds. Therefore, the actual metering time and stop time taken were measured and recorded for each combination of the set material supply speed and screw rotation speed. This was also used in the simulation described below.

[0310] <Simulation 1>

[0311] The gas concentration of the molten resin was calculated using the gas concentration estimation method of the first embodiment. Specifically, simulations were performed using equations (2-6) and (6-1) under the same conditions as the experiments. Furthermore, in the simulation based on the gas concentration estimation method of the first embodiment, the stopping process of the screw 18 was not considered; the calculation was performed only when it was rotating. Figure 13B The simulation results are shown in the figure.

[0312] <Simulation 2>

[0313] The gas concentration of the molten resin was calculated using the gas concentration estimation method of the third embodiment. That is, according to... Figure 9 The flowchart was calculated. Furthermore, the mesh division for the threaded ejection of molten resin 29a is as follows: That is, the number of mesh divisions in the x-direction is 2, the number of divisions in the y-direction is 200, and the mesh length in the z-direction is 3.63 × 10⁻⁶. -3 [m]. Similarly, in Simulation 2, the stopping process of screw 18 is not considered; only the rotating state is considered as the object in the calculation. Figure 13C The simulation results are shown in the figure.

[0314] <Simulation 3>

[0315] The gas concentration estimation method of the third embodiment and the gas concentration estimation method of the fourth embodiment were combined to calculate the gas concentration of the molten resin. That is, the calculation was performed using the gas concentration estimation method of the third embodiment while the screw 18 was rotating, and the calculation was performed using the gas concentration estimation method of the fourth embodiment when the screw 18 was stopped. Furthermore, the grid division for the threaded ejection of the molten resin 29a was changed during the rotation and stopping of the screw 18. Specifically, when the screw 18 was rotating, the number of grid divisions in the x-direction was 2, the number of divisions in the y-direction was 200, and the length of the grid in the z-direction was 3.63 × 10⁻⁶. -3 [m]. On the other hand, when screw 18 stops, the number of grid divisions in the x direction is 200, the number of grid divisions in the y direction is 200, and the length of the grid in the z direction is 3.63 × 10⁻⁶. 3 [m]. In other words, the number of segments in the x-direction was switched. Figure 13D The simulation results are shown in the figure.

[0316] <Research>

[0317] As for the simulations 1, 2, 3, it was confirmed that gas concentrations close to those obtained in the experiment were obtained. Also, it was known that, compared with the gas concentration estimation method of the first embodiment, the gas concentration estimation method of the third embodiment was able to calculate the gas concentration with a value closer to the result obtained in the experiment. That is, it was confirmed that, in the estimation of the gas concentration, in the case where not only the dissolution of gas from the gas-liquid interface but also the flow of the molten resin was taken into consideration, the gas concentration could be estimated with higher accuracy.

[0318] On the other hand, as for the simulation 3, which was calculated while taking into consideration the diffusion of gas during the stop of the screw 18, a value larger than the gas concentration obtained in the experiment was calculated. In the simulations 1, 2, 3, the length of the non-full section 27 was set to be fixed and calculation was performed, but in reality, the length of the non-full section 27 varies. It is presumed that, as a result of the simulation performed without taking into consideration the length variation, the calculated gas concentration becomes large. Therefore, for estimating the gas concentration with higher accuracy, it is preferable to perform simulation using a model in which the length of the non-full section 27 varies. As for the variation of the length of the non-full section 27, it can be obtained actually through experiment, or it can be obtained by calculation using a flow analysis software.

[0319] The above explained the application completed by the present inventors based on the embodiments, but the present application is not limited to the embodiments already explained, and various modifications can be made without departing from the gist thereof. The multiple examples explained above can also be implemented by being appropriately combined.

Claims

1. A gas concentration estimation method characterized by comprising: A gas concentration in molten resin is estimated in an injection device for foam molding, the injection device for foam molding comprising: a heating cylinder; a screw inserted in the heating cylinder and formed with a thread; and a gas supply mechanism, when the screw is rotated in the heating cylinder to melt and convey resin downstream, the molten resin is depressurized by the shape of the thread, a non-full section in a non-full state is formed in the heating cylinder, gas supplied from the gas supply mechanism is dissolved in the molten resin in the non-full section, the gas concentration estimation method is used in the injection device for foam molding, in the rotation of the screw, a change rate dC / dt of the gas concentration in the molten resin changed by dissolution of gas into the molten resin from a gas-liquid interface between the gas and the molten resin in the non-full section is provided by the following (c1) formula, wherein Gas concentration change rate in molten resin [g / (m 3 s)] k: constant [ / s] C * : solubility of gas [g / m 3 ] C: gas concentration in the molten resin [g / m 3 ] the gas concentration in the molten resin is estimated from the (c1) formula and a passing time T required for resin to pass through the non-full section.

2. The gas concentration estimation method according to claim 1, wherein the gas concentration in the molten resin is estimated from the following formula based on the (c1) formula, C = (1 - exp(-kT))C * (c4) where k: constant [ / s] T: passing time of the non-full section [s] C * : solubility of gas [g / m 3 ].

3. The gas concentration estimation method according to claim 1 or 2, wherein In the non-full section with respect to the molten resin pushed out by the thread, it is provided that the gas-liquid interface is renewed by flow, and the amount of gas dissolved into the molten resin per unit time N from the gas-liquid interface is provided using the following equation gs , where N gs : average solubility of the gas [g / (m 2 s)] D m : Diffusion coefficient of the gas [m 2 / s] τ: exposure time to gas [s] C * : solubility of gas [g / m 3 ] C: gas concentration in the molten resin [g / m 3 ] k in the (c1) formula is obtained to estimate the gas concentration in the molten resin.

4. The gas concentration estimation method according to claim 1 or 2, wherein In a case where one of the pair of wall surfaces of the screw thread from which the molten resin is pushed out by rotation of the screw is set as a push side surface and the other is set as a pull side surface, it is assumed that the molten resin is in contact with the push side surface and is pushed out in the non-full section, and the thickness w of the pushed-out molten resin in a direction orthogonal to the screw thread is fixed, k is provided by the following equation, and the gas concentration in the molten resin is estimated. p w = 2.5 x 10"4 (mm) wherein W p : thickness of molten resin in the push flank of the thread [m] D m : Diffusion coefficient of the gas [m 2 / s] D b : inner diameter of heating cylinder [m] N: rotational speed of the screw [ / s] θ: thread angle [rad] h: distance between a groove and an inner peripheral surface of the heating cylinder [m].

5. The gas concentration estimation method according to claim 1, wherein with respect to the molten resin pushed out in the non-full section, the gas concentration C in the molten resin increased by the amount of dissolved gas is calculated based on the (c1) formula at a prescribed time interval, and the calculation is repeated until the passing time T is reached to estimate the gas concentration in the molten resin.

6. The gas concentration estimation method according to claim 5, wherein In a case where one of the pair of wall surfaces of the screw thread from which the molten resin is pushed out by rotation of the screw is set as a push side surface and the other is set as a pull side surface, it is assumed that the molten resin is in contact with the push side surface and is pushed out in the non-full section, and the thickness w of the molten resin pushed out in the direction orthogonal to the screw thread is fixed, k is provided by the following equation, and the gas concentration in the molten resin is estimated. p w = k (1) where w p : thickness of molten resin in the push flank of the thread [m] D m : Diffusion coefficient of the gas [m 2 / s] D b : inner diameter of heating cylinder [m] N: rotational speed of the screw [ / s] θ: thread angle [rad] h: distance between a groove and an inner peripheral surface of the heating cylinder [m].

7. The gas concentration estimation method according to claim 1, wherein when one of a pair of wall surfaces of the thread from which the molten resin is pushed out by the rotation of the screw is set as a push side and the other is set as a pull side, the molten resin is pushed out by the push side in the non-full section at a prescribed thickness, and gas is filled between the molten resin and the pull side to form a gas-liquid interface, the prescribed thickness of the molten resin pushed out by the push side is set as a plurality of element resins divided into a plurality of portions in a direction of a helix along the thread, a thickness direction of the molten resin, and a height direction of the thread, respectively, and is processed as the gas concentration is uniform in the inside of each of the element resins at any instant, For the dissolution of the gas from the gas-liquid interface into the molten resin, only with respect to the element resins of the plurality of element resins that are in contact with the gas, the calculation is performed using the (cl) formula, and it is assumed that the plurality of element resins move and mix with the rotation of the screw to be processed, thereby estimating the gas concentration in the molten resin.

8. The gas concentration estimation method according to claim 7, wherein In a case where one of the pair of wall surfaces of the screw thread from which the molten resin is pushed out by rotation of the screw is set as a push side surface and the other is set as a pull side surface, it is assumed that the molten resin is in contact with the push side surface and is pushed out in the non-full section, and the thickness w of the molten resin pushed out in the direction orthogonal to the screw thread is fixed p with respect to the plurality of elements of resin segmented in a manner that the thickness d x is fixed, k is provided by the following equation, and the gas concentration in the molten resin is estimated. where d x : thickness of the element resin, i.e. depth from the gas-liquid interface [m] D m : Diffusion coefficient of the gas [m 2 / s] D b : inner diameter of heating cylinder [m] N: rotational speed of the screw [ / s] θ: thread angle [rad] h: distance from the groove to the inner circumferential surface of the heating cylinder [m].

9. The gas concentration estimation method according to claim 7 or 8, wherein In the non-full section, it is assumed that the film-like molten resin adhering to the inner circumferential surface of the heating cylinder and in contact with the gas is brought into the molten resin pushed out by the thread with the rotation of the screw to be processed, thereby estimating the gas concentration in the molten resin.

10. The gas concentration estimation method according to claim 9, wherein The film-like molten resin is assumed to have a gas concentration of the solubility C* of the gas to be processed, thereby estimating the gas concentration in the molten resin.

11. The gas concentration estimation method according to claim 7 or 8, wherein It is assumed that the change in the gas concentration in the molten resin due to the penetration of the gas into the molten resin in the non-full section at the time when the rotation of the screw is stopped is provided by the following formula, thereby estimating the gas concentration in the molten resin, wherein D m : diffusion coefficient of the gas [m 2 / s] x: thickness direction of the molten resin pushed out by the thread, i.e., the direction orthogonal to the thread C=C in gas-liquid interface * .

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