Method of analyzing resin molding, analyzer, analyzing program, and storage medium

Abstract

To accurately divide a volumetric shrinkage ratio into three axial directions to enhance analysis accuracy even when a resin material that includes a crystalline resin is targeted, in a method of analyzing a resin molding, an analyzer, an analyzing program, and a storage medium.SOLUTION: In a method of analyzing a resin molding by a computer simulation, a volumetric shrinkage ratio in a solidification region of a resin material including a crystalline resin is divided into linear shrinkage ratios in three axial directions of the plate thickness, fluid flow, and perpendicular direction on the basis of the following formula, where εND: a linear shrinkage ratio in a plate thickness direction, εMD: a linear shrinkage ratio in a fluid flow direction in a plane, εTD: a linear shrinkage ratio in a perpendicular direction in a plane, εV : a volumetric shrinkage ratio, ΔT: a temperature difference, αND: a linear expansion coefficient in a plate thickness direction, αMD: a linear expansion coefficient in a fluid flow direction in a plane, and αTD: a linear expansion coefficient in a perpendicular direction in a plane. εND=αND×ΔT (1), εMD=(εV-εND)×αMD / (αMD+αTD) (2), εTD=(εV-εND)×αTD / (αMD+αTD) (3).SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to a method, an apparatus, a program, and a recording medium for analyzing a resin molded product. [Background technology]

[0002] Conventionally, in order to improve the accuracy, efficiency, and cost reduction of product design for resin molded products, CAE (Computer-Aided-Engineering) has been used to analyze the behavior of resin inside a mold and the warpage deformation of the final product.

[0003] For example, when conducting flow analysis and structural analysis of resin in injection molding, it is necessary to accurately reproduce the solidification shrinkage of the resin material in order to improve prediction accuracy.To do this, it is necessary to distribute the isotropic volumetric shrinkage rate obtained from the pressure-specific volume-temperature (PVT) characteristics, taking into account the anisotropy in three axial directions: the plate thickness direction (ND), the in-plane flow direction (MD), and the transverse direction (TD).

[0004] For example, Non-Patent Document 1 describes that the volume expansion coefficient is expressed as the sum of the linear expansion coefficients in three axial directions, which means that the linear contraction coefficients in the three axial directions can be obtained by dividing the volume contraction coefficient by the ratio of the linear expansion coefficients in each direction.

[0005] Furthermore, Patent Documents 1 and 2 disclose methods for predicting the deformation of injection-molded products, which predict the behavior of molten resin in a mold during each process of filling, dwelling, and cooling using basic equations formulated by the finite element method, and predict the shrinkage rates in the thickness and in-plane directions based on the volumetric shrinkage rates determined during the prediction of each process. These documents disclose that the shrinkage rate εZ in the thickness direction and the shrinkage rate εP in the in-plane direction are expressed by the formulas εZ = A + B eV and εP = (eV - εZ) / 2 (where eV is the volumetric shrinkage rate, and A and B are the shrinkage coefficients). [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Japanese Patent Application Publication No. 07-186228 [Patent Document 2] Japanese Patent Application Publication No. 08-230008 [Non-patent literature]

[0007] [Non-Patent Document 1] Masahiro Seto et al., Molding Processing, Vol. 15, No. 2, 2003, pp. 148-154 Summary of the Invention [Problem to be solved by the invention]

[0008] However, the inventors' verification of the relationship described in Non-Patent Document 1 showed that it was inconsistent with actual phenomena, at least when targeting resin materials containing crystalline resins, and there was a problem in that the solidification shrinkage of the resin material could not be accurately reproduced.

[0009] Furthermore, Patent Document 1 does not describe in detail how the above-mentioned calculation formulas described in Patent Documents 1 and 2 were derived. On the other hand, Patent Document 2 describes that the calculation formulas were derived based on the dimensions of the mold and the dimensions of the actual molded product by actually performing injection molding using a polycarbonate resin.

[0010] However, the polycarbonate resin used in Patent Document 2 is an amorphous resin, and has a relatively small shrinkage rate during the molding process. For example, when targeting a resin material containing a crystalline resin that has a relatively large shrinkage rate during the molding process, the above calculation formula does not accurately reproduce the linear shrinkage rate in each direction, resulting in a problem of reduced prediction accuracy.

[0011] Therefore, the objective of this disclosure is to provide an analysis method, analysis device, analysis program, and recording medium for resin molded products that accurately distributes the volumetric shrinkage rate in three axial directions, even when targeting resin materials that include crystalline resins, thereby improving analysis accuracy. [Means for solving the problem]

[0012] In order to solve the above problems, one aspect of the analysis method for a resin molded product disclosed herein is to: A method for analyzing a resin molded product by computer simulation, comprising: The volumetric shrinkage rate in the solidified region of the resin material containing the crystalline resin is divided into linear shrinkage rates in three axial directions, namely, the thickness direction, the in-plane flow direction, and the perpendicular direction in the in-plane direction, based on the following formulas (1) to (3): ε ND =α ND ×ΔT (1) ε MD =(ε V -ε ND )×α MD / (α MD +α TD ) ···(2) ε TD =(ε V -ε ND )×α TD / (α MD +α TD ) ···(3) (However, in the above formulas (1) to (3), ε ND : Linear shrinkage rate in the thickness direction, ε MD : Linear shrinkage rate in the flow direction in the plane, ε TD : Linear shrinkage rate in the perpendicular direction in the plane, ε V : volumetric shrinkage rate, ΔT: temperature difference, α ND : Linear expansion coefficient in the thickness direction, α MD : Linear expansion coefficient in the flow direction in the plane, α TD : Coefficient of linear expansion in the perpendicular direction within the plane) It is characterized by:

[0013] As a result of extensive research, the present inventors discovered that when targeting resin materials containing crystalline resins, not only primary crystallization of the crystalline resin but also secondary crystallization affects the anisotropy of linear shrinkage. Specifically, isothermal TMA measurements (described below) revealed that secondary crystallization of the crystalline resin progresses even at constant temperature, and that the progress of this secondary crystallization leads to shrinkage in the in-plane direction while shrinkage in the thickness direction hardly progresses. In this configuration, the linear shrinkage rate in the thickness direction takes into account shrinkage due to primary crystallization, and the linear shrinkage rate in the in-plane direction takes into account shrinkage due to primary and secondary crystallization, and the volumetric shrinkage rate is distributed using the above formulas (1) to (3). This improves analysis accuracy by calculating the linear shrinkage rate in each direction by taking into account the anisotropy of shrinkage due to secondary crystallization of the crystalline resin.

[0014] Preferably, the crystalline resin is a resin whose volume shrinkage rate when changed from a molten state at 250° C. and 50 MPa to a solidified state at 25° C. and 0 MPa is 10% or more.

[0015] This analysis method can be suitably used for resin materials containing crystalline resins whose volume shrinkage rate is 10% or more when the entire process from the molten region to the solidified region is taken into consideration.

[0016] The crystalline resin preferably includes a polypropylene resin.

[0017] One aspect of the resin molded product analysis device disclosed herein is: An apparatus for analyzing a resin molded product by computer simulation, The apparatus is provided with a calculation unit that distributes the volumetric shrinkage rate in the solidified region of the resin material containing the crystalline resin into linear shrinkage rates in three axial directions, namely, the thickness direction, the in-plane flow direction, and the perpendicular direction in the in-plane direction, based on the following formulas (1) to (3). ε ND =α ND ×ΔT (1) ε MD =(ε V -ε ND )×α MD / (α MD +αTD ) ···(2) ε TD =(ε V -ε ND )×α TD / (α MD +α TD ) ···(3) (However, in the above formulas (1) to (3), ε ND : Linear shrinkage rate in the thickness direction, ε MD : Linear shrinkage rate in the flow direction in the plane, ε TD : Linear shrinkage rate in the perpendicular direction in the plane, ε V : volumetric shrinkage rate, ΔT: temperature difference, α ND : Linear expansion coefficient in the thickness direction, α MD : Linear expansion coefficient in the flow direction in the plane, α TD : Coefficient of linear expansion in the perpendicular direction within the plane) It is characterized by:

[0018] According to this configuration, the linear shrinkage rate in each direction is calculated taking into consideration the anisotropy of shrinkage due to secondary crystallization of the crystalline resin, thereby improving the accuracy of the analysis.

[0019] One aspect of the program for analyzing a resin molded product disclosed herein is: A program for analyzing a resin molded product by computer simulation, The computer is caused to execute a procedure for distributing the volumetric shrinkage rate in the solidified region of the resin material containing the crystalline resin into linear shrinkage rates in three axial directions, namely, the thickness direction, the in-plane flow direction, and the perpendicular direction in the in-plane direction, based on the following formulas (1) to (3): ε ND =α ND ×ΔT (1) ε MD =(ε V -ε ND )×α MD / (α MD +α TD ) ···(2) ε TD =(ε V -ε ND )×α TD / (α MD +α TD) ···(3) (However, in the above formulas (1) to (3), ε ND : Linear shrinkage rate in the thickness direction, ε MD : Linear shrinkage rate in the flow direction in the plane, ε TD : Linear shrinkage rate in the perpendicular direction in the plane, ε V : volumetric shrinkage rate, ΔT: temperature difference, α ND : Linear expansion coefficient in the thickness direction, α MD : Linear expansion coefficient in the flow direction in the plane, α TD : Coefficient of linear expansion in the perpendicular direction within the plane) It is characterized by:

[0020] According to this configuration, the linear shrinkage rate in each direction is calculated taking into consideration the anisotropy of shrinkage due to secondary crystallization of the crystalline resin, thereby improving the accuracy of the analysis.

[0021] One aspect of the recording medium disclosed herein is: A computer-readable recording medium storing the above-mentioned program for analyzing resin molded products. [Effects of the Invention]

[0022] As described above, according to the present disclosure, the shrinkage rate in each direction is calculated taking into consideration the anisotropy of linear shrinkage due to secondary crystallization of the crystalline resin, thereby improving the accuracy of analysis. [Brief explanation of the drawings]

[0023] [Figure 1] 1A to 1C are diagrams for explaining each step in resin injection molding and graphs showing an example of the history of pressure and temperature of resin. [Figure 2] FIG. 1 is a diagram showing an example of the configuration of an analysis device for a resin molded product according to the present disclosure. [Figure 3] 1 is a flowchart showing an example of a method for analyzing a resin molded product according to the present disclosure. [Figure 4] PVT diagram obtained by PVT measurement 1 for PP in the measurement temperature range from 80°C to 20°C. [Figure 5] FIG. 2 is a diagram schematically showing the shape of an L-shaped molded product. [Figure 6]A diagram showing an outline of a thermomechanical analyzer (TMA). [Figure 7] Graph showing the results of TMA measurement 2. [Figure 8] FIG. 1 is a diagram for explaining the progress of secondary crystallization in the in-plane direction. [Figure 9] 1 is a graph showing the relationship between the volumetric shrinkage rate εV and the thickness direction shrinkage rate εND obtained from the results of PVT measurement 1 and TMA measurements 1 and 2. [Figure 10] PVT diagram of PP under various pressures obtained by PVT measurement 2. DETAILED DESCRIPTION OF THE INVENTION

[0024] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the accompanying drawings. The following description of the preferred embodiments is merely exemplary in nature and is not intended to limit the present disclosure, its applications, or its uses.

[0025] <Method for molding resin materials> The technology of the present disclosure can be applied to general molding methods using a mold that uses a molten resin material as a raw material. Specific molding methods include, for example, injection molding, press molding, blow molding, etc. Below, an overview of injection molding will be provided as an example of a molding method.

[0026] In this specification, the term "resin material" refers to a resin composition containing a crystalline resin and, if necessary, an optional amorphous resin and optional additives. In addition, the term "resin material" may be simply referred to as "resin."

[0027] [Resin injection molding] FIG. 1 is a diagram for explaining each step in resin injection molding and a graph showing an example of the history of pressure and temperature of the resin.

[0028] As shown in FIG. 1, the resin injection molding process includes an injection step S51, a pressure holding step S52, and a cooling step S53.

[0029] First, a molten resin material heated to a temperature T1 is injected into a cavity formed by clamping the molds M1 and M2 (injection step S51).

[0030] Once the entire cavity is filled with resin, supplementary injection of additional resin begins (time A1) to reduce excessive shrinkage of the resin due to temperature drop. Then, a pressure exceeding atmospheric pressure P0 is applied to the resin in the cavity. Then, the amount of additional resin is adjusted to maintain the resin pressure at approximately a predetermined pressure P1 (pressure holding step S52).

[0031] After a certain time or a certain amount of additional resin has been added, the addition of additional resin is stopped (time A2). As a result, the resin pressure in the cavity gradually decreases from P1 and eventually reaches atmospheric pressure P0 (time A3). After being cooled in the mold, the mold is opened and removed, and then cooled in the air (cooling step S53).

[0032] Although not shown in FIG. 1, the molded product thus obtained is cooled to room temperature T0, and then goes through post-processing such as deburring to become a finished product.

[0033] In the injection process S51, shear flow of the resin causes molecular orientation of the polymer chains. In the pressure holding process S52, crystallization progresses as the temperature drops in this molecularly oriented state, causing volumetric shrinkage. During mold cooling in the cooling process S53, the resin shrinks, but mold constraints cause residual stress in the molded product. During atmospheric cooling in the cooling process S53, the residual stress is released by demolding, causing deformation of the molded product.

[0034] It is known that there are two types of resin crystallization processes: primary crystallization and secondary crystallization. In this specification, "primary crystallization" refers to crystallization in which spherulites are formed, each consisting of a crystalline layer formed by the folding of polymer chains and a laminated structure (lamellar structure) of an amorphous layer sandwiched between adjacent crystalline layers. "Secondary crystallization" refers to further thickening and growth of the crystalline layer in the lamellar structure formed by primary crystallization and completion of the lamellar structure due to further folding of the polymer chains.

[0035] As a result of extensive research, the inventors of the present application have found that the crystallization of the resin that progresses from the pressure holding step S52 to the mold cooling in the cooling step S53 is primarily primary crystallization in a non-isothermal process, but that secondary crystallization also progresses in a non-isothermal process. They have also found that further crystallization progresses during atmospheric cooling in the cooling step S53, but that this crystallization is primarily secondary crystallization in an isothermal process.

[0036] <Resin molded products> The resin molded product is not particularly limited as long as it is a molded product including a plate-shaped portion produced by the various molding methods described above. The resin molded product may be a thick-walled molded product or a thin-walled molded product, and the present disclosure is preferably applicable to thin-walled molded products having a plate thickness of 1 mm or less. Specific examples of resin molded products include automobile parts, rocket and aircraft parts, sporting goods, etc. Preferred examples include plate-shaped injection molded products such as interior and exterior components of vehicles. The resin molded product may also be an insert molded product.

[0037] The resin material contains a crystalline resin, preferably containing a crystalline resin as a main component. The crystalline resin is not particularly limited, and any well-known crystalline resin may be used. Specific examples include polypropylene (PP) resin, polyethylene (PE) resin, polyacetal (POM) resin, and polyamide (PA) resin, and polypropylene resin is preferred. These resins may be used alone or in combination of two or more.

[0038] Although not intended to be limiting, a crystalline resin can be defined as a resin whose volume shrinkage rate is, for example, 7% or more when it changes from a molten state at 250°C and 50 MPa to a solidified state at 25°C and 0 MPa. In particular, the crystalline resin contained in the resin material targeted by this analysis method is preferably a resin whose volume shrinkage rate is 10% or more when it changes from a molten state at 250°C and 50 MPa to a solidified state at 25°C and 0 MPa.

[0039] The resin material may also contain amorphous resins other than crystalline resins. Examples of amorphous resins include thermoplastic resins such as polycarbonate (PC) resin, polystyrene (PS) resin, polymethyl methacrylate (PMMA) resin, and acrylonitrile butadiene styrene (ABS) resin. These resins may be used alone or in combination.

[0040] Although not intended to be limiting, an amorphous resin can be defined as a resin whose volume shrinkage rate when changed from a molten state at 250°C and 50 MPa to a solidified state at 25°C and 0 MPa is, for example, less than 7%, or even less than 10%.

[0041] The resin material may contain additives such as reinforcing fibers, fillers, pigments, dyes, impact modifiers, and UV absorbers. The reinforcing fibers are not particularly limited, and well-known fibers can be used, including, for example, glass fibers, carbon fibers, and cellulose nanofibers. These fibers can be used alone or in combination of two or more. The fiber diameter, fiber length, and content of the reinforcing fibers, as well as the specifications and content of other additives, are not particularly limited, and can be generally used conditions. These additives can be added alone or in combination.

[0042] <Analysis equipment for resin molded products> 2 shows an example of the configuration of an analysis device 100 for resin molded products (hereinafter also referred to as "analysis device 100") according to the present disclosure. The analysis device 100 is a CAE (Computer Aided Engineering) system that basically includes a computer 110. The analysis device 100 is a device that analyzes the behavior of resin during resin molding using a finite element method through computer simulation.

[0043] In this specification, analysis of resin behavior refers to at least one of flow analysis and structural analysis (also called "warpage analysis"). Flow analysis is a method for analyzing the flow behavior of resin in molding methods such as injection molding, in which molten resin is injected into a cavity. Structural analysis is a method for analyzing the solidification behavior of resin in a cavity, regardless of the molding method.

[0044] Here, an example of an apparatus for predicting warpage of a resin injection molded product by performing flow analysis and structural analysis will be described. Note that the analysis apparatus 100 in Fig. 2 is merely an example of an analysis apparatus for a resin molded product according to the present disclosure, and the configuration of the apparatus is not limited to this example.

[0045] The analysis device 100 includes a storage unit 120 including, for example, a ROM, RAM, and hard disk, and a processor 130 (computing unit) including, for example, a CPU. The analysis device 100 also includes a display unit 140 including, for example, a display, an input unit 150 including, for example, a keyboard, and a reading unit 160 for acquiring information stored on various recording media 170. The storage unit 120 and / or the recording media 170 store information such as programs for computation and various analytical data. The processor 130 can function as a model creation unit, a flow analysis unit, a structural analysis unit, and the like. The processor 130 performs various computational processes based on the information stored in the storage unit 120, information input via the input unit 150, and information acquired from the recording media 170 via the reading unit 160. The analysis device 100 is configured to be able to communicate with external devices via an interface (not shown).

[0046] The analysis device 100 uses a model creation unit to divide shape data, such as 3D CAD data that defines a mold cavity, into a plurality of minute elements to create a flow analysis model and a structural analysis model. The flow analysis model is a finite element model used in the flow analysis, which will be described later. The structural analysis model is a finite element model used in the structural analysis, which will be described later. The flow analysis model and the structural analysis model may be the same model or different models.

[0047] The model creation unit can use commercially available automatic mesh creation software, etc., and specifically, CAE preprocessors such as 3D TIMON (registered trademark)-Pre / Post manufactured by Toray Engineering D Solutions Co., Ltd., FEMAP (registered trademark) manufactured by NST Corporation, Patran (registered trademark) manufactured by MSC Software Co., Ltd., and Hypermesh (registered trademark) manufactured by Altair can be used. The shape and size of the elements are not particularly limited and are set appropriately depending on the product specifications, material composition, calculation efficiency, and calculation accuracy. A finite element model of the mold may also be created and used for analysis. When creating a finite element model of the mold, for example, a finite element model of only the surface forming the mold cavity or a portion of the mold including that surface may be created.

[0048] The analysis conditions are set based on material property data regarding the type of resin, blend, additives, and various physical properties, as well as boundary condition data describing molding conditions such as injection speed and resin temperature during injection.

[0049] The flow analysis unit uses the above-described flow analysis model to perform flow analysis to analyze the behavior of the resin in the injection process S51, the pressure holding process S52, and the cooling process S53. The flow analysis unit then calculates various data, including temperature information (temperature change over time) and pressure information (pressure change over time) of the resin for each element and for each micro-time period, through the flow analysis. The calculated data is stored in the memory unit 120. The flow analysis unit may use injection molding CAE software such as 3D TIMON (registered trademark) manufactured by Toray Engineering D Solutions Co., Ltd. The micro-time period is the analysis unit time for the flow analysis and structural analysis, and is not particularly limited and is set appropriately depending on the product specifications, material configuration, calculation efficiency, and calculation accuracy level.

[0050] The structural analysis unit uses the structural analysis model described above to perform structural analysis of the resin, i.e., calculates the shrinkage behavior of the resin based on the temperature information and pressure information of the resin calculated by the flow analysis unit, to calculate the amount of shrinkage of the resin, and finally calculates the deformed shape and amount of deformation of the molded product. The structural analysis unit may use its own software, or may use a solver such as Abaqus by Dassault Systemes or 3D TIMON (registered trademark)-WARP by Toray Engineering D Solutions, Inc. as its base.

[0051] The structural analysis unit functions as, for example, a specific volume calculation unit, a volumetric shrinkage calculation unit, a linear shrinkage calculation unit, a shrinkage amount calculation unit, a deformation amount calculation unit, etc. The specific volume calculation unit calculates specific volume information (change in specific volume over time) of the resin for each element and for each short time period based on temperature information and pressure information. The volumetric shrinkage calculation unit calculates the volumetric shrinkage of the resin for each element and for each short time period based on the specific volume information. The linear shrinkage calculation unit calculates the linear shrinkage in three axial directions for each element and for each short time period based on the volumetric shrinkage information. The shrinkage amount calculation unit calculates the shrinkage amount of the resin for each element and for each short time period based on the linear shrinkage in the three axial directions. The deformation amount calculation unit calculates the deformation amount and deformed shape of the molded product from the design shape obtained by integrating the above shrinkage amounts. The specific volume information, volumetric shrinkage information, linear shrinkage information, shrinkage amount information, deformed shape / deformation amount information, etc. obtained by the structural analysis, as well as linear expansion coefficient information required for calculating the linear shrinkage rate, are also stored in the memory unit 120.

[0052] The minute time is the analysis unit time for flow analysis and structural analysis, and is not particularly limited, but is set appropriately depending on the product specifications, material configuration, calculation efficiency, and calculation accuracy level.

[0053] <Analysis method for resin molded products> The resin molded product analysis method according to the present disclosure (hereinafter also referred to as "the present analysis method") is a method for analyzing a resin molded product using the finite element method through computer simulation, and is carried out using, for example, the above-mentioned analysis device 100.

[0054] Figure 3 is a flowchart showing an example of this analysis method, which is a method for analyzing warpage of a resin injection molded product. Note that this analysis method is not limited to application to warpage analysis of resin injection molded products. For example, it can also be applied to structural analysis of the above molding methods other than injection molding, and this analysis method can also be applied to flow analysis when analyzing the behavior of the solidified region in flow analysis of various molding methods.

[0055] As shown in FIG. 3, this analysis method includes, for example, a model creation step S1, a flow analysis step S2, and a structure analysis step S3.

[0056] First, in the model creation step S1, as described above, the model creation unit divides the shape data of the mold cavity created using 3D CAD or the like into minute elements for numerical analysis to create a flow analysis model and a structural analysis model. The model creation method is not particularly limited, and a generally known method can be used.

[0057] Next, in the flow analysis step S2, analysis conditions such as material property data and boundary condition data are set, and flow analysis is performed using the above-mentioned flow analysis model. Then, temperature and pressure information for each resin element and for each minute time is obtained in each step of the resin injection molding, i.e., the injection step S51, the pressure holding step S52, and the cooling step S53.

[0058] The flow analysis method is not particularly limited, and generally known methods can be used. Specifically, for example, pressure information and flow velocity information for each element and for each minute time during the flow and solidification process of the resin are obtained using input information such as the initial flow velocity (injection velocity), the dynamic viscosity coefficient of the resin material, boundary conditions, etc., and governing equations such as the Navier-Stokes equation and the continuity equation. Furthermore, in addition to information on the shear rate of the resin based on the flow velocity information, information on the initial temperature (injection temperature) of the resin, the specific heat, density, thermal conductivity of the resin material, etc. are also input, and temperature information for each element and for each minute time during the flow and solidification process of the resin is obtained using the heat conduction equation as governing equation.

[0059] Then, using the structural analysis model described above, the shrinkage behavior of the resin is calculated based on the temperature information and pressure information acquired in the flow analysis step S2, and the amount of shrinkage of the resin in the pressure holding step S52 and the cooling step S53 is calculated.Then, the deformed shape and amount of deformation of the finally obtained molded product are calculated (structural analysis step S3).

[0060] Specifically, the structural analysis step S3 includes a specific volume calculation step S31, a volumetric shrinkage rate calculation step S32, a linear shrinkage rate calculation step S33, a shrinkage amount calculation step S34, and a deformation amount etc. calculation step S35.

[0061] The amount of resin shrinkage can be calculated based on the volume change associated with changes in resin temperature and pressure. Specifically, based on the temperature and pressure information for each element and each time interval acquired in the flow analysis step S2, a state equation such as the Tait equation is used as the governing equation to calculate the specific volume for each element and each time interval (specific volume calculation step S31). Then, based on the specific volume information for each element and each time interval, the volumetric shrinkage rate for each element and each time interval is calculated (volume shrinkage rate calculation step S32). From the obtained volumetric shrinkage rates, the linear shrinkage rates in the three axial directions are calculated (linear shrinkage rate calculation step S33), and the shrinkage amounts in the three axial directions for each element and each time interval are calculated (shrinkage amount calculation step S34). After performing calculations for all time steps, the final warpage deformation amount and warpage shape of the molded product are calculated using equations such as Generalized Hooke's Law based on the shrinkage amounts, elastic moduli, stress, etc. (deformation amount calculation step S35).

[0062] Here, the present analysis method is characterized by the linear shrinkage calculation step S33.

[0063] Specifically, in the linear shrinkage calculation step S33 in this analysis method, the volumetric shrinkage is divided into linear shrinkages in three axial directions based on the following formulas (1) to (3).

[0064] ε ND =α ND ×ΔT (1) ε MD =(ε V -ε ND )×α MD / (α MD +α TD ) ···(2) ε TD =(ε V -ε ND )×α TD / (α MD +α TD ) ···(3) However, in the above formulas (1) to (3), ε ND : Linear shrinkage rate in the thickness direction, ε MD : Linear shrinkage rate in the flow direction in the plane, ε TD : Linear shrinkage rate in the perpendicular direction in the plane, ε V : volumetric shrinkage rate, ΔT: temperature difference, α ND : Linear expansion coefficient in the thickness direction, α MD : Linear expansion coefficient in the flow direction in the plane, α TD : Linear expansion coefficient in the perpendicular direction within the plane. ND , α MD , α TD is a value obtained experimentally by TMA measurement or the like.

[0065] As shown in the Reference Examples, Examples, and Comparative Examples described below, the inventors of the present application have, as a result of extensive research, discovered that when targeting a resin material containing a crystalline resin, not only the primary crystallization of the crystalline resin but also the secondary crystallization affects the anisotropy of linear shrinkage. Specifically, by TMA measurement 2 (isothermal TMA measurement) described below, they discovered that the secondary crystallization of the crystalline resin progresses even at a constant temperature, and that the progress of this secondary crystallization leads to shrinkage in the in-plane direction, while shrinkage in the plate thickness direction hardly progresses.

[0066] In the above configuration, the linear shrinkage rate in the thickness direction takes into account shrinkage due to primary crystallization, and the linear shrinkage rate in the in-plane direction takes into account shrinkage due to primary and secondary crystallization, and the volumetric shrinkage rate is distributed using the above formulas (1) to (3).With this configuration, the linear shrinkage rate in each direction is calculated taking into account the anisotropy of shrinkage due to secondary crystallization of the crystalline resin, thereby improving the accuracy of the analysis.

[0067] <Analysis program for resin molded products and its recording medium> At least some of the steps of the analysis method described above are programmed as a program for analyzing resin molded products. That is, the analysis program for resin molded products according to the present disclosure is a program that causes a computer to execute at least the linear shrinkage calculation step S33 among the steps described above. The analysis program may also be configured to cause a computer to execute other steps in addition to the linear shrinkage calculation step S33. Specifically, for example, the analysis program may be configured to execute the steps of the structural analysis step S3 described above, or the steps of the model creation step S1 to the structural analysis step S3 described above. This analysis program may be stored in, for example, the storage unit 120 and executed by the processor 130. The analysis program is not limited to being stored in the storage unit 120, but may also be recorded on various well-known computer-readable recording media, such as optical disk media and magnetic tape media. The analysis program can be executed by loading such a recording medium into the reading unit 160 and reading the analysis program. [Example]

[0068] The experiments carried out will be specifically described below. First, Table 1 shows the results of the Reference Examples, Examples, and Comparative Examples described below.

[0069] [Table 1]

[0070] <Forming method> As the molding method, injection molding was used and assumed.

[0071] <Material> In the Reference Examples, Examples, and Comparative Examples, the following material (1) was used. (1) Polypropylene (PP, manufactured by Prime Polymer Co., Ltd., Prime Polypro (registered trademark) J708UG) In addition to the above material (1), the following materials (2) to (4) were used in PVT measurement 2, which will be described later. (2) Polyamide 6 (PA6, manufactured by BASF, Ultramid® B3S) (3) Polyacetal (POM, manufactured by Polyplastics Co., Ltd., DURACON (registered trademark) M90-44) (4) Polycarbonate (PC, manufactured by Sumika Polycarbonate Co., Ltd., 301-15) <Reference example> [PVT measurement 1] Using a commercially available capillary rheometer (known piston method), the temperature of a molten PP sample was lowered from 300°C to 10°C (cooling rate 3°C / min) under a pressure of 1 MPa (atmospheric pressure) to measure the PVT characteristics. The region of the PVT diagram obtained, from measurement temperatures of 20°C to 80°C, is shown in Figure 4. The volumetric shrinkage of the solidified region, calculated from the solidified portion measured at temperatures between 26°C and 76°C, was 3.08% (see the PVT measurement 1 row in Table 1).

[0072] [TMA measurement 1 (non-isothermal TMA measurement)] An L-shaped molded product W (2 mm thick, symbol G indicates the gate position) with the shape shown in Figure 5 was actually produced by injection molding using PP as the resin material, and after demolding, it was annealed at 140°C for 24 hours. Then, a test piece measuring approximately 10 mm in the MD direction, approximately 10 mm in the TD direction, and 2 mm in the ND direction (plate thickness) was cut out from the obtained L-shaped molded product W, centered at position W1, 20 mm from the end.

[0073] Using a TMA30 (thermomechanical analyzer TMA8310 manufactured by Rigaku Corporation) shown in Figure 6, the linear expansion coefficients (at temperatures from 26°C to 76°C) of the above-mentioned test piece, designated by the symbol TP, in the three axial directions (MD, TD, ND) were measured. In the TMA30, symbols 31 and 32 represent detection rods, symbol 33 represents a glass plate (diameter 5 mm × thickness 1 mm), symbol 34 represents a glass pillar (diameter 5 mm × height 0 to 10 mm (adjusted depending on the size of the test piece TP)), and symbol 35 represents a glass pillar (diameter 5 mm × height 11 to 13 mm (adjusted depending on the size of the test piece TP)). A compressive load of 20 mN was applied to the test piece TP using the detection rod 31, and the temperature was raised from 26°C to 76°C at a heating rate of 1°C / min, and the thermal expansion coefficients in each direction were measured. The results are shown in the cells for the linear expansion coefficient of TMA measurement 1 in Reference Example in Table 1.

[0074] The linear shrinkage ε in the three axes directions was calculated by multiplying the obtained thermal expansion coefficient by a temperature change of 50°C (=76°C - 26°C). MD1 , ε TD1 , ε ND1 and the sum of these ε MD1 +ε TD1 +ε ND1 are also shown in Table 1. The sum of the linear shrinkage rates was 2.24%, which is about 0.8% different from the volumetric shrinkage rate of 3.08% obtained in PVT measurement 1 (an error of about 20%), and it was found that the two are not consistent. In other words, the linear shrinkage rate obtained from the linear expansion coefficient may not reflect the effects of secondary crystallization, in particular, that progress in the solidified region of the actual crystallized resin.

[0075] [TMA measurement 2 (isothermal TMA measurement)] Therefore, the influence of secondary crystallization that progresses in the solidified region of the crystalline resin was investigated by performing isothermal TMA measurements using unannealed test pieces.

[0076] Specifically, an L-shaped molded product W (2 mm thick, symbol G indicates the gate position) with the shape shown in Figure 5 was actually produced by injection molding using PP as the resin material. Then, immediately after demolding (immediately after molding), a test piece measuring approximately 10 mm in MD, approximately 10 mm in TD, and 2 mm (plate thickness) in ND was cut out from the L-shaped molded product W at a position W1 20 mm from the end. The test piece TP was held at a constant temperature of 40°C for at least three days using the TMA30 shown in Figure 6, and the dimensional changes during that time were measured in each of the MD, TD, and ND directions. The linear shrinkage in each direction was calculated from the dimensional changes in each direction. The results are shown in Figure 7 and Table 1. The linear shrinkage in the TD and ND directions after 130 hours from the start of measurement was measured using the ε values ​​shown in Table 1. TD2 , ε ND2 The linear shrinkage in the MD direction after 90 hours is shown in Table 1. MD2 The time from immediately after demolding the test piece TP to the start of the isothermal TMA measurement was approximately 2 hours (i.e., time 0 in FIG. 7 is 2 hours after demolding).

[0077] As shown in Figure 7, it was found that shrinkage progressed in the in-plane directions, MD and TD, at a constant temperature of 40°C. On the other hand, it was found that there was almost no shrinkage in the ND.

[0078] Linear shrinkage ratio ε in the three axes obtained by TMA measurement 1 MD1 , ε TD1 , ε ND1 and the linear shrinkage in the three axes directions ε obtained by TMA measurement 2 MD1 , ε TD1 , ε ND1 Adding these together, the linear shrinkage ε shown in Table 1 is obtained. MD , ε TD , ε ND The linear shrinkage factor ε MD , ε TD , ε ND The sum of the values ​​of ε MD +ε TD +ε ND was 3.13%, which was found to be consistent with the result of PVT measurement 1 (3.08%).

[0079] [Consideration] The above can be explained as follows: As shown in Figure 8, immediately after molding, the molecular orientation of the resin material occurs in the MD and TD directions within the plane (the molecular chains extend in the in-plane direction). Then, with the passage of time, the molecular chains are folded into a stable state in the in-plane direction (particularly as secondary crystallization progresses), and shrinkage only progresses in the MD and TD directions, while shrinkage in the ND direction hardly progresses at all.

[0080] Furthermore, it can be considered that the linear shrinkage rate obtained from the linear expansion coefficient of TMA measurement 1 mainly reflects the influence of primary crystallization, while the linear shrinkage rate obtained from TMA measurement 2 mainly reflects the influence of secondary crystallization.

[0081] From the above, considering the results of TMA measurement 2, which showed that shrinkage progressed in the in-plane direction but not in the thickness direction, it is reasonable to consider that the shrinkage due to secondary crystallization is distributed in the MD and TD directions.

[0082] In other words, it can be assumed that shrinkage due to secondary crystallization does not progress in the thickness direction, so the linear shrinkage rate in the thickness direction is the linear expansion coefficient α ND The linear shrinkage factor ε was calculated from ND1 In other words, the above formula (1) is derived as the formula for calculating the linear shrinkage rate in the plate thickness direction.

[0083] On the other hand, shrinkage due to secondary crystallization progresses in the in-plane direction, so the volumetric shrinkage rate ε obtained in PVT measurement 1 V From ε ND1 The remainder after subtracting is distributed according to the ratio of the linear expansion coefficients in the in-plane direction. In other words, the above formulas (2) and (3) are derived as the formulas for calculating the linear shrinkage rate in the in-plane direction.

[0084] According to the above formulas (1) to (3), the volume expansion coefficient can be distributed accurately in the three axial directions, taking into account the secondary crystallization in the in-plane direction.

[0085] <Example> Volumetric shrinkage rate ε obtained from PVT measurement 1 V, the linear expansion coefficient α obtained by TMA measurement 1 MD , α TD , α ND Based on the following equations (1) to (3), the linear shrinkage ratio ε in the three axial directions is calculated using MD , ε TD , ε ND The results are shown in Table 1. The calculated values ​​were 0.97%, 1.16%, and 0.95%, respectively, and the linear shrinkage ε in the three axes directions of the Reference Example MD , ε TD , ε ND The maximum difference between the values ​​was 0.05%, and it was found that the accuracy of the distribution of anisotropic shrinkage was high (○).

[0086] ε ND =α ND ×ΔT (1) ε MD =(ε V -ε ND )×α MD / (α MD +α TD ) ···(2) ε TD =(ε V -ε ND )×α TD / (α MD +α TD ) ···(3) <Comparative Example> Volumetric shrinkage rate ε obtained from PVT measurement 1 V , the linear expansion coefficient α obtained by TMA measurement 1 MD , α TD , α ND Using the above, the linear shrinkage ratio ε in the three axial directions was calculated based on the following equations (4) to (6). MD , ε TD , ε ND The equations (4) to (6) are calculation formulas based on the description in Non-Patent Document 1, which simply divide the volumetric shrinkage rate by the ratio of the linear expansion coefficients. The results are shown in Table 1. The calculated values ​​were 0.80%, 0.96%, and 1.31%, respectively, and the linear shrinkage rate ε in the three axial directions of the Reference Example MD , ε TD , ε ND The maximum difference between the values ​​of ε TD than ε NDThe value became larger. From these facts, it was found that simply distributing the volume shrinkage rate according to the linear expansion coefficient results in low distribution accuracy for anisotropic shrinkage (×).

[0087] ε ND = ε V × α ND / (α MD + α TD + α ND ) ···(4) ε MD = ε V × α MD [[ID=2�]] / (α MD + α TD + α ND ) ···(5) ε TD = ε V × α TD / (α MD + α TD + α ND ) ···(6) <Comparison between the calculation formula of the linear shrinkage rate in the plate thickness direction in Patent Documents 1 and 2 and Equation (1) of the present disclosure> As a result of PVT measurement 1, the volume shrinkage rate ε obtained from the results of TMA measurements 1 and 2 V and the linear shrinkage rate ε in the plate thickness direction ND are shown in FIG. 9. In FIG. 9, a temperature of 60° C. is used as a reference (shrinkage rate 0%), and it is assumed that cooling is performed to 40° C. As shown in FIG. 9, until the temperature reaches 40° C. from 60° C., the linear shrinkage rate in the plate thickness direction increases proportionally with the increase in the volume shrinkage rate. On the other hand, after the temperature becomes constant at 40° C., the linear shrinkage rate in the plate thickness direction becomes a constant value, while the volume shrinkage rate continues to increase. When fitting the data points in FIG. 9 with a linear equation, the coefficient of determination is about 0.72, and the fitting accuracy becomes low. From this result, it was found that the calculation formula εZ = A + B·eV for the linear shrinkage rate in the plate thickness direction in Patent Documents 1 and 2 is not appropriate when the resin material contains a crystalline resin.

[0088] <PVT measurement 2> Using a commercially available capillary rheometer, the temperature of a molten PP sample was lowered from 300°C to 10°C at a constant cooling rate of 3°C / min under pressures of 0 MPa, 50 MPa, 100 MPa, 150 MPa, and 200 MPa, and the PVT properties were measured. The measurement results under pressures of 0 MPa, 50 MPa, 100 MPa, 150 MPa, and 200 MPa are shown in Figure 10.

[0089] It is assumed that the state of the resin material changes from a molten state at 250°C and 50 MPa to a solidified state at 25°C and 0 MPa during each injection molding process, and the volumetric shrinkage of the PP sample accompanying this change was calculated from the PVT diagram in Figure 10.

[0090] Additionally, for the resin materials PA6, POM, and PC, the volumetric shrinkage rate of each material due to the above changes was calculated under the above assumptions based on the PVT properties published by each manufacturer. However, for the specific volume of PA6 at 25°C, a value of 10 MPa was substituted for 0 MPa.

[0091] The results are shown in Table 2.

[0092] [Table 2]

[0093] As shown in Table 2, it was found that the volume shrinkage rate of PC, which is an amorphous resin, is less than 7%, while the volume shrinkage rate of crystalline resin is 7% or more. [Industrial Applicability]

[0094] The present disclosure is extremely useful in that it provides an analysis method, analysis device, analysis program, and recording medium for resin molded products, and is capable of accurately distributing the volumetric shrinkage rate in three axial directions, thereby improving analysis accuracy, even when targeting resin materials including crystalline resins. [Explanation of symbols]

[0095] 100 Resin molding analysis device 130 Processor (arithmetic unit) 170 Recording Media S2 Flow analysis process S3 Structural analysis process S31 Specific volume calculation process S32 Volumetric shrinkage calculation process S33 Linear shrinkage calculation process S34 Shrinkage calculation process S35 Deformation amount calculation process

Claims

1. A method for analyzing a resin molded product by computer simulation, comprising: The volumetric shrinkage rate in the solidified region of the resin material containing the crystalline resin is divided into linear shrinkage rates in three axial directions, namely, the thickness direction, the in-plane flow direction, and the perpendicular direction in the in-plane direction, based on the following formulas (1) to (3): e ＮＤ =a ＮＤ ×ΔT ・・・(1) e ＭＤ =(e Ｖ -e ＮＤ )×a ＭＤ / (a ＭＤ +a ＴＤ ) ・・・(2) e ＴＤ =(e Ｖ -e ＮＤ )×a ＴＤ / (a ＭＤ +a ＴＤ ) ・・・(3) (However, in the above formulas (1) to (3), ε ＮＤ : Linear shrinkage rate in the thickness direction, ε ＭＤ : Linear shrinkage rate in the flow direction in the plane, ε ＴＤ : Linear shrinkage rate in the perpendicular direction in the plane, ε Ｖ : volumetric shrinkage rate, ΔT: temperature difference, α ＮＤ : Linear expansion coefficient in the thickness direction, α ＭＤ : Linear expansion coefficient in the flow direction in the plane, α ＴＤ : Coefficient of linear expansion in the perpendicular direction within the plane) A method for analyzing a resin molded product, comprising:

2. In claim 1, The crystalline resin is a resin whose volume shrinkage rate when changed from a molten state at 250°C and 50 MPa to a solidified state at 25°C and 0 MPa is 10% or more. A method for analyzing a resin molded product, comprising:

3. In claim 1 or claim 2, The crystalline resin includes a polypropylene resin. A method for analyzing a resin molded product, comprising:

4. An apparatus for analyzing a resin molded product by computer simulation, The apparatus includes a calculation unit that distributes the volumetric shrinkage rate in the solidified region of the resin material containing the crystalline resin into linear shrinkage rates in three axial directions, namely, the thickness direction, the in-plane flow direction, and the perpendicular direction in the in-plane direction, based on the following formulas (1) to (3): e ＮＤ =a ＮＤ ×ΔT ・・・(1) e ＭＤ =(e Ｖ -e ＮＤ )×a ＭＤ / (a ＭＤ +a ＴＤ ) ・・・(2) e ＴＤ =(e Ｖ -e ＮＤ )×a ＴＤ / (a ＭＤ +a ＴＤ ) ・・・(3) (However, in the above formulas (1) to (3), ε ＮＤ : Linear shrinkage rate in the thickness direction, ε ＭＤ : Linear shrinkage rate in the flow direction in the plane, ε ＴＤ : Linear shrinkage rate in the perpendicular direction in the plane, ε Ｖ : volumetric shrinkage rate, ΔT: temperature difference, α ＮＤ : Linear expansion coefficient in the thickness direction, α ＭＤ : Linear expansion coefficient in the flow direction in the plane, α ＴＤ : Coefficient of linear expansion in the perpendicular direction within the plane) 1. A resin molding analysis device comprising:

5. A program for analyzing a resin molded product by computer simulation, A computer is caused to execute a procedure for distributing the volumetric shrinkage rate in a solidified region of a resin material containing a crystalline resin into linear shrinkage rates in three axial directions, namely, the thickness direction, the in-plane flow direction, and the perpendicular direction in the in-plane direction, based on the following formulas (1) to (3): e ＮＤ =a ＮＤ ×ΔT ・・・(1) e ＭＤ =(e Ｖ -e ＮＤ )×a ＭＤ / (a ＭＤ +a ＴＤ ) ・・・(2) e ＴＤ =(e Ｖ -e ＮＤ )×a ＴＤ / (a ＭＤ +a ＴＤ ) ・・・(3) (However, in the above formulas (1) to (3), ε ＮＤ : Linear shrinkage rate in the thickness direction, ε ＭＤ : Linear shrinkage rate in the flow direction in the plane, ε ＴＤ : Linear shrinkage rate in the perpendicular direction in the plane, ε Ｖ : volumetric shrinkage rate, ΔT: temperature difference, α ＮＤ : Linear expansion coefficient in the thickness direction, α ＭＤ : Linear expansion coefficient in the flow direction in the plane, α ＴＤ : Coefficient of linear expansion in the perpendicular direction within the plane) A program for analyzing resin molded products, comprising:

6. 6. A computer-readable recording medium on which the resin molding analysis program according to claim 5 is recorded.

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