Method for predicting coating state, prediction device, prediction program, and recording medium

Abstract

This method improves the accuracy of predicting the state of a coating film by considering the behavior of the solvent and particulate components during the drying process, targeting coating films containing particulate matter. [Solution] In a drying model, the steps include: dividing the computational domain into multiple computational grids; performing a calculation of the movement of particulate components; assuming that the solvent volatilizes from the top surface of the computational grid located in the outermost layer, and that the solvent concentration decreases as it moves from the substrate side to the surface layer computational grid; taking the diffusion coefficient of the solvent, the volatilization rate, and the interaction coefficient of each solvent in the mixed solvent as input information; calculating the volatilization flux using the diffusion coefficient of the solvent; and calculating the amount of volatilization using the product of the volatilization rate, the area of ​​the top surface of the computational grid located in the outermost layer, the solvent concentration, and the interaction coefficient of each solvent in the mixed solvent; and performing a calculation of the solvent diffusion state and the amount of volatilization.

Description

[Technical Field]

[0001] This disclosure relates to a method for predicting the state of a coating film, a prediction apparatus, a prediction program, and a recording medium. [Background technology]

[0002] One painting technique involves a coating process in which a solvent-containing paint is applied to a substrate, followed by a drying process in which the solvent is evaporated by heat, thereby forming a paint film on the substrate. In such painting techniques, the state of the paint film after drying can affect the performance of the painted parts. Therefore, conventionally, computer simulations have been performed on models of the coating process and drying process to predict the state of the paint film, with the aim of obtaining the conditions necessary to obtain an appropriate paint film in a short time.

[0003] For example, Patent Document 1 discloses a method for determining the solvent drying rate of a coating solution containing a solvent and a polymer as an actual measured value, deriving the solvent diffusion coefficient from that solvent drying rate using the Regular Regime theory and the flux comparison method, and simulating the residual solvent ratio in the coating solution.

[0004] Patent Document 2 describes a method for obtaining a porous coating film (porous body) by applying a paste containing particles, a solvent, and a binder to a substrate, and then drying the solvent to form voids between the particles. Furthermore, in this method, it is disclosed that the drying state of the coating film is predicted by considering solvent movement driven by capillary pressure within the porous body, phase change from liquid to gas phase of the solvent, and solvent movement by diffusion in the gas phase during the decay drying period in which the evaporation rate of the solvent decreases. [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Patent No. 5273591 [Patent Document 2] Patent No. 5673570 [Overview of the project] [Problems that the invention aims to solve]

[0006] Incidentally, various particulate components are sometimes added to paints for the purpose of imparting various functions to the paint film, such as heat resistance, heat shielding, aesthetic appeal, and rust prevention. When the content of such particulate components in a paint increases, even if the surface smoothness is ensured in the wet paint film immediately after formation, a problem arises in the dry paint film after drying: the smoothness of the surface decreases due to the generation of voids caused by residual solvent in the paint film and the protrusion of particulate components from the surface. Surface smoothness of a paint film is one of the factors that affects the performance of painted parts. For example, it is known that when a paint film containing particulate components is formed on a part facing the combustion chamber of an engine, the smoothness of the paint film surface affects the engine's fuel efficiency.

[0007] The simulation described in Patent Document 1 does not take into account the case where particulate components are present. Furthermore, the prediction method described in Patent Document 2 relates to coating films containing particles, but since it is a calculation method for obtaining porous coating films, it is not suitable as a calculation method for obtaining smooth coating films.

[0008] Therefore, this disclosure aims to improve the accuracy of analysis in a coating film state prediction method, prediction device, prediction program, and recording medium, by considering the behavior of solvents and particulate components during the drying process, targeting coating films containing particulate components. [Means for solving the problem]

[0009] To solve the above problems, one aspect of the coating state prediction method disclosed herein is: A method for predicting the state of a dry coating film after drying using computer simulation, In a drying model in which a wet coating film formed by applying a paint containing particulate components and a solvent to a substrate surface is dried to obtain a dry coating film, Step of dividing the calculation region of the wet coating film into a plurality of calculation grids Step of performing calculation of movement of the particulate component in the paint It is assumed that the solvent volatilizes from the upper surface of the calculation grid located in the outermost layer, and the concentration of the solvent decreases as it goes from the calculation grid on the substrate side to the calculation grid on the surface layer side. The diffusion coefficient of the solvent, the evaporation rate, and when the solvent is a mixed solvent of a plurality of types, the interaction coefficient of each solvent in the mixed solvent are used as input information. Calculation of the evaporation flux using the diffusion coefficient of the solvent, and calculation of the evaporation amount using the product of the evaporation rate, the area of the upper surface of the calculation grid located in the outermost layer, the concentration of the solvent, and the interaction coefficient of each solvent in the mixed solvent. The area is determined based on the coordinates of the particulate component obtained by the calculation of the movement of the particulate component. The step of performing calculation of the diffusion state and the evaporation amount of the solvent

[0010] As a result of intensive research, the inventors of the present application have found that when simulating the drying process of a wet coating film formed by applying a paint containing a particulate component and a solvent to the surface of a substrate, considering the movement of the particulate component in the calculation grid and the concentration difference of the solvent between the calculation grids in the z-axis direction and performing calculation of the state and evaporation amount of the solvent is useful for improving the estimation accuracy of the state of the dry coating film after drying.

[0011] In a wet coating film containing a particulate component, the evaporation amount of the solvent decreases because the particulate component narrows the surface area where the solvent can volatilize. Therefore, by calculating the movement of the particulate component and incorporating into the evaporation amount calculation equation the fact that the evaporation amount of the solvent changes according to the coordinates where the particulate component has moved, it becomes possible to derive a calculation result closer to the actual measurement.

[0012] Also, when using a plurality of types of solvents, since the interaction coefficient of the mixed solvent serves as the driving force for the movement and diffusion of the solvent, by considering the interaction between the solvents in the mixed solvent in the calculation of the evaporation amount using the interaction coefficient, it becomes possible to further improve the calculation accuracy.

[0013] Preferably, the area is obtained by subtracting the sum of the areas occupied by the particulate components protruding from the upper surface of the computational grid located in the outermost layer on the upper surface.

[0014] When the particulate component protrudes from the surface of the computational grid, the area where the solvent can volatilize is reduced by the area occupied by the particulate component. Therefore, by performing calculations considering this, it becomes possible to obtain a solvent evaporation amount closer to the actual value and improve the prediction accuracy.

[0015] In a coating model in which a coating material containing a particulate component and a solvent is applied to a substrate surface to form a wet coating film, it is preferable to have a step of setting coating conditions and performing a calculation of the coating state of the coating material applied from the coating device to the substrate surface, and using the film thickness of the wet coating film and the coating solid content of the coating material obtained by this step as input information for performing computer simulation in the above drying model.

[0016] According to this aspect, by setting appropriate calculation models for the coating model and the drying model and analyzing them in a linked manner, it becomes possible to improve the calculation accuracy of a series of processes from coating to drying. Also, by inputting the information obtained from the simulation of the coating model into the simulation of the drying model and continuously performing two types of simulations, the calculation efficiency can be improved.

[0017] The movement of the particulate component is preferably derived using Stokes' equation for deriving the terminal velocity of the particle.

[0018] Since the coordinates where the particulate component moves affect the solvent evaporation amount, by calculating the detailed behavior considering the floating and sinking of the particulate component, the coordinates of the particulate component can be accurately calculated, and by considering those coordinates, it becomes possible to obtain a solvent evaporation amount closer to the actual value.

[0019] It is preferable to use equation (1) below as the equation used to calculate the amount of volatilization, and equation (2) below as the equation used to calculate the volatilization flux.

[0020]

number

[0021] In equation (1), n ​​is an integer greater than or equal to 1, indicating that n types of solvents, from the first solvent to the nth solvent, are used. Jn is the amount of solvent n volatilized in the computational grid located at the outermost layer, Rn is the volatilization rate when solvent n is a single solvent, S is the area of ​​the top surface of the computational grid located at the outermost layer, Δt is the time step, Cn is the molar concentration of solvent n, and αn is the interaction coefficient of solvent n in the mixed solvent when the solvents are mixed solvents. In equation (2), J'n is the amount of solvent n transferred between layers (between computational grids), Dn is the diffusion coefficient of solvent n, x is the position in the z-axis direction in the computational grid, and Cn is the molar concentration of solvent n.

[0022] According to this embodiment, when using multiple types of solvents, by considering the interactions between solvents in the mixed solvent and inputting the interaction coefficient α of each solvent in the mixed solvent, which is experimentally obtained from the mole fraction of each solvent in the mixed solvent and the volatilization rate of the mixed solvent, the calculation accuracy can be improved compared to when only the volatilization rate and diffusion coefficient are used in the case of a single solvent. By using equations (1) and (2), the interaction coefficient α of the mixed solvent and the concentration difference dc between the computational grids become the driving forces for solvent movement and diffusion, and by including these in the volatilization flux J, it is possible to improve the prediction accuracy.

[0023] The steps include updating the volume of each computational grid, the coordinate values ​​of the particulate components, and the concentration of the paint based on the diffusion state and volatilization amount of the solvent derived using the above formulas (1) and (2), Preferably, after repeatedly performing each of the above steps until a specified time step, the system has a step of outputting one or more of the following: the film thickness as the z-axis length of the entire calculation domain, the surface roughness calculated on the upper surface of the calculation grid located at the outermost layer, and the amount of remaining solvent in the calculation domain.

[0024] In the calculation of the movement of the particulate components, if it is detected that the diameter of one particulate component is within the diameter range of another particulate component based on the coordinates and diameters of the particulate components, it is preferable to have a step in which it is determined that the two particulate components are overlapping, the interparticle distance is calculated using the coordinates of the two particulate components, and the coordinates of each of the two particulate components are shifted by a distance obtained by the product of a random number, a coefficient, and the ratio of the overlapping distance to the interparticle distance, on a straight line connecting the centers of the two particulate components.

[0025] The content of the particulate component in the dry coating is preferably more than 30 vol%.

[0026] When the particulate component content exceeds 30 vol% in a dry coating, the particulate component has a significant impact on the solvent's volatilization behavior during the drying process, and surface roughness issues are also pronounced. Therefore, the prediction method of this disclosure is particularly useful when the particulate component content is such that it is important to use it.

[0027] One embodiment of the coating state prediction device disclosed herein is: A device for predicting the state of a dry coating film after drying using computer simulation, In a drying model in which a wet coating film formed by applying a paint containing particulate components and a solvent to the surface of a substrate is dried to obtain a dry coating film, A computational grid forming unit that divides the computational area of ​​the wet coating into a plurality of computational grids, A particle coordinate calculation unit that performs calculations of the movement of the particulate components in the paint, The solvent volatilizes from the top surface of the computational grid located at the outermost layer, and the concentration of the solvent decreases as it moves from the computational grid on the substrate side to the computational grid on the surface side. The diffusion coefficient of the solvent, the volatilization rate, and, if the solvent is a mixture of multiple solvents, the interaction coefficient of each solvent in the mixture are used as input information to perform calculations of the volatilization flux using the diffusion coefficient of the solvent, and calculations of the amount of volatilization using the product of the volatilization rate, the area of ​​the top surface of the computational grid located at the outermost layer, the concentration of the solvent, and the interaction coefficient of each solvent in the mixture, with the area being determined based on the coordinates of the particulate components obtained by the calculation of the movement of the particulate components. The volatilization amount calculation unit performs calculations of the diffusion state and the amount of volatilization of the solvent. It is characterized by the following:

[0028] According to this embodiment, by considering the movement of particulate components in the computational grid, the concentration difference of the solvent between computational grids, and the surface area of ​​the computational grid from which the solvent can volatilize, the accuracy of calculating the thickness of the dry coating film, the surface roughness, and the amount of residual solvent in the dry coating film after drying can be improved.

[0029] One aspect of the coating state prediction program disclosed herein is: A program for predicting the state of a dry coating film after drying using computer simulation, On the computer, Using a drying model in which a wet coating film formed by applying a paint containing particulate components and a solvent to the surface of a substrate is dried to obtain a dry coating film, The computational domain of the wet coating is divided into multiple computational grids, The solvent is assumed to volatilize from the top surface of the computational grid located at the outermost layer, and the concentration of the solvent decreases as it moves from the computational grid on the substrate side to the computational grid on the surface side. The diffusion coefficient of the solvent, the volatilization rate, and, if the solvent is a mixture of multiple solvents, the interaction coefficients of each solvent in the mixture are used as input information. The volatilization flux is calculated using the diffusion coefficient of the solvent, and the amount of volatilization is calculated using the product of the volatilization rate, the area of ​​the top surface of the computational grid located at the outermost layer, the concentration of the solvent, and the interaction coefficients of each solvent in the mixture. The area is determined based on the coordinates of the particulate components obtained by the calculation of the movement of the particulate components. The diffusion state and amount of volatilization of the solvent are then calculated. It is characterized by the following:

[0030] According to this embodiment, by considering the movement of particulate components in the computational grid, the concentration difference of the solvent between computational grids, and the surface area of ​​the computational grid from which the solvent can volatilize, the accuracy of calculating the thickness of the dry coating film, the surface roughness, and the amount of residual solvent in the dry coating film after drying can be improved.

[0031] One aspect of the recording medium disclosed herein is: This is a computer-readable recording medium on which the above-mentioned program for predicting the state of the coating film is stored. [Effects of the Invention]

[0032] As described above, according to this disclosure, the solvent state and evaporation rate are calculated considering the diffusion of the solvent between computational grids and the surface area of ​​the computational grid from which the solvent can volatilize. This improves the accuracy of calculating the film thickness, surface roughness, and amount of residual solvent in the dry coating after drying. [Brief explanation of the drawing]

[0033] [Figure 1] This is a diagram illustrating the coating process, the drying process, and their models. [Figure 2] This figure shows an example of the configuration of a coating state prediction device related to this disclosure. [Figure 3]This is an example of a flowchart for the coating process of the coating film state prediction method described herein. [Figure 4] This is an example of a flowchart for the drying process of the coating film state prediction method related to this disclosure. [Figure 5] This figure shows an example of a computational grid. [Figure 6] This diagram illustrates the particle duplication correction process. [Figure 7] This graph shows the volatilization rates of mixed solvents prepared at various mixing ratios. [Figure 8A] This is a schematic front view of a computational grid and a hollow particle protruding from its top surface. [Figure 8B] This is a schematic top view of a computational grid and a hollow particle with its head protruding from its top surface. [Figure 9] This figure shows the top surface of an engine piston used as the base material. [Figure 10] This graph compares experimental results with calculated results for film thickness. [Figure 11] This is a graph comparing experimental results and calculated results for surface roughness. [Figure 12] This graph compares experimental results with calculated results regarding the change in solid content concentration. [Figure 13] This graph shows the relationship between particulate matter content and surface roughness based on experimental results. [Modes for carrying out the invention]

[0034] Embodiments of the present disclosure will be described in detail below with reference to the drawings. The following description of preferred embodiments is illustrative in nature and is not intended to limit the present disclosure, its applications or uses in any way.

[0035] The technology disclosed herein comprises a coating step of applying a paint containing a solvent onto a substrate, and a drying step of drying and curing the paint while volatilizing the solvent by heat, and can be applied to all methods of forming a coating film on a substrate.

[0036] <coating film> The coating film used as the target of the prediction method of this disclosure is formed by drying a paint containing particulate components, a solvent, and a resin binder. The paint is not particularly limited as long as it can form a coating film by volatilizing the solvent, but examples include paints used to impart heat shielding, heat resistance, design properties, etc., to a substrate. In the following description, the coating film containing the solvent before drying is referred to as a wet coating film, and the coating film after drying, when the solvent has been volatilized, is referred to as a dry coating film.

[0037] The type, shape, and particle size of the particulate components can be appropriately selected depending on the application of the coating film, and are not particularly limited, but those on the order of μm smaller than the thickness of the coating film are preferred. For example, they are preferably 30 μm or less, and hollow particles with an average particle size of 10 μm or less are more preferred. They can be solid or hollow, but if they are hollow particles or particles with a density lower than that of the fluid, they tend to protrude from the surface of the coating film and have a large impact on the volatilization of the solvent. Therefore, the usefulness of using the prediction method of this disclosure is high when the particulate components include hollow particles or particles with a density lower than that of the fluid. The paint may also contain nanoparticles. In the prediction method of this disclosure, spherical particles on the order of μm are treated as particulate components, and nanoparticles are treated as solids in the same way as resins. The usefulness of the prediction method of this disclosure is particularly remarkable when targeting coating films with a relatively high content of particulate components, and it is preferable that the content of particulate components in the formed coating film exceeds 30 vol%, and it is preferable that the content of particulate components in the paint exceeds 15 vol%.

[0038] As the solvent, various organic solvents capable of dissolving the resin binder can be used. One solvent may be used alone, or two or more may be mixed. Examples of solvents include hydrocarbon solvents such as xylene, toluene, hexane, and heptane; ester solvents such as ethyl acetate, butyl acetate, and ethylene glycol monomethyl ether acetate; ether solvents such as ethylene glycol monomethyl ether and ethylene glycol diethyl ether; alcohol solvents such as butanol, propanol, octanol, cyclohexanol, and diethylene glycol; and ketone solvents such as methyl ethyl ketone and methyl isobutyl ketone. While not intended to limit the solvents, hydrocarbon solvents and alcohol solvents are preferred.

[0039] The resin binder is not particularly limited as long as it can form a coating film, but for example, if the purpose of the paint is to provide heat shielding or heat resistance, a silicone-based resin can be preferably used.

[0040] The base material is not particularly limited, and various shapes and applications can be used. Although not intended to be limiting, it is preferable that the base material has heat-shielding and heat-resistant properties. Examples include the top surface of an engine piston and the walls forming the combustion chamber of an engine. High heat-shielding properties are required for engine pistons and combustion chambers, and it is common to form a coating film that acts as a heat-shielding material.

[0041] <Coating film formation method> Figure 1 shows a series of steps in which a coating step S1 is performed in which a paint 20 containing a solvent 21 and particulate components 22 is applied to a substrate 10, followed by a drying step S2 in which the paint is dried and cured while the solvent is evaporated by heat, thereby forming a dry coating film on the substrate.

[0042] [Coating process] In coating step S1, a wet coating film 40 is formed by applying paint 20 to the substrate 10 using a coating device 30. The coating method is not particularly limited, and coating may be done using a brush or spatula, but here we give an example in which a spray gun is used as the coating device 30 to spray and coat the substrate 10, which rotates around the z axis, from above. In the prediction method of this disclosure, a simulation is performed to calculate the coating state of the paint applied from the coating device to the substrate surface in the coating model of coating step S1. Details of the calculation will be described later, but the coating model analyzed in coating step S1 includes a paint atomization model that calculates the spray gun 30 and the sprayed paint, a mist paint volatilization model that calculates the paint after it has been sprayed from the spray gun 30, and a coating bounce model of paint particles on the substrate surface.

[0043] [Drying process] The drying step S2 includes a step of drying the wet coating 40 at room temperature and a step of accelerating the hardening of the wet coating 40 by volatilizing the solvent with heat. Heat drying is generally carried out by placing the substrate in a heating oven, for example, but it may also be carried out by placing heat sources on both sides of the substrate. In the prediction method of this disclosure, following the calculation of the coating step S1, calculations regarding the behavior of particulate components in the wet coating, solvent diffusion and volatilization are performed in the drying step S2. Details of the calculations will be described later, but the drying model analyzed in this drying step S2 includes a particle motion model and a solvent diffusion model that use the wet coating as the calculation target.

[0044] <Coating film state prediction device> Figure 2 shows an example of the configuration of the coating state prediction device 100 (hereinafter also referred to as "prediction device 100") according to this disclosure. The prediction device 100 is a CAE (Computer Aided Engineering) system with a computer 110 as its basic configuration. The prediction device 100 is a device that predicts the state of a dry coating after drying by analyzing the particulate components and solvent in the coating using the finite element method through computer simulation.

[0045] This prediction device 100 predicts the film thickness, surface roughness, and residual solvent amount of a dry coating formed by spraying paint with a spray gun and drying it by heat, using computer simulation. Note that the prediction device 100 shown in Figure 2 is merely an example of a coating state prediction device according to this disclosure, and the device configuration is not limited to this example.

[0046] The prediction device 100 includes a storage unit 120 consisting of, for example, ROM, RAM, or a hard disk, and a processor 130 (arithmetic unit) consisting of, for example, a CPU. The prediction device 100 also includes a display unit 140 consisting of, for example, a display, an input unit 150 consisting of, for example, a keyboard, and a reading unit 160 for acquiring information stored in various recording media 170. The storage unit 120 and / or recording media 170 store information such as programs for arithmetic processing and various analysis data. The processor 130 can function as a wet coating information calculation unit 131 for executing a coating model, a calculation grid formation unit 132 for executing a drying model, a particle coordinate calculation unit 133, a volatility calculation unit 134, and a dry coating information calculation unit 135, etc. The processor 130 performs various arithmetic processing based on the above 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. Furthermore, this prediction device 100 is configured to communicate with external devices via an interface (not shown).

[0047] The memory unit 120 stores various programs. It also stores model information, including coating models and drying models. This model information also includes information that visualizes the substrate material to be coated. The memory unit 120 stores information regarding coating and drying conditions. The data stored in the memory unit 120 can be modified and added by the user. Furthermore, the memory unit 120 also stores various calculation results generated by the execution of various programs.

[0048] <Method for predicting the state of the coating film> The method for predicting the state of a coating film according to this disclosure (hereinafter also referred to as "this prediction method") is a method for analyzing a coating film using the finite element method through computer simulation, and is performed, for example, using the prediction device 100 described above. In the following, an example of forming a coating film as a heat shield on the top surface of an engine piston will be given for explanation.

[0049] [Coating Model] The wet coating film formation process in the coating process is calculated using a coating model. Figure 3 is an example of a flowchart for the coating film state prediction method in the coating process according to this disclosure. In the coating process S1, this prediction method performs three-dimensional fluid analysis (3D-CFD) using the coating model. The Navier-Stokes equations are used as the governing equations for the fluid analysis. In this embodiment, the thermal fluid analysis program CONVERGE from Convergent Science Inc. was used as the calculation software for this simulation, but other software such as icon-CFD from IDAJ Corporation, and Star-CD or Star-CCM+ from Siemens can also be used. As shown in Figure 3, in the coating process, this prediction method comprises a coating condition setting process S11, a numerical analysis process S12, a wet coating film information calculation process S13, and a wet coating film information output process S14.

[0050] Specifically, first, various physical properties of the paint are input, along with the spray particle size and spray speed obtained from actual measurements using a spray gun. Then, in the coating condition setting step S11, coating conditions such as the spray angle of the spray gun, the rotation speed of the substrate, the distance from the tip of the spray gun to the substrate surface (gun distance), the viscosity coefficient of the paint, surface tension, heat of vaporization, vapor pressure, thermal conductivity, density, specific heat, and viscosity after coating are set. As an example of coating conditions, the conditions used in this embodiment are shown in Table 1.

[0051] [Table 1]

[0052] Next, in numerical analysis step S12, the coating state of the paint applied from the spray gun to the substrate surface is calculated by three-dimensional fluid analysis using a coating model. The coating model includes a paint atomization model that calculates the spray gun and the sprayed paint, a mist paint volatilization model that calculates the paint after it has been sprayed, and a coating bounce model of paint particles on the substrate surface.

[0053] The paint atomization model simulates how paint particles atomized at the tip of a spray gun are further atomized due to instability caused by the density difference between the spray and gas phases. Specifically, the RT (Rayleigh-Taylor) model was used. The calculation formulas used in the paint atomization model are shown in equations (3) and (4) below.

[0054]

number

[0055] In equations (3) and (4), r c C is the particle size of the paint particles. RT g is a constant, t ρ is acceleration. f is paint density, ρ g σ is the gas phase density, and σ is the surface tension of the paint.

[0056] The atomized paint volatilization model simulates how paint particles volatilize from the tip of a spray gun to the substrate surface, specifically using the Frossling model. Considering mass transfer between droplets and vapors, the atomized paint volatilization model uses equations (5) to (8) below.

[0057]

number

[0058] In equations (5) to (8), D is the mass diffusion coefficient between liquid droplets and vapor, and Y k * Y is the mass fraction of vapor on the droplet surface. kis the mainstream vapor mass fraction, Sh d is the Sherwood number, M is the molecular weight, p is the vapor pressure, X is the mole fraction, and T is the temperature of the droplet. B is a coefficient used in the mathematical formula for evaporation, and the mainstream vapor mass fraction Y k is the vapor mass fraction Y at the droplet surface k * If it is smaller than, the droplet radius represents a decreasing relationship. The evaporation rate depends on the mass fraction Y k * Y depends on k * Y is input from the literature value for each solvent and is determined by the vapor pressure p vap and the molecular weight M.

[0059] The model of the deposition and bounce of paint particles on the substrate surface is calculated using the Weber number (We number), which is a dimensionless number representing the deposition behavior of droplets, as shown in Equation (9) below.

[0060] [Equation]

[0061] In Equation (9), L is the particle diameter of the paint particle, V is the velocity of the paint particle, ρ is the paint density, and σ is the surface tension of the paint.

[0062] When the numerical analysis step S12 ends, based on the analysis result of the numerical analysis step S12, the wet coating film information calculation step S13 calculates wet coating film information such as the film thickness and deposition solids content (NV) of the wet coating film.

[0063] The wet coating film information calculated by the wet coating film information calculation step S13 is output in the wet coating film information output step S14. Among the wet coating film information, the film thickness and deposition solids content (NV) of the wet coating film are used as input information for performing simulations in the drying model. In Figure 3, the flowchart ends at the wet coating film information output step S14, but the coating model and the drying model may also be connected in series.

[0064] [Drying Model] The dry coating film formation process during drying is calculated using a drying model. In the embodiments described below, the wet coating film is assumed to contain hollow particles on the order of several micrometers as particulate components. The wet coating film also contains nanoparticles, but these nanoparticles are not treated as particulate components but as solid components, similar to the resin binder.

[0065] Figure 4 is an example of a flowchart in the drying process of the coating state prediction method according to the present disclosure. As shown in Figure 4, the prediction method uses a drying model and comprises a drying condition setting step S21, a computational grid creation step S22, a porosity calculation step S23, a Brownian motion calculation step S24, a particle terminal velocity calculation step S25, a particle overlap correction step S26, a porosity calculation step for each layer S27, a solvent volatilization amount calculation step S28, a solvent transfer calculation step S29, a film thickness update step S30, a drying process completion determination step S31, a dry coating information calculation step S32, and a dry coating information output step S33.

[0066] Specifically, the following are inputs: the film thickness and coated solids content (NV) of the wet coating obtained from the analysis of the coating model, the maximum and minimum particle diameters of the hollow particles, the viscosity of components other than hollow particles (solvent, resin binder, nanoparticles, etc.), the density of each component, the volatilization rate and diffusion coefficient of the solvent, and the interaction coefficient of each solvent in the mixed solvent. Note that the viscosity of components other than hollow particles (solvent, resin binder, nanoparticles, etc.) is the viscosity corresponding to the change in solvent volume and is an experimentally obtained value. The diffusion coefficient of the solvent is the diffusion coefficient corresponding to the change in solvent volume and is an experimentally obtained value. When the coating model and drying model are coupled, the information obtained from the analysis of the coating model can be applied to the drying model, and input information other than the information obtained from the coating model may be input at the start of the coating model. When the coating model and drying model are not coupled, the inputs required for the drying model may be values ​​obtained by separate calculations or experiments. As an example of input information, Table 2 shows the input information used in this embodiment. Table 2 includes the setting conditions set in the drying condition setting step S21.

[0067] [Table 2]

[0068] Then, in the drying condition setting step S21, drying conditions are set such as the initial cell (computational grid) size reflecting the information on the film thickness of the wet coating, the number of time steps and step intervals, temperature setting, pressure setting, the volume fraction of each component reflecting the information on the amount of solids coated (NV), and the contribution of hollow particles that protrude from the surface of the coating to the solvent evaporation rate.

[0069] Next, in the computational grid creation step S22, a computational grid with the cell size set in the drying condition setting step S21 is created as the computational domain for the wet coating film. An example of a computational grid is shown in Figure 5. The computational grid is created with width x, depth y, and height z as the film thickness, and is divided into multiple computational grids in the xy and z directions. It is assumed that a mixed solvent of multiple types of solvents is diffused and present at the set concentration. Furthermore, it is assumed that there are a number of hollow particles within these multiple computational grids calculated by the volume ratio and particle diameter, and that they are randomly placed using the random number generation command XSRAND and the random number seed Xorshift. Since the random number seed is a constant value, the position of each particle is reproduced each time the same program is run.

[0070] Next, in the porosity calculation step S23, the porosity of each layer within the computational grid is calculated. Here, porosity is the proportion of components other than hollow particles and nanoparticles, i.e., the resin binder and solvent, within the computational grid. Porosity = (Volume of resin binder and solvent) / Volume of the entire calculation grid That is the case.

[0071] Next, in the Brownian motion calculation process S24, the movement of particulate components in the paint is calculated. Specifically, hollow particles are moved in their x, y, and z directions by Brownian motion, and their coordinates after movement are calculated using the random number generation command XSRAND and the diffusion coefficient. The formula for Brownian motion is shown in equation (10), and the formula for the coordinates after movement is shown in equation (11).

[0072]

number

[0073] In equation (10), D is the diffusion coefficient of the hollow particle, k is the Boltzmann constant, T is the temperature, μ is the viscosity, and a is the radius of the hollow particle. In equation (11), D is the diffusion coefficient of the hollow particle, s is the time step (seconds), x int The initial x-axis cell size (m), V x This represents the partial coordinate position relative to the cell size.

[0074] Next, in the particle terminal velocity calculation step S25, the movement of particulate components in the paint is calculated. Specifically, using Stokes' equation (12) below, the movement of hollow particles by floating and sinking is calculated from the difference between the settling of hollow particles due to gravity and the flow of solvent around the particles. In equation (12), if the viscosity η (Pa·s) is high, the resistance increases and the particles become more difficult to move.

[0075]

number

[0076] In formula (12), ν s p is the terminal velocity of the hollow particle. p D is the density of hollow particles. p p is the particle size of the hollow particle. f η is the fluid density (components of the coating other than hollow particles), and η is the viscosity.

[0077] Next, in the particle overlap correction step S26, if overlap of multiple hollow particles is detected from the coordinates after the movement of the hollow particles, the overlap is resolved by moving those hollow particles relative to each other. Specifically, as shown in Figure 6, for example, based on the coordinates of the particles and their diameters, the diameter 2r of particle i is determined. i Within the range, particle j has a diameter of 2r jIf an overlap exists between two particles, that is, if an overlap is detected, the inter-particle distance R is calculated using the coordinates of the two particles from equation (13) below, and the overlap between the particles is resolved by shifting the coordinates x,y,z of each particle by a random number XSRND × coefficient × (ratio of overlap distance to inter-particle distance) on the straight line connecting the centers of the two particles i and j from equation (14) below. This process allows the particles to be moved in a state closer to reality, thereby improving the accuracy of the calculation.

[0078]

number

[0079] In equation (13), R is the interparticle distance, x i y i z i x is the coordinate of particle i, x j y j z j is the coordinate of particle j. In equation (14), X is the initial x-direction cell size (m), r i r is the radius of particle i. j is the radius of particle j. Equation (14) gives the x-coordinate of particle i after its movement. The y-coordinates and z-coordinates of particle i, and the x-coordinates, y-coordinates and z-coordinates of particle j can be found in the same way as in equation (14).

[0080] Next, in the porosity calculation step S27 for each layer, the porosity is calculated for the computational grid of each layer in the z-axis direction. The porosity is the ratio of components other than hollow particles and nanoparticles within the computational grid, similar to the porosity calculation step S23.

[0081] Next, in the solvent volatilization calculation step S28, the amount of solvent volatilizing from the top surface of the computational grid, which is located at the outermost layer, is calculated, assuming that the solvent volatilizes from the top surface. Specifically, the volatilization rate of a single solvent, or, if the solvent is a mixture of multiple solvents, the interaction coefficients of each solvent in the mixture, are used as input information, and the amount of solvent volatilizing from the top surface of the computational grid is calculated by calculating the following equation (1) as the volatilization calculation equation.

[0082]

number

[0083] In equation (1), n ​​is an integer greater than or equal to 1, indicating that n types of solvents, from the first solvent to the nth solvent, are used. Jn is the amount of solvent n volatilized in the computational grid located at the outermost layer, Rn is the volatilization rate when solvent n is a single solvent, S is the area of ​​the top surface of the computational grid located at the outermost layer, Δt is the time step, Cn is the molar concentration of solvent n, and α is the interaction coefficient of solvent n in the mixed solvent when the solvents are mixed solvents. The interaction coefficient α is the driving force for solvent movement and diffusion.

[0084] In equation (1), the interaction coefficient α is an experimentally determined value. Figure 7 shows graphs of experimentally obtained and calculated volatilization rates when a mixed solvent of hydrocarbon solvent A and alcohol solvent B is prepared at various mole fractions. As shown by the dashed line in Figure 7, if we assume that solvents A and B are an ideal solution with no interaction between them, the volatilization rate and mole fraction are proportional. However, in reality, interactions exist between the solvents, so the volatilization rate and mole fraction are not proportional. Experimentally, the weight change was measured while volatilizing a mixed solvent of solvents A and B at room temperature, and the value of the volatilization rate as a function of the mole fraction of the mixed solvent was obtained. As shown in Figure 7, the interaction coefficient α of each solvent in the mixed solvent can be derived from the experimentally obtained relationship between the volatilization rate and the mole fraction of the mixed solvent. For example, in this example of a mixed solvent of solvents A and B, the volatilization rate of solvent A is 0.067 g / (m³). 2 s) In a mixed solvent of solvent A and solvent B, the interaction coefficient of solvent A is 0.92, and the volatilization rate of solvent B is 0.052 g / (m³). 2 s) The interaction coefficient of solvent B in a mixed solvent of solvent A and solvent B is 0.69.

[0085] In equation (1), the area S is determined based on the coordinates of the hollow particles obtained by hollow particle movement calculations such as the Brownian motion calculation step S24, the particle terminal velocity calculation step S25, and the particle overlap correction step S26. Figures 8A and 8B show schematic diagrams of a computational grid A located in the outermost layer and hollow particles 22 protruding from the top surface a of the computational grid, with Figure 8A being a front view and Figure 8B being a top view. The solvent can volatilize in the area of ​​the top surface a of the computational grid located in the outermost layer, but as shown in Figures 8A and 8B, when hollow particles 22 protrude from the top surface a, the volatilization of the solvent is hindered by the area occupied by the hollow particles. Therefore, when hollow particles 22 protrude from the top surface a, it is preferable that the area from which the solvent can volatilize is the area occupied by the hollow particles protruding from the top surface a of the computational grid located in the outermost layer, minus the sum of the areas occupied by the top surface a (shaded area in Figure 8).

[0086] Next, in the solvent transfer calculation step S29, the solvent concentration is assumed to decrease as it moves from the calculation grid on the substrate side to the calculation grid on the surface side (in the z-axis direction of the calculation grid), and the calculation of solvent transfer and diffusion is performed. Specifically, the diffusion coefficient as a single solvent is experimentally determined and input, and the solvent transfer and diffusion state is calculated by calculating the following equation (2) as the volatile flux calculation equation (Fick equation).

[0087]

number

[0088] In equation (2), Dn is the diffusion coefficient of solvent n, x is the position in the z-axis direction on the computational grid, J'n is the amount of solvent n transferred between layers (between computational grids), and Cn is the molar concentration of solvent n. Since the solvent concentration decreases from the computational grid on the substrate side to the computational grid on the surface side (in the z-axis direction of the computational grid), in equation (2), the concentration c with respect to position x has a negative gradient, and J has a positive value.

[0089] Next, in the film thickness update step S30, based on the calculation results of the solvent volatilization calculation step S28 and the solvent transfer calculation step S29, the volume of the computational grid reduced by the amount of volatilization, the coordinate values ​​of the hollow particles, and the concentration of the paint are updated, and the film thickness (the z-axis length of the entire computational grid) is also updated.

[0090] Next, in the drying process completion determination step S31, it is determined whether the drying process is complete based on whether the specified number of steps have been executed. If the specified number of steps have not yet been executed, the process returns to the porosity calculation step S23 and performs calculations for all time steps. At this point, various film thickness information may be output in time history format.

[0091] Once calculations for all time steps are complete, the dry coating information calculation step S32 calculates the dry coating information from the final calculation results. Specifically, for example, the z-axis length of the entire final calculation domain is calculated as the dry coating thickness t (μm), the surface roughness Ra (μm) is calculated by randomly measuring the top surface of the calculation grid located at the outermost layer, and the amount of residual solvent in each layer is calculated for each solvent type.

[0092] Next, in the dry coating information output step S33, for example, the dry film thickness, surface roughness, and the amount of remaining solvent for each solvent type are output.

[0093] In the above configuration, the solvent state and volatilization rate are calculated by considering the movement of particulate components in the computational grid and the concentration difference of the solvent between computational grids in the z-axis direction, thereby improving the accuracy of the prediction of the state of the dry coating film after drying. In a wet coating film containing particulate components, the particulate components reduce the surface area from which the solvent can volatilize, which can lead to a decrease in the amount of solvent volatilized. Therefore, by calculating the movement of particulate components and incorporating into the volatilization rate calculation equation that the amount of solvent volatilized changes depending on the coordinates to which the particulate components move, it is possible to derive calculation results that are closer to actual measurements. Furthermore, when using multiple types of solvents, the interaction coefficient of the mixed solvent becomes the driving force for the movement and diffusion of the solvent. Therefore, by considering the interaction between the solvents in the mixed solvent in the volatilization rate calculation equation, it is possible to further improve the calculation accuracy.

[0094] <Program for predicting coating state and recording medium thereof> At least a portion of each step of the prediction method described above is programmed as a program for predicting the state of the coating film. That is, the program for predicting the state of the coating film according to this disclosure is a program that causes a computer to execute the computational grid creation step S22, the Brownian motion calculation step S24 and / or the particle terminal velocity calculation step S25, the solvent volatilization amount calculation step S28 and the solvent transfer calculation step S29 of the above steps. The analysis program may also be configured to cause the computer to execute the steps of other steps in addition to the above steps. Specifically, for example, the analysis program may be configured to execute each step of the drying step S2 following each step of the coating step S1, or it may be configured to execute only the drying step S2 independently. This analysis program is stored in, for example, a storage unit 120 and can be executed by a processor 130. Furthermore, the analysis program is not limited to being stored in the storage unit 120, but can also be recorded on various well-known computer-readable recording media such as optical discs or magnetic tape media. Then, by attaching such a recording medium to the reading unit 160 and reading the analysis program, the program can be executed. [Examples]

[0095] The following describes the specific experiments conducted and the comparison between the actual experimental results and the calculation results obtained using the prediction method described herein.

[0096] An engine piston was used as the base material, and the following materials were used as the paint. The input information used for the calculations is shown in Tables 1 and 2. A photograph of the top surface of the piston is shown in Figure 9. • Resin binder: Silicone-based resin • Hollow particles: Ceramic hollow particles • Nanoparticles: Silica nanoparticles • Solvent: Hydrocarbon solvent A: Alcohol solvent B = α:β mixed solvent, or low boiling point hydrocarbon solvent C: Alcohol solvent B = α:β mixed solvent A wet coating was formed on the top surface of a piston using a spray gun while rotating it, and a dry coating was obtained by drying it in a 120°C heating oven for 3 hours. The thickness (μm), surface roughness (Ra), and solid content concentration (%) of the obtained dry coating were measured. The thickness was measured using an electromagnetic / eddy current thickness gauge, and the average value of the measurement results at multiple points was calculated. The surface roughness Ra of the coating film was measured using a contact roughness meter in accordance with JIS B0633. The solid content concentration was calculated in accordance with JIS K 5601, by measuring the weight of the wet coating film and the weight of the coating film after curing using an electronic balance.

[0097] The film thickness (μm), surface roughness (Ra), and solid content concentration (%) of the dry coating were calculated using the prediction method described herein under the same conditions, and these values ​​were compared with experimental values.

[0098] Figure 10 shows a comparison of experimentally measured and calculated results for the film thickness (μm) of the dry coating. The letters on the horizontal axis in Figure 10 correspond to the positions on the piston top surface in Figure 9. The results demonstrate a correlation between the calculated and measured values.

[0099] Figure 11 shows a comparison of experimentally measured surface roughness (Ra) results and calculated results. A strong correlation was observed between the calculated and measured values.

[0100] Figure 12 shows experimental and calculated data comparing the change in solid content concentration when using a mixed solvent of hydrocarbon solvent A and alcohol solvent B (α:β), and when using a mixed solvent of low-boiling-point hydrocarbon solvent C and alcohol solvent B (α:β). A strong correlation was observed between the calculated and experimental values.

[0101] Figure 13 shows experimental results regarding the relationship between particulate matter content in the coating film and surface roughness. As shown, when the particulate matter content in the coating film exceeds 30 vol%, the surface roughness increases. Converted to the content in the paint, the problem of surface roughness may become significant when it exceeds approximately 15 vol. [Industrial applicability]

[0102] This disclosure is extremely useful because it can improve the accuracy of analysis when dealing with coatings formed by paints containing particulate components, in a method for predicting the state of a coating, a prediction device, a prediction program, and a recording medium. [Explanation of Symbols]

[0103] 10 Base material 20 paint 21 Solvent 22 Hollow particles (particulate component) 100 Coating film state prediction device 130 Processor (Arithmetic Unit) 131 Wet coating information calculation unit 132 Computational grid formation part 133 Particle Coordinate Calculation Unit 134 Volatility calculation unit 135 Dry coating information calculation unit 170 Recording media S1 Coating process S2 Drying process S11 Setting of coating conditions S12 Numerical Analysis Process S13 Wet coating information calculation process S14 Wet coating information output process S21 Drying condition setting process S22 Computational grid creation process S23 Porosity calculation process S24 Brownian motion calculation process S25 Particle terminal velocity calculation process S26 Duplicate correction process S27 Porosity calculation process S28 Solvent Volatilization Calculation Process S29 Solvent transfer calculation process S30 Film thickness renewal process S31 Termination Decision Process S32 Dry coating information calculation process S33 Dry coating information output process

Claims

1. A method for predicting the state of a dry coating film after drying using computer simulation, In a drying model in which a wet coating film formed by applying a paint containing particulate components and a solvent to a substrate surface is dried to obtain a dry coating film, The steps include dividing the computational domain of the wet coating into multiple computational grids, The steps include: performing a calculation of the movement of the particulate components in the paint; The solvent volatilizes from the top surface of the computational grid located in the outermost layer, and the concentration of the solvent decreases as it moves from the computational grid on the substrate side to the computational grid on the surface side. The diffusion coefficient of the solvent, the volatilization rate, and, if the solvent is a mixture of multiple solvents, the interaction coefficient of each solvent in the mixture are used as input information to perform calculations of the volatilization flux using the diffusion coefficient of the solvent, and the amount of volatilization using the product of the volatilization rate, the area of ​​the top surface of the computational grid located in the outermost layer, the concentration of the solvent, and the interaction coefficient of each solvent in the mixture, wherein the area is determined based on the coordinates of the particulate components obtained by the calculation of the movement of the particulate components. The steps include performing calculations of the diffusion state and the amount of volatilization of the solvent. A method for predicting the state of a coating film, characterized by the following features.

2. In claim 1, The aforementioned area is obtained by subtracting the sum of the areas occupied on the upper surface by the particulate components that protrude from the upper surface of the computational grid located in the outermost layer. A method for predicting the state of a coating film, characterized by the following features.

3. In a coating model in which a coating containing the particulate component and the solvent is applied to the surface of a substrate to form the wet coating film, The method includes a step of setting coating conditions and performing a fluid analysis to calculate the coating state of the paint applied to the substrate surface from the coating device, and using the film thickness of the wet coating and the solid content of the coated paint obtained in this step as input information for performing the prediction method described in claim 1. A method for predicting the state of a coating film, characterized by the following features.

4. In claim 1, A method for predicting the state of a coating film, characterized in that the movement of the particulate components is derived using Stokes' equation for deriving the terminal velocity of the particles.

5. In claim 1, A method for predicting the state of a coating film, characterized by using equation (1) below as the equation used to calculate the amount of volatilization, and equation (2) below as the equation used to calculate the volatilization flux. [Math 1] (In equation (1), n ​​is an integer greater than or equal to 1, indicating that n types of solvents, from the first solvent to the nth solvent, are used. Jn is the amount of solvent n volatilized in the computational grid located at the outermost layer, Rn is the volatilization rate when solvent n is a single solvent, S is the area of ​​the upper surface of the computational grid located at the outermost layer, Δt is the time step, Cn is the molar concentration of solvent n, and αn is the interaction coefficient of solvent n in the mixed solvent when the solvents are mixed solvents. In equation (2), J'n is the amount of solvent n transferred between layers, Dn is the diffusion coefficient of solvent n, x is the position in the z-axis direction in the computational grid, and Cn is the molar concentration of solvent n.)

6. In claim 5, The steps include updating the volume of each computational grid, the coordinate values ​​of the particulate components, and the concentration of the paint based on the diffusion state and volatilization amount of the solvent derived using the above formulas (1) and (2), The process involves repeatedly performing each of the above steps until a specified time step is reached, and then outputting one or more of the following: the film thickness as the z-axis length of the entire calculation domain, the surface roughness calculated on the upper surface of the calculation grid located at the outermost layer, and the amount of residual solvent in the calculation domain. A method for predicting the state of a coating film, characterized by the following features.

7. In the calculation of the movement of the particulate components, if it is detected that the diameter of one particulate component is within the diameter range of another particulate component based on the coordinates and diameters of the particulate components, it is determined that the two particulate components are overlapping, the interparticle distance is calculated using the coordinates of the two particulate components, and the coordinates of each of the two particulate components are shifted by a distance calculated by the product of a random number, a coefficient, and the ratio of the overlapping distance to the interparticle distance, along a straight line connecting the centers of the two particulate components. The method for predicting the state of a coating film according to feature 1.

8. In claim 1, The content of the particulate component in the dry coating film exceeds 30 vol% A method for predicting the state of a coating film, characterized by the following features.

9. A device for predicting the state of a dry coating film after drying using computer simulation, In a drying model in which a wet coating film formed by applying a paint containing particulate components and a solvent to the surface of a substrate is dried to obtain a dry coating film, A computational grid forming unit that divides the computational area of ​​the wet coating into a plurality of computational grids, A particle coordinate calculation unit that performs calculations of the movement of the particulate components in the paint, The solvent volatilizes from the top surface of the computational grid located at the outermost layer, and the concentration of the solvent decreases as it moves from the computational grid on the substrate side to the computational grid on the surface side. The diffusion coefficient of the solvent, the volatilization rate, and, if the solvent is a mixture of multiple solvents, the interaction coefficient of each solvent in the mixture are used as input information to perform calculations of the volatilization flux using the diffusion coefficient of the solvent, and calculations of the amount of volatilization using the product of the volatilization rate, the area of ​​the top surface of the computational grid located at the outermost layer, the concentration of the solvent, and the interaction coefficient of each solvent in the mixture, with the area being determined based on the coordinates of the particulate components obtained by the calculation of the movement of the particulate components. The volatilization amount calculation unit performs calculations of the diffusion state and the amount of volatilization of the solvent. A device for predicting the state of a coating film, characterized by the following features.

10. A program for predicting the state of a dry coating film after drying using computer simulation, On the computer, Using a drying model in which a wet coating film formed by applying a paint containing particulate components and a solvent to the surface of a substrate is dried to obtain a dry coating film, The computational domain of the wet coating is divided into multiple computational grids, The calculation of the movement of the particulate component in the paint is performed. The solvent is assumed to volatilize from the top surface of the computational grid located at the outermost layer, and the concentration of the solvent decreases as it moves from the computational grid on the substrate side to the computational grid on the surface side. The diffusion coefficient of the solvent, the volatilization rate, and, if the solvent is a mixture of multiple solvents, the interaction coefficients of each solvent in the mixture are used as input information. The volatilization flux is calculated using the diffusion coefficient of the solvent, and the amount of volatilization is calculated using the product of the volatilization rate, the area of ​​the top surface of the computational grid located at the outermost layer, the concentration of the solvent, and the interaction coefficients of each solvent in the mixture. The area is determined based on the coordinates of the particulate components obtained by the calculation of the movement of the particulate components. The diffusion state and amount of volatilization of the solvent are then calculated. A program for predicting the state of a coating film, characterized by the following features.

11. A computer-readable recording medium that stores a program for predicting the state of a coating film as described in claim 10.

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