JP2009074972A - Film forming process analyzer, its analysis method and memory medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an analyzer for spraying process that can analyze flatting/solidification phenomena of spraying particles unable to easily analyze by conventional Euler method and can treat deforming behavior of multiphase material and also even pore forming process induced by incorporating surrounding gas phase that have been unanalyzable until now. <P>SOLUTION: The analyzer, which is used for processes to form a film on a substrate by applying a thermal/kinetic energy to spraying particles, comprises an input section to input properties of spraying particles, shape and velocity of spraying particles prior to colliding the substrate, a model preparing section to exchange the spraying particles into a plurality of model particles having the same total mass with the spraying particles, a computing section to solve a dynamic equation that is expressed by a coordinate system fixed to the model particles with respect to the movement of each model particle, and an output section to represent a deforming behavior of the spraying particles from the resulting data of velocity, pressure, etc. of each model particle. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to a film forming process analysis apparatus, an analysis method thereof, and a storage medium that can handle the deformation behavior of a multiphase material and the formation process of pores by taking in a surrounding gas phase.

  The thermal spraying method that forms a film by depositing thermal spray particles on a substrate by heating and spraying is a method of wear resistance, corrosion resistance, and heat resistance on members such as energy equipment, transportation equipment, semiconductor related equipment, and building structural materials. It is used for various purposes such as imparting sex.

  The characteristics of the coating formed by the thermal spraying method (porosity, residual stress, corrosion resistance, heat resistance, electrical conductivity, etc.) vary greatly depending on the flat behavior of the individual thermal spray particles and the state of stacking of the thermal spray particles. Techniques for analyzing these phenomena are important in practice.

  Until now, many attempts have been made to analyze the particle flatness of the thermal spraying method experimentally and numerically.

  For example, as a classic analysis model, the Madjeski model in which the shape after flattening of a particle is approximated to a disk shape is well known.

ここで、ζｍは、初期の粒子径と扁平後のディスクの幅との比、ReはReynolds数、WeはWeber数である。 According to this model, the shape of the particles after flattening is given by the following equation (1).

Here, ζm is the ratio between the initial particle diameter and the width of the disk after flattening, Re is the Reynolds number, and We is the Weber number.

  This model has been reported to be able to express the actual behavior relatively well, and various corrections have been made based on the material and process based on this model.

  In addition, many analyzes using numerical fluid analysis methods have been made, and many reports have been made centering on methods combining the SOLA method, which is an analysis scheme for incompressible fluids, and the VOF function representing the existence rate of fluids. ing.

  In the conventional numerical fluid analysis method, a method is used in which a region occupied by the fluid is divided into grids, and variable values such as velocity and pressure at each grid position are analyzed at each time step.

  However, for example, in the numerical analysis method using a grid based on the Euler method, it is difficult to analyze a phenomenon in which initial particles such as the flattening behavior of a sprayed droplet are greatly deformed or scattered (so-called splash phenomenon). It was.

  For this reason, the ALE (Arbitrary Lagrangian Eulerian) method, which moves the lattice with the deformation of the thermal spray particles, and the Adaptive Mesh method, which re-divides the lattice sequentially, are used. In order to obtain this, many trials and errors are required, and a general-purpose calculation method that can be used by general process engineers has not yet been found.

  In addition, when handling a free surface, such as the flat behavior of a target droplet, a problem has been pointed out that the surface is gradually blurred due to problems such as numerical diffusion.

  On the other hand, as an analysis method that does not use a lattice, a particle method is being developed in which a fluid is replaced with a plurality of equivalent model particles and the flow is analyzed by the interaction of the model particles.

  For example, the MPS method (Moving Particle Semi-Implicit Method) is attracting attention as a calculation method for non-statistically expressing the fluid flow phenomenon using the particle method (Japanese Patent Laid-Open Nos. 7-334484 and 2002-137272). ).

ここで、ｕは流速、Ｐは圧力、ρは密度、νは動粘性係数、fは外力、Dはラグランジュ微分を示す。 The MPS method uses a governing equation such as the following equation (2) that describes the flow of an incompressible fluid.

Here, u is a flow velocity, P is a pressure, ρ is a density, ν is a kinematic viscosity coefficient, f is an external force, and D is a Lagrange derivative.

Except for the pressure term of the first term on the right side of the above equation (2), the pressure gradient generated from the temporary velocity and position of the model particle obtained by this is implicitly solved separately from the Poisson equation for pressure. The time is developed while correcting the speed and position of the model particle.
JP-A-7-334484 JP 2002-137272 A

  Since such particle method belongs to (1) Lagrangian method, calculation of convection term which is a problem in discretization of governing equation of general Euler method is unnecessary, and problems of numerical diffusion and numerical vibration occur. (2) It is not necessary to consider the distortion of the lattice accompanying deformation as in the lattice method, and it is possible to easily reproduce phenomena such as droplet breakup and scattering, (3) Model particles Since the free surface is represented by the presence or absence, there is an advantage that there is no problem that the surface shape blurs as the calculation progresses.

  However, there is no example of applying this particle method to the flattening and solidification behavior of particles by thermal spraying, and problems such as modeling of actual materials remain to express the thermal spraying process.

  As mentioned above, in the analysis of the flattening and solidification process of spray particles, the conventional analysis method based on the grid division based on the Euler method is a failure of calculation due to large deformation of the object, difficulty in handling a free surface, etc. Therefore, it is necessary to establish a general-purpose analysis method for actual materials.

  Therefore, the present invention analyzes the flattening / solidification phenomenon of thermal spray particles, which could not be easily analyzed by the conventional Euler method, and the deformation behavior of the multiphase material, which could not be analyzed before, and the surrounding gas phase. An object of the present invention is to provide a film formation process analysis apparatus, analysis method, and storage medium that can handle the formation process of pores due to the incorporation of.

  In order to achieve the above-described object, the film formation process analysis apparatus according to claim 1 is a process analysis apparatus for forming a film on a substrate by applying thermal and kinetic energy to the spray particles, A data input unit that inputs the properties of the sprayed particles, the shape of the sprayed particles before collision with the substrate, and the velocity, a model creation unit that replaces the sprayed particles with multiple model particles whose total mass is equal to the sprayed particles, and these individual models A calculation unit that solves the equation of motion described by a coordinate system in which the particle motion is fixed to the model particle, and an output unit that expresses the deformation behavior of the sprayed particle from the obtained data such as velocity and pressure of the model particle. It is characterized by that.

  According to a seventh aspect of the present invention, there is provided a thermal spraying apparatus based on the analysis result of the flat behavior of particles by the analytical apparatus, in addition to the above-described analytical apparatus for the film forming process. A feedback circuit for controlling process conditions such as speed is provided.

  The method for analyzing a film forming process according to claim 8 is a process for forming a film on a substrate by applying thermal and kinetic energy to the sprayed particles. The step of inputting the shape and velocity of the previous sprayed particles and the calculation unit replaced the sprayed particles with a plurality of model particles whose sum of mass is equal to the sprayed particles, and fixed the motion of these individual model particles to the model particles. The step of solving the equation of motion described by the coordinate system and the step of expressing the deformation behavior of the sprayed particles from the obtained data such as the velocity and pressure of each model particle are provided in the output unit.

  Furthermore, the storage medium according to claim 10 records each step used in the analysis method.

  According to the present invention, it is possible to stably solve the flattening / solidification phenomenon of thermal spray particles that could not be easily analyzed by the Euler method using a conventional mesh. In addition, it is possible to handle the deformation behavior of multiphase materials that could not be analyzed until now and the formation process of pores by taking in the surrounding gas phase, and realize an analysis device for thermal spraying process that has never existed before Is possible.

  DESCRIPTION OF EMBODIMENTS Hereinafter, an analysis apparatus, an analysis method, a recording medium, and a thermal spray apparatus according to an embodiment of the present invention will be described with reference to the drawings.

  FIG. 1 shows an exemplary embodiment of the present invention. The film formation process analysis apparatus 40 of the present invention mainly includes a data input unit 1, a model creation unit 2, a calculation unit 3, and an output unit 4.

  First of all, the data input unit 1 determines the shape of the sprayed particles and the base material, the film forming process conditions such as the speed and temperature of the sprayed particles before the base material collision, the density, viscosity coefficient, surface tension coefficient, specific heat, heat of various materials. This is a site where material properties such as conductivity, interfacial thermal resistance, and latent heat of solidification are input.

  Although it is possible to input values for various material property values for each analysis, it is generally more efficient to provide a data storage unit for storing data in the input unit.

  Particle velocity and temperature can be easily measured at the time of thermal spraying due to recent advances in sensor technology, so if these measurement data are used as input values for the film formation process, thermal spraying is possible. Sometimes analysis can be done online.

  Next, the model creation unit 2 models particles and substrate shapes using model particles based on the shape data input by the data input unit 1.

  FIG. 2 shows an example in which spherical spray particles and a base material are modeled by model particles 7 drawn with dots. In the figure, 5 indicates spray particles, 6 indicates a base material, and dots indicate model particles 7.

  In the subsequent calculation, in order to give a constraint condition due to the incompressibility of the fluid, the analysis proceeds to keep the number density (number of particles per unit area) of the model particles 7 constant. At least in the same material, it is necessary to arrange so that the density is constant.

  FIGS. 3A and 3B show a method for arranging the model particles 7 for this purpose.

  In FIG. 3A, model particles 7 are arranged on lattice points of orthogonal lattices, and this arrangement is the easiest to model. However, since such an arrangement is not a close-packed structure, when an impact force such as a collision / flattening phenomenon of thermal spray particles is applied to the material, the pressure fluctuation due to the analysis method increases, resulting in a result. As a result, the analysis error may increase.

  In such a case, it is possible to take measures to reduce the pressure fluctuation by using a staggered arrangement as shown in FIG.

  The calculation unit 3 performs flow analysis and heat conduction / solidification analysis using the particle method, and from the obtained results, the deformation shape of the particles, solidification rate, residual stress, porosity inside the film, adhesion strength, etc. Estimation is performed.

  The particle method algorithm is not limited to a specific method as long as it is an analysis method based on a meshless Lagrangian method. However, from the viewpoint of versatility, stability, and analysis accuracy of the analysis, Koshizuka mentioned above. The MPS method (Moving Particle Semi-Implicit Method) developed by J. et al. Is suitable.

  FIG. 4 shows a calculation flow of flow analysis by the MPS method.

ここで、ｕは流速、Ｐは圧力、ρは密度、νは動粘性係数、ｆは外力、Ｄはラグランジュ微分を示す。 When the flow analysis is started in step S1, various calculation conditions are input in step S2, and the initial arrangement, initial velocity, and pressure of the particles are set in step S3. Then, in step S4, the following formula (3) is set. In the governing equation, the viscosity term of the second term on the right side and the external force term of the third term (mainly the gravity term and the surface tension term) are calculated.

Here, u is a flow velocity, P is a pressure, ρ is a density, ν is a kinematic viscosity coefficient, f is an external force, and D is a Lagrangian derivative.

ここで、rは着目する粒子とそれ以外の粒子との距離である。MPS法によるラプラシアンモデルを用いると、粘性項における速度のラプラシアンは、次式（５）のように計算される。

FIG. 5 shows the positional relationship between the target model particle 19 and the adjacent model particle 20. The range where the interaction between the central target model particle 19 and the adjacent model particle 20 works is denoted by r _e. Then, a weighting function w like the following equation (4) is introduced.

Here, r is the distance between the focused particle and the other particles. Using the Laplacian model by the MPS method, the Laplacian of the velocity in the viscosity term is calculated as in the following equation (5).

Here, d is the number of dimensions, n ₀ is the initial particle number density, and λ is a constant for matching the distribution of the physical quantity distribution with the analytical solution.

  In step S5, the temporary position of the particle is updated by the viscosity term and the external force term by these methods.

ここで、ｋは計算ステップ、Δｔは時間刻み、ρは密度を表す。 In the particle coordinates updated by the viscosity term and the external force term in step S6, the condition of constant particle number density, which is an incompressible condition, is not satisfied. Therefore, the provisional particle number density n * and the number of particles in the initial arrangement are used. Consider the Poisson equation for pressure with the difference from density n ₀ as the source term.

Here, k is a calculation step, Δt is a time step, and ρ is a density.

  In step S7, the Laplacian of the pressure on the left side is described by the Laplacian model by the MPS method as described above, and the pressure field is updated by implicitly solving the Poisson equation. Then, the velocity and position of the particle are corrected from the gradient of the pressure field, and the first calculation step of the flow analysis is completed in step S8.

  Furthermore, in step S9, the time is updated, the process returns to before step S4, the calculation is repeated twice or more, and finally, in step S10, the flow analysis is completed by repeating a predetermined number of times.

ここで、Ｔは温度、ｋは熱伝導率、Ｃｐは比熱、Ｑは熱源である。 On the other hand, in the heat conduction analysis, a heat conduction equation such as the following equation (7) is solved by an interaction model by the MPS method.

Here, T is temperature, k is thermal conductivity, Cp is specific heat, and Q is a heat source.

  As for the latent heat of solidification, it is incorporated into the heat conduction equation by changing the enthalpy (so-called enthalpy method) or by correcting the specific heat (so-called specific heat conversion method), and by setting the solid fraction for each model particle, Can be handled by the particle method.

  Moreover, in the calculation part 3 in FIG. 1, from the result of the coupled analysis of the flow analysis and the heat conduction / solidification analysis as described above, the particle width after solidification is calculated from the coordinate value of the particles attached on the substrate. Estimate shape data such as thickness, estimate the solidification rate from the time when the solid phase ratio is 100% for all particles, or introduce a linear spring between the particles immediately after solidification and the surrounding solid phase particles Further, the value of the residual stress can be estimated from the energy accumulated in the spring after further deformation.

  Further, the output unit 4 in FIG. 1 outputs data of time-series model particle positions and temperature changes and various predicted values.

  FIG. 6 shows, as an example of analysis, the state of flattening and solidification when the sprayed particles 5 are heated to a temperature just above the melting point and collide with the base material 6, and the model particles 7 drawn with dots are plotted in time steps. This is shown as a change in density.

  If the particle method is used in this way, it is possible to analyze the flattening behavior of the thermal sprayed particle 5 without breaking the calculation, and the spread after deformation of the particle by this method has been widely used until now. It has been clarified that the model agrees well quantitatively with an error of about 30%.

  FIGS. 7A and 7B show modeling of a multiphase material in which a high melting point phase is treated as a rigid body. FIG. 7B shows the coordinates of particles in FIG. Is corrected.

  In the present embodiment, a method for modeling the flat behavior of the thermal spray particles 5 composed of at least two phases having different chemical compositions (melting points) will be described. Incidentally, 21 is a low melting point model particle, and 22 is a high melting point model particle.

  The simplest handling of such a system is to treat the phase model particle 22 on the high melting point side as a rigid body in the flow analysis.

  Therefore, after all the model particles are equally analyzed, the relative positional relationship of the high melting point phase model particles 22 from the centroid of the high melting point phase does not change. As shown in FIG. 7B, the coordinates of the particles are corrected so that only rotational movement around the center of gravity is allowed.

  By such a method, it is possible to analyze the flattening and solidification behavior of the model particles 21 and 22 composed of phases having different melting points. As the high melting point phase, compounds such as tungsten carbide and chromium carbide, low melting point phase If chrome, cobalt, nickel, etc. are targeted, analysis of cermet materials widely used as thermal spraying materials for wear resistance can be realized.

  FIG. 8 shows a state in which the gas phase model particles 26 are entrained in the model particles 25 of the sprayed particles 5 on the base material 27 during the thermal spraying, and pores are generated. When air is analyzed together, the situation of pores formed at the interface is schematically shown.

  As described above, when the particle method is used, it is possible to estimate the porosity and the distribution of the pores of the coating by obtaining the region where the sprayed particles 26 modeled of air remain in the coating.

  Since there is a large density difference between spray particles and air, a calculation algorithm for a two-stage pressure field that calculates the behavior of only the model particles 25 of the spray particles that are heavy particles and then calculates the pressure of the model particles 26 of air. If is used, stable calculation is possible.

  In addition, the calculation of the particle method can obtain the arrangement of the model particles at the interface. However, if an appropriate spring element is assumed between the model particles of the thermal spray particles and the substrate, the adhesion strength of the thermal spray coating can be improved. Estimation is possible.

  FIG. 9 shows an intelligent thermal spraying apparatus equipped with an on-line thermal spray particle velocity / temperature measurement apparatus at the time of thermal spraying, a thermal spray particle deformation analysis apparatus of the present invention, and a feedback circuit to the thermal spraying apparatus of the analysis result. The overall configuration is shown.

  In FIG. 9, reference numeral 28 denotes a welding robot provided with a thermal spray gun 29, and the coordinate position and the like are controlled by the robot control device 38. In addition, the spray gun 29 is controlled by the spray gun control device 39 in terms of the conditions of the spray frame 30 and the flying spray particles 31 included in the spray frame 30, and the flying spray particles 31 in the spray frame 30 are placed on the surface of the substrate 32. Thermally spray on.

  Reference numeral 34 denotes a camera that employs a CCD or the like as an image sensor, and images the thermal spray frame 30 and the flying thermal spray particles 31. The captured image is input to the image analysis device 35 and analyzed.

  The analysis result of the image analysis device 35 and the analysis result of the flattening / solidification analysis device 36 are accumulated in the thermal spray construction data accumulation unit 37, respectively. The data stored in the thermal spray construction data storage unit 37 is fed back to the robot controller 38 and the spray gun controller 39.

  Radiation thermometers are often used for on-line thermal spray particle temperature measurement. On the other hand, particle velocity can be measured by measuring the locus of radiated light emitted from individual particles by image analysis, measuring from the time variation of the spectrum of radiated light emitted from the measurement region, Although it is well known to measure light by irradiating light and capturing the trajectory of reflected light coming out of the particle, as input data to the analysis device of the present invention, any particle velocity measurement method is used. Also good.

  Compare the analysis results by the analysis device with, for example, the deformation data of the sprayed particles in the best coating formation, and based on the difference between them, process parameters such as spray gun output, gas flow rate, spray distance, gun traverse speed, etc. By providing a feedback mechanism that controls the thermal spraying, it is possible to achieve an unprecedented intelligent spraying apparatus.

  It is possible to stably solve the flattening and solidification phenomena of spray particles that could not be easily analyzed by the conventional Euler method, and the deformation behavior of multiphase materials, which could not be analyzed before, and the surrounding gas phase It can be applied to any application where it is indispensable to handle the process of pore formation by uptake.

It is a typical example of the flattening / solidification analyzing apparatus for thermal spray particles of the present invention. It is an example of modeling by the particle method of a thermal spray particle and a base material. It is an example of the initial arrangement of model particles. It is the calculation flow of the flow analysis by MPS method. It is an example which shows the positional relationship of an attention model particle and an adjacent model particle. It is an example of the flattening / solidification analysis of a thermal spray particle by the analysis device of the present invention. It is an example of modeling of a multiphase material (handling of a high melting point phase as a rigid body). It is an example which shows generation | occurrence | production of the pore by entrainment of the model particle | grains of a gas phase. It is an Example of the thermal spraying apparatus which has an online measurement mechanism and a process feedback mechanism.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 ... Data input part, 2 ... Model preparation part, 3 ... Calculation part, 4 ... Output part, 5 ... Sprayed particle, 6 ... Base material, 7 ... Initial arrangement of model particle using orthogonal lattice, 8 ... Houndstooth lattice 19 ... model particle of interest, 20 ... model particle of interest, 20 ... adjacent model particle, 21 ... low melting point phase model particle, 22 ... high melting point phase model particle, 23 ... time step 1, 24 ... time step 2, 25 ... sprayed particle model particles, 26 ... ambient gas phase model particles, 27 ... substrate, 28 ... sprayed robot, 29 ... sprayed gun, 30 ... sprayed frame, 31 ... flying sprayed particle, 32 ... substrate, 33 ... coating, 34 DESCRIPTION OF SYMBOLS ... CCD camera, 35 ... Image analysis device, 36 ... Flatness / solidification analysis device, 37 ... Thermal spraying construction data storage unit, 38 ... Robot control device, 39 ... Thermal spray gun control device, S1 ... Analysis step 1, S2 ... Analysis step 2 , S3 ... Analysis Step 3, S4 ... analysis step 4, S5 ... analysis step 5, S6 ... analysis step 6, S7 ... analysis step 7, S8 ... analysis step 8, S9 ... analysis step 9, S10 ... analysis step 10

Claims (10)

An analysis device for the process of applying thermal and kinetic energy to thermal spray particles to form a film on a substrate,
A data input unit for inputting the physical properties of the sprayed particles, the shape of the sprayed particles before the base material collision, and the velocity,
A model creating unit that replaces the spray particles with a plurality of model particles having a total mass equal to that of the spray particles;
An arithmetic unit for solving a motion equation described by a coordinate system in which the motion of each individual model particle is fixed to the model particle;
An apparatus for analyzing a film forming process, comprising: an output unit that represents deformation behavior of the sprayed particles from data such as velocity and pressure of each of the obtained model particles. The input unit further inputs the solidification latent heat data of the sprayed particles and the initial temperature distribution of the sprayed particles before the substrate collision,
2. The film formation process analyzing apparatus according to claim 1, wherein the calculation unit analyzes a temperature distribution and a solidification region by solving a heat conduction equation sequentially in addition to an equation of motion of the model particle. The said calculating part predicts the residual stress which generate | occur | produces in a membrane | film | coat by the displacement amount after the solidification of the said model particle in addition to the equation of motion and heat conduction equation of the said model particle. Deposition process analysis equipment. Further, when analyzing the deformation behavior of the thermal spray particles having a plurality of phases having different chemical compositions, the calculation unit is configured such that the model particle representing the high melting point phase has the center of gravity of the high melting point phase as an origin. The film deposition process analyzing apparatus according to any one of claims 1 to 3, wherein the position of the model particle is corrected so that the relative positional relationship between the particles does not change. The computing unit is further formed at the interface at the time of film formation by using the model particles expressing the gas phase existing in the periphery during the film forming process by model particles and expressing any irregularities on the substrate. The film formation process analyzing apparatus according to any one of claims 1 to 4, wherein the shape and amount of pores are estimated. A temperature measurement unit that measures the temperature of the sprayed particles at the time of thermal spraying with a radiation thermometer, and the velocity of the sprayed particles, the time change of the bright spot coordinates of the emitted light emitted by the individual sprayed particles, or the time of the spectrum of the emitted light A film forming process according to any one of claims 1 to 5, further comprising: a speed measuring unit that measures a change or a time change of a bright spot coordinate due to reflected light when irradiated with a laser. Analysis device. In addition to the film formation process analysis apparatus according to claim 6, process conditions such as a spray gun output, a gas flow rate, a spray distance, and a gun traverse speed are controlled based on the analysis result of the flattening behavior of particles by the analysis apparatus. A thermal spraying device comprising a feedback circuit for In the process of forming a film on a substrate by applying thermal and kinetic energy to the spray particles,
An input unit that inputs the physical properties of the sprayed particles, the shape of the sprayed particles before the base material collision, and the speed;
A calculation unit replacing the sprayed particles with a plurality of model particles having a total mass equal to the sprayed particles, and solving a motion equation described by a coordinate system in which the motions of the individual model particles are fixed to the model particles; ,
And a step of expressing the deformation behavior of the sprayed particles from the obtained data such as velocity and pressure of each model particle. The said calculating part has a step which estimates contact | adhesion intensity | strength from the contact | adherence area of a film | membrane based on the analytical value of the form and quantity of a pore formed in an interface at the time of film-forming. Analysis method of film formation process.   A storage medium in which each step used in the analysis method according to claim 8 or 9 is recorded.

Images