JP2008171145A - Air pocket simulation method and simulation program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To more precisely analyze behavior of particles in fluid, to obtain simulation result approximate to actual situations. <P>SOLUTION: N air bubble particles are generated inside/outside a work (S4). The moving amount ΔZ of the air bubble particles is computed based on the balance of forces acting on the air bubble particles (S5). When there is no interference with the work, the air bubble particles are moved, and when there is interference, the air bubble particles are moved along the member surface of the work (S7). Furthermore, when there is a collision between the particles, move by the collision between the particles is calculated, and the speed and direction after the collision are computed (S11). After finishing the calculation, the process proceeds to a post process (S14). The locus of the air bubble particles and the deposition state inside the work are visualized. The volume of an air pocket is computed from the deposition state of the air bubble particles. Thereby, behavior of the particles in fluid is more precisely analyzed, to obtain the simulation result approximate to actual situations. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to an air pool simulation method and a simulation program for simulating an air pool generated in a workpiece when a dipping process is performed.

  In general, in the work dipping process in electrodeposition coating or plating, it is important not to cause air pockets (air pockets) in the work in order to form a uniform coating film or plating film. This air pocket is a recess that can be formed when a workpiece having a complicated shape is immersed, for example, if it is a vehicle body such as an automobile, air remains in a space such as a recess such as the inner surface of the hood, the inner surface of the roof, or the lower surface of the floor. If this air pocket is generated, poor coating and poor plating will occur.

  Therefore, a method for simulating a state in which a workpiece is immersed using a computer and predicting the occurrence of air pockets has been proposed. As one of the methods, as disclosed in Patent Document 1, immersion is performed. There is a technique for predicting the generation of air pockets from bubble particles accumulated inside a workpiece by analyzing the process in which the bubble bubbles rise in the immersion liquid, assuming that air bubbles in the liquid are bubble particles.

As shown in FIG. 18, the technique of Patent Document 1 generates bubble particles Bk from below or around the work Wk and calculates the trajectory of the bubble particles. When it hits the wall, it further rises along the bottom of the wall surface, and as shown in FIG. 19, it stays in the convex region above the workpiece Wk and becomes stagnant particles Bkt. Finally, the position of the stagnant particle Bkt becomes the position where the air pocket is generated, and the size of the air pocket is simply displayed by the density of the stagnant particle Bk.
JP 2006-116385 A

  However, the technique of Patent Document 1 focuses on reducing the calculation load and quickly grasping the position where the air pocket is generated, such as the influence of various forces acting on the bubble particles and the collision between the bubble particles. The analysis is simplified by omitting the influence of mutual interference, and finally the location where the air pocket is generated is highlighted by deformation and coloring of stagnant particles. For this reason, it is difficult to accurately predict the size and shape of the air pocket, and the development of more precise analysis remains as an issue.

  The present invention has been made in view of the above circumstances, and provides a simulation method and simulation program for an air reservoir that can analyze the behavior of particles in a fluid more precisely and develop a simulation that closely approximates the actual situation. It is intended to provide.

  In order to achieve the above object, the air pool simulation method according to the present invention generates particles that simulate air bubbles in an analysis region including a virtual work in which a work to be dipped is represented by shape data, In the simulation method of the air pool that simulates the air pool by calculating the behavior of the particle in the fluid imitating the immersion liquid in which the workpiece is immersed, the particle has an arbitrary shape and physical property, Based on the relationship between the forces acting on the particles, the step of calculating the movement trajectory accompanied by the collision between the particles and the particles stopped moving due to interference with the virtual work or other particles are deposited without coalescing each other. And a step of determining the deposited particle group as an air pocket.

  The simulation program of an air pool according to the present invention generates particles that simulate air bubbles in an analysis region including a simulated workpiece in which a workpiece to be dipped is represented by shape data, and the workpiece is immersed. A computer-executable air pool simulation program that calculates the behavior of the particles in a fluid simulating a liquid and simulates the air pool, wherein the particles have an arbitrary shape and physical properties, and the particles in the fluid Based on the relationship between the forces acting on the particles, the step of calculating the movement trajectory accompanied by the collision of the particles and the particles stopped moving due to the interference with the simulated work or other particles without being combined with each other, And a step of determining the deposited particle group as an air pocket.

  According to the present invention, the behavior of particles in a fluid can be analyzed more precisely, and the actual situation can be developed into a simulation that closely approximates the actual situation.

  Embodiments of the present invention will be described below with reference to the drawings. 1 to 9 relate to a first embodiment of the present invention, FIG. 1 is a basic configuration diagram of a simulation apparatus, FIG. 2 is a schematic explanatory view of a painting line of a vehicle body, and FIG. 3 is an explanatory view showing a generation position of bubble particles. FIG. 4 is an explanatory view showing the state of accumulation of bubble particles, FIG. 5 is an explanatory view showing the state of accumulation of bubble particles having different particle diameters, FIG. 6 is an explanatory view showing the uneven deposition of bubble particles, and FIG. FIG. 8 is an explanatory diagram showing the collision between bubble particles, and FIG. 9 is a flowchart of an air pocket simulation program.

  As shown in FIG. 1, the simulation apparatus 1 according to the present embodiment creates an air pocket (air pocket) generated in a work when an immersion process such as electrodeposition coating or plating is performed on a work such as a body shell of an automobile. To simulate. The air pocket simulation apparatus 1 is configured using a single computer such as a microcomputer or a personal computer, or a plurality of computers connected to each other via a network.

  Below, the example which comprises the simulation apparatus 1 with a single computer for convenience is demonstrated. The simulation apparatus 1 includes an arithmetic device 10, an input device 11 such as a keyboard and a mouse, a display device 12 such as a CRT and a liquid crystal display, an external storage device 13 such as a magnetic disk and an optical disk, and the like.

  The arithmetic device 10 includes an internal memory such as a CPU, a ROM and a RAM, an input / output interface, and the like, and includes a simulation program stored in an internal ROM, an external storage device 13 and an external storage medium, or a network (not shown) A simulation program loaded from the outside via the communication device is executed by the CPU, and the workpiece (object) to be analyzed instructed via the input device 11 is immersed in the immersion bath in a pseudo manner, and the object is obtained by the immersion. The air pocket generated in the simulation is simulated, and the simulation result is output to the display device 12 for display. The display device 12 may display not only the simulation result but also the simulation process.

  For example, as an application example of the simulation according to the present invention, there is a simulation in which the distribution of the electrodeposition liquid and air during the electrodeposition coating of the vehicle body is numerically analyzed to predict the occurrence of air pockets in the object to be coated. Here, the painting line of the vehicle body will be briefly described with reference to FIG.

  As shown in FIG. 2, a vehicle body body 20 of an automobile configured by joining a plurality of vehicle body panels to each other by welding or the like is transported in a substantially horizontal direction on a painting line while being mounted on a hanger of a transport device 21. The In the painting line, as a pretreatment for electrodeposition coating, the body panel is subjected to treatments such as degreasing, water washing, surface adjustment, film formation, water washing and the like.

  After these processes, the vehicle body 20 descends toward the electrodeposition tank 22 and moves substantially horizontally while being immersed in the electrodeposition liquid 23. In this state, paint is deposited on the vehicle body panel by applying a voltage to the vehicle body 20 and electrodes (not shown) in the electrodeposition tank 22. Thereafter, the vehicle body 20 is pulled up from the electrodeposition tank 22 by the transfer device 21, and the electrodeposition liquid 23 adhering to the vehicle body panel without being electrodeposited is removed by washing.

  In the simulation of air pockets in the present invention, a pseudo air bubble generated in the immersion liquid is assumed to be particles (bubble particles), and a method for simulating the generation of air pockets by analyzing the behavior of the bubble particles is developed. It is possible to predict the shape and size of the air pocket. In order to predict the shape and size of the air pocket, the air pocket simulation of the present invention takes into account the balance of forces acting on the bubble particles in the fluid simulating the immersion liquid and the collision of the bubble particles. The behavior is analyzed.

  In consideration of collisions between the bubble particles, the bubble particles in the fluid exhibit a rigid behavior under the influence of the surface tension under a predetermined condition. The physical properties as a solid having a predetermined rigidity are set without being limited to the physical properties. Furthermore, the bubble particles can have any shape such as an ellipsoid or a polyhedron as well as a sphere, and each of the plurality of bubble particles may have a different size.

  The arithmetic unit 10 generates an arbitrary number of bubble particles at an arbitrary position in a calculation area set for the workpiece, and analyzes the behavior of the bubble particles rising against gravity. Finally, an aggregate of bubble particles that stop moving and accumulate inside the members constituting the workpiece is determined as an air pocket, and the shape and size thereof are calculated.

  The behavior of the bubble particles can be basically analyzed by considering the buoyancy acting on the bubble particles and the gravity, but further conditions need to be set in order to improve the simulation accuracy. For example, the particle stiffness, the coefficient of restitution in the collision between particles, the friction coefficient of the particle surface, etc. are set, and the viscosity of the fluid, the surface tension at the boundary surface, the acting force from the fluid, the influence of other external forces other than the fluid By setting conditions in consideration of the above, it is possible to improve the simulation accuracy of the air pocket that is finally determined.

  In the present embodiment, the following conditions (1) to (4) are set in consideration of the calculation amount and calculation speed required for the analysis and the simulation accuracy.

(1) It is assumed that bubble particles are spherical rigid bodies, and deformation due to mutual collision does not occur.

(2) In the collision between the bubble particles, the coefficient of restitution is set to “0”, and the bubble particles that have collided are coupled to each other and moved. However, it is possible to separate the bubble particles from the combined state.

(3) The coefficient of friction of the bubble particle surface is set to “0”.

(4) The diameter of the bubble particles is set to a diameter equal to or larger than a set value in consideration of the influence of the surface tension in the gas-liquid two-phase flow.

  The conditions (1) and (2) mean that the bubble particles do not coalesce with each other and are deposited while maintaining their respective sizes when the movement is stopped and stopped, and the conditions of (3) Means that even if the bubble particles collide with each other, the bubble particles do not rotate and there is no energy loss. The condition of (4) is that even if there are gaps or holes in the workpiece, if the gap is narrow or the holes are too small, the air inside the workpiece will not escape due to surface tension and air pockets will be generated. By setting the bubble particle size according to the condition of (4), it is possible to overlook the occurrence of air pockets even when the gaps or holes in the workpiece are inappropriate. I can grasp without.

  The function of the simulation program using the above bubble particles can be expressed by dividing the function of the arithmetic unit 10 into an analysis region setting unit 10a, a bubble particle setting unit 10b, a particle behavior calculation unit 10c, and a post processing unit 10d. . Hereinafter, functions of each unit will be described.

  The analysis region setting unit 10a sets the analysis region (calculation region) for analyzing the behavior of the bubble particles as a three-dimensional region that is digitized including the shape data of the workpiece to be determined as an air pocket. As the workpiece shape data, CAD data for design, STL (Stereo Lithography) data, FEM (finite element method) data obtained by dividing the workpiece shape into a plurality of elements such as meshes and nodes, and the like can be used.

  For example, when mesh data is used as shape data, an analysis region is set using a mesh set for a workpiece and a spatial mesh set around the workpiece, and each mesh has, for example, a mesh number for identifying itself, Coordinate values (coordinate values on the XYZ coordinate axes in the three-dimensional space) of a mesh node (node) with respect to a predetermined reference point, mesh attributes, and the like are assigned. These data are stored in the external storage device 13, and for example, in a database composed of attribute record groups with individual identification numbers (record numbers) for each object, mesh numbers and node point coordinates of each mesh. Values, attribute data, etc. are described in association with each other.

  The bubble particle setting unit 10b artificially generates bubble particles at an arbitrary position in the analysis region, and sets initial conditions. As initial conditions, calculation conditions such as the diameter (diameter) dp of bubble particles, the number N of generations, the number M of calculations, the time increment Δt of calculation, etc. are set, and the direction of gravity with respect to the posture of the workpiece is determined.

  The generation position of the bubble particles is set as shown in FIG. 3, for example. In FIG. 3, the position indicated by the black circle disposed below the workpiece W in the analysis region A is the generation position of the bubble particles B, and the state where the bubble particles B are arranged in a row in the horizontal axis direction for convenience. It is shown. As for the generation position of the bubble particles B, an arbitrary position may be designated using a mouse or the like while referring to the display device 12, or it can be automatically generated at a preset position or a random position. is there. Furthermore, the generation position of the bubble particles can be set inside the workpiece, and by setting the inside of the workpiece, the most noticed portion can be intensively analyzed.

  As will be described below, the bubble particles B generated in the analysis region A are moved in a predetermined distance and direction by the acting force applied to the bubble particles and the collision with each other for each calculation time step width Δt. Finally, as shown in FIG. 4, an aggregate (particle group) B_P of bubble particles B that is prevented from moving by interference with the workpiece W or other bubble particles and accumulates inside the workpiece W is an air pocket. Thus, the shape and size of the air pocket are calculated.

  In FIG. 4, the diameters of the respective bubble particles B are shown to be the same, but bubble particles having various sizes may be used. By using bubble particles having different sizes and shapes, as shown in FIG. 5, small bubble particles BS are accumulated between large bubble particles BL, and the shape of the gas-liquid boundary surface can be expressed smoothly. Become.

The diameter dp of the bubble particles is not more than a value set in consideration of the influence of the surface tension σ in the gas-liquid two-phase flow. The influence of the surface tension σ can be determined based on two dimensionless numbers, the Weber number We and the Reynolds number Re. The Weber number We and the Reynolds number Re are the fluid density ρ, kinematic viscosity coefficient ν, fluid velocity. Let u be expressed by the following equations (1) and (2), respectively.
We = (ρ × dp × u ² ) / σ (1)
Re = u × dp / ν (2)

In the immersion treatment that is the subject of this simulation, the flow state of the immersion liquid is relatively slow, but in many cases, the state of Re> 1, that is, the influence of inertial force is larger than that of viscous force. When Re> 1, the influence of the surface tension cannot be ignored when We> 1. Therefore, by setting the diameter dp of the bubble particles so as to satisfy the condition of the following expression (3), the simulation can be performed without overlooking the air pocket due to the influence of the surface tension generated in a narrow gap or a small hole.
dp ≧ σ / (ρ × u ² ) (3)

The particle behavior calculation unit 10c calculates the bubble particle movement speed (vector) up for each time step width Δt, and moves the bubble particles using the movement speed up for each time step width Δt as the movement amount ΔZ. The moving speed up of the bubble particles is obtained from a relational expression representing the acting force per unit mass applied to the spherical particles. As the force acting on the bubble particles, an external force such as a viscous force, a buoyancy, a centrifugal force or an electromagnetic force is considered as shown in the following equation (4). Note that the fluid velocity u in the equation (4) may be a value calculated from the specifications of the actual immersion tank, but may be a value obtained from a fluid analysis result or an experimental result to be performed separately. good.
(Dup / dt) = fD × (u−up) + g × (ρp−ρ) / ρp + Fx (4)
Where fD: Viscous resistance coefficient of particles
g: Gravity acceleration
ρp: Particle density
Fx: External force other than viscous force and buoyancy

  The movement speed up of the bubble particles according to the equation (4) is a speed obtained from the balance of forces acting on the bubble particles. However, due to the influence of the disturbance generated when the bubble particles move in the fluid, FIG. As shown, the bubble particles B may be unevenly deposited inside the workpiece W. For this reason, when it is expected that the influence of the bubble particle turbulence cannot be ignored, the movement amount in the direction perpendicular to the movement direction of the bubble particles (or the horizontal plane direction when only gravity acts on the bubble particles) should be set. You may do it.

  Specifically, in the equation (4) representing the relationship between forces acting on the bubble particles, as shown in FIG. 7, the size (movement) is on the xy plane perpendicular to the movement direction of the bubble particles B at the speed up. Amount) External force Ftx in Δr and direction θ is set. This external force Ftx expresses turbulence of bubbles, and is set for each bubble particle using, for example, a random number. By introducing the external force Ftx, it is possible to simulate a state in which the bubble particles rise while the bubble particles fluctuate, and it is possible to mitigate the influence of the bubble particles being unevenly deposited in the work.

When the bubble particles interfere with the member with the movement amount ΔZ obtained as described above, the bubble particles are moved along the member surface from the position of the interference. Further, as shown in FIG. 8, when the bubble particle B1 with mass m1 and velocity up1 collides with the bubble particle with mass m2 and velocity up2, the following equation (5) is obtained based on the conservation law of momentum. The magnitude of the obtained speed up is calculated as the movement amount ΔZ. In the equation (5), up, up1, and up2 are velocity vectors.
up = m1 / (m1 + m2) × up1 + m2 / (m1 + m2) × up2 (5)

  The post processing unit 10d performs visualization processing and data output of the simulation result so that the progress of the simulation and the simulation result can be easily grasped. That is, data for visualizing the movement state of the bubble particles with respect to the workpiece is generated, and the collection of bubble particles accumulated inside the workpiece by stopping the movement due to the interference with the member is used as the bubble particles forming the air pocket. Identification is displayed by shading. Also, the shape and size (volume) of the air pocket are calculated, and data display processing and file storage processing are performed.

  Next, an air pocket simulation program executed by the CPU of the arithmetic unit 10 will be described with reference to the flowchart shown in FIG.

  In the simulation program of FIG. 9, first, in step S <b> 1, workpiece shape data is input, and analysis is performed to analyze the behavior of bubble particles by combining the member existing space and the space filled with the immersion liquid based on the workpiece shape data. Set the area. Next, proceed to step S2, set the physical properties of the fluid simulating bubble particles and immersion liquid, and the direction of gravity. In step S3, input calculation conditions such as the diameter dp of bubble particles, the number N of generated particles, and the number M of calculations. To do.

  Further, the process proceeds to step S4, and when the positions of N bubble particles generated around the member (inside and outside of the workpiece) are set, in step S5, according to the above equation (4), that is, to balance the acting force applied to the bubble particles. Based on this, the movement amount ΔZ of the bubble particles is calculated including the movement direction. In step S6, it is determined whether or not the movement trajectory of the bubble particles with the movement amount ΔZ interferes with the workpiece in the analysis region.

  The interference between the bubble particles and the workpiece is determined, for example, based on whether or not the movement trajectory of the bubble particles overlaps with the workpiece shape data at the same coordinates. If they do not overlap at the same coordinates, it is determined that they do not interfere with the workpiece even if the bubble particles are moved. If they overlap at the same coordinates, it is determined that if the bubble particles are moved, they interfere with the workpiece. If it is determined in step S6 that there is no interference, the bubble particles are moved by the movement amount ΔZ and jumped to step S8. If it is determined that there is interference, the bubble particles are moved to the workpiece member surface in step S7. And move to step S8.

  In step S8, it is checked whether or not the number of bubble particles i whose movement has been calculated (hereinafter referred to as “number of particles”) i has reached the initially generated number N. If i <N, the number i of particles is incremented in step S9 to select the bubble particle to be subjected to the next movement calculation, and the process returns to step S5. In step S8, when the number i of particles reaches the number N generated (i ≧ N), the process proceeds from step S8 to step S10 to check whether there is a collision between the bubble particles. The collision between the bubble particles is similarly determined based on whether or not there is a point that overlaps at the same coordinate in the trajectory with the movement amount ΔZ, and the trajectory intersects.

  As a result, if there is no collision between particles in step S10, the process jumps to step S12. If there is a collision between particles, movement calculation due to the collision between particles is performed in step S11. As described above, this calculation is performed using equation (5) based on the conservation law of momentum, and the speed and direction after the collision are calculated, and the process proceeds to step S12.

  In step S12, it is checked whether or not the number of calculations j has reached the specified number M. If j <M, the specified number has not been reached, so in step S13 the number of calculations j is incremented and the number of particles i is cleared. Then, the process returns to step S5 to execute the next movement calculation.

  Thereafter, in step S12, when the number of calculations j reaches the specified number M (j ≧ M), the process proceeds from step S12 to step S14, and post processing is executed. In this post processing, the bubble particle trajectory is animated by post processing, visualization processing such as displaying the accumulation state of the bubble particles inside the workpiece, etc., and the volume of the air pocket is calculated from the accumulation state of the bubble particles Then, output to the display device 12, data output to a simulation result file, and the like are performed.

  As described above, according to the present embodiment, the behavior of the bubble particles in the immersion liquid is considered in consideration of the influence of various forces acting on the bubble particles and the influence of mutual interference such as collision between the bubble particles. The air pocket can be analyzed accurately and the air pocket can be evaluated in a state close to the actual dipping process reflecting the state of the actual dipping process such as a painting line. In addition, the size and shape of the air pocket can be known, and it is possible to develop a more practical simulation without stopping at a mere guide.

  In addition, by setting the physical property value of the fluid simulating the immersion liquid to gas (air) and the physical property value of the bubble particles to liquid (immersion liquid), measures against liquid accumulation that occur when pulling up the workpiece from the immersion tank are taken. Can be taken.

  Next, a second embodiment of the present invention will be described. 10 and 11 relate to the second embodiment of the present invention, FIG. 10 is an explanatory diagram showing stagnant particles, FIG. 11 is a flowchart of an air pocket simulation program, and FIG. 12 is an explanatory diagram showing extraction from stagnant particles, FIG. 13 is an explanatory view showing the average height of the air pockets.

  In the second form, in the bubble particle movement calculation, the bubble particle that has been in a state where the movement distance is 0 continues for a certain period of time is defined as a “stagnation particle” that cannot move due to a workpiece or the like, and its attribute is changed. At the same time, among the stagnant particles, the particles that are in contact with the work wall surface at three or more points are defined as “topmost stagnant particles” and their attributes are changed.

  The most stagnant particle means the stagnant particle at the highest position in the direction opposite to the gravitational direction. As shown in FIG. 10, one air pocket of the workpiece W is formed by two convex portions Wt1 and Wt2. In this case, two uppermost stagnant particles Btmax are defined for a plurality of stagnant particles Bt forming one air pocket.

  The simulation program of the second form adds a slight change to the simulation program of the first form (FIG. 9) according to the setting of “stagnant particles” and “topmost stagnant particles”. Hereinafter, the simulation program of the second embodiment will be described with reference to the flowchart of FIG.

  In the simulation program shown in FIG. 11, the first steps S21 to S24 are the same as steps S1 to S4 of the first embodiment, and the workpiece shape data input, physical property and gravity direction setting, calculation condition input, N pieces Set the bubble particles. Next, in step S25 and subsequent steps, bubble particle movement calculation including determination of stagnant particles is performed.

  That is, it is determined in step S25 whether or not the bubble particles are stagnant particles. If they are stagnant particles, the movement calculation is terminated and the process jumps to step S29. If not, the process proceeds to step S26. The amount of movement ΔZ of the bubble particles is calculated. The calculation of the movement amount Z is the same as in the first embodiment.

  In step S27, it is determined whether or not the movement trajectory of the bubble particles with the movement amount ΔZ interferes with the workpiece in the analysis region. This interference determination is the same as in the first embodiment. When it is determined that there is no interference, the bubble particles are moved by the movement amount ΔZ and the process proceeds to step S29. When it is determined that there is interference, the bubble particles are moved to the workpiece in step S28. Then, the process proceeds to step S29.

  In step S29, it is checked whether or not the number of particles i has reached the generated number N. If i <N, the number i of particles is incremented in step S30 to select a bubble particle to be subjected to the next movement calculation. Then, the process returns to step S25. In step S29, when the number i of particles reaches the number N generated (i ≧ N), the process proceeds from step S29 to step S31, and whether or not there is a collision between bubble particles as described in the first embodiment. Find out.

  In step S31, if there is no collision between particles, the process jumps to step S37. If there is a collision between particles, the process proceeds to step S32, and as described in the first embodiment, based on the momentum conservation law (5 ) To calculate the movement due to the collision between the particles, and the process proceeds to step S33.

  In the collision of bubble particles, when a certain bubble particle collides (or comes into contact) with stagnant particles, an external force similar to the vertical force Ftx representing the disturbance of the bubble particles described in the first embodiment is applied. This external force means a lateral force in the horizontal plane direction when only gravity acts on the bubble particles, and when the bubble particles come into contact with the stagnant particles, the bubble particles skid to form the gas-liquid interface shape. Can be smooth.

  Next, in step S33, it is checked whether or not the current particle position is the same as the previous step in the particle position calculation. If the particle position is not the same position as the previous calculation, the process jumps to step S37. If the particle position remains at the same position, the process proceeds from step S33 to step S34, and the corresponding bubble particle is changed to a stagnant particle. Set and change attributes.

  Furthermore, it progresses to step S35 from step S34, and the contact state with the workpiece | work of stagnant particle | grains is investigated. In this embodiment, assuming that the bubble particles are spheres, it is checked whether or not the stagnant particles are in contact with the workpiece at three points. If not, the process jumps to step S37 and contacts at three points. If so, in step S36, the stagnant particle is set as the most stagnant particle, the attribute is changed, and the process proceeds to step S37.

  In step S37, as in the first embodiment, it is checked whether or not the number of calculations j has reached the specified number M. If j <M, the specified number has not been reached, and therefore the number of calculations j is incremented in step S38. At the same time, the number of particles i is cleared, and the process returns to step S25 to execute the next movement calculation.

  Thereafter, in step S37, when the number of calculations j reaches the specified number M (j ≧ M), the process proceeds from step S37 to step S39, where the number of stagnant particles is counted. Output data of simulation results.

  In this post processing, when air pockets are generated, the position of the air holes to be provided in the workpiece can be clearly grasped from the position of the most stagnant particles. Moreover, when it is desired to immediately grasp the approximate size of the air pocket, an approximate volume of the air pocket can be quickly calculated from the number of stagnant particles, and a quick response can be made.

  Furthermore, in order to obtain the air pocket volume precisely, as shown in FIG. 12, when looking up the stagnant particles Bt group inside the work W from below, the representative points of the particles such as the center of gravity and the lowest point of the particle surface can be recognized. The stagnant particles are extracted, and the gas-liquid interface shape of the air pocket is determined as a smoother shape that is closer to reality.

  FIG. 12 exemplifies a simulation result using bubble particles having different particle diameters, and stagnant particles Bti that are darkly displayed in the drawing indicate particles that can recognize representative points. From the extracted stagnant particles Bti, the average height of the air pockets is calculated by weighted averaging the representative point positions with the representative size (for example, particle diameter or projected area) of the bubble particles.

For example, as shown in FIG. 13, i stagnant particles Bt1, Bt2,..., Bti are extracted, and the center position of each particle from the reference position (Z = 0) is set as the representative point height Zp1, Zp2,. When Zpi and the diameters dp1, dp2,..., Dpi of each particle are representative sizes, the air pocket average height ZAP is calculated by the following equation (6) (Σ in the equation is the sum of i).
ZAP = (ΣZpi × d ² pi) / Σd ² pi (6)

  Then, a plane perpendicular to the direction of the force acting on the bubble particle at the air pocket average height ZAP (or a horizontal plane when only gravity acts on the bubble particle) is obtained, and this is obtained as the air pocket interface (the air-liquid boundary of the air pocket). Surface). By defining the shape formed by the air pocket interface and the workpiece as the air pocket shape and determining the air pocket volume from the air pocket shape, the exact shape and volume of the actually generated air pocket can be predicted.

  In this case, the air pocket interface may be obtained by correcting the average height ZAP of the air pocket in consideration of the flow of the paint in the immersion tank and the shaking of the work. That is, the corrected average height ZAPr is calculated by adding at least one of the correction amount due to the paint flow and the correction amount due to the shaking of the workpiece to the average height ZAP so that the corrected average height ZAPr is obtained. Remove bubble particles from stagnant particles.

  In the second mode, by defining the bubble particles that have stopped moving as “stagnation particles”, it is possible to quickly find the bubble particles that stop moving and stop the movement calculation quickly, thereby improving the processing speed. be able to. Also, by defining the stagnant particle at the highest position among stagnant particles as the “topmost stagnant particle”, it is possible to clearly grasp the position of the air holes to be provided in the workpiece, and when air pockets occur In addition, it is possible to develop a practical simulation that can be quickly handled and is not limited to a mere guide.

  Next, a third embodiment of the present invention will be described. 14 to 17 relate to a third embodiment of the present invention, FIG. 14 is an explanatory view showing initial bubble particles, FIG. 15 is an explanatory view showing disappearance of bubble particles outside the workpiece, and FIG. 16 is a bubble inside the workpiece. FIG. 17 is an explanatory diagram showing bubble particles left inside the workpiece.

  In the third embodiment, a predetermined space region surrounding the work in the analysis region is set as an initial condition for generating N bubble particles, and the air bubbles initially set in this space region (including the inside of the work) are set. The particle rise is calculated, and the air pocket is finally determined from the bubble particles remaining inside the workpiece.

  In this embodiment, a rectangular parallelepiped is assumed as a space region surrounding the work, and the minimum and maximum coordinate positions (Xmin, Xmax, Ymin, Ymax, Zmin, Zmax) of the work in the three axis directions of XYZ are obtained, and from this coordinate position Set the cuboid to be constructed. As shown in FIG. 14, N bubble particles B are uniformly arranged in a rectangular parallelepiped L surrounding the workpiece W. In this case, the maximum value of the number of particles is inevitably determined from the particle diameter of the bubble particles and the size of the rectangular parallelepiped.

  The simulation program of this embodiment is different from the simulation program of the second embodiment described above (see FIG. 11) only in the process of setting a rectangular parallelepiped as the calculation condition in step S23, and the other processes are the same as those of the second embodiment. .

  For example, as shown in FIG. 14, when N bubble particles are initially set in a rectangular parallelepiped L surrounding a work W having a vent hole H, calculation is performed first as shown in FIG. Bubble particles (bubble particles Bout indicated by the wavy line in the figure) rise and disappear from the analysis region A.

  Thereafter, as shown in FIG. 16 (a), the bubble particles B1 under the air holes H of the workpiece W rise out of the workpiece and rise, and as shown in FIG. 16 (b), the bubble particles B1 rise. The bubble particles B2, B3,... Around the bubble particle B1 sequentially escape from the vent hole H to the outside of the workpiece. Finally, as shown in FIG. 17, it can be seen that air pockets are formed by the bubble particle groups Bt remaining inside the workpiece W.

  In the third mode, calculation of the movement trajectory until bubble particles are accumulated inside the workpiece can be omitted, and the bubble particles left inside the workpiece can be grasped with a smaller amount of calculation, and the calculation load can be calculated efficiently. , The size of the air pocket can be easily grasped, and a more practical simulation can be achieved.

A basic configuration diagram of a simulation apparatus according to the first embodiment of the present invention. Same as above, schematic illustration of car body painting line Same as above, explanatory diagram showing the generation position of bubble particles Same as above, explanatory diagram showing the state of accumulation of bubble particles Same as above, explanatory diagram showing the accumulation state of bubble particles having different particle diameters Same as above, explanatory diagram showing the bias in the accumulation of bubble particles Same as above, explanatory diagram of external force considering turbulence of bubble particles Same as above, explanatory diagram showing collision between bubble particles Same as above, air pocket simulation program flowchart Explanatory drawing which shows stagnant particle in connection with 2nd Embodiment of this invention. Same as above, air pocket simulation program flowchart Same as above, explanatory diagram showing extraction from stagnant particles Same as above, explanatory diagram showing the average height of the air pocket Explanatory drawing which shows initial stage bubble particle concerning 3rd Embodiment of this invention. Same as above, explanatory diagram showing the disappearance of bubble particles outside the workpiece Same as above, explanatory diagram showing the escape of bubble particles inside the workpiece Same as above, explanatory diagram showing bubble particles left inside the workpiece Explanatory drawing showing the state of bubble particle generation in the conventional method Explanatory drawing showing simulation results in the conventional method

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Simulation apparatus 10 Arithmetic apparatus 10a Analysis area | region setting part 10b Bubble particle | grain setting part 10c Particle behavior calculation part 10d Post-processing part

Claims (22)

In the analysis region including the virtual work that expresses the work to be dipped in the shape data, a pseudo particle of air bubbles is generated, and the particle in the fluid imitating the dipping liquid in which the work is dipped is generated. In the simulation method of the air pool that calculates the behavior and simulates the air pool,
Setting an arbitrary shape and physical properties to the particles, and calculating a movement trajectory accompanied by collision between the particles based on a relationship of forces acting on the particles in the fluid;
Depositing particles that have stopped moving due to interference with the virtual workpiece or other particles without coalescing each other, and determining the accumulated particle group as an air pocket.   2. The method of simulating an air pocket according to claim 1, wherein the particle is a rigid body, the friction coefficient of the surface is set to zero, the coefficient of restitution between the particles is set to zero, and the movement trajectory is calculated.   3. The method for simulating air accumulation according to claim 1, wherein the particle is a sphere, and the diameter of the sphere is not less than a value calculated from the Weber number.   4. The method of simulating an air pocket according to claim 1, wherein the movement trajectory is calculated in a state where particles of different sizes coexist, and the particles that have stopped moving are accumulated.   5. The method of simulating an air pocket according to any one of claims 1 to 4, wherein a direction of gravity acting on the particles is set based on a hanging posture of the workpiece.   6. The air pocket simulation method according to claim 1, wherein a force in a direction perpendicular to the moving direction of the particles is applied when calculating the moving trajectory.   The attribute is changed by setting the particles deposited by stopping the movement as stagnant particles, and further changing the attribute by setting the particles in contact with the simulated work at three or more points among the stagnant particles as the most stagnant particles. The simulation method of the air pocket as described in any one of Claims 1-6.   8. When the moving particles collide with the stagnant particles, the particles are caused to skid under the stagnant particles by a force perpendicular to the direction of the force acting on the particles. A simulation method for air pockets.   The initial generation position of the particles is set in a region having a size including the virtual workpiece, and the particles are uniformly distributed in the region to be generated initially. 2. A method for simulating air accumulation according to 1.   Extract the particles that can recognize the representative points of the particles from below from the particle group that accumulates in the virtual workpiece, and average the height of the extracted representative points by the representative size of each particle. 10. The air according to claim 1, wherein a plane perpendicular to the direction of the force acting on each particle at the average height is defined as a boundary surface of the air pocket. A simulation method for pooling.   11. The method of simulating an air pocket according to claim 10, wherein the average height of the air pocket is corrected by a correction amount based on at least one of the shaking of the workpiece and the flow of the immersion liquid. In the analysis region including the simulated work that expresses the work to be dipped in the shape data, pseudo particles of air bubbles are generated, and the particles in the fluid imitating the immersion liquid in which the work is immersed are generated. In a simulation program for a puddle that can be executed by a computer that calculates the behavior and simulates a puddle,
Setting an arbitrary shape and physical properties to the particles, and calculating a movement trajectory accompanied by collision between the particles based on a relationship of forces acting on the particles in the fluid;
Depositing particles that have stopped moving due to interference with the simulated workpiece or other particles without coalescing each other, and determining the accumulated particle group as an air pocket.   13. The air retention simulation program according to claim 12, wherein the particle is a rigid body, the friction coefficient of the surface is set to zero, the restitution coefficient between the particles is set to zero, and the movement trajectory is calculated.   14. The air retention simulation program according to claim 12, wherein the particle is a sphere, and the diameter of the sphere is equal to or greater than a value calculated from the Weber number.   15. The air retention simulation program according to any one of claims 12 to 14, wherein the movement trajectory is calculated in a state where particles of different sizes coexist, and the particles that have stopped moving are accumulated.   The air retention simulation program according to any one of claims 12 to 15, wherein a direction of gravity acting on the particles is set on the basis of a hanging posture of the workpiece.   The air reservoir simulation program according to any one of claims 12 to 16, wherein a force in a direction perpendicular to the moving direction of the particles is applied in the calculation of the moving trajectory.   The attribute is changed by setting the particles deposited by stopping the movement as stagnant particles, and further changing the attribute by setting the particles in contact with the simulated work at three or more points among the stagnant particles as the most stagnant particles. An air reservoir simulation program according to any one of claims 12 to 17.   19. When the moving particles collide with the stagnant particles, the particles are slid under the stagnant particles by a force in a direction perpendicular to the direction of the force acting on the particles. Air pool simulation program.   The initial generation position of the particles is set in a region having a size including the simulated workpiece, and the particles are uniformly distributed in the region to be initially generated. The air reservoir simulation program according to 1.   Extract the particles that can recognize the representative points of the particles from below from the particle group that accumulates in the simulated workpiece, and average the heights of the extracted representative points by the representative size of each particle. 21. The air according to claim 12, wherein a plane perpendicular to the direction of a force acting on each particle at the average height is defined as a boundary surface of the air pocket. A pool simulation program.   The simulation program of an air pocket according to claim 21, wherein the average height of the air pocket is corrected by a correction amount based on at least one of the shaking of the workpiece and the flow of the immersion liquid.

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