WO2016199211A1

WO2016199211A1 - Void behavior analysis method and apparatus therefor

Info

Publication number: WO2016199211A1
Application number: PCT/JP2015/066535
Authority: WO
Inventors: 遼太郎島田; 河野　務; 眞行美野
Original assignee: 株式会社日立製作所
Priority date: 2015-06-09
Filing date: 2015-06-09
Publication date: 2016-12-15
Also published as: JPWO2016199211A1

Abstract

A void behavior analysis method for analyzing, by means of a computer, the behavior of a void generated in the process of molding a liquid material injected into a space inside a mold comprises: an input step of inputting or generating a shape corresponding to a filling part of a product to be analyzed, a physical property value of a filling material, and an initial condition of a void particle, assuming the existence of a void; and a calculation step of calculating an amount of movement of the void particle at prescribed time intervalf, using data from the input step. In the calculation step, a determination is made as to whether the void particle is in contact with a wall surface, for each time step. If it is determined that the void particle is in contact with a wall surface, a resistance coefficient of the void is calculated as a function including the movement speed of the void, the diameter of the void, the viscosity of a resin material, and the angle of inclination of the wall surface.

Description

Void behavior analysis method and apparatus

The present invention relates to a void behavior analysis method and apparatus among information processing techniques such as flow analysis of a molding process by a computer.

Residual voids in molded products such as casting, injection molding, casting, etc., which are formed by injecting liquid materials (including those heated at the melting temperature) in addition to liquid materials at room temperature. It can be a cause of defects such as cracking of the molded product and dielectric breakdown. Therefore, an analysis system that predicts defects at the product and mold design stages and selects product shapes, molding conditions, mold structures, etc. by performing flow analysis including void behavior for the molding process is used. .

As a technique for analyzing the behavior of voids generated continuously or intermittently, there is a technique described in Patent Document 1. This technology is a method of analyzing the behavior of voids generated by bubbles entrained in a molten material using a computer when filling the mold with the molten material. For each divided minute space, the flow rate of the molten material is calculated using the elapsed time from the start of filling of the molten material as a parameter, assuming the position where voids are likely to occur in any one of the minute spaces. Trace particles are virtually generated at the void generation position, and since it is assumed that the trace particles flow together with the molten material, the flow rate of the molten material is calculated at predetermined time intervals. It is a method of calculating the position where the trace particles exist after the predetermined time interval and analyzing the behavior of the void.

JP-A-5-337999

The technology of Patent Document 1 analyzes voids as trace particles, and assumes that the molten material and the trace particles flow together. For this reason, the influence of the force applied to the void other than the flow rate of the molten material is not considered. Therefore, it gives good results when the material flow rate is fast like injection molding, but when the material flow rate is slow, such as casting, the effect of force on voids such as buoyancy cannot be ignored and the error is large. Become. In particular, when the void comes into contact with the inner wall of the mold or a wall surface of a part, the error is the largest because it is affected by deformation of the void or friction with the wall surface. However, since the moving speed of the void is the slowest in the vicinity of the wall surface, it is important to predict the behavior of the void in the vicinity of the wall surface with high accuracy in order to apply to the design of a wide range of molded products.

Therefore, an object of the present invention is to provide an analysis method and apparatus capable of accurately predicting the behavior of a void contacting a wall surface.

In order to solve the above problems, the void behavior analysis method of the present invention is used to analyze the behavior of voids generated in the molding process of the liquid material injected into the space in the mold using information processing by a computer. In the method, the process of dividing the model space in which the liquid material is filled in the mold for molding the product to be analyzed into three-dimensional solid elements, and the generation of void particles assuming the physical properties of the liquid material, mold, and parts, and voids. Inputting or reading initial conditions, boundary conditions for setting the initial temperature of liquid material, pressure, and initial temperature of the mold, as well as initial time increments and analysis conditions for setting analysis end conditions, and the time increment interval The flow analysis of the liquid material filled in the mold at each analysis time after the time increment is performed, and the liquid in each three-dimensional solid element is analyzed. In the step of calculating the state quantity and viscosity of the material, and in the calculation of the amount of movement caused by buoyancy acting on the void particles riding on the flow of the liquid material in each analysis time, the void particles are the inner wall or part of the mold If so, calculate the drag coefficient of the void particle as a function including the moving speed of the void particle, the void particle diameter, the viscosity of the liquid material, and the inclination angle θ of the wall surface. And calculating the state quantity of each void from the state quantity of the liquid material and the amount of movement of the void particles, and after the satisfaction of the analysis end condition, each recorded analysis time and each void at the analysis end time And a step of displaying the state quantity on the screen.

As another feature of the present invention, in the void behavior analysis method, the viscosity of the liquid material is calculated as a function including the temperature and elapsed time of the liquid material.

Further, as still another feature of the present invention, in the void behavior analysis method, the drag coefficient of the void is calculated as a function including a Reynolds number Re, an Ebeth number Eo, a Morton number Mo, and a wall inclination angle θ.

In order to solve the above-mentioned problems, the void behavior analyzing apparatus according to the present invention uses the information processing by a computer to analyze the void behavior generated in the molding process of the liquid material injected into the space in the mold. In the analysis device, set the analysis target product shape, mold shape, liquid material, mold and part physical property values, initial conditions for void particle generation assuming voids, liquid material initial temperature, pressure, and mold initial temperature. Data input processing unit that inputs boundary conditions to be performed, initial time increment, and analysis conditions for setting analysis end conditions, stores each data in the storage unit, and reads from the storage unit during processing of each unit, and an analysis target A model shape / element creation unit that divides a model space in which a liquid molding material is filled into a mold for molding a product into three-dimensional solid elements; A liquid material flow analysis processing unit for performing a flow analysis of the liquid material filled in the mold at each analysis time after increment and calculating a state quantity and a viscosity of the liquid material in each of the three-dimensional solid elements; In each analysis time, in the calculation of the amount of movement caused by buoyancy acting on the void particles riding on the flow of the liquid material, it is determined whether the void particles are in contact with the inner wall of the mold or the wall of the part. And calculating the drag coefficient of the void particle as a function including the moving speed of the void particle, the void particle diameter, the viscosity of the liquid material, and the inclination angle θ of the wall surface, and the state quantity of each void is calculated as the state of the liquid material. A void movement analysis processing unit which is calculated from the amount and the movement amount of the void particles, each analysis time recorded after the completion of the analysis end condition, and each void state at the analysis end time An analysis result output processing unit for displaying the amount on the screen.

According to the present invention, it is possible to predict the behavior of a void that floats along a wall surface with high accuracy.

It is a schematic block diagram of the void behavior analysis apparatus which analyzes the behavior of the void which generate | occur | produces in the process of filling a liquid material into a type | mold and using a computer. It is a flowchart showing the analysis process of the behavior of the void at the time of inject | pouring a liquid material into a type | mold and shape | molding. It is process drawing which shows an example of the shaping | molding process and model space which the void behavior analysis apparatus of a present Example makes into analysis object. The analysis method for the rising speed of voids (bubbles) in liquid materials is as follows: (A): Behavior of free-floating voids (bubbles), (B): Void (bubbles) in the direction of rising It is a figure explaining the comparison of the behavior of voids (bubbles) when contacting a wall surface. It is a block diagram which shows the structure of the experimental apparatus for verifying the analysis result of the void behavior analysis apparatus of a present Example. It is a scatter diagram for comparing the analysis value of the void behavior analysis apparatus of a present Example with the experimental value of the experimental apparatus shown in FIG.

Hereinafter, examples will be described with reference to the drawings.

First, as an example of the analysis target of this embodiment, a semiconductor package injection molding process is given. This is a process in which a liquid resin material is filled in a mold and molded in order to seal a component (an element on a lead frame) installed between the upper mold and the lower mold with a resin material. In this case, air bubbles are entrained in the resin material during the filling of the liquid resin material, and voids are generated. The voids flow in the mold as the filling proceeds, and the voids may remain in the molded product. FIG. 1 shows a schematic configuration diagram of a void behavior analyzing apparatus 100 that analyzes the behavior of the void using an electronic computer.

The void behavior analysis apparatus 100 can be configured on a general-purpose computer, and the hardware configuration thereof includes a calculation unit 110 including a CPU (Central Processing Unit), a RAM (Random Access Memory), and a ROM (Read Storage unit 120 composed of only memory (HDD), hard disk drive (HDD), etc., input unit 130 composed of input devices such as keyboard and mouse, display devices such as LCD (Liquid Crystal Display), organic EL display, etc. A display unit 140 configured by an output device or the like, a media reading unit 150 for reading information of a portable storage medium having portability such as a CD-ROM or a USB memory, a communication unit 160 configured by a NIC (Network Interface Card) or the like. , Etc.
The communication unit 160 is connected to an external CAD device 180 and an external computer 190 via a network 170.

The storage unit 120 is a storage area 121 for storing a void behavior analysis program, and an analysis target of a molded product designed by an external CAD device 180 or a three-dimensional CAD system (not shown) mounted in the same device 100. An analysis target model shape data storage area 122 for storing a model, shape data of a molding die, and the like; a three-dimensional element data storage area 123 for storing a three-dimensional solid element of the analysis target model created by the finite element analysis method; Analyzes that store physical properties such as density, specific heat, thermal conductivity, surface tension, and viscosity of liquid materials such as resin materials, molded parts, and equations such as exothermic formula and viscosity formula Object property / equation storage area 124 and boundary / molding condition data such as initial temperature of mold, initial temperature of liquid material, pressure, etc. A data storage area 125, an analysis condition data storage area 126 including information such as an initial time increment (time width Δt) and an analysis end condition (end time, etc.) at the time of analysis, and an initial void condition for generating a void are generated. It comprises an initial void condition data storage area 127 that stores data such as time, position, number, diameter, and density, and each analysis result storage area 128.

The calculation unit 110 implements the following functional units by loading the void behavior analysis program stored in the void behavior analysis program storage area 121 of the storage unit 120 into the RAM and executing it by the CPU.
The molded product molding process analysis processing unit 111 performs control for simulating the entire molding process of the analysis target model, and controls the analysis time interval of the liquid material flow analysis processing unit 114 and the void movement analysis processing unit 115 according to the analysis conditions. The entire system is controlled until the analysis end condition is satisfied.

The data input processing unit 112 is configured so that the molded product molding process analysis processing unit 111 simulates the entire molding process of the analysis target model, or the user (operator) in advance analyzes the analysis target model, mold shape CAD data, and the analysis target model. Various physical property values, equations, boundary / molding condition data, analysis condition data, initial void condition data, and the like are received via the input unit 130 and the media reading unit 150, and are input to each storage area of the storage unit 120. Remember. In addition, data created in the external CAD device 180 and the external computer 190 is received via the network 170 and the communication unit 160 and stored in the storage unit 120. Further, when necessary data is already registered in the storage unit 120 during the processing of the molded product molding process analysis processing unit 111, the data input processing unit 112 reads the data from the storage unit 120.

The model shape / element creation unit 113 targets the analysis region 207, which is a space in which the liquid material flows, from the shape data of the molded product stored in the analysis target model shape data storage region 122 and the shape data of the molding die. Are divided into a plurality of three-dimensional solid finite element regions (hereinafter referred to as elements), and the shape data of each element is created and stored in the three-dimensional element data storage region 123.

The liquid material flow analysis processing unit 114 is executed at predetermined time intervals under the control of the molded product molding process analysis processing unit 111, and each element of the liquid material injected into the analysis region 207 at the time of the analysis time t. The state quantity such as velocity (flow velocity), pressure, temperature, etc., and physical properties such as viscosity are calculated.

The void movement analysis processing unit 115 is executed at predetermined time intervals under the control of the molded product molding process analysis processing unit 111. At the time of the analysis time t, each void element generated according to the initial void condition is the flow of the liquid material. And the position moved by buoyancy is calculated.

The analysis result output processing unit 116 records the analysis results for each analysis time t in the liquid material flow analysis processing unit 114 and the void movement analysis processing unit 115 in the analysis result storage area 128. After the analysis processing is completed, the analysis results are recorded. The data is output to the display unit 140 or the external computer 190.

FIG. 2 is a flowchart showing an embodiment in which the molded product molding process analysis processing unit 111 performs analysis processing of the behavior of voids when a liquid material is injected into a mold to mold a molded product. In the present embodiment, the analysis processing is processing such as analysis, design support, and evaluation (molded product void evaluation) related to a molding process (injection / flow / curing process) in which a liquid material is injected into a mold to obtain a molded product. Indicates.

FIG. 3 is an example of the molding process and model space to be analyzed in this embodiment. In a state before injection of the liquid material 205 shown in FIG. 3A, the component 202 is installed inside the mold 201. A space 204 in the mold 201 is formed according to the shape of the mold 201 and the part 202.
At the initial stage of the liquid material 205 injection step shown in FIG. 3B, the liquid material 205 is injected from the gate 203 for injecting the liquid material 205 into the space 204 in the mold 201. At this time, the initial void 206 flows in due to air entrainment at the inlet or the like.

In the state before the filling process of the liquid material 205 shown in FIG. 3C, the void 206 comes into contact with the wall surface of the component 202 and floats along the wall surface while being deformed into an elliptical sphere.
In a state in which the liquid material 205 is filled in the space 204 in the mold 201 shown in FIG. 3D, the viscosity increases in the process of curing the liquid material 205, so that the void 206 cannot move freely, and molding is performed. It remains as a void 206 in the product. After the liquid material 205 is cured, an integrally molded product composed of the part 202 and the cured (liquid) material 205 is taken out from the mold 201. In the above process, the (liquid) material 205 is integrally formed with the component 202 included therein. If it is not integral molding, molding is performed without the component 202. In the present embodiment, an area including the space 204 surrounded by a dotted line in FIG. If the structures of the mold 201 and the part 202 are symmetric as shown in FIG. 3, an area where the symmetry can be secured can be set as the analysis area 207 to shorten the calculation time.

As the mold 201, a mold or a sand mold can be used. The component 202 can use various inorganic or organic materials. As the liquid material 205, a material that is solid at room temperature and melts by heating (inorganic material or thermoplastic resin material) or a material that cures by heating at room temperature (thermosetting resin material) is used. Can do.

The operation in which the molded product molding process analysis processing unit 111 controls the entire simulation of the molding process of the model to be analyzed based on the flowchart of FIG. 2 is as follows.

In step S101, the data input processing unit 112 guides the input of the analysis target model, the operator inputs the model shape of the analysis region 207 via the input unit 130 or the media reading unit 150, and the analysis target model shape data Store in the storage area 122. Alternatively, when the data is already stored in the analysis target model shape data storage area 122 of the storage unit 120, the data input processing unit 112 reads the data. The shape of the mold 201 and the part 202 (model shape of the analysis region 207) is stored in advance in the storage unit 122 from the external CAD device 180 via the network 170 or from the external recording medium via the media reading unit 150 to the storage unit 122. It can also be stored and read out.

In step S102, the model shape / element creation unit 113 divides the analysis region 207 stored in the analysis target model shape data storage region 122 into a plurality of three-dimensional solid finite element regions (hereinafter referred to as elements). A process of creating shape data and storing it in the three-dimensional element data storage area 123 of the storage unit 120 is performed. The division process into elements is a known technique.

In step S103, the data input processing unit 112 guides the input of material property values, and the operator inputs the property values of the mold 201, the part 202, and the liquid material 205 via the input unit 130 or the media reading unit 150. And stored in the storage unit 124. Alternatively, when the data has already been stored in the analysis target physical property / equation storage area 124, the data input processing unit 112 reads the data. The physical property values can be stored in the storage unit 124 in advance and read out from data created by the external computer 190 via the network 170 or from an external recording medium via the media reading unit 150.

The physical property values of the part 202 to be input include initial temperature, heat capacity, density, thermal conductivity, and specific heat. The physical property values of the input liquid material 205 include thermal conductivity, specific heat, density, surface tension, and viscosity. In addition, about the physical property value which has temperature dependence, it is necessary to input the physical property value in the temperature range of the mold 201 at the time of molding at least. In this case, an experimentally calculated actual value may be input, or a value calculated from a physical model equation may be input. When the liquid material 205 is a resin material, the viscosity of the resin material can be calculated as a function including the temperature and elapsed time of the resin. As an example, the exothermic behavior and viscosity accompanying the curing of the resin material can be calculated from the following exothermic equations (Equation 1 to Equation 5) and viscosity equations (Equation 6 to Equation 9). In this case, Expressions 1 to 9 are also input as physical property values of the liquid material 205.

The meanings of the symbols used in the above formula are as follows (the same applies hereinafter).
α: reaction rate, dα / dt: reaction rate, t: time, T: temperature, K ₁ , K ₂ : coefficient as a function of temperature, M, N: order of reaction, Ka, Kb: reaction rate constant, Ea , Eb: activation energy, Q: amount of heat generated up to an arbitrary time, Qo: total amount of heat generated until the end of the reaction, dQ / dt: heat release rate, mu _L: viscosity of the liquid material 205, mu _L0: the liquid material 205 Initial viscosity, t ₀ : Gelation time of liquid material 205, C (T): Specific heat of liquid material 205, a, b, d, e, f, g: Constants specific to liquid material

In step S <b> 104, the data input processing unit 112 guides the input of the boundary / molding condition, and the operator inputs the boundary / molding condition via the input unit 130 or the media reading unit 150 and stores it in the storage unit 125. . Alternatively, when the data has already been stored in the boundary / molding condition data storage area 125, the data input processing unit 112 reads the data. As the boundary / forming conditions, data created by the external computer 190 can be stored in the storage unit 125 and read in advance via the network 170 or an external recording medium. The input boundary and molding conditions include the initial temperature and pressure of the liquid material 205 and the initial temperature of the mold 201.

In step S 105, the data input processing unit 112 guides the input of the initial void condition, and the operator inputs the initial void condition via the input unit 130 or the media reading unit 150, and the initial void condition data storage area 127 is input. Store. Alternatively, when the data has already been stored in the initial void condition data storage area 127, the data is read out. Input initial void conditions include time of occurrence, location, number, diameter and density. It can also be input assuming that voids are continuously generated at a certain analysis time t. In the present embodiment, the void is assumed to be a void particle having the input initial void condition. Therefore, in the fluid analysis described later, a single-phase flow analysis of only the liquid phase is performed. As the initial void condition, data created by the external computer 190 can be stored and read in advance in the storage unit 127 via the network 170 or an external recording medium.

In step S <b> 106, the data input processing unit 112 guides the input of the analysis condition, and the operator inputs the analysis condition via the input unit 130 or the media reading unit 150 and stores it in the analysis condition data storage area 126. Alternatively, when the data is stored in advance in the analysis condition data storage area 126, the data input processing unit 112 reads the data. The input analysis condition includes information such as an initial time increment (time width Δt) and an analysis end condition (such as an end time).
The operator inputs an analysis start instruction via the input unit 130 after the necessary data input (input process) has been completed. Alternatively, an analysis start instruction is issued when the molded product molding process analysis processing unit 111 starts.

The molded product molding process analysis processing unit 111 sets the initial value of the analysis time t as Δt (at the analysis time t = 0, the molded product molding process is started, and analyzes the state after the initial time increment (time width Δt). Therefore, the subsequent loop from step S107 to step S115 is repeated until the analysis end condition is satisfied. (One loop from step S107 to step S115 is hereinafter referred to as one analysis step.)

In step S107, the liquid material flow analysis processing unit 114 reads the mathematical formula stored in the storage unit 124. The mathematical formulas to be read out are the following continuous formula (Formula 10), Naviestokes formula (Formula 11), and energy conservation formula (Formula 12).

The meanings of the symbols used in the above formula are as follows (the same applies hereinafter).
ρ _L : density of the liquid material 205, v _L : flow velocity of the liquid material 205, P: pressure, T: temperature, G: gravitational acceleration, C: constant pressure specific heat, k: thermal conductivity, γ: shear rate, ∇: vector Differential operator

The liquid material flow analysis processing unit 114 receives the values (time width Δt, initial temperature, heat capacity, density, thermal conductivity, specific heat of the mold 201 and the part 202, the liquid that has been input or read from the storage unit 120 until step S106. Substituting the initial temperature, pressure, density, specific heat, thermal conductivity, exothermic formula (Formula 1 to Formula 5), viscosity formula (Formula 6 to Formula 9) of the material 205 into Formula 10 to Formula 12, and analyzing time The physical properties such as the velocity, pressure, temperature, and other physical quantities, and the viscosity of the liquid material 205 positioned in each element of the analysis region 207 at t are calculated.

In step S108, the analysis result output processing unit 116 stores the calculation result in step S107 in the analysis result storage area 128 in a format associated with the position of each element divided in step S102.

In step S109, the void movement analysis processing unit 115 causes the void position at the analysis time (t−Δt) before the time width Δt from the analysis time t (when t−Δt = 0, the time of t = 0 in the initial void condition) Is defined from the initial void condition data 127 of the storage unit 120 or the analysis result 128. Depending on whether the position of the called void is in a positional relationship where the wall surface of the part 202 or the mold 201 and the surface of the void are in contact with the surface of the void, or not, the flying speed of the void (at the analysis time t) The prediction formula of the ascending speed is distinguished and read from the storage unit 120.

FIG. 4 illustrates a method for analyzing the rising speed of voids (bubbles) in a liquid material.
FIG. 4 (A), as a prediction equation of the behavior of the free floating to voids (air bubbles), the prediction formula for drag coefficient C _D in the liquid material in a wide range of physical properties have been reported in the literature as known. Ascent rate v _B of the voids can be predicted by the prediction equation of C _D at any bubble diameter d.

In FIG. 4B, when the void (bubble) comes into contact with the inner wall of the mold 201 or the wall surface of the component 202 in the flying direction, it is affected by deformation of the void (bubble) or friction with the wall surface. for the shows prediction expression the prediction accuracy of the moving speed v _B of the voids improves to become low in the prediction equation of drag coefficient C _D of the free floating to voids (air bubbles). Assuming that voids (bubbles) are particles, it is determined whether the void (bubbles) particles are in contact with the part 202 or the wall surface of the mold 201. 1), calculates the moving velocity v _B of (equation 2), and (void by the resistance coefficient C _D, derived by the equation 3) (bubbles).

Returning to the description of the flowchart of FIG. 2, in step S109, the void movement analysis processing unit 115 causes the component 202 in the void rising direction at the void position of the analysis time (t−Δt) before the analysis time t by the time width Δt. Alternatively, it is determined whether or not the wall surface of the mold 201 is in contact with the surface of the void. If they are in contact, the process proceeds to step S111. If not, the process proceeds to step S110.
In the case where voids (bubbles) there are a plurality performs determination processing in step S109 for all the voids, reads a prediction equation of the moving speed V _T of the voids by the process of step S111 or step S110,, followed by The process up to the void movement analysis process in step S112 is executed.

In step S <b> 110, the void movement analysis processing unit 115 reads out from the storage unit 124 an evaluation formula for the drag coefficient of a free-floating void. Incidentally, it is possible to use those known as an evaluation formula for drag coefficient C _D voids freely floating. As an example, there is Equation 13 below.

The meanings of the symbols used in the above formula are as follows (the same applies hereinafter).
C _D : drag coefficient, Re: Reynolds number, Eo: Etobes number

The Reynolds number and the Etobeth number are dimensionless numbers defined by the following formulas 14 and 15.

The meanings of the symbols used in the above formula are as follows (the same applies hereinafter).
σ: Surface tension of liquid material 205, v _R : Void-liquid phase relative velocity, d: Void equivalent volume diameter, G: Gravitational acceleration, Δρ: Density difference between liquid material 205 and void

Note that the void-liquid correlation relative velocity v _R and the density difference Δρ between the liquid material 205 and the void are expressed by the following equations 16 and 17.

The meanings of the symbols used in the above formula are as follows (the same applies hereinafter).
v _B : Void ascent rate, ρ _G : Void density

In step S111, the void movement analysis processing unit 115 reads from the storage unit 124 an evaluation formula for the drag coefficient of the void that rises along the wall surface. As an evaluation formula for the drag coefficient of the void floating along the wall surface, a function including the moving speed of the void, the void diameter, the viscosity of the liquid material 205, and the inclination angle θ of the wall surface is used. When the liquid material 205 is a resin material, as described above, a value obtained by calculating the viscosity using a function including the temperature and elapsed time of the resin can be used. The inclination angle θ of the wall surface is calculated as an angle formed by the vertical vector of the void and the normal vector of the wall surface.

More preferably, Equation 18 which is a function including the Reynolds number Re, the Etobeth number Eo, the Morton number Mo, and the inclination angle θ of the wall surface is used as an evaluation formula of the drag coefficient of the void floating along the wall surface. The Molton number Mo is a dimensionless number defined by the following Equation 19.

Equation 18 is more preferably used in the form of Equation 20 below. When the Reynolds number Re is small, it is calculated as a function of the Reynolds number Re and the Morton number Mo, which is the first term of Equation 20. Further, when the Reynolds number Re is large, the calculation is performed as a function of the Eteves number Eo, the Morton number Mo, and the wall surface inclination angle θ, which are the second terms of the equation (20). This is a fact obtained by the inventors as a result of experimentally observing the behavior of voids floating along the wall surface.

Formula 20 is more preferably used in the form of Formula 21 below. The expression 21 is more preferably used in the form of the expression 22. Furthermore, the expression 22 is more preferably used in the form of the expression 23. The effect of using the above Equations 18 to 23 is clarified by comparing the output of the analysis processing described later and the experimental results.

The meanings of the symbols used in the above formula are as follows (the same applies hereinafter).
h, i, j, l, m, o, p, q, r, s, u, w: constants

In step S112, the void movement analysis processing unit 115 calls the mathematical formula stored in the storage unit 124. The formula to be called includes the following equation of motion of the void (Formula 24).

The meanings of the symbols used in the above formula are as follows (the same applies hereinafter).
C _VM : virtual mass coefficient, C _L : lift coefficient, F _W : wall force

Evaluation formula for determining the virtual mass coefficient C _VM, the lift coefficient C _L and the wall surface force F _W can each known ones. As an example, there are the following formulas 25 to 27.

The meanings of the symbols used in the above formula are as follows (the same applies hereinafter).
x: distance between void center of gravity position and wall surface, k: vertically upward unit vector, n: unit normal vector from wall surface to flow path, C _W1 , C _W2 : coefficient

As the evaluation formulas for _{obtaining the} coefficients C _W1 and C _W2 , known formulas can be used. As an example, there are the following Expression 28 and Expression 29.

The void movement analysis processing unit 115 assumes voids (bubbles) as particles in the void behavior analysis processing, and treats them as mass points that do not deform. The reason for this is that when performing a gas-liquid two-phase analysis, it is necessary to solve the two fluids with the liquid material using the void as a gas. By defining a particle as a kind of marker that has no analytical mass for a single laminar flow of liquid, and how it behaves in a liquid material Processing to analyze. In order to consider the buoyancy acting on the void moving on the flow of the liquid material, the spherical volume equivalent diameter d of the void is defined and used in the initial condition. (However, when the void (bubble) 206 shown in FIG. 3 or the like is in contact with the wall surface, the shape is changed to a flat shape so as to notify the operator that it is in contact.

The void movement analysis processing unit 115 adds the state quantities such as the void position, diameter, density, and velocity at each value (time width Δt, analysis time (t−Δt)) input from the step S101 to the step S111. , And state quantities such as flow velocity, viscosity, surface tension and density of the liquid resin 205 at the analysis time t) are substituted, and the void state quantities (position, diameter, density, velocity) at the analysis time t are calculated. At this time, as the evaluation formula for the drag coefficient, the equation read from the storage unit 124 in step S110 or step S111 is used.

Further, the inclination angle θ of the wall surface is calculated as an angle formed by the vertical vector of the void and the normal vector of the wall surface. When there are a plurality of voids, the calculation is performed for all the voids.
In addition, the void movement analysis processing unit 115 generates a new void whose occurrence is defined between the analysis time t−Δt and the analysis time t according to the initial void condition, at the defined position, with the defined diameter and initial velocity of 0. To generate.

In step S113, the analysis result output processing unit 116 stores the calculation result of each void in step S112 in the analysis result storage area 128 in a form associated with the position of each element divided in step S102. If there are a plurality of voids, the calculation results are stored for all the voids.

In step S114, the analysis time t is advanced by the initial time increment (time width Δt).

In step S115, the molded product molding process analysis processing unit 111 determines whether the analysis time t incremented by the initial time increment (time width Δt) has reached the analysis end condition (end time), and the analysis time t If the analysis end condition (end time) is not reached, the process proceeds to step S107, the analysis steps from step S107 to step S115 are repeated, and if the analysis time t reaches the analysis end condition (end time) or more, the analysis is performed. It determines with complete | finishing and progresses to step S116.

In step S116, the analysis result output processing unit 116 reads out from the analysis result storage area 128 the state quantities including the positions and velocities of all the voids in each analysis step. Further, state quantities such as speed, pressure and temperature of the liquid material 205 and physical properties such as viscosity are read out. According to the read data, data in accordance with the operator's request is output to the display unit 140. Further, the analysis result is output to the external computer 190 as necessary.

The operator determines whether or not the residual position of the void obtained by the output process in step S116 is within the range of the target location. For example, it is determined whether it is within a range that is removed from the final molded product. If a void remains outside this range, for example, the process returns from step S101 to the input process of step S106, and the operator reattempts or modifies the design so that the void remains within the target location range. I do.

According to the above flow chart, in the analysis when the liquid material 205 is injected into the mold 201 and molded, the physical properties and state quantities of the liquid material 205 with respect to the void 206 generated inside the liquid material 205 filled in the mold 201, In addition, it is possible to calculate and predict the void behavior that changes in accordance with the state quantity of the void within a realistic time. In the analysis processing of the present embodiment, the presence or absence of contact of the voids (bubbles) with the wall surface is determined, and if they are in contact, the evaluation process of the drag coefficient on the wall surface is used to form the liquid material 205. It is possible to calculate the void behavior when the void 206 generated in step S3 comes into contact with the mold 201 or the part 202 with higher accuracy than in the conventional evaluation formula in a realistic time.

Further, for example, in order to accumulate the voids remaining in the molded product at a position where the void is removed from the final molded product, by using this analysis method, molding conditions such as the shape of the molded product, the initial temperature of the mold 201, In addition, it is possible to optimize the mold structure such as the filling position (gate position) of the liquid material 205 and to support its design. In addition, compared with the gas-liquid two-phase flow analysis model that calculates the void as the gas phase, the analysis model is simplified by assuming that the void is a void particle. Etc. can be predicted in a realistic calculation time. Therefore, there are effects such as cost reduction and development period shortening with respect to a molding method in which a liquid material is injected into a mold. In addition, since defects due to voids can be reduced, it contributes to improving the reliability of products.

In the above description of the embodiment, as an example of the liquid material 205, the thermosetting resin material that is liquid at room temperature and is cured by heating has been mainly described. However, the liquid material 205 is heated in solid at room temperature. Even if it is the material (an inorganic material or a thermoplastic resin material) which melt | dissolves by this and becomes a liquid, the void behavior analysis apparatus 100 of a present Example can analyze similarly.

<< Verification of analysis result of analysis method of this embodiment >>
Hereinafter, the effect of the void behavior analysis apparatus 100 will be described in more detail with an analysis example using the analysis apparatus of the present embodiment. FIG. 5 is a configuration diagram showing a configuration of an experimental apparatus for verifying the analysis result of the present analysis method. FIG. 5A shows a front view of the experimental apparatus 300, and FIG. 5B shows a right side view thereof. A container (made of transparent acrylic) having a width of 100 mm and a depth of 20 mm was used, and a predetermined liquid material 205 was filled to a position of 100 mm from the bottom of the container. A flat plate 301 (made of aluminum) having a length of 95 mm, a width of 15 mm, and a thickness of 2 mm was placed at a height of 50 mm from the bottom of the container. The inclination angle θ of the flat plate 301 was 5 °, 15 °, and 30 °.

Also, a light source 306 (three 500 W halogen lamps) was irradiated from the front and back of the container, respectively. An air blow nozzle 304 having an inner diameter of 1 mm was installed at the bottom of the container, and a compressed air 302 whose flow rate was adjusted by a flow rate adjusting valve 303 was sent to generate a void. Since the size of the void 206 generated from the nozzle 304 is random, a large amount of the void 206 is accumulated in a hemispherical cup 305 having an inner diameter of 8 mm, and then the cup 305 is inverted and floated. Generated. The behavior when the void 206 rises after colliding with the inclined flat plate 301 is measured using a high-speed camera 307 (high-speed camera: Phototron FASTCAM-1024PCI (R), lens: Nikon 50 mm / F2.8) Images were taken under the conditions of a frame rate of 250 fps, a resolution of 1024 × 1024 pixels, a lens aperture value F11, and a shutter speed of 1/10000 seconds. Experimental values of the spherical volume equivalent diameter and velocity of the void 206 were calculated by image processing of the captured moving image. In addition, Reynolds number and drag coefficient when the velocity of the void 206 rising along the wall surface became constant were calculated. As the liquid material 205, silicon oil KF-96L-2cs (R) (Molton number Mo = 1.7E-08) and KF96-1000cs (R) (Molton number Mo = 9.4E + 02) manufactured by Shin-Etsu Silicone are used. The temperature was constant at 20 ° C.

In addition, the region filled with the liquid material 205 in FIG. 5 is modeled as an analysis region, and the analysis processing is performed with the flowchart shown in FIG. 2 to calculate the analysis value of the velocity of the void 206 at various sphere volume equivalent diameters. did. Reynolds number and drag coefficient when the velocity of the void 206 rising along the wall surface became constant were calculated. It should be noted that Formula 23 is used as an evaluation formula for the drag coefficient of the void floating along the inclined flat plate, and the values of the coefficients and constants of the formula are respectively o = 8.5, q = 11, w = 18, r = -0. .17, and u = 2.9. As the physical property value of the liquid material 205, the physical property value of the silicon oil used in the above experiment was used. The temperature was kept constant at 20 ° C. as in the above experiment, and the resin pressure was 0. As the initial void condition, the setting was made so that the spherical volume equivalent diameter of 0.2 to 10 mm was continuously and randomly generated with the position in the vicinity of the nozzle as in the above experiment and the density as the value of air. The initial time width Δt was set to 0.01 s. In addition, as a comparative example, as an evaluation formula for the drag coefficient of a void that floats along an inclined flat plate, an analysis process similar to that in the above analysis example is performed using Formula 13 that is an evaluation formula for an existing free-floating void. Similar analysis values were calculated.

FIG. 6 shows experimental values and analysis values of the Reynolds number and drag coefficient when the void 206 rising along the wall surface rises at a constant speed. FIGS. 6A to 6C show the results when silicon oil having a Morton number Mo = 9.4E + 02 is used and the inclination angle θ of the flat plate 301 is 30 °, 15 °, and 5 °, respectively. 6 (D) to 6 (E) show the results when silicon oil having a Morton number Mo = 1.1E-09 is used and the inclination angle θ of the flat plate 301 is 30 °, 15 °, and 5 °, respectively. is there. The point (plot) is an experimental value, the dotted line is an analytical value using the conventional equation 13 as an evaluation formula for the drag coefficient of a void floating along the inclined flat plate, and the solid line is the drag coefficient of the void 206 floating along the inclined flat plate. The analysis values using Expression 23 of the present embodiment are shown as the evaluation expressions. From the figure, in any case, the analysis value using Equation 23 of the present embodiment is in good agreement with the experimental value, and the behavior of the void 206 that floats along the wall surface with higher accuracy than the conventional Equation 13 is shown. It can be seen that can be calculated. When the correlation coefficient R between the experimental value and the analysis value was compared, in any case, the value of the correlation coefficient R was higher in the analysis value using Expression 23 of this embodiment. From the above, it was shown that the behavior of the void 206 that floats along the wall surface can be calculated with high accuracy in the analysis processing of the present embodiment.

As described above, since the movement speed of the void is the slowest in the vicinity of the wall surface, by making it possible to predict the behavior of the void in the vicinity of the wall surface with high accuracy, the residual position of the void in the mold 201 can be determined with higher accuracy than before. Predictable. Thereby, optimization of the above-described molded product and process and design support thereof can be performed more efficiently. In particular, when the material flow rate is slow, such as casting, the effect of the force (buoyancy, drag, etc.) applied to the void on the material flow increases, so that the analysis processing effect of this embodiment can be obtained more remarkably. Can do.

DESCRIPTION OF SYMBOLS 100 Void behavior analysis apparatus 110 Operation part 111 Molding part formation process analysis process part 112 Data input process part 113 Model shape and element preparation part 114 Liquid material flow analysis process part 115 Void movement analysis process part 116 Analysis result output process part 120 Storage part 121 Void behavior analysis program storage area 122 Analysis target model shape data storage area 123 Three-dimensional element data storage area 124 Analysis target physical property / equation storage area 125 Boundary / forming condition data storage area 126 Analysis condition data storage area 127 Initial void condition data storage Area 128 Analysis result storage area 130 Input unit 140 Display unit 150 Media reading unit 160 Communication unit 170 Network 180 CAD device 190 External computer 201 Type 202 Part 203 Gate 204 Space 205 Liquid material 206 Void 207 Analysis Area 300 Experimental apparatus 301 Flat plate (aluminum)
302 Compressed air 303 Flow control valve 304 Nozzle 305 Cup 306 Light source 307 High-speed camera

Claims

A void behavior analysis method for analyzing the behavior of voids generated in the molding process of a liquid material injected into a space in a mold using information processing by a computer,
Dividing a model space in which a liquid material is filled into a mold for molding an analysis target product into three-dimensional solid elements;
Properties of liquid materials, molds and parts, initial conditions of void particle generation assuming voids, boundary conditions for setting initial temperature, pressure and mold temperature of liquid materials, initial time increment, and analysis end Entering or reading analysis conditions for setting conditions; and
Performing flow analysis of the liquid material filled in the mold at each analysis time after the time increment at the time increment interval and calculating a state quantity and a viscosity of the liquid material in each three-dimensional solid element When,
In the calculation of the amount of movement caused by buoyancy acting on the void particles riding on the flow of the liquid material in each analysis time, it is determined whether the void particles are in contact with the inner wall of the mold or the wall surface of the part. The drag coefficient of the void particle is calculated as a function including the moving speed of the void particle, the void particle diameter, the viscosity of the liquid material, and the inclination angle θ of the wall surface, and the state quantity of each void is calculated. Calculating from the amount of state and the amount of movement of the void particles;
And a step of displaying on the screen each recorded analysis time and a state quantity of each void at the analysis end time after the analysis end condition is satisfied.
2. The void behavior analysis method according to claim 1, wherein the viscosity of the liquid material is calculated as a function including a temperature and an elapsed time of the liquid material.
2. The void behavior analysis method according to claim 1, wherein the drag coefficient of the void is calculated as a function including a Reynolds number Re, an Etobes number Eo, a Morton number Mo, and a wall inclination angle θ.
The drag coefficient of the void is calculated by Equation 22.

Here, C D : drag coefficient, Re: Reynolds number, Eo: Etobes number, Mo: Morton number, θ: wall inclination angle, h, i, j, l, m, o, p, q, r, s , U: constant,
The void behavior analysis method according to claim 1, wherein:
The drag coefficient of the void is calculated by Equation 23.

Here, C D : drag coefficient, Re: Reynolds number, Eo: Etobes number, Mo: Molton number, θ: wall inclination angle, o, q, r, u, w: constant,
The void behavior analysis method according to claim 1, wherein:
The liquid material is a material that is solid at room temperature and melts by heating (inorganic material, thermoplastic resin material), or a material that cures by heating at liquid temperature (thermosetting resin material). The void behavior analysis method according to claim 1 or 2.
A void behavior analysis device for analyzing the behavior of voids generated in the molding process of a liquid material injected into the space in a mold using information processing by a computer,
Analysis target product shape, mold shape, liquid material, mold and part physical property value, initial condition of void particle generation assuming void, boundary condition to set initial temperature, pressure of liquid material, and initial temperature of mold, And an initial time increment, and an analysis condition for setting an analysis end condition, storing each data in the storage unit, and reading out from the storage unit during processing of each unit;
A model shape / element creation unit that divides a model space in which a liquid material is filled into a mold for molding an analysis target product into three-dimensional solid elements;
The flow rate of the liquid material in each three-dimensional solid element is calculated by performing a flow analysis of the liquid material filled in the mold at each analysis time after the time increment at the time increment interval. A material flow analysis processing unit;
In the calculation of the amount of movement caused by buoyancy acting on the void particles riding on the flow of the liquid material in each analysis time, it is determined whether the void particles are in contact with the inner wall of the mold or the wall surface of the part. The drag coefficient of the void particle is calculated as a function including the moving speed of the void particle, the void particle diameter, the viscosity of the liquid material, and the inclination angle θ of the wall surface, and the state quantity of each void is calculated. A void movement analysis processing unit that calculates the state quantity and the movement amount of the void particles;
A void behavior analysis device comprising: an analysis result output processing unit that displays each analysis time recorded and a state quantity of each void at the analysis end time after the analysis end condition is satisfied.