JPH07236923A - Simulation method for forming plate - Google Patents

Abstract

PURPOSE:To provide a simulation method for forming a plate, in which a die holding force can be taken into consideration through a simple calculation, in a finite-element analysis for a plate forming. CONSTITUTION:In a present time step, a contact discrimination is carried out between a base material 1 and a wrinkle holding die 4 by S210; a die holding pressure is determined from the contact area obtained in the conditions of the contact discrimination and from a specific wrinkle holding force by S215; a nodal contact force imparting to each contact nodal point is determined by S240; and a finite element analysis is performed by using these results as boundary conditions in the following time step.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for numerically simulating a plastic deformation process of a plate material.

[0002]

2. Description of the Related Art For example, FIG. 21 shows a first multi-step drawing process.
FIG. 22 shows a second step which follows, and these figures are obtained by finite element method analysis by a method in which the clearance C ₀ between the wrinkle holding die 4 and the die 3 is kept constant. .

The finite element analysis procedure is shown in the flowchart of FIG. In the calculation of the current time step, first, a stiffness matrix is created in S110, the created stiffness matrix is solved, and the nodal velocity is obtained. Next, S1
At 20, the strain rate, strain, stress, nodal force, etc. are sequentially obtained from the nodal velocity. Further, in S130, the nodal coordinates are updated to the nodal coordinates used for the calculation of the next time step, and S1
The boundary condition is changed at 40, and the calculation of the next time step is started. These series of calculations are repeated until a predetermined stroke is reached.

[0004]

As described above, the system in which the clearance C ₀ between the wrinkle holding die 4 and the die 3 is constant, that is, the displacement of the surface node contacting the wrinkle holding die follows the die. The following two problems occur when the finite element method analysis is performed by the method of restraining by.

The first problem is that, as shown in FIG. 21, when the plate thickness t of the material 1 is increased from the initial plate thickness t ₀ , the wrinkle holding effect is reflected, but it is added to the material 1. The wrinkle pressing force F depends largely on the size of the clearance C ₀ and is not constant during molding. That is, at the initial stage of molding (FIG. 21 (a)), since the increase in the plate thickness t is small, the reaction force R applied to the wrinkle holding die 4 by the material 1, that is, the wrinkle holding force F is small, and the middle stage ( In FIG. 21B, the wrinkle pressing force F increases as the plate thickness t increases. Furthermore, the end of molding (Fig. 21 (c))
In, the wrinkle holding force F becomes smaller again due to the reduction of the material of the flange portion. Thus, the clearance C
_{When the} finite element method analysis is performed by the method of keeping ₀ constant, it is inevitable that the wrinkle pressing force F fluctuates. However, in actual processing, the wrinkle pressing force F ₀ is a load that is applied by hydraulic pressure or an elastic deformation force of a spring, urethane, or the like and increases at a constant rate or at a constant rate. Therefore, assuming that the clearance C ₀ between the wrinkle holding die 4 and the die 3 is constant, the finite element method analysis is contrary to the actual phenomenon and becomes a problem.

As a second problem, as shown in FIG. 22, assuming that the clearance C ₀ between the wrinkle holding die 4 and the die 3 is constant, the wrinkle holding die 4 is formed at the initial stage of the second step. And the material 1 are separated from each other, and the effect of pressing the wrinkle is not reflected. However, in actual processing, a predetermined wrinkle pressing force F ₀
Since is always added during molding, the analysis goes against the actual phenomenon and becomes a problem.

The present invention has been made in order to solve such a problem, and an object thereof is to obtain a plate forming simulation method for performing a finite element method analysis of a plate forming process in consideration of a wrinkle holding force.

[0008]

A method for simulating plate forming according to claim 1 by a finite element method analysis determines whether or not there is contact between a die and each material surface node, as shown in the flow chart of FIG. Step 210 for judging, step 215 for calculating a contact area between the die and the material based on the result of the above judgment, and calculating die pressing pressure applied to this contact area, and contacting the die pressing pressure with the die. It is characterized in that it has a step 240 of converting into a nodal force at each material surface nodal point, and uses the nodal force as a boundary condition for analysis at the next time step.

The simulation method according to claim 2 is
Check whether there is contact between the die and each material surface node (i),
It is determined whether or not (i) is within a predetermined distance D ₀ from the mold, and the total contact area S between the mold and the material is obtained from the above determination result. The contact area S and the predetermined pressing force F _The average pressing force (Pe = F ₀ / S) is calculated from ₀ and this average pressing force Pe is calculated by using the contact area Si represented by each material surface node (i) in contact with the mold. (Gi = Pe × S
After being converted into i), this nodal force Gi is used as a boundary condition for analysis in the next time step.

The simulation method according to claim 3 is
Check whether there is contact between the die and each material surface node (i),
(i) a step of determining whether or not the die is within a predetermined distance D ₀ from the die, a step of determining a contact area between the die and the material based on the determination result, and At the material surface node (i), a step of obtaining a weight Wi depending on a predetermined distance Di from the mold, the weight Wi, and a contact area Si represented by each contacting material surface node (i) , Using a predetermined pressing force F ₀ , the weighted average value of the mold pressing pressure (Pwe = F ₀ / (ΣWiS
i)), a step of calculating a die pressing pressure (Pi = WiPwe) at each contact surface node (i), and a step of converting the die pressing pressure Pi into a node force Gi. The feature is that the nodal force Gi is used as a boundary condition for analysis in the next time step.

According to a fourth aspect of the simulation method,
Check whether there is contact between the die and each material surface node (i),
The next time step is determined from the step of determining whether (i) exists within a predetermined distance D ₀ from the mold, and the total contact area Sb in the previous time step and the total contact area S in the current time step. Total contact area Sf
Extrapolating step, and the extrapolated total contact area Sf
And a predetermined pressing force F ₀ , the average wrinkle pressing pressure (Pe = F ₀
/ Sf) calculation step, and the average pressing pressure Pe
Is converted into a nodal force (Gi = Pe × Si) by using the contact area Si represented by each material surface nodal point (i) in contact with the die, and the nodal force Gi is converted to the next time. It is characterized by being used as a boundary condition for analysis in steps.

A simulation method according to claim 5 is
In determining whether or not there is contact between the die and the material surface node (i), a predetermined distance D ₀ from the die is set with respect to the initial plate thickness t ₀ .
It is characterized in that it is set to 0.005t _{0 to} 0.015t ₀ .

According to a sixth aspect of the simulation method,
The step of calculating the reaction force R that the mold receives from the material by the deformation calculation at the current time step, and the reaction force R
And a step of changing the moving speed of the die in the next time step based on the predetermined die pressing force F ₀ , and controlling the reaction force R received from the material by the die in the next time step. A plate forming simulation method characterized by the above.

[0014]

In the simulation method according to the first aspect, the mold pressing pressure is taken into consideration by obtaining the mold pressing pressure applied to the contact area between the mold and the material and giving it in the form of the boundary condition of nodal force. High-precision finite element method analysis can be performed.

In the simulation method according to the second aspect, the contact judgment between the die and the material and the average pressing pressure Pe can be obtained by a simple calculation, and the pressure Pe is given in the form of a boundary condition called a nodal force. , It is possible to perform high-precision finite element method analysis taking into account the mold pressing pressure.

In the simulation method according to the third aspect, the weight Wi that depends on a predetermined distance Di from the mold is used.
And the die holding pressure Pi taking this weight Wi into consideration.
By calculating and converting into a nodal force, it is possible to consider the die pressing pressure close to the actual working state, and it is possible to perform a highly accurate finite element method analysis.

In the simulation method according to the fourth aspect, since the total contact area Sf of the next time step is extrapolated and the nodal force is converted based on this, the finite element method analysis at the next time step is accurately performed. Highly accurate simulation is possible.

Further, by setting a predetermined distance D ₀ from the mold to 0.005t _{0 to} 0.015t ₀ with respect to the initial plate thickness t ₀ ,
The contact determination becomes accurate, and the actual processing state can be reproduced with higher accuracy.

In the simulation method according to claim 6, the moving speed of the mold in the next time step is changed based on the reaction force R received by the mold from the material and a predetermined mold pressing force F _0. Thus, the reaction force R received from the material by the wrinkle pressing die at the next time step can be controlled so as to be within the allowable value (± ΔF) of the predetermined wrinkle pressing force F ₀ .

[0020]

【Example】

Example 1. 2 is a flow chart of the plate forming simulation according to the first embodiment of the present invention, and FIG. 3 is a block diagram of the plate forming simulation apparatus used in the present embodiment.

The outline of the present embodiment will be described with reference to FIGS. 2 and 3. First, initial data, boundary conditions, etc. are input from the data input unit 10, and in the calculation of the current time step, the stiffness matrix of S110 is calculated. Create / solve (rigidity matrix creating / solving unit 20), strain in S120,
Calculate the stress etc. (calculation unit 30 for strain / stress etc.) in S13
At 0, the nodal coordinates are updated (nodal coordinate updating unit 50). Next, in S210, contact determination between the die and the material (contact determination unit 6
0), and the total contact area between the die and the material at the current time step is calculated at S220 (contact area calculation unit 70) at S23.
Calculate the average wrinkle presser pressure with 0 (Average presser foot pressure calculation unit 8
0) is converted to the nodal force in S240 (the nodal force conversion unit 9
0) is performed. Finally, in S140, the boundary condition is changed (boundary condition changing unit 100), and the calculation of the next time step is performed. These series of calculations are repeated until a predetermined stroke is reached, and the simulated result is output from the output unit 40.

The formulation of the rigid-plastic FEM used in the analysis of this example is to use the constitutive equation (compressive property method) of a slightly compressible rigid-plastic body proposed by Kosakada and Mori. This method has the advantage of enabling high-speed analysis. This is briefly described below ("Plasticity and processing", Journal of Japan Society for Plasticity Processing, Vol. 34, No. 390).

According to the upper bound theorem, among the dynamically acceptable velocity fields, the one that minimizes the functional of Equation 1 below gives the correct answer.

[0024]

[Equation 1]

Further, the equivalent stress and the equivalent plastic strain rate are expressed by the following mathematical formula 2.

[0026]

[Equation 2]

The relationship between the stress and the strain rate is expressed by the following equation (3).

[0028]

[Equation 3]

These equations are discretized using the finite element method. The displacement velocity vector and the strain velocity vector are expressed by the following equation 4 using the nodal velocity vector.

[0030]

[Equation 4]

Substituting the equations (2-1) and (4) into the equation (1) and further setting the variation of Φ as {0}, the equation to be solved is the following equation (5).

[0032]

[Equation 5]

The above equation (5) is equivalent to the nodal force balance equation derived from the principle of virtual work.

Next, the analysis processing of S210 to S250 will be described in detail with reference to FIG. First, as shown in FIG. 8A, the distance Di between the wrinkle pressing die 4 and each material surface node (i) is calculated, and this distance Di and a predetermined distance D ₀ set in advance.
The presence or absence of contact between the material surface node (i) and the crease presser die 4 is determined by comparing with. That is, it is determined that the contact is made if the distance Di ≦ D ₀ and the non-contact is made if Di> D ₀ . Then, the contact area A between the wrinkle holding die 4 and the material 1 is determined.

Next, from said determined contact area A, determine the total contact area S between the blank-holding die 4 and the material 1, average wrinkle presser foot pressure from a predetermined blank holding force F ₀ (Pe = F ₀ / S)
Is calculated (FIG. 8 (b)). Further, at each material surface node (i) in contact with the wrinkle pressing die 4, a contact area Si represented by the node, for example, the average value of the surface area of the elements sharing the material surface node (i) is used. Then, the average wrinkle pressing pressure Pe is converted into the nodal force Gi = Pe × Si. Finally,
These are added to the nodal force of each material surface node (i) obtained in the calculation step of strain, stress, etc. in S120 and used as a boundary condition in the next time step of each material surface node (i).

Example 2. FIG. 4 is a flow chart of a plate forming simulation according to the second embodiment of the present invention, and FIG. 5 is a block diagram of a plate forming simulation apparatus used in this embodiment.

The outline of this embodiment will be described with reference to FIGS. 4 and 5. First, initial data, boundary conditions, etc. are input from the data input unit 10, and in the calculation of the current time step, the rigidity matrix is calculated in S110. Create / solve (rigidity matrix creating / solving unit 20), strain in S120,
Calculate the stress etc. (calculation unit 30 for strain / stress etc.) in S13
At 0, the nodal coordinates are updated (nodal coordinate updating unit 50). Next, in S210, contact determination between the die and the material (contact determination unit 6
0), the total contact area between the die and the material at the current time step is calculated in S220 (contact area calculator 70). Then, in the presser foot pressure calculation unit 85, the weight is calculated (S
310), calculation of weighted average value of wrinkle holding pressure (S32
0), the wrinkle holding pressure Pi (S330) is calculated. Then, based on this wrinkle pressing pressure Pi, conversion to nodal force (nodal force conversion unit 90) is performed in S240. Finally, S1
At 40, the boundary condition is changed (the boundary condition changing unit 100), and the calculation of the next time step is performed. It is characterized in that the series of calculations are repeated until a predetermined stroke is reached to give a distribution to the wrinkle holding pressure Pi.

Next, the analysis process of S310 to S330 will be described in detail with reference to FIG. First, in the calculation of the weight in S310, a predetermined distance D ₀ from the wrinkle holding die at each material surface node (i) determined to be in contact with the wrinkle holding die 4 in the contact determination (S210). Compute a coefficient that depends on. For example, with respect to the distance Di from the wrinkle holding die 4 to each material surface node (i), it becomes 1 when Di = 0 as shown in the following formula (6), and 0 when Di = D _0. Like one
Calculate using the following function. Wi = (D ₀ −Di) / D ₀ (6)

The coefficients thus obtained are weighted by Wi
In step S320, the weighted average value {Pwe = F ₀ / (ΣWiSi)} of the wrinkle holding pressure is calculated at all material surface nodes (i) in contact with the wrinkle holding die 4. And
In S330, the wrinkle holding pressure {Pi = Wi at each contact surface node (i) is calculated from the weighted average value Pwe and the weight Wi.
Calculate Pe}. As a result, as shown in FIG. 9, it is possible to give a distribution of the wrinkle holding pressure according to the distance Di from the wrinkle holding die.

Example 3. 6 is a flow chart of a plate forming simulation according to the third embodiment of the present invention, and FIG. 7 is a block diagram of a plate forming simulation apparatus used in the present embodiment.

In the present embodiment, in the calculation of the current time step, after determining the contact between the mold and the material in S210, the total contact area of the current time step is calculated in S220 (calculation of contact area). Part 70). And S4
It is characterized in that the total contact area of the next time step is extrapolated at 10 (contact area extrapolation section 75), and the average wrinkle pressing pressure is calculated at S420 (average pressing pressure calculating section 80). .

Details of the analysis processing of S410 and S420 of this embodiment will be described. First, the total contact area S between the wrinkle presser die 4 and the material 1 at the current time step obtained at S220 and the total contact area Sb at the previous time step.
And the total contact area S at the next time step
Extrapolate f to obtain. For example, as shown in FIG.
It is obtained by linearly extrapolating f with Sb and S. Next, using the total contact area Sf of the next time step extrapolated in S420 instead of the total contact area S of the current time step, the average wrinkle holding pressure {Pe = F ₀ / S
f} is calculated.

Then, in step S240, the average wrinkle pressing pressure Pe is converted into the nodal force. Finally, S14
The boundary condition is changed at 0, and the process moves to the calculation of the next time step. These series of calculations are repeated until a predetermined stroke is reached.

Example 4. Furthermore, in the determination of the presence or absence of contact between the wrinkle holding die 4 and the material surface node (i) in Examples 1 to 3 (S210), a predetermined distance D ₀ from the wrinkle holding die is set to the initial plate of the material 1. The thickness t ₀ is set to a value of 0.005t ₀ to 0.015t ₀ . As a result, the actual processing can be reproduced more accurately.

Example 5. FIG. 11 shows a flow chart of a plate forming simulation according to the fifth embodiment of the present invention.
In the present embodiment, the moving speed of the wrinkle holding die at the next time step is calculated based on the difference between the reaction force received by the material 1 and the predetermined wrinkle holding force at the current time step. It is intended to correct and control the reaction force. That is, in the calculation of the current time step, first, S
At 500, the initial movement speed of the wrinkle presser die 4 is set.
Then, in S110, the stiffness matrix is created and solved.
Strain, stress, etc. are calculated in S120, and the nodal coordinates are updated in S130. Next, in S510, the reaction force is calculated by S5.
At 20, the wrinkle presser die moving speed is changed. Finally, S
The boundary condition is changed at 140, and the calculation of the next time step is started. These series of calculations are repeated until a predetermined stroke is reached.

The details of the analysis processing in S510 and S520 will be described with reference to FIG. First, calculation of strain, stress, etc. of each material surface node (i) in contact with the wrinkle pressing die 4 (S12
0) Wrinkle presser die 4 is made of material 1 from the nodal force
Calculate the reaction force R received from. Next, based on the difference between the reaction force R and the predetermined wrinkle holding force F ₀ , the moving speed of the wrinkle holding die at the next time step is changed. By changing the moving speed of the wrinkle press die, the reaction force R received from the material by the wrinkle press die at the next time step, that is,
The wrinkle holding force F actually applied to the material is controlled so as to be within the allowable value (± ΔF) of the predetermined wrinkle holding force (F ₀ ).

Experimental Example 1. The cylindrical deep drawing of a disc-shaped material (SPCC) having a blank diameter of 120 mm and a plate thickness of 1.0 mm was analyzed by the finite element method using the method of Example 2 or 4. Predetermined distance D ₀ from the wrinkle press die is 0.01 m
m, the predetermined wrinkle pressing force F ₀ is 1000 kgf, the weight Wi of the node is calculated using the following linear function, Wi = (D ₀ −Di) / D ₀ , and the friction coefficient is the punch shoulder R Part and die shoulder R part were set to μ = 0.23, and other parts were set to μ = 0.10. Considering symmetry, the model is ½ and the total number of elements is 1.
It was set to 000. Material constant is σ = 5 corresponding to SPCC material
7.2ε ^0.23 was used.

FIG. 13 shows how the material is deformed by the finite element method analysis. FIG. 13A shows a state at the initial stage of molding,
FIG. 13B shows a state in the middle stage of molding, and FIG. 13C shows a state in the final stage of molding. It was possible to simulate a situation in which sink marks were generated at the punch shoulder R portion in the middle stage of molding and fracture occurred at that part at the end of molding.

Further, by changing the blank diameter and the wrinkle pressing force F ₀ , a plurality of similar finite element method analyzes of cylindrical deep drawing were carried out. FIG. 14 is a summary of the analysis results. FIG. 15 shows a comparison between the analysis result and the experimental result. The analytical results are in good agreement with the experimental results. Therefore, it was found that the plate forming process using the wrinkle holding die can be analyzed with the finite element method with sufficient accuracy by the method considering the wrinkle holding force F _0, and it can be effectively used for prediction of forming defects such as sink marks and breaks. .

FIG. 16 shows a comparison between the analysis result and the experimental result when the predetermined distance D ₀ from the wrinkle holding die is changed from 0.005 mm to 0.015 mm. Than this,
Predetermined distance D ₀ from the wrinkle press die within the above range (0.0
05t0 ≦ D ₀ ≦ 0.015t0; by setting the initial thickness t0), it was found that the experimental results agree well with the analytical results.

Experimental Example 2. Blank diameter 96mm, plate thickness 1.
The multi-step drawing of a 5 mm disk-shaped material (assuming SPCC) was analyzed by the finite element method using the method of Example 2 or 4. A predetermined wrinkle pressing force F ₀ is set to 200 in the first step.
0 Kgf, 1500 Kgf in the second step, the predetermined distance D ₀ from the wrinkle holding die is 0.015 mm, and the weight Wi
Is calculated using the following linear function, Wi = (D ₀ −Di) / D ₀ , and the friction coefficient is μ = 0.23 for the punch R part and the die R part, and μ = 0 for the other parts. It was set to 10. Considering the symmetry, the model is ½ and the total number of elements is 500. Material constant is σ = 57.2ε corresponding to SPCC material
^0.23 was used. FIG. 17 shows how the material is deformed as a result of the analysis in the first step, and FIG. 18 shows an analysis result in the second step. Compared with the analysis result (see FIG. 21 and FIG. 22) obtained by the finite element method analysis in which the conventional clearance C ₀ is fixed, the wrinkle presser die moves due to the deformation of the material, and the actual machining phenomenon is It turned out to be reproducible.

Experimental Example 3. Using the method of Example 3, the finite element method analysis was performed on the cylindrical deep drawing of a disk-shaped material (SPCC) having a blank diameter of 120 mm and a plate thickness of 1.0 mm. Predetermined distance D ₀ from the wrinkle holding die is 0.01 mm,
When the predetermined wrinkle pressing force F ₀ is 1000 Kgf, the weight Wi
Is calculated using the following linear function, Wi = (D ₀ −Di) / D ₀ , and the friction coefficient is μ = 0.23 for the punch shoulder R part and the die shoulder R part, and the other parts are It was set to μ = 0.10. Considering symmetry, the model is ½ and the total number of elements is 1.
It was set to 000. Material constant is σ = 5 corresponding to SPCC material
7.2ε ^0.23 was used. A plurality of finite element method analyzes of similar cylindrical deep drawing were performed by changing the blank diameter and the wrinkle pressing force F ₀ . FIG. 19 shows a comparison between the analysis result and the experimental result. The analysis result is in good agreement with the experiment result from the analysis result of Experimental Example 1 (FIG. 15), and if the extrapolated total contact area (Sf) of the next time step is used, the finite element method analysis can be performed with higher accuracy. I understood.

Experimental Example 4. In the fifth embodiment, the moving speed of the wrinkle presser die at the current time step is V, the moving speed at the next time step is Vf, and K is a constant, and a linear function Vf = V−K (F _0- R) is used to change the moving speed of the wrinkle presser die, the reaction force R received by the wrinkle presser die from the material at the next time step is within the permissible value of the predetermined wrinkle presser force F ₀ (± It was possible to control so as to fall within ΔF).

[0054]

As described above, according to the invention of claim 1,
By obtaining the die pressing pressure applied to the contact area with the material and giving this pressing pressure in the form of the boundary condition called the nodal force, it is possible to perform a high-precision finite element analysis and a phenomenon close to the actual process deformation process. Can be predicted. Further, the above analysis result is effectively used for prediction of molding defects such as sink marks and breaks, and it becomes possible to set the optimum processing conditions without trial and error. Further, the cost of the mold and the manufacturing period can be shortened.

According to the invention of claim 2, in addition to the effect of the invention of claim 1, it is possible to determine the contact between the die and the material and the average pressing pressure Pe by a simple calculation, and it is possible to obtain a higher accuracy. Finite element method analysis can be performed.

According to the third aspect of the invention, in addition to the effect of the first aspect of the invention, the weight Wi depending on the predetermined distance Di from the die is obtained, and the die taking this weight Wi into consideration is taken into consideration. By calculating the pressing force Pi and converting it into the nodal force, it is possible to perform a highly accurate finite element method analysis in consideration of the pressing force of the mold which is close to the actual machining phenomenon.

According to the invention of claim 4, in addition to the effect of claim 1, the total contact area S of the next time step is
Since f is extrapolated and the nodal force is converted based on the extrapolated f, the finite element method analysis at the next time step is accurately performed, and high-precision simulation is possible.

Further, by setting the predetermined distance D ₀ from the mold to 0.005t _{0 to} 0.015t ₀ with respect to the initial plate thickness t ₀ ,
The contact determination becomes accurate, and the actual processing state can be reproduced with higher accuracy.

According to the sixth aspect of the invention, the moving speed of the mold in the next time step is changed based on the reaction force R received by the mold from the material and the predetermined mold pressing force F _0. Therefore, the reaction force R received from the material by the wrinkle holding die at the next time step is within the allowable value of the predetermined wrinkle holding force F ₀ (±
It can be controlled to fall within ΔF).

[Brief description of drawings]

FIG. 1 is a flow chart for explaining the invention of a plate forming simulation method according to claim 1.

FIG. 2 is a flowchart of a plate forming simulation method according to the first embodiment.

3 is a block diagram of a plate forming simulation device used in Example 1. FIG.

FIG. 4 is a flowchart of a plate forming simulation method according to a second embodiment.

FIG. 5 is a block diagram of a plate forming simulation device used in a second embodiment.

FIG. 6 is a flowchart of a plate forming simulation method according to a third embodiment.

FIG. 7 is a block diagram of a plate forming simulation device used in a third embodiment.

FIG. 8 is a conceptual diagram showing an average wrinkle holding pressure calculation method in the first embodiment.

FIG. 9 is a conceptual diagram showing a wrinkle holding pressure calculation method in the second embodiment.

FIG. 10 is a conceptual diagram showing an extrapolation method of the total contact area in the third embodiment.

FIG. 11 is a flowchart of a plate forming simulation method according to a fifth embodiment.

FIG. 12 is a conceptual diagram of a method for controlling the moving speed of the wrinkle holding die in the fifth embodiment.

13 is a diagram showing a finite element method analysis result of cylindrical deep drawing according to Experimental Example 1. FIG.

FIG. 14 is a graph showing the relationship between the blank diameter and the wrinkle holding force of the analysis result in Experimental Example 1.

FIG. 15 is a graph showing a comparison between the analysis result of the relationship between the blank diameter and the wrinkle pressing force in Experimental Example 1, and the actual experimental result.

FIG. 16 is a graph showing a comparison between the analysis result of the relationship between the blank diameter and the wrinkle holding force and the actual experimental result when the predetermined distance D ₀ from the wrinkle holding die in Experiment Example 1 is changed.

FIG. 17 is a diagram showing an analysis result of a first drawing process according to Experimental Example 2.

FIG. 18 is a diagram showing an analysis result of a second drawing process according to Experimental Example 2;

FIG. 19 is a graph showing a comparison between the analysis result of the relationship between the blank diameter and the wrinkle pressing force in Experimental Example 3 and the actual experimental result.

FIG. 20 is a flowchart showing a conventional plate forming simulation method.

FIG. 21 is a diagram showing an analysis result of a first step of multi-step drawing by a conventional simulation method.

FIG. 22 is a diagram showing an analysis result of a second step of multi-step drawing by a conventional simulation method.

[Explanation of symbols]

1 Material 2 Punch 3 Die 4 Wrinkle presser die A A Wrinkle presser die and material contact area D ₀ Wrinkle presser die predetermined distance F Wrinkle presser force F ₀ Predetermined wrinkle presser force ΔF Wrinkle presser force allowable value Pe Average wrinkle presser pressure Pwe Weighted average wrinkle presser pressure (i) Material surface node number Si Contact area represented by nodes Di Wrinkle presser die to contact node (i) distance Pi Wrinkle presser pressure Wi Weight

Claims (6)

[Claims] 1. A method for simulating plate forming by a finite element method analysis, determining the presence / absence of contact between a die and each material surface node, and determining the contact area between the die and the material based on the determination result. The step of calculating the die pressing pressure applied to this contact area and the step of converting the die pressing pressure into the nodal force at each surface node of each material in contact with the die, Plate forming simulation method characterized by being used as a boundary condition for analysis in the time step of. 2. In a method for simulating plate forming by finite element method analysis, the presence or absence of contact between the die and each material surface node (i) is determined by a distance D ₀ between each node (i) and the die. determining the presence or absence within, the determination result by the search of the total contact area S between the mold and the material, the average pressing pressure from the contact area S and a predetermined pressing force F ₀ Metropolitan (Pe =
F ₀ / S) calculation step, and the above-mentioned average pressing pressure Pe
Is converted into a nodal force (Gi = Pe × Si) by using the contact area Si represented by each material surface nodal point (i) in contact with the die, and the nodal force Gi is converted to the next time. A plate forming simulation method characterized by being used as a boundary condition for analysis in steps. 3. In a method for simulating plate forming by finite element method analysis, the presence / absence of contact between a die and each material surface node (i) is determined by each node (i) being a predetermined distance D ₀ from the die. Determining whether or not it exists in the mold, and determining a weight Wi depending on a predetermined distance Di from the mold at each material surface node (i) that is judged to be in contact with the mold, Calculating a die pressing pressure Pi in consideration of the weight Wi at each contact surface node (i),
A plate forming simulation method comprising a step of converting the die pressing pressure Pi into a nodal force Gi, and using the nodal force Gi as a boundary condition for analysis in the next time step. 4. In a method for simulating plate forming by a finite element method analysis, the presence or absence of contact between the die and each material surface node (i) is determined by each node (i) being a predetermined distance D ₀ from the die. A step of determining whether or not the total contact area Sf in the next time step is extrapolated from the total contact area Sb in the previous time step and the total contact area S in the current time step, Calculating an average wrinkle pressing pressure (Pe = F ₀ / Sf) from the extrapolated total contact area Sf and a predetermined pressing force F ₀ ;
Using the contact area Si represented by each material surface node (i) in contact with the die, the average pressing force Pe is applied to the node force (G
i = Pe × Si), and the above-mentioned nodal force Gi is used as a boundary condition for analysis in the next time step. 5. A predetermined distance D ₀ from the mold is 0.005t _{0 to} 0.015t ₀ with respect to the initial plate thickness t _{0 in} the determination of the presence or absence of contact between the mold and the material surface node (i). The plate forming simulation method according to claim 1, wherein the plate forming simulation is performed. 6. A method of simulating plate forming by a finite element method analysis, a step of calculating a reaction force R received from a material by a mold from a deformation calculation at a current time step, the reaction force R and a predetermined value. It has a step of changing the moving speed of the die at the next time step based on the die pressing force F ₀ , and controls the reaction force R received from the material by the die at the next time step. Sheet forming simulation method.