JP2626496B2 - Method of bending metal plate by linear heating - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention is used to finish a curved member of a ship, bridge, or other metal structure from an initial shape subjected to a primary processing such as a flat plate material or a press to a target curved surface shape. The present invention relates to a method for bending a metal plate by linear heating.

[0002]

2. Description of the Related Art Generally, when a metal plate used for a ship, a bridge or the like is bent, it is often performed by linear heating. This bending by linear heating is performed by applying linear heating to a predetermined position on a flat plate or a metal plate that has been primarily processed by a press, and using in-plane shrinkage and angular deformation of the plate due to the generated plastic strain. To create the desired three-dimensional shape.

In the bending by linear heating, the amount of in-plane shrinkage and the amount of angular deformation are determined by the heating position, direction and heating conditions of the linear heating. Therefore, these heating positions, directions and heating conditions are important. is there.

[0004] At the current processing site, there is no technology based on a theoretical approach focusing on the target intrinsic strain distribution obtained by calculation for forcibly deforming the initial shape to the target shape. The actual situation is that the heating position, the direction, and the heating conditions are determined based on the intuition and skill of a skilled person while detecting the deviation from the target shape by temporarily disposing the heater on the top.

However, in recent years, problems such as the aging of these skilled workers and the accompanying decrease in the number of workers have become remarkable.

Therefore, in recent years, in view of such a situation, a method of bending a plate by linear heating can be performed without requiring special skills, and the processing capability can be improved without requiring special skills. Has been proposed and a patent application has been filed (Japanese Patent Application No. 3-237948).

The recently proposed method determines the position, direction and generated intrinsic strain (intensive strain distribution) of a linear heating wire based on an elastic analysis of a finite element method (FEM). As shown in FIG. 22, first, after inputting geometric information relating to the initial shape and the final formed shape (step I), mesh division of the FEM corresponding to the initial shape is performed (step II). Next, forcibly elastically deform from the initial shape to the final shape, calculate the strain that occurs in the process, separate the calculated strain into in-plane components and bending components, and display the main strain distribution on the graphic screen Display (Step III). Next, paying attention to the strain distribution in the plane, the area where the main strain of compression is large is selected as the heating area, and the direction of heating is perpendicular to the direction of the main strain (step IV). Attention is paid to the region where the absolute value of the bending strain is large, as a heating region, and the direction of heating is set to a direction perpendicular to the main direction where the absolute value of the strain is the maximum (step V).

Next, in order to determine the magnitude of the intrinsic strain to be generated, a forced deformation FEM elasticity analysis in which the stiffness of the elements belonging to the heating region is made smaller than that of the remaining portion is performed again, and the strain concentrated in the heating region is determined. The value of the generated intrinsic distortion is calculated from the value of (step VI). Thereafter, based on these calculations, linear heating is performed to generate an intrinsic strain, thereby processing into a predetermined final shape (step VII).

[0009]

The method proposed and filed recently has the advantage that the bending of the plate by linear heating can be carried out easily, so that it can be carried out without relying on the expert's intuition. However, as shown in (a) to (b) of FIG.
When elasticity analysis is performed, generally, the in-plane component of the target intrinsic strain may show not only a contraction strain (compression strain) but also an extension strain as shown in FIG. In addition, forcible deformation F in which the rigidity of the heating section is reduced to determine the magnitude of the intrinsic strain.
In the EM elasticity analysis, the elongation strain may appear similarly. Bending by linear heating is a method of processing using compression plastic strain generated in a heating portion, and cannot impart elongation strain (← → mark) shown in the lower part of FIG. Therefore, in order to be able to work on the target shape only by linear heating, the above FEM calculation results must all be shrinkage strain (→ ← mark). In FIG. 23 (c), it is necessary to apply a uniform contraction strain at least to the stretch strain portion or as a whole. This corresponds to reducing the target shape or increasing the initial shape. Similarly, in order to achieve a certain amount of bending strain by heating from one side, some in-plane shrinkage is inevitable. Due to these extra shrinkages, the finished target shape has insufficient in-plane dimensions. Although this has been known qualitatively in the past, these cannot be compensated quantitatively, so at the present time, a sufficient margin based on empirical rules must be taken in advance and the final There is a possibility that extra work for trimming and, in some cases, insufficient dimensions may occur. It is well known that in the case of linear heating, not only the contraction strain in the direction perpendicular to the heating wire but also the contraction strain in the heating line direction is always small, but it always accompanies it. Then, it is considered difficult to accurately realize the target eigendistortion distribution. Also, the quantitative relationship between the heating conditions and the generated intrinsic strain is not mentioned in the recently proposed and filed method, so it can be inferred from experience and intuition from the current field technology, bending template and initial shape. The method of selecting and implementing the heating conditions that will generate the necessary deformation amount of each part based on experience is adopted, but as a result of accumulating multiple stages of estimation based on experience and intuition, difficulties, errors, There are problems such as large variations, limited number of people who can do it, and long time to learn. In order to form a curved surface from a flat plate, it is necessary to give a predetermined bending strain and an in-plane strain by some method. However, when focusing on bending strain, the bending strain distribution is relatively simple as shown in FIG. Yes, the main direction is almost constant, so there is no particular problem in creating a work procedure for imparting bending strain, and a substantial part of the actual bending is performed by a machine using bending rollers etc. It can be understood that it can be performed by bending, and it is sufficient to perform bending by partial linear heating. However, it is very difficult to apply the in-plane strain to the plate by mechanical means, and linear heating is an ideal means for such an operation.
As shown in the figure, the direction is not uniform. Further, as described above, tensile strain (elongation strain) cannot be given by linear heating, and shear strain cannot be created by linear heating. Therefore, in order to give the strain shown in FIG. Heating must be performed in the direction of the strain, and the heating wire is directed in various directions, which makes the work difficult and complicated.

Therefore, the present invention further advances the above-mentioned recently proposed and filed plate bending method by linear heating to eliminate the above-mentioned problems, and can be practiced by a layman when a target shape is given. In addition, it is intended to achieve the target intrinsic strain only under desired heating conditions, and to facilitate the work and simplify the equipment.

[0011]

SUMMARY OF THE INVENTION In order to solve the above-mentioned problems, the present invention provides a method for bending a metal plate from an initial shape to a final target shape. Input, perform mesh division by the finite element method based on the initial shape, map the divided shape onto the target shape, and then forcibly deform from the initial shape to the target shape to calculate the target eigendistortion distribution Then, the obtained target eigenstrain distribution is expressed by generated eigenstrain generated by a plurality of grid-like heating lines orthogonal to each other, and at this time, heating conditions and generated eigenstrain for the combination of the heating device and the workpiece are Then, a method of bending a metal plate is used. Also, a method of performing a bending process on a metal plate after performing an elastic simulation for confirming a bent shape by giving the generated intrinsic strain determined when the above-described heating conditions are given to the initial shape. Good.

[0012]

The desired eigenstrain distribution in each element is obtained by forcibly elastically deforming the metal plate from the initial shape to the desired shape, and then the desired eigenstrain distribution is generated by a plurality of mutually orthogonal grid-like heating wires. When the generated eigenstrain is given based on the quantitative relationship and the generated eigenstrain is given based on the quantitative relationship, the heating condition corresponding to the eigenstrain is determined. It is not necessary to rely on a skilled engineer. In addition, it is possible to predict in advance how the target shape is achieved by giving the generated intrinsic strain to the initial shape. Further, since the bending process is performed by heating in a lattice shape, the work becomes easy, and accordingly, the apparatus can be simplified.

[0013]

Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 shows the present invention in which a flat plate having an arbitrary peripheral shape or a steel plate or a metal plate other than steel having an arbitrary curved surface as an initial shape is bent into a target shape (another arbitrary peripheral shape and a curved surface shape). In the flowchart showing the method, after inputting geometric information regarding the initial shape and the target shape (step 1), FIG.
As shown in (a), the mesh is divided by the finite element method (FEM) (step 2), and the divided shape is formed by a suitable mapping method for mapping the initial shape to the target shape as shown in FIG. Mapping onto target shape of plate P (step 3)
I do. Next, each element node position in the initial shape is forcibly elastically deformed by FEM calculation to a corresponding element node position in the target shape, and a strain distribution (target intrinsic strain distribution) in each element is calculated. Then, using the obtained strain distribution as a starting point, by focusing on the in-plane strain and eliminating the elongation strain and the shear strain, an iterative calculation algorithm that is orthogonal and converges on the in-plane intrinsic strain of compression is performed. The target eigendistortion distribution is obtained, and it is possible to determine a shrinkage allowance associated with the mapping method and the processing method (step 4).

Next, as a heating method, the target eigen-strain distribution in the element obtained in the above step 4 is converted into a concentrated strain distribution (generation eigen) generated by a plurality of grid-like heating lines orthogonal to each other. (Distortion) (step 5). In this case, when realizing the target eigenstrain distribution with the generated eigenstrain in step 5 above, for a given combination of a heater (gas flame, high-frequency induction heater, laser light, etc.) and a workpiece, Since a quantitative relationship between the heating conditions (heat input amount per unit time, moving speed, etc.) and the generated intrinsic strain is required, this relationship is determined (step 6). The quantitative relationship between the heating conditions and the generated intrinsic strain is generally determined by accumulating experimental data or by using thermo-elastic plastic FE.
It is obtained by calculating the intrinsic strain generated on the metal plate when the heat input condition (heat input distribution or temperature distribution changing in a time series) is given by M analysis. That is, when calculating the relationship between the above-mentioned heating conditions and the generated intrinsic strain using a thermo-elastic-plastic FEM program whose validity was confirmed by a demonstration experiment, as described later, the problem of thermo-elastic-plastic deformation due to linear heating was considered. When a heating condition is given by developing an efficient calculation method that uses the similarity rule that holds and the governing parameters derived from it, and arranging the calculated results or measured data in a generalized form with those parameters We have devised a means that can efficiently determine the generation intrinsic strain of.

Next, by applying the generated intrinsic strain when the heating conditions obtained in steps 5 and 6 are given to the initial shape, an elasticity simulation of the bent shape is performed and confirmed (step 7). Thereafter, linear heating using a manual or NC controlled heater is performed according to the heating method determined in step 6 (step 8).

The metal plate is formed into a target shape by imparting a generated intrinsic strain by the heating method determined in the steps 1 to 8 described above.

The details will be described below.

Steps 1 to 3 correspond to steps I and II in FIG.

In step 4, by appropriately selecting a mapping method for forcibly deforming and adopting a newly-considered algorithm of iterative convergence calculation, an in-plane compression strain and bending in which in-plane elongation strain and shear strain components are eliminated. A target eigendistortion distribution composed of distortion is obtained, and a shrinkage allowance associated with the mapping method and the processing method can be determined. The simplest example of a method of obtaining the objective eigendistortion will be described. That is, since linear heating cannot give an elongational strain as described above and does not produce a shearing strain, it gives a complicated and in-plane in-plane strain as shown in FIG. Since the heating direction becomes a plurality of different directions and the work becomes difficult, it is necessary to realize a curved surface by in-plane strain composed of only two components of ε _x and ε _y orthogonal to each other, and only compressive strain. I do. For this purpose, an algorithm for calculating an eigen-distortion distribution that is orthogonal and that is composed only of the compressed components is adopted below. A method of calculating the target eigendistortion distribution in which the in-plane distortion is orthogonalized will be described with reference to a numerical example for an actual example of a saddle-shaped surface.

In order to eliminate the elongational strain and the shearing strain components and obtain the orthogonal and compressional intrinsic strain, the following algorithm was considered. The bending strain ε _b and the in-plane strain ε _m when the bending W corresponding to the target shape is forcibly applied to the flat plate are calculated as the large elastic bending problem. Focusing on the in-plane strain, if ε _mx <0, ε ^* _mx = ε _mx ε _mx > 0, ε ^* _mx = 0 if ε _my <0, then ε ^* _my = ε _mx ε _my > 0. If so, ε ^* _my = 0, but γ ^* _mxy = 0. Here, ε ^* _mx , ε ^* _my , and γ ^* _mxy are the first approximations of the intrinsic strain to be obtained. The elastic strains ε _b and Δε _m (Δε _m when the intrinsic strains ε ^* _mx and ε ^* _my at the present stage are given as initial strains at the same time as the deflection W are forcibly given to the flat plate are given by applying the intrinsic strains. Value becomes smaller). Focused on the in-plane strain, with Δε _mx <if it is ^{_{0 Δε * mx = Δε mx Δε}} mx> if it is 0 Δε ^* _my = 0 Δε <if it is ^{_{0 Δε * my = Δε mx Δε}} my> my 0 If so, Δε ^* _my = 0, where Δγ ^* _mxy = 0, and a new intrinsic strain is calculated according to the following equation.

Ε ^* _mx = ε ^* _mx + Δε ^* _mx ε ^* _my = ε ^* _my + Δε ^* _my , where γ ^* _mxy = 0 The above calculations are performed with the correction amounts Δε ^* _mx and Δε ^* _my sufficiently small. The elongation strain is repeated three or four times until the elongation strain becomes zero, the compression strain is left as it is, and only the orthogonal component and the compression component are used. The finally obtained ε ^* _mx and ε ^* _my are the orthogonal compression intrinsic strains. In order to confirm whether or not the correct target eigenstrain distribution is obtained, the bending strain ε _b and the in-plane strain ε ^* _mx ,
ε ^* _my is given to the flat plate as an intrinsic strain and freely deformed, and it is confirmed that the shape matches the target bending W and that no stress is generated in the flat plate.

FIG. 6A shows the orthogonal compression distortion obtained for the curved surface of FIG. 3 according to the above procedure. FIG. 3 shows a shape in which a metal plate P having a long side length L of 2000 mm and a short side length B of 1000 mm is bent to form a saddle-shaped curved surface. In FIG. 6A, focusing on the strain in the Y-axis direction, the absolute value is large at the center of the plate, which corresponds well to the heating procedure performed at the shipyard site. When attention is paid to the strain in the X-axis direction, a large compressive strain is recognized as a feature on the side parallel to the Y-axis of the plate. On the other hand, in order to confirm that the intrinsic strain obtained here was suitable for the purpose of creating a curved surface, verification was performed according to the procedure shown in the steps. In this verification, the bending intrinsic strain is uniquely determined from the curvature of the curved surface. Therefore, the bending strain ε _b obtained in the step is directly given as the intrinsic strain, and the orthogonal strain shown in FIG. Compression intrinsic strain ε ^* _mx , ε
^* The bending and stress distribution when _my was given to a flat plate and freely deformed were calculated. As for the deflection, as shown in Table 1, the relative error from the target curved surface is about 1%.

[0024]

[Table 1] FIG. 7A shows the relative stress distribution of Mises. The magnitude of the stress is on the order of 10 ^-1 (kgf / mm ² ), and the magnitude of the absolute value of each stress component shown in Table 1 is also small. As shown by these deflections W and residual stress, the orthogonal compressive intrinsic strain (ε ^* _mx , ε ^* _my ) obtained by the above procedure is an in-plane intrinsic strain to be given to the plate in order to create a target shape. You can see that there is. FIG. 8 is a contour diagram of a deformed shape when the shape is confirmed based on the in-plane strain of FIG. 6A obtained after the iterative calculation and the bending strain of FIG. 4, and the initial target shape shown in FIG. It can be seen that they match well.

Next, a description will be given of the case where the orthogonal compressive eigenstrains are gathered in a grid or parallel lines as shown in Table 1. If the eigenstrain is applied by linear heating, the eigenstrains are spaced at intervals. Given in the form. Therefore, a more practical characteristic strain distribution is a distribution concentrated on the heating wire, and such a distribution can be calculated by the following method. That is, basically, the calculation is performed in the same procedure as described above, but the elastic modulus of the element corresponding to the heating line is simply set to be smaller than about 1/1000 of the other part, and the elastic strain is reduced. Focus on the line. The eigenstrain distribution obtained in this way is as shown in FIGS. 6 (b) and 6 (c). In other words, the eigenstrain distribution shown in FIG. 6 (b) is a case where the orthogonal compression eigenstrains aggregated in a lattice shape are given, that is, a case where the eigenstrains are concentrated on the lattice-shaped heating wires.
The eigenstrain distribution shown in (c) is a case in which orthogonal compression eigenstrains converged in a parallel line shape are given, that is, a case in which eigenstrains are concentrated on a heating wire in only one direction. When the intrinsic strain is concentrated on the heating line in this way, the orthogonal compression intrinsic strain (ε ^* _mx ) distributed along the edge of the plate, which is observed in FIG.
The results correspond well to linear heating by skilled workers. Further, the error caused in the bending when these inherent strains are applied to the flat plate is small as shown in Table 1. Therefore, it can be seen that a curved surface can be created from the intrinsic strains gathered in a lattice or parallel lines. FIG. 9 is a contour diagram of the deformed shape when the shape is confirmed based on FIG.

On the other hand, when attention is paid to the stress, as shown in Table 1 or FIG. 7 (b) showing the stress distribution when the intrinsic strain is concentrated on the grid-shaped heating wire, the grid-shaped heating becomes almost stress-free. However, in the case of unidirectional parallel heating, only the shear stress value was 4.1 kgf / as shown in Table 1 or FIG.
It is as large as mm ^2. This indicates that heating in only one direction cannot completely impart in-plane strain required for bending.

Next, the formulation of the heating method in step 5 will be described. Several methods are conceivable for creating a work procedure for linear heating based on the intrinsic strain distributions obtained in the forms shown in FIGS. First, by appropriate selection of the heating device and heating conditions, the heating conditions of small heat input dominated by bending strain and the heating conditions of large heat input dominated by in-plane shrinkage strain are assumed. A method of applying in-plane strain, which is provided by a combination of heat or press working, will be described. For example, in the first method, one reference heating condition for the purpose of drawing is selected, and the density or number of actual heating wires at each position is determined based on the amount of shrinkage per heating wire. As a second method, the position of the heating wire is determined by providing a groove a as shown in FIG. 6B, and the heating conditions on each heating wire are changed continuously or stepwise. This is a method of changing the amount of contraction.

Also, if the magnitude and distribution of the strain to be given by the aperture are apparent in advance as shown in FIGS. 6A, 6B, and 6C, the shrinkage that must be expected for linear heating. Can be calculated. In this case, the additional amount of shrinkage generated to give bending strain is negligible, but can be considered if necessary.

Based on the above, plate bending by grid heating or parallel heating becomes possible, and FIG. 6 (a) (b) (c)
The heating temperature, heating time, heating rate, heat input and other heating conditions are selected and heated according to the amount of shrinkage determined based on the intrinsic strain distribution shown in the above, and the target curved shape is formed. Is displayed.

Next, a specific embodiment for obtaining a quantitative relationship between the heating condition in step 6 and the generated intrinsic strain will be described. (A) In the case of obtaining the generated intrinsic strain by giving a heating condition Assuming a gas flame of input heat quantity Q = 985.6 cal / sec, heating is given as a forced heat flux q from the plate surface,
q is an axisymmetric Gaussian distribution such as

[0031]

(Equation 1) And has a spread of κ = 7.75 × 10 ⁻⁴ mm ⁻² . Heat source moving speed v = 1mm / sec and thickness h = 16mm
Shows an example of obtaining a transverse shrinkage [delta] _m and angular distortion φ plate of when heated linear. In this case, the following material physical property values are used.

Λ = 0.160 cal / mm · sec. ° C. Cp = 0.098 cal / g · ° C. ρ = 0.00782 g / mm ^{3 When the} heat penetration coefficient p and the heat diffusion coefficient k are obtained, p = (λCpρ) ^{1 / 2} = 0.0035 cal / mm ² · ° C k = λ / Cpρ = 20.9 mm ² / sec where λ: thermal conductivity of metal plate Cp: specific heat of metal plate ρ: specific gravity of metal plate The dominating parameters β and ζ are β = Q / (p ² vh ³ ) ^1/2 = 4.4 × 10 ³ ζ = (vh / k) ^1/2 = 0.88. β is a parameter proportional to the maximum temperature of the surface of the plate heated by the heat source, and ζ is a parameter corresponding to the heat source moving speed.

FIG. 15 shows the change in the amount of angular deformation by the parameters β and ζ, and FIG. 16 shows the change in the amount of in-plane lateral contraction by the parameters β and ζ. Reading _m , it can be seen that φ = 0.006 rad δ _m = 0.025 mm.

When the similarity rule of the thermal elasto-plastic deformation due to the moving heat source is introduced, the shape of the target plate and the width of the heat source are geometrically similar, and the material of the metal plate is the same, and the thermal and mechanical properties are the same. , The above parameters β, β
Are the same, the temperature distributions at the similarized time and position match, and similar deformation occurs.

FIG. 10A shows an example of the application of the similarity rule.
Table 2 shows the results of setting specific numerical values for the two types of models shown in (b).

[0036]

[Table 2] In this example, an axially symmetric heat source is shown as shown in the figure, but various methods can be considered as the heat source. The method proposed here can be utilized corresponding to those heat source shapes.

Here, the plate thickness 8 mm and the width 3 shown in FIG.
M8 is a model having a thickness of 00 mm and a length of 300 mm, and M1 is a model having a thickness of 16 mm, a width of 600 mm and a length of 600 mm shown in FIG.
Call it 6.

As can be seen from Table 2, the geometric shape is 2
In the case of double, in order to generate similar deformation, heat input Q
It should be understood that は must be twice and the heat source moving speed v must be 1/2 times.

FIGS. 11 and 12 show the heating line of each of the plates M8 and M16, the cross-sectional position at the center in the plate length direction, and the temperature history accompanying the movement of the heat source occurring on the front and back surfaces of the plates.

The vertical axis of the graph indicates the temperature of the section. The horizontal axis of the graph is the standardized relative time, but also corresponds to the position in the plate length direction. Τ = 0.5 is the center in the plate length direction (Y direction in FIG. 10), τ = 1 .0 is the end. β,
It can be seen that in M8 and M16 where ζ is equal, the temperatures at the corresponding positions match.

FIG. 13 shows the history of the angular deformation associated with the movement of the heat source in the cross section at the center in the longitudinal direction of the heating wire M8 and M16. The vertical axis is the amount of angular deformation (radian),
The horizontal axis is the same as in FIGS.

FIG. 14 shows the history of contraction deformation in the sheet width direction in the cross section at the center in the sheet length direction of the heating lines M8 and M16.

13 and 14, it is clear that the change with time and the difference in the amount of deformation itself when the heat source moving speed is fast (ζ = 4.4) and when it is slow (ζ = 1.9). I can take it.

FIG. 15 is a graph in which the series calculation results obtained by changing β and ζ are arranged.

Β is 3.2 × 10 ³ (corresponding to the maximum temperature on the plate surface of about 445 ° C.) 4.4 × 10 ³ (corresponding to the maximum temperature of the plate surface of about 615 ° C.) 5.7 × 10 ³ ( (Corresponding to the maximum temperature of the plate surface of about 785 ° C).

The vertical axis represents the amount of angular deformation (radian), and the horizontal axis represents ζ.
It can be seen that the larger the β (the higher the surface temperature), the greater the amount of angular deformation (corresponding to the heat source moving speed).

FIG. 16 shows the relationship between the amount of shrinkage in the horizontal direction and the parameters in the cross section at the center in the longitudinal direction of the plate on the heating line.

The vertical axis is the contraction amount, and the horizontal axis is the same as FIG.

FIG. 17 shows the relationship between the shrinkage strain in the width direction and the parameter at the center position in the width direction on the same cross section as in FIG. The amount of bending strain is represented by a difference in plastic strain between the plate surface and the center of the plate thickness. FIG. 17 shows FIG.
15 can be considered as a figure that can be read in a unified manner.

FIG. 18 is similar to FIG.
The relationship between the amount of angular deformation (radian) and the lateral shrinkage (mm) when the degree of concentration κ of the distribution is changed is considered, considering an axially symmetric heating source as shown in FIG. Assuming that heating is given as a forced heat flux q from the plate surface, q is an axisymmetric Gaussian distribution as

[0051]

(Equation 2) Here, r is the distance from the center of the heat source qmax: κ in the case of the heat flux at the center of the heat source is plotted on the horizontal axis. in this case,
κ represents the degree of spread of q (r). The larger κ is, the more concentrated, and the smaller κ, the more diffuse.

The relationship between q and Q is Q = πqmax / κ.

According to this graph, even when the heat input amount and the heating rate are the same, the deformation is different if the heat input distribution pattern of the heat source is different. That is, an important finding that the efficiency of bending is greatly changed is provided. (B) When the heating condition is obtained from the generated intrinsic strain An example in which a heating method is determined from the target intrinsic strain obtained in step 4 is shown. The target intrinsic strain in the plane as shown in FIG. 6B is calculated, and the amount of shrinkage in the Y direction to be given is obtained by multiplying the target intrinsic strain by the element width. In this case, it is possible to know what heating conditions (Q, v) should be used for heating. When the plate thickness is 16 mm, the characteristic value of the generated intrinsic strain is
It is assumed that the contraction amount δ _{m in the} Y direction is specified to be 0.05 mm.

In FIGS. 15 and 16, a position is searched for where the angular deformation is as small as possible and the shrinkage is 0.05 mm.

In FIG. 21 where FIG. 16 is reproduced, a line parallel to the horizontal axis is drawn so that the amount of lateral contraction becomes 0.05 mm, and β
If = 5.7 × 10 ³ , ζ = about 0.9. FIG.
20, where β = 5.7 × 10 ³ , ζ
Looking at the angular deformation at the position of = 0.9, it is sufficiently small at about 0.001 rad, and it can be seen that almost only in-plane distortion can be given.

[0056]

(Equation 3) Therefore, a gas flame having a strength of 1339 cal / sec is 1.1 mm /
If linear heating is performed at a moving speed of sec, the required δ _m = 0.0
5 mm is achieved, and the angular deformation φ is sufficiently small.

Steps 5 and 6 as described above
When bending the metal plate by the heating method determined in the above,
Given the required generated intrinsic strain, it can be bent into the target shape. In addition, if necessary, the intrinsic shape generated by heating by the heating method obtained in the above steps 5 and 6 is given to the initial shape in step 7 and the elasticity of the bent shape is simulated for confirmation. Can be.

[0058]

As described above, according to the method of bending a metal plate by linear heating of the present invention, the following excellent effects can be obtained. (i) Calculate the target intrinsic strain distribution in each element and separate it into the in-plane component and the bending component. If the bending component is applied by pressing or linear heating with small heat input, the remaining in-plane component will be represented by the bending method according to the flow shown in FIG. Can be found even by amateurs, and because the heating direction can be fixed in two fixed directions, the work is easy and the equipment can be simplified. In addition, the characteristic value of the generated intrinsic strain to be given in the element is specified. In this case, it is possible to determine the heating condition using a data bank that gives the relationship between the heating condition and the generated intrinsic strain as given in FIGS. (ii) Due to the above (i), the conventional linear heating bending method which had to rely on a skilled engineer because it was a complicated phenomenon containing many trial and error elements, was converted to an apparatus or an optimal processing method. Can now be selected.

[Brief description of the drawings]

FIG. 1 is a flowchart illustrating an embodiment of the method of the present invention.

FIGS. 2A and 2B show mapping from an initial shape to a target shape and forced deformation. FIG. 2A is a diagram of FEM mesh division, and FIG.

FIG. 3 is a diagram showing a shape of a curved surface aimed at performing an experiment on an actual plate.

FIG. 4 is a vector diagram showing a bending strain distribution given when a curved surface is formed from a flat plate.

FIG. 5 is a vector diagram showing an in-plane strain distribution given when a curved surface is formed from a flat plate.

6A and 6B show in-plane eigendistortion, where FIG. 6A shows a case where distributed orthogonal compression eigenstrain is given, and FIG. 6B shows a case where distributed orthogonal compression eigenstrain is given in a grid pattern. (C) is a diagram in the case where the orthogonal compression eigen-distortion converged in parallel lines is given.

FIG. 7 shows a stress distribution, in which (a) is a diagram of a stress distribution calculated when a distributed orthogonal compression intrinsic strain is given;
(B) is a diagram of the stress distribution calculated when the orthogonal compressive eigenstrains are aggregated in a lattice, and (c) is a diagram of the stress distribution calculated when the orthogonal compressive eigenstrains are aggregated in a parallel line. It is.

8 is a contour diagram of a deformed shape showing a confirmed shape due to the in-plane strain shown in FIG. 6A and the bending strain shown in FIG.

FIG. 9 is a contour diagram of a deformed shape showing the confirmed shape according to FIG.

10A and 10B show an application example of the similarity rule. FIG. 10A is a perspective view of a model M8, and FIG. 10B is a perspective view of a model M16.

FIG. 11 is a diagram showing a comparison of temperature histories at corresponding positions of models M8 and M16 when parameter ζ = 4.4.

FIG. 12 is a diagram showing a comparison of temperature histories at corresponding positions of models M8 and M16 when parameter ζ = 1.9.

FIG. 13 is a diagram showing a comparison of temporal changes in angular deformation at corresponding positions of models M8 and M16.

FIG. 14 is a diagram showing a temporal change of an in-plane lateral contraction amount at a corresponding cross section of models M8 and M16.

FIG. 15 is a diagram showing a change in the amount of angular deformation according to parameters β and ζ.

FIG. 16 is a diagram illustrating a change in an in-plane lateral shrinkage amount according to parameters β and ζ.

FIG. 17 shows parameters β and の of plastic strain in a central section.
FIG. 6 is a diagram showing a change due to

FIG. 18 is a diagram showing the influence of the spread of a heat source on deformation.

FIG. 19 is a diagram showing a change in maximum temperature depending on parameters β and ζ.

FIG. 20 is a diagram showing angular deformation and reading β from a parameter ζ.

FIG. 21 is a view showing heat shrinkage and reading of β from a parameter ζ.

FIG. 22 is a flowchart showing an embodiment of a method of bending a plate by linear heating, which has been recently filed.

23A and 23B show in-plane distortion components when forcibly deformed from an initial shape to a target shape, where FIG. 23A is a diagram showing the initial shape, FIG. 23B is a diagram showing the target shape, and FIG. It is an inner principal distortion vector diagram.

[Explanation of symbols]

 1 Step 1 2 Step 2 3 Step 3 4 Step 4 5 Step 5 6 Step 6 7 Step 7 8 Step 8 P Metal plate

Continued on the front page (72) Inventor Yukio Ueda 11-1 Mihogaoka, Ibaraki-shi, Osaka Pref., Osaka University Welding Engineering Laboratory (72) Inventor Eiichi Murakawa 11-1 Mihogaoka, Ibaraki-shi, Osaka Pref. Inventor Rashwan Ahmed Mohamed 11-1 Mihogaoka, Ibaraki City, Osaka Prefecture Welding Engineering Laboratory, Osaka University (56) References JP-A-5-76947 (JP, A) JP-A-6-226360 (JP, A)

Claims (2)

(57) [Claims] In order to bend a metal plate from an initial shape to a final target shape, first, geometric information of the initial shape and the target shape is input, and mesh division by the finite element method is performed based on the initial shape. Then, the divided shape is mapped onto the target shape, the target specific strain distribution is calculated by forcibly deforming from the initial shape to the target shape, and the obtained target specific strain distribution is converted into a plurality of mutually orthogonal grids. It is expressed by the generated eigenstrain generated by the heating wire of the shape, and at this time, the quantitative relation between the heating condition and the generated eigenstrain for the combination of the heating device and the workpiece is used. A method for bending a metal plate by linear heating. 2. In order to bend a metal plate from an initial shape to a final target shape, first, geometric information of the initial shape and the target shape is input, and mesh division by the finite element method is performed based on the initial shape. Then, the divided shape is mapped onto the target shape, the target specific strain distribution is calculated by forcibly deforming from the initial shape to the target shape, and the obtained target specific strain distribution is converted into a plurality of mutually orthogonal grids. It is expressed by the generated intrinsic strain generated by the heating line in a shape, and at this time, the quantitative relation between the heating condition and the generated intrinsic strain for the combination of the heating device and the workpiece is used, and then the heating condition is given. After performing elasticity simulation for confirming the bent shape by applying the generated intrinsic strain obtained at the time to the initial shape, bending the metal plate is characterized by performing bending processing of the metal plate Song Processing method.