JPH0760368A - Bending method of metal plate by linear heating - Google Patents

Abstract

PURPOSE:To execute bending by means of linear heating of a metal plate without depending on skilled engineer. CONSTITUTION:After the geometrical information of initial shape and objective shape is inputted (step 1), the mesh dividing of objective shape by the infinite element method is executed (step 2), the divided shape is mapped on the objective shape (step 3). The initial shape is forcedly elastic-deformed to the objective shape so as to obtain objective specific strain in each element (step 4). The obtained objective specific strain is realized to a caused specific strain by means of plural intersecting lattice state heating lines (step 5). By seeking the quantative relationship between heating condition and causing specific strain, the caused specific strain under the provided heating condition is obtained (step 6). By the heating method obtained by step 5, 6, the bending is executed by imparting the caused specific strain to the objective shape.

Description

Detailed Description of the Invention

[0001]

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

[0002]

2. Description of the Related Art In general, bending of a metal plate used for ships, bridges and the like is often performed by linear heating. This bending by linear heating uses linear heating at a predetermined position of a flat plate or a metal plate that is primarily processed by a press, and uses 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 process by the linear heating, the in-plane shrinkage amount and the angular deformation amount are determined by the heating position, the direction and the heating condition of the linear heating. Therefore, these heating position, direction and heating condition are important. is there.

At the current processing site, there is no technology based on a theoretical approach focusing on the distribution of the target intrinsic strain obtained by the calculation of forced deformation from the initial shape to the target shape. It is the actual situation that the heating position, direction, and heating condition are determined by the intuition and skill of an expert while detecting the deviation from the target shape by temporarily disposing it above.

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 view of the above circumstances, a method of bending a plate by linear heating which enables the linear heating work requiring skill to be performed without requiring special skill and the processing capacity can be improved recently. Has been proposed and a patent application has been filed (Japanese Patent Application No. 3-237948).

The recently proposed method is to determine the position, direction and generated intrinsic strain (concentrated strain distribution) of the linear heating wire based on the elastic analysis of the finite element method (FEM). As shown in FIG. 22, first, geometric information about the initial shape and the final shape is input (step I), and then the FEM mesh division corresponding to the initial shape is performed (step II). Then, as the determination of the heating position and direction, forcibly elastically deform from the initial shape to the final shape, after calculating the strain that occurs in the process, the calculated strain is separated into in-plane component and bending component, respectively. The principal strain distribution of is displayed on the graphic screen (step III). Next, paying attention to the in-plane strain distribution, select the region where the main strain of compression is large as the heating region, and set the heating direction at right angles to the direction of the principal strain (step IV), and also in the distribution of bending strain. Paying attention, a region having a large absolute value of bending strain is added to the heating region, and the heating direction is perpendicular to the main direction having the maximum absolute strain value (step V).

Next, in order to determine the magnitude of the intrinsic strain to be generated, the forced deformation FEM elastic analysis in which the rigidity of the element 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 re-executed. The value of the generated intrinsic distortion is calculated from the value of (step VI). Then, based on these calculations, linear heating is performed to generate an intrinsic strain, thereby processing into a predetermined final shape (step VII).

[0009]

In the case of the method proposed and applied recently, the plate can be easily bent by linear heating, which is advantageous in that it can be carried out without resorting to the intuition of a skilled person. However, forced deformation FEM as shown in (a) to (b) of FIG.
In the case of performing elastic analysis, in general, the in-plane component of the target intrinsic strain may appear not only the contraction strain (compressive strain) but also the extension strain as shown in FIG. In addition, the forced deformation F in which the rigidity of the heating part is lowered to determine the magnitude of the intrinsic strain
Elongation strain may also appear in the EM elasticity analysis. Bending by linear heating is a method of processing by utilizing compressive plastic strain generated in a heated portion, and extension strain (← → mark) seen in the lower portion of FIG. 23C cannot be applied. Therefore, in order to be able to process the target shape only by linear heating, all the above FEM calculation results must be shrinkage strains (→ ← marks). In FIG. 23 (c), it is necessary to apply a uniform shrinkage strain at least to the stretch strain portion or as a whole. This corresponds to shrinking 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 unavoidable. Due to these extra contractions, the finished target shape has insufficient in-plane dimensions. Although this is qualitatively known in the past, it is not possible to compensate them quantitatively, so at the present time, a sufficient margin based on an empirical rule is set in advance and the final There is a possibility that extra work for trimming and alignment, or in some cases, insufficient dimensions may occur. When linear heating is performed, it is well known that not only the contraction strain in the direction perpendicular to the heating line but also the contraction strain in the direction of the heating line is small, but it is well known. In addition, it is considered difficult to accurately realize the target intrinsic strain distribution. Further, since the quantitative relationship between the heating conditions and the generated intrinsic strain is not mentioned in the method recently proposed and applied, it is inferred from experience and intuition from the bending site and the initial shape, which is the current field technology. The heating condition that will generate the required deformation amount for each part is selected based on experience, and the method is adopted.However, as a result of accumulating multiple stages of estimation based on experience and intuition, difficult, error, There are problems such as large variation, limited number of people, and long learning time. In order to form a curved surface from a flat plate, it is necessary to give a predetermined bending strain and in-plane strain by some method. However, focusing on the bending strain, the bending strain distribution is relatively simple as shown in FIG. Since the main direction is almost constant, there is no particular problem in creating a work procedure for imparting bending strain, and in actual bending, a considerable part of the processing is done by a machine such as a bending roller. It can be seen that it can be performed by bending, and it suffices to partially perform bending by linear heating. However, as for the in-plane strain, it is very difficult to apply it to the plate by mechanical means, and linear heating is an ideal means for such work, but the in-plane strain distribution is as shown in FIG.
As shown in, it is complicated and the directions are not constant. Furthermore, as described above, tensile strain (elongation strain) cannot be applied by linear heating, and shear strain cannot be created by linear heating. Therefore, in order to apply the strain of FIG. Since heating must be performed in the direction of strain, the heating wire faces various directions, which makes the work difficult and the equipment becomes complicated.

Therefore, the present invention eliminates the above-mentioned problems by further advancing the above-mentioned recently proposed and applied method of bending a plate by linear heating, and can be carried out even by an amateur even if a target shape is given, At the same time, it is intended to realize the objective intrinsic strain only with desired heating conditions, and to facilitate the work and simplify the equipment.

[0011]

In order to solve the above-mentioned problems, the present invention first bends a metal plate from an initial shape to a final target shape by first providing geometric information of the initial shape and the target shape. Input, perform mesh division of the finite element method based on the initial shape, map the divided shape onto the target shape, then forcibly deform from the initial shape to the target shape and calculate the target intrinsic strain distribution Then, the obtained target intrinsic strain distribution is expressed by the generated intrinsic strain generated by a plurality of grid-shaped heating wires that are orthogonal to each other, and at this time, the heating conditions and the generated intrinsic strain for the combination of the heating device and the workpiece are Using the quantitative relation of, the elastic characteristic for confirming the bent shape is given by applying the generated intrinsic strain obtained when the heating condition is given to the initial shape, and Song And how to do the processing.

[0012]

[Function] The metal plate is forcibly elastically deformed from the initial shape to the target shape to obtain the target intrinsic strain distribution in each element, and then the target intrinsic strain distribution is generated by a plurality of grid-like heating wires that intersect at right angles. It is expressed as an intrinsic strain, and when the generated intrinsic strain is given based on the quantitative relationship, the heating condition corresponding to it is obtained.Therefore, by giving this generated intrinsic strain to the initial shape, It is only necessary to predict the degree of achievement in advance and perform heating with a plurality of heating wires under the required heating conditions, and it is not necessary to rely on a skilled engineer. Further, since the bending is performed by heating in a grid pattern, the work is facilitated, and the device can be simplified accordingly.

[0013]

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

FIG. 1 shows a flat plate having an arbitrary peripheral shape, a steel plate having an initial shape of an arbitrary curved surface, or a metal plate other than steel as a target shape (another arbitrary peripheral shape and curved surface shape). In the flowchart showing the method, geometric information about the initial shape and the target shape is input (step 1), and then, based on the initial shape of the metal plate P, as shown in FIG.
As shown in (a), mesh division of the finite element method (FEM) is performed (step 2), and the divided shape is converted into a metal as shown in FIG. 2 (b) by an appropriate mapping method that maps the initial shape to the target shape. Map onto the target shape of plate P (step 3)
To do. Then, each element node position in the initial shape is forcibly elastically deformed to the corresponding element node position in the target shape by FEM calculation, and the strain distribution (target intrinsic strain distribution) in each element is calculated. Next, using the obtained strain distribution as a starting point, by focusing on the in-plane strain and excluding the extension strain and the shear strain, an iterative calculation algorithm that is orthogonal and converges to the in-plane intrinsic strain of compression The target intrinsic strain distribution is obtained, and it becomes possible to determine the shrinkage margin associated with the mapping method and the processing method (step 4).

Next, as a method of designing the heating method, the target intrinsic strain distribution in the element obtained in step 4 is set to the concentrated strain distribution (generation intrinsic strain distribution) generated by a plurality of grid-shaped heating lines orthogonal to each other. The distortion is approximately expressed (step 5). In this case, when the target intrinsic strain distribution is realized by the generated intrinsic strain in step 5, for a given combination of the heater (gas flame, high frequency induction heater, laser light, etc.) and the work material, 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 should be obtained (step 6). The quantitative relationship between the heating conditions and the generated intrinsic strain is generally obtained by accumulating experimental data or by thermoelastic-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 that changes in time series) is given by M analysis. That is, when calculating the relationship between the heating conditions and the generated intrinsic strain using the thermo-elasto-plastic FEM program, the validity of which has been confirmed by empirical experiments, as described later, regarding the thermo-elasto-plastic deformation problem due to linear heating, By developing an efficient calculation method using the applicable similarity rule and the governing parameters derived from it, and organizing the calculated results in a generalized form with those parameters, the generation eigenvalue when the heating condition is given We devised a means to obtain the distortion efficiently.

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

By applying the generated intrinsic strain to the metal plate by the heating method obtained in the procedure from step 1 to step 8 above, the metal plate can be bent into a target shape.

The details will be described below.

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

In step 4, the orthogonal in-plane compressive strain and bending in which the in-plane elongation strain and shear strain components are eliminated by appropriately selecting the mapping method when forcedly deforming and adopting a newly-considered iterative convergence calculation algorithm. The objective intrinsic strain distribution consisting of the distortion and the strain can be obtained, and the shrinkage allowance associated with the mapping method and the processing method can be determined. The simplest example of the method for obtaining this objective intrinsic distortion is shown. That is, since the linear heating cannot give elongation strain or shear strain as described above, in order to give in-plane strain which is complicated and whose direction is not constant as shown in FIG. In addition, since the heating direction becomes different directions and the work becomes difficult, it is necessary to realize a curved surface with in-plane strain composed of two orthogonal components ε _x and ε _y and only compression strain. To do. Therefore, an algorithm for calculating an intrinsic distortion distribution which is orthogonal and is composed only of compressed components is adopted below. A method for calculating the target intrinsic strain distribution by orthogonalizing the in-plane strain will be described while showing numerical examples for the saddle-shaped curved surface as an example.

The following algorithm was considered in order to eliminate the elongation strain and shear strain components and obtain the orthogonal and compressive intrinsic strain. The bending strain ε _b and the in-plane strain ε _m when the deflection W corresponding to the target shape is forcibly given to the flat plate are calculated as a large elastic deflection problem. _Paying attention to the in-plane strain, if ε _mx <0, then ε ^* _mx = ε _mx ε _mx > 0, then 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. Elastic strains ε _b and Δε when the inherent strains ε ^* _mx and ε ^* _my are applied to the plate at the same time and the deflection W is forcibly given.
Calculate _m (Δε _m becomes smaller in absolute value by giving intrinsic strain). 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 there is Δε ^* _my = 0, however, 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 However, γ ^* _mxy = 0 The above-mentioned calculation of the correction amounts Δε ^* _mx and Δε ^* _my are sufficiently small. Repeating 3 to 4 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 obtained, and ε ^* _mx and ε ^* _my finally obtained are orthogonal compression intrinsic strains. To confirm whether the correct target intrinsic strain distribution is obtained, the bending strain ε _b and the in-plane strain ε ^* _mx obtained in the step,
Give ε ^* _my as an intrinsic strain to a flat plate and allow it to freely deform, and confirm that its shape matches the desired flexure W and that no stress is generated on the plate.

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

[0024]

[Table 1] In addition, FIG. 7A shows the Mice's relative stress distribution. The magnitude of 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, and it can be considered that there is almost no stress. As shown by these deflections W and residual stresses, the orthogonal compression intrinsic strain (ε ^* _mx , ε ^* _my ) obtained by the above procedure is the in-plane intrinsic strain to be given to the plate in order to produce the desired shape. I know there is. FIG. 8 is a contour diagram of the deformed shape when the shape is confirmed based on the in-plane strain of FIG. 6 (a) and the bending strain of FIG. 4 obtained after the iterative calculation. You can see that they agree well.

Next, description will be made on the case where the orthogonal compression intrinsic strains gathered in the lattice shape or the parallel line shape shown in Table 1 are given. When the intrinsic strain is given by the linear heating, the intrinsic strains are lined at intervals. Given to you. Therefore, a more practical intrinsic strain distribution is a distribution concentrated on the heating line, and such a distribution can be calculated by the following method. That is, basically, the calculation is performed by the same procedure as described above, but simply setting the elastic coefficient of the element of the portion corresponding to the heating wire to be about 1/1000 smaller than that of the other portion, and the elastic strain is heated. Try to focus on the line. The intrinsic strain distribution thus obtained is as shown in FIGS. 6B and 6C. That is, the intrinsic strain distribution shown in FIG. 6B is a case where the orthogonal compression intrinsic strains gathered in a lattice form are given, that is, the intrinsic strain is concentrated in the lattice heating wire.
The intrinsic strain distribution shown in (c) is when the orthogonal compression intrinsic strains gathered in parallel lines are given, that is, when the intrinsic strain is concentrated on the heating wire in only one direction. When the intrinsic strain is concentrated on the heating wire in this way, the orthogonal compression intrinsic strain (ε ^* _mx ) distributed along the edge of the plate observed in FIG.
The results correspond well with the linear heating by skilled workers. Further, as shown in Table 1, the error that occurs in bending when these intrinsic strains are applied to the flat plate in the opposite direction is small. Therefore, it can be seen that a curved surface can be formed also from the intrinsic strain aggregated in a lattice shape or a parallel line shape. FIG. 9 is a contour diagram of the deformed shape when the shape is confirmed based on FIG.

On the other hand, paying attention to the stress, as shown in Table 1 or FIG. 7B showing the stress distribution when the intrinsic strain is concentrated on the grid-shaped heating wire, the grid-shaped heating results in almost no stress. However, in the case of unidirectional parallel heating, only the value of shear stress is 4.1 kgf / as shown in Table 1 or Fig. 7 (c).
It is as large as mm ² . This indicates that heating in only one direction cannot completely give the in-plane strain required for bending.

Next, the formulation of the heating method in step 5 will be described. Several methods are conceivable in order to create a work procedure for linear heating based on the inherent strain distribution obtained in the shapes shown in FIGS. 6 (a), 6 (b), and 6 (c). First, by appropriately selecting the heating device and heating conditions, the heating conditions for small heat input that is as dominant as possible and the heating conditions for large heat input where only in-plane contraction strain are dominant are assumed, and the bending strain distribution is small. The method of applying in-plane strain will be described assuming that the application is performed by a combination of heat or press working. For example, the first method is to select one standard heating condition for diaphragm and
This is a method of determining the actual density or number of heating wires at each position based on the shrinkage amount per heating wire of the book. The second method is to provide a groove a as shown in FIG. This is a method of changing the shrinkage amount by determining the position of the heating wire and changing the heating condition on each heating wire continuously or stepwise.

Further, if the magnitude and distribution of the strain to be applied by the diaphragm are clear in advance as shown in FIGS. 6 (a), (b) and (c), the shrinkage margin that must be estimated for linear heating. Can be calculated. In this case, the addition amount of the shrinkage margin generated to give the bending strain is negligible, but it can be considered if necessary.

Based on the above, plate bending by lattice heating or parallel heating becomes possible, and FIG. 6 (a) (b) (c)
If the heating conditions such as heating temperature, heating time, heating rate, and heat input are selected according to the size of the compressive strain, the points determined based on the intrinsic strain distribution shown in Fig. 2 will be molded into the desired curved surface shape. Is displayed.

Next, a specific embodiment for obtaining a quantitative relationship between the heating condition of step 6 and the generated intrinsic strain will be described. (A) When obtaining the generated intrinsic strain under heating conditions Assuming a gas flame with an input heat quantity Q = 4335 cal / sec, heating is given as a forced heat flux q from the plate surface, and q
Is an axisymmetric Gaussian distribution such that

[0031]

[Equation 1] Therefore, it is assumed that it has a spread of κ = 7.75 × 10 ^-4 mm ^-2 . Heat source moving speed v = 1mm / sec, plate thickness h = 16mm
An example of obtaining the lateral contraction δ _m and the angular deformation φ when the plate of FIG. In this case, the following physical property values of steel should be used.

Λ = 0.160cal / mm · sec · ° C. Cp = 0.098cal / g · ° C. ρ = 0.00782g / mm ^{3 When the} heat penetration coefficient p and the thermal diffusion coefficient k are calculated, p = (λCpρ) ^{1 / 2 = 0.0035cal / mm 2 ·} ℃ k = λ / Cpρ = 20.9mm 2 / sec where, lambda: the thermal conductivity of the metal plate Cp: specific heat of the metal plate [rho: density of the metal plate thus the similarity rule The governing 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.

From FIG. 15 showing changes in the amount of angular deformation due to the parameters β and ζ, and FIG. 16 showing changes in the amount of in-plane lateral contraction due to the parameters β and ζ, the angular deformation φ and the lateral contraction δ with respect to these parameters β and ζ. Reading _m , it can be seen that φ = 0.006 rad δ _m = 0.025 mm.

Introducing the similarity law of thermo-elasto-plastic deformation by a moving heat source, 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 also the same. Assuming that
If the values are the same, the temperature distributions at the time and the position of the similarities are the same, and similar deformation occurs.

As an application example of the similarity rule, FIG.
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 axisymmetric heat source is shown as shown in the figure, but various methods are conceivable as the heating source. The method proposed here can be utilized corresponding to the shape of the heat source.

Here, the plate thickness 8 mm and width 3 in FIG.
A model with a length of 00 mm and a length of 300 mm is M8, and a model with a thickness of 16 mm, a width of 600 mm and a length of 600 mm shown in FIG.
Call 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 can be seen that the heat source moving speed v must be twice and the heat source moving speed v must be half.

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

The vertical axis of the graph shows the temperature of the part. The horizontal axis of the graph is the standardized relative time, but at the same time, it corresponds to the position in the plate length direction, and τ = 0.5 is the center of 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 the same, the temperatures at the corresponding positions are the same.

FIG. 13 shows the history of angular deformation due to the movement of the heat source in the transverse section at the center of the heating wire upper plate length direction of M8 and M16. The vertical axis is the amount of angular deformation (radian),
The horizontal axis is the same as in the case of FIGS.

FIG. 14 shows the history of shrinkage deformation of the M8 and M16 in the plate width direction in the transverse section at the center in the plate length direction on the heating wire.

In FIGS. 13 and 14, it is clear that the state of change with time and the difference in the amount of deformation itself are high when the heat source moving speed is fast (ζ = 4.4) and when it is slow (ζ = 1.9). Can be taken.

FIG. 15 is a graph summarizing the results of series calculation performed by changing β and ζ.

Β is 3.2 × 10 ³ (corresponding to the maximum temperature of 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 a maximum temperature of about 785 ° C on the plate surface).

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

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

The vertical axis is the amount of shrinkage, and the horizontal axis is the same as in 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 expressed by the difference in plastic strain between the plate surface and the center of plate thickness. FIG. 17 shows FIG.
It can be considered that the tendency shown in FIG.

FIG. 18 is the same as FIG. 10 in the above-mentioned embodiment (A).
Considering an axially symmetric heating source like this, the relation between the amount of angular deformation (radian) and lateral contraction (mm) when the concentration degree κ of the distribution is changed is shown. Assuming that the heating is given as the forced heat flux q from the plate surface, let q be the axisymmetric Gaussian distribution

[0051]

[Equation 2] However, r is the distance from the center of the heat source, qmax is the horizontal axis, and κ is the heat flux at the center of the heat source. in this case,
κ represents the spread of q (r), and the larger κ is, the more concentrated it is, and the smaller it is, the more diffuse it is.

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

From this graph, even if the amount of heat input and the heating rate are the same, the manner of deformation differs if the heat input distribution pattern of the heat source is different. That is, an important finding is given that the efficiency of bending significantly changes. (B) When obtaining heating conditions from the generated intrinsic strain An example of formulating the heating method from the objective intrinsic strain obtained in step 4 is shown. The in-plane target intrinsic strain as shown in FIG. 6B is calculated, and the Y-direction shrinkage amount to be given is obtained by multiplying it by the element width. In this case, it is possible to know what heating conditions (Q, v) should be used for heating. The characteristic value of the intrinsic strain generated when the plate thickness is 16 mm is
It is assumed that the shrinkage amount in the Y direction δ _m = 0.05 mm is specified.

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

In FIG. 21 in which FIG. 16 is reproduced again, a line parallel to the horizontal axis is drawn so that the lateral contraction amount becomes 0.05 mm, and β
= 5.7 × 10 ³ , ζ = 0.9. Figure 1
In FIG. 20 in which 5 is reproduced again, β = 5.7 × 10 ³ , ζ
Looking at the angular deformation at the position of = 0.9, it is found that it is sufficiently small at about 0.001 rad, and it is possible to give almost in-plane strain only.

[0056]

[Equation 3] Therefore, with a gas flame with an intensity of 1340 cal / sec, 1.1 mm /
If linear heating is performed at a moving speed of sec, the required δ _m = 0.0
5mm is achieved, and the angular deformation φ is also sufficiently small.

As described above, step 5 and step 6
When the metal plate is bent by applying the inherent strain generated by heating by the heating method obtained in step 8 to the initial shape in step 8 and performing an elastic simulation of the bent shape for confirmation, the obtained heating method is obtained. By giving the generated intrinsic strain in, it is possible to bend into a target shape.

[0058]

As described above, according to the method for 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 in-plane and bending components, pay attention only to the in-plane target intrinsic strain distribution, and heat them into a plurality of mutually orthogonal grid-shaped heating elements. Since it is expressed by the generated intrinsic strain generated by the line, if the bending component is applied by pressing or linear heating with a small heat input, the remaining in-plane component is bent according to the flow shown in FIG. Can be found even by an amateur, and since it only requires two heating directions that are orthogonal to each other, it has the effect that the work is easy and the device can be simplified, and the characteristic value of the generated intrinsic strain to be given in the element is specified. In such a case, it becomes possible to determine the heating condition by using the data bank that gives the relationship between the heating condition and the generated intrinsic strain as shown in FIGS. (ii) Due to the above (i), the linear heating bending method that had to rely on a skilled engineer because it was a complicated phenomenon that conventionally included many elements of trial and error It became possible to choose.

[Brief description of drawings]

1 is a flow chart showing an embodiment of the method of the present invention.

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. 2B is a state diagram mapped onto the target shape.

FIG. 3 is a diagram showing the shape of a curved surface intended when an experiment is performed on an actual plate.

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

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

6A and 6B show in-plane intrinsic strains, where (A) is a diagram when distributed orthogonal compression intrinsic strains are given, and (B) is a diagram when orthogonal compression intrinsic strains aggregated in a lattice are given. , (C) are diagrams when the orthogonal compression intrinsic strains gathered in parallel lines are applied.

FIG. 7 shows a stress distribution, where (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 compression intrinsic strain aggregated in a grid is given, and (C) is a diagram of the stress distribution calculated when the orthogonal compression intrinsic strain aggregated in a parallel line is applied. Is.

FIG. 8 is a contour diagram of a deformed shape showing a confirmation 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 confirmation shape according to FIG.

FIG. 10 shows an application example of the similarity rule, (a) is a perspective view of a model M8, and (b) is a perspective view of a model M16.

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

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

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

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

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

FIG. 16 is a diagram showing changes in in-plane lateral contraction amount due to parameters β and ζ.

FIG. 17 shows parameters β and ζ of plastic strain in the central cross section.
It is a figure which shows the change by.

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

FIG. 19 is a diagram showing changes in maximum temperature due to parameters β and ζ.

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

FIG. 21 is a diagram showing thermal contraction and reading of β from a parameter ζ.

FIG. 22 is a flowchart showing an example of a method of bending a plate by linear heating that has been recently applied.

23A and 23B show in-plane strain components when the initial shape is forcibly deformed to a target shape, where (A) shows the initial shape, (B) shows the target shape, and (C) shows the surface. 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

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Inventor Yukio Ueda 11-1 Mihogaoka, Ibaraki City, Osaka Prefecture, Research Institute for Welding Engineering, Osaka University (72) Inventor, Eiichi Murakawa 11-1, Mihogaoka, Ibaraki City, Osaka Prefecture, Welding Engineering, Osaka University Inside the Institute (72) Inventor Rashwan Ahmed Mohamed 11-1 Mihogaoka, Ibaraki City, Osaka Prefecture Inside the Institute for Welding Engineering, Osaka University

Claims (1)

[Claims] 1. 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 of the finite element method is performed based on the initial shape. Then, the divided shape is mapped onto the target shape, then the target characteristic strain distribution is calculated by forcibly deforming from the initial shape to the target shape, and the obtained target characteristic strain distribution is divided into multiple mutually orthogonal grids. It is expressed by the generated intrinsic strain generated by a linear heating line. At this time, the quantitative relationship 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 elastic simulation for confirming the bent shape by giving the generated intrinsic strain to the initial shape, the bending of the metal plate is characterized by the linear heating of the metal plate. Song Processing method.