JPH0760368A - Bending method of metal plate by linear heating - Google Patents
Bending method of metal plate by linear heatingInfo
- Publication number
- JPH0760368A JPH0760368A JP23216893A JP23216893A JPH0760368A JP H0760368 A JPH0760368 A JP H0760368A JP 23216893 A JP23216893 A JP 23216893A JP 23216893 A JP23216893 A JP 23216893A JP H0760368 A JPH0760368 A JP H0760368A
- Authority
- JP
- Japan
- Prior art keywords
- strain
- shape
- heating
- intrinsic
- bending
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
Landscapes
- Bending Of Plates, Rods, And Pipes (AREA)
Abstract
Description
【0001】[0001]
【産業上の利用分野】本発明は船舶、橋梁、その他の金
属製構造物の曲面状部材を平板状の素材あるいはプレス
等の一次加工を施された初期形状から目的曲面形状へ仕
上げるために用いる線状加熱による金属板の曲げ加工方
法に関するものである。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】[0002]
【従来の技術】一般に船舶、橋梁等に用いられる金属板
の曲げ加工を行う場合は、線状加熱により行われている
場合が多い。この線状加熱による曲げ加工は、平板状素
材あるいはプレスで一次加工された形状の金属板の所定
の位置に線状加熱を施し、生じた塑性歪による板の面内
収縮や角変形を利用して目的とする三次元形状を作り出
すものである。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.
【0003】上記線状加熱による曲げ加工では、面内収
縮量や角変形量が線状加熱の加熱位置、方向、加熱条件
によって決定されるため、これらの加熱位置、方向、加
熱条件が重要である。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.
【0004】現状の加工現場では、初期形状から目的形
状へ強制変形させる計算によって得られる目的固有歪分
布に着目した理論的なアプローチに基づく技術は存在せ
ず、複数個の曲げ型板を金属板上に仮配置することで目
的形状とのずれを検知しながら熟練者の勘や技能によっ
て加熱位置、方向、加熱条件を決めているのが実状であ
る。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.
【0005】しかしながら、近年では、これら熟練者の
高齢化とこれに伴う作業従事者の減少等の問題が顕著に
なって来ている。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.
【0006】そのため、最近、かかる状況に鑑み、熟練
を要する線状加熱作業を特別な技能を要せずに実施でき
て処理能力を向上させることができるような線状加熱に
よる板の曲げ加工方法が提案され且つ特許出願されてい
る(特願平3−237948号)。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).
【0007】上記最近提案された方法は、有限要素法
(FEM)の弾性解析に基づいて線状加熱線の位置、方
向及び生成固有歪(集中的な歪分布)を決定するように
したもので、図22に示す如く、先ず、初期形状と最終
成形形状に関する幾何学情報のインプット(ステップ
I)をした後、初期形状に対応したFEMのメッシュ分
割を行う(ステップII)。次いで、加熱位置及び方向の
決定として、初期形状から最終形状まで強制的に弾性変
形させ、その過程で生じる歪を計算した後、計算された
歪を面内成分と、曲げ成分に分離し、それぞれの主歪分
布をグラフィック画面に表示する(ステップIII )。次
に、面内の歪分布に注目し、圧縮の主歪が大きい領域を
加熱領域に選び、加熱の方向は主歪の方向に直角の方向
とし(ステップIV)、又、曲げ歪の分布に注目し、曲げ
歪の絶対値が大きい領域を加熱領域に加え、加熱の方向
は歪の絶対値が最大である主方向に直角の方向とする
(ステップV)。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).
【0008】次に、生成すべき固有歪の大きさを決める
ために、加熱領域に属する要素の剛性を残りの部分より
も小さくした強制変形FEM弾性解析を再度実施し、加
熱領域に集中した歪の値から生成固有歪の値を算定する
(ステップVI)。しかる後に、これらの計算に基づき線
状加熱を施して固有歪を発生させることによって所定の
最終形状に加工する(ステップVII )ものである。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】[0009]
【発明が解決しようとする課題】上記最近提案され且つ
出願されている方法の場合、線状加熱による板の曲げ加
工が容易に行えるため、熟練者の勘に頼らなくても実施
可能という利点があるが、 図23の(イ)から(ロ)のように強制変形FEM
弾性解析を行う場合には、一般に、目的固有歪の面内成
分は、図23(ハ)に示すように収縮歪(圧縮歪)だけ
でなく、伸び歪も現われることがある。又、固有歪の大
きさを決めるための加熱部の剛性を低くした強制変形F
EM弾性解析においても同様に伸び歪が表われることが
ある。線状加熱による曲げ加工は、加熱部に生ずる圧縮
塑性歪を利用して加工する方法であり、図23(ハ)の
下部に見られる伸び歪(←→印)を付与することができ
ない。よって、目的形状に線状加熱だけによって加工す
ることができるためには、上記のFEM計算結果がすべ
て収縮歪(→←印)となっていなければならない。同図
23(ハ)において少なくとも伸び歪の部分に限定し
て、あるいは、全体として一様な収縮歪を加える必要が
ある。このことは、目的形状を縮めること、あるいは初
期形状を大きくすることに対応している。同様に、ある
量の曲げ歪を片側からの加熱によって達成するために
は、ある程度の面内縮みが伴うことは避けられない。こ
れらの余分の収縮によって、仕上った目的形状は面内の
寸法不足となる。このことは定性的には従来から知られ
ているが、これらを定量的に補償することが出来ないの
で、現状では予め経験則に基づいた十分な余裕をとって
おいた上で、最終的な切り揃えの余分の作業や、場合に
よっては寸法不足を生じるおそれが考えられる。 線状加熱を行った場合には、加熱線と直角方向の収
縮歪だけでなく、加熱線方向の収縮歪も割合は少ないが
必ず伴うことがよく知られており、両方向の生成固有歪
を考慮した上で目的固有歪分布を正確に実現させること
が難しいと考えられる。 又、加熱条件と生成固有歪との定量的関係について
は、最近提案され出願された方法では言及されていない
ので、現状の現場技術である、曲げ型板と初期形状から
経験と勘で推測される各部必要変形量を発生させるであ
ろう加熱条件を、経験をベースに選択し実施する方法が
採用されているが、多段の推測を経験と勘をベースに積
み重ねる結果として、難しいこと、誤差、バラツキが大
きいこと、出来る人が限られること、習得に時間がかか
ること、等の問題がある。 平板から曲面を成形するためには、何等かの方法で
所定の曲げ歪と面内歪を与える必要があるが、曲げ歪に
注目すると、曲げ歪分布は、図4に示す如く比較的単純
であり、主方向はほぼ一定の方向になっているため、曲
げ歪を付与するための作業手順作成については特に問題
はなく、又、実際の曲げ加工も加工のかなりの部分をベ
ンディングローラ等による機械曲げによって行うことが
でき、部分的に線状加熱による曲げを施せばよいことが
わかる。しかし、面内歪については、これを機械的手段
で板に与えることは非常に難しく、このような作業には
線状加熱が理想的な手段となるが、面内歪分布は、図5
にも示されるように複雑であり、方向も一定していな
い。更に、前述したように、線状加熱では引張の歪(伸
び歪)を与えることができず、又、線状加熱では剪断歪
が作れないので、図6の歪を付与するためには、主歪の
方向に加熱しなければならず、加熱線が種々の方向を向
くことになり、作業が大変となり、又、設備も複雑とな
る。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.
【0010】そこで、本発明は、上述した最近提案され
且つ出願されている線状加熱による板の曲げ加工方法を
更に進めて上述した問題点をなくし、目的形状が与えら
れると素人でも実施でき、且つ、希望する加熱条件だけ
で目的固有歪を実現できるようにすると共に、作業の容
易さ、設備の単純化を図るようにしようとするものであ
る。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】[0011]
【課題を解決するための手段】本発明は、上記課題を解
決するために、金属板を初期形状から最終の目的形状に
曲げ加工するために、先ず、初期形状と目的形状の幾何
学情報をインプットし、初期形状に基づいて有限要素法
のメッシュ分割を行って、その分割形状を目的形状の上
に写像し、次いで、初期形状から目的形状まで強制的に
変形させて目的固有歪分布を計算し、得られた目的固有
歪分布を複数の互いに直交する格子状の加熱線によって
生成される生成固有歪で表現し、このとき加熱装置と被
加工材の組合わせに対する加熱条件と生成固有歪との定
量的関係を用い、次に、加熱条件が与えられたときに求
められた生成固有歪を初期形状に付与することによって
曲り形状の確認のための弾性シミュレーションを行った
上で、金属板の曲げ加工を行う方法とする。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】[0012]
【作用】金属板を初期形状から目的形状に強制的に弾性
変形させて各要素内の目的固有歪分布を求めてから、こ
の目的固有歪分布を複数の互いに直交する格子状の加熱
線による生成固有歪として表現させ、又、定量的関係に
基づいて生成固有歪が与えられると、それに対応した加
熱条件を求めるようにすることから、この生成固有歪を
初期形状に付与させることにより目的形状の達成具合を
事前に予測するとともに、求められた加熱条件での複数
の加熱線による加熱を行えばよく、熟練技術者に頼らな
くてもよくなる。又、格子状の加熱で曲げ加工すること
から、作業が容易となり、これに伴い装置を単純化でき
ることになる。[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】[0013]
【実施例】以下、本発明の実施例を図面を参照して説明
する。Embodiments of the present invention will be described below with reference to the drawings.
【0014】図1は任意の周辺形状をした平板あるいは
任意曲面を初期形状とする鋼板あるいは鋼以外の金属板
を、目的形状(別の任意の周辺形状及び曲面形状)に曲
げ加工する本発明の方法を示すフローチャートで、初期
形状と目的形状に関する幾何学情報のインプット(ステ
ップ1)をした後、金属板Pの初期形状に基づいて図2
(イ)の如く、有限要素法(FEM)のメッシュ分割を
行い(ステップ2)、その分割形状を、初期形状を目的
形状に写像する適切な写像方法によって図2(ロ)に示
すように金属板Pの目的形状の上に写像(ステップ3)
する。次いで、初期形状における各要素節点位置を目的
形状における対応する各要素節点位置にFEM計算によ
って強制的に弾性変形させ、各要素内での歪分布(目的
固有歪分布)を計算する。続いて、求められた歪分布を
出発点とし、面内歪に注目して伸び歪と剪断歪を排除す
ることによって、直交ししかも圧縮の面内固有歪に収束
するような反復計算のアルゴリズムにより目的固有歪分
布が得られ、写像法と加工法に付随した縮み代を定める
ことが可能となる(ステップ4)。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).
【0015】次に、加熱方法の策定として、上記ステッ
プ4で求められた要素内での目的固有歪分布を複数の互
いに直交する格子状の加熱線によって生成される集中的
な歪分布(生成固有歪)で近似的に表現する(ステップ
5)ようにする。この場合、上記ステップ5で目的固有
歪分布を生成固有歪で実現する際に、与えられた加熱器
(ガス炎、高周波誘導加熱器、レーザ光等)と被加工材
の組合わせに対して、加熱条件(単位時間当りの入熱
量、移動速度等)と生成固有歪との定量的関係が必要と
なるので、この関係を求めておくようにする(ステップ
6)。この加熱条件と生成固有歪との定量的関係は、一
般には実験データを蓄積するか、あるいは熱弾塑性FE
M解析により入熱条件(入熱分布又は時系列的に変化す
る温度分布)を与えたときの金属板上の生成固有歪を計
算することによって得られる。すなわち、実証実験によ
りその妥当性が確認された熱弾塑性FEMプログラムを
用いて上記加熱条件と生成固有歪との関係を計算するに
際して、後述するように、線状加熱による熱弾塑性変形
問題について成立する相似則とそれから導かれる支配パ
ラメータを用いた効率的な計算方法を開発し、計算され
た結果をそれらのパラメータで一般化した形で整理する
ことにより加熱条件が与えられたときの生成固有歪を効
率よく求めることができる手段を考案した。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.
【0016】次に、ステップ5とステップ6で求められ
た加熱条件が与えられたときの生成固有歪を初期形状に
付与することによって、曲り形状の弾性シミュレーショ
ンを行い確認を行う(ステップ7)。しかる後、ステッ
プ6で定められた加熱方法に従って手動あるいはNC制
御の加熱器を用いた線状加熱を行う(ステップ8)。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).
【0017】上記ステップ1からステップ8までの手順
で求められた加熱方法で金属板に生成固有歪を与えるこ
とによって目的形状に曲げ加工することができるように
する。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.
【0018】以下、詳述する。The details will be described below.
【0019】ステップ1〜ステップ3は、図22のステ
ップI、IIに相当するものである。Steps 1 to 3 correspond to steps I and II in FIG.
【0020】ステップ4では強制的に変形させるときの
写像法の適切な選択と新しく考えた反復収束計算のアル
ゴリズムの採用により面内の伸び歪と剪断歪成分を排除
した直交面内圧縮歪と曲げ歪とで構成される目的固有歪
分布が得られ、写像法と加工法に付随した縮み代を定め
ることができるが、この目的固有歪を求める方法につい
て最も簡単な例を示す。すなわち、線状加熱は、前述し
たように伸び歪を与えることができず、又、剪断歪が作
れないので、図5に示す如き複雑で且つ方向が一定して
いない面内歪を付与するためには、加熱方向が複数の異
なる方向となり、作業が大変となることから、直交する
εx とεy の2成分で、しかも圧縮歪だけで構成される
面内歪により曲面を実現させるようにする。そのため
に、以下に、直交し、しかも圧縮成分からのみ構成され
る固有歪分布を計算するためのアルゴリズムを採用す
る。鞍型曲面の実例を対象に数値例を示しながら、面内
歪を直交化した目的固有歪分布を算出する方法について
説明する。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.
【0021】伸び歪と剪断歪成分を排除し、直交ししか
も圧縮の固有歪を求めるため、次のようなアルゴリズム
を考えた。 目的の形状に対応した撓みWを平板に強制的に与え
たときの曲げ歪εb と面内歪εm を弾性大撓み問題とし
て計算する。 面内歪に注目し、 εmx<0であればε* mx=εmx εmx>0であればε* mx=0 εmy<0であればε* my=εmx εmy>0であればε* my=0 ただし γ* mxy =0 とする。ここで、ε* mx、ε* my、γ* mxy は、求める
べき固有歪の第1近似である。 平板に現段階での固有歪ε* mx、ε* myを与えると
同時に撓みWを強制的に与えたときの弾性歪εb とΔε
m (Δεm は固有歪を与えることにより絶対値が小さく
なる)を計算する。 面内歪に注目し、 Δεmx<0であればΔε* mx=Δεmx Δεmx>0であればΔε* my=0 Δεmy<0であればΔε* my=Δεmx Δεmy>0であればΔε* my=0 ただし、 Δγ* mxy =0 とし、新しい固有歪を次式に従い計算する。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.
【0022】ε* mx=ε* mx+Δε* mx ε* my=ε* my+Δε* my ただし、γ* mxy =0 上記〜の計算を、修正量Δε* mx、Δε* myが
十分に小さくなるまで3〜4回繰り返して伸び歪を零に
し、圧縮歪はそのまま残すようにして直交成分と圧縮成
分だけとし、最終的に得られたε* mx、ε* myが直交圧
縮固有歪である。 正しい目的固有歪分布が得られているかどうかの確
認として、段階で求めた曲げ歪εb と面内歪ε* mx、
ε* myを固有歪として平板に与え自由に変形させ、その
形状が目的とする撓みWと一致し、しかも、板には応力
が生じないことを確認する。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.
【0023】上記の手順に従い図3の曲面を対象に求め
た直交圧縮歪を図6(イ)に示す。なお、図3は、長辺
の長さLが2000mm、短辺の長さBが1000mmの金
属板Pを曲げ加工して鞍型曲面とした形状を示すもので
ある。図6(イ)において、Y軸方向の歪に注目する
と、板の中央部でその絶対値が大きくなっており、造船
所の現場で実施されている加熱要領とよく対応してい
る。又、X軸方向の歪に注目すると、板のY軸に平行な
辺上に大きな圧縮歪が特徴として認められる。一方、こ
こで求められた固有歪が、曲面を作り出すという目的に
かなったものであることを確認するため、段階に示さ
れた手順に従い検証を行った。この検証では、曲げの固
有歪は曲面の曲率から唯一に決るので、段階で求めら
れた曲げ歪εb を直接固有歪として与え、面内の固有歪
として図6(イ)に示された直交圧縮固有歪ε* mx、ε
* myを平板に与え自由に変形させたときの撓みと応力分
布を計算した。撓みについては、表1に示すように目的
とする曲面からの相対的誤差は約1%である。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】[0024]
【表1】 又、図7(イ)には、Misesの相対応力分布が示さ
れている。応力の大きさは10-1(kgf/mm2 )のオーダ
ーであり、表1に示された各応力成分の絶対値の大きさ
も小さく、ほとんど無応力の状態とみなして差し支えな
い。これらの撓みW及び残留応力が示すように、上記の
手順で求めた直交圧縮固有歪(ε* mx、ε* my)は、目
的の形状を作り出すために板に与えるべき面内の固有歪
であることがわかる。図8は反復計算の後に得られた図
6(イ)の面内歪と図4の曲げ歪に基づき形状確認をし
た際の変形形状の等高線図であり、図3に示す初期の目
的形状によく一致していることがわかる。[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.
【0025】次に、表1に示した格子状又は平行線状に
集約した直交圧縮固有歪を与える場合について説明する
と、線状加熱で固有歪を与える場合は、固有歪は間隔を
置いて線状に与えられる。したがって、より実際的な固
有歪分布は、加熱線に集中した分布であり、そのような
分布は次のような手法で計算することができる。すなわ
ち、基本的には、前記したのと同じ手順で計算を行う
が、単に、加熱線に相当する部分の要素の弾性係数を他
の部分の1/1000程度に小さく設定し、弾性歪が加
熱線に集中するようにする。このようにして求めた固有
歪分布は、図6(ロ)及び図6(ハ)に示すとおりであ
る。すなわち、図6(ロ)に示す固有歪分布は、格子状
に集約した直交圧縮固有歪を与えた場合、つまり、格子
状の加熱線に固有歪を集中させた場合であり、図6
(ハ)に示す固有歪分布は、平行線状に集約した直交圧
縮固有歪を与えた場合、つまり、一方向のみの加熱線に
固有歪を集中させた場合である。このように固有歪を加
熱線に集中させた場合は、図6(イ)に認められた板の
縁に沿って分布する直交圧縮固有歪(ε* mx)は消え、
熟練工による線状加熱とよく対応した結果が得られてい
る。更に、これらの固有歪を逆に平板に与えたときの撓
みに生じる誤差は、表1に示されるように小さい。した
がって、格子状あるいは平行線状に集約された固有歪か
らも曲面が作れることがわかる。図9は図6(ロ)に基
づき形状確認をした際の変形形状の等高線図である。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.
【0026】一方、応力に注目すると、表1あるいは格
子状加熱線に固有歪を集中させた場合の応力分布を示す
図7(ロ)に示す如く、格子状加熱ではほぼ無応力状態
となっているが、一方向平行加熱の場合は、表1あるい
は図7(ハ)に示す如く剪断応力の値のみが4.1kgf/
mm2 と大きくなっている。これは、一方向のみの加熱で
は、曲げに必要な面内歪を完全には与えることができな
いことを示している。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.
【0027】次に、ステップ5の加熱方法の策定につい
て説明する。図6(イ)(ロ)(ハ)のような形で得ら
れた固有歪分布に基づいて線状加熱の作業要領を作成す
るためには、いくつかの方法が考えられる。まず、加熱
装置や加熱条件の適切な選択により、できるだけが支配
的な小入熱の加熱条件と面内収縮歪だけが支配的な大入
熱の加熱条件を想定し、曲げ歪分布は小入熱の組合せ又
はプレス加工によって付与するものとし、面内歪を付与
する方法について説明する。たとえば、第1番目の方法
は、絞りを目的とした基準の加熱条件を1個選択し、1
本の加熱線当りの収縮量を基にして各位置での実際の加
熱線の密度あるいは本数を決める方法であり、第2の方
法としては図6(ロ)のように溝aを設けることによっ
て加熱線の位置を決め、各加熱線上での加熱条件を連続
的あるいは段階的に変化させることによって収縮量を変
化させる方法である。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.
【0028】又、絞りで与えるべき歪の大きさと分布が
図6(イ)(ロ)(ハ)のように事前に明らかである
と、線状加熱のために見込んでおかなければならない縮
み代の計算が可能となる。この場合、曲げ歪を与えるた
めに生ずる縮み代の付加分は無視できる程度のものであ
るが、必要となれば考慮することもできる。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.
【0029】以上に基づき、格子状加熱あるいは平行加
熱による板曲げが可能となり、図6(イ)(ロ)(ハ)
に示す固有歪分布に基づき決められたところを圧縮歪の
大きさに合わせて加熱温度、加熱時間、加熱速度、入熱
量などの加熱条件を選んで加熱すれば、目的とする曲面
形状に成形させられることが表示される。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.
【0030】次に、ステップ6の加熱条件と生成固有歪
との定量的関係を求める具体的な実施例を説明する。 (A) 加熱条件を与えて生成固有歪を求める場合 投入熱量Q=4335cal/sec のガス炎を想定し、加熱
を板表面からの強制熱流束qとして与えるものとし、q
を次のような軸対称ガウス分布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】[0031]
【数1】 と考え、κ=7.75×10-4mm-2なる広がりをもつも
のとする。熱源移動速度v=1mm/secで板厚h=16mm
の板を線状加熱した際の横収縮δm と角変形φを求める
例を示す。この場合、鋼の材料物性値として下記のもの
を用いるようにする。[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.
【0032】λ=0.0160cal/mm・sec ・℃ Cp=0.098cal/g ・℃ ρ=0.00782g/mm3 熱侵入係数p、熱拡散係数kを求めると、 p=(λCpρ)1/2 =0.0035cal/mm2 ・℃ k=λ/Cpρ=20.9mm2 /sec 但し、λ:金属板の熱伝導率 Cp:金属板の比熱 ρ:金属板の比重 よって、相似則を支配するパラメータβ、ζは、 β=Q/(p2 vh3 )1/2 =4.4×103 ζ=(vh/k)1/2 =0.88 である。βは熱源により加熱された板の表面の最高温度
に比例するパラメータ、ζは熱源移動速度に対応するパ
ラメータである。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.
【0033】パラメータβ、ζによる角変形量の変化を
示す図15、パラメータβ、ζによる面内横収縮量の変
化を示す図16から、これらのパラメータβ、ζに対す
る角変形φと横収縮δm を読みとると、 φ=0.006 rad δm =0.025mm となることがわかる。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.
【0034】移動熱源による熱弾塑性変形の相似則を導
入すると、対象となる板の形状と熱源の幅が幾何学的相
似で、且つ金属板の材質は同一で熱的、力学的性質も同
じであることを前提にしたとき、上記パラメータβ、ζ
が同じであれば、相似化された時間と位置における温度
分布が一致し、相似の変形が起ることになる。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.
【0035】相似則の適用例として、図10(イ)
(ロ)に示す2種類のモデルについて具体的な数値を設
定した結果を表2に示す。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】[0036]
【表2】 なお、この例では、図にみるとおり軸対称の熱源が示し
てあるが、加熱源としてはさまざまな方法が考えられ
る。ここで提案する方法は、それらの熱源形状にも対応
して活用することができる。[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.
【0037】ここでは、図10(イ)の板厚8mm、幅3
00mm、長さ300mmのモデルをM8、図10(ロ)の
板厚16mm、幅600mm、長さ600mmのモデルをM1
6と呼ぶ。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.
【0038】表2からわかるように、幾何学的形状が2
倍の場合、相似の変形を発生させるためには、入熱量Q
は2倍、熱源移動速度vは 1/2倍でなくてはならないこ
とがわかる。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.
【0039】図11、図12はM8、M16の各板の加
熱線上、板長さ方向の中央での横断面位置、板表面及び
裏面で起る熱源移動に伴う温度履歴を示している。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.
【0040】グラフの縦軸は該部温度を示す。グラフの
横軸は標準化された相対時間であるが、同時に板長さ方
向の位置に対応しており、τ=0.5は板長さ方向(図
10のY方向)の中央、τ=1.0は終端に当る。β、
ζが等しいM8、M16では対応する位置での温度が一
致していることがわかる。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.
【0041】図13はM8、M16の加熱線上板長さ方
向の中央での横断面における熱源移動に伴う角変形の履
歴を示すものである。縦軸は角度変形量(ラジアン)、
横軸は図11、図12の場合と同じである。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.
【0042】図14はM8、M16の加熱線上板長さ方
向中央での横断面における板幅方向の収縮変形の履歴を
示すものである。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.
【0043】図13、図14において、熱源移動速度が
速い場合(ζ=4.4)と遅い場合(ζ=1.9)の時
間に伴う変化の様子及び変形量そのものの違いが明確に
よみとれる。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.
【0044】図15はβ及びζを変えて行ったシリーズ
計算結果を整理したグラフである。FIG. 15 is a graph summarizing the results of series calculation performed by changing β and ζ.
【0045】βを3.2×103 (板表面での最高温度
約445℃に相当) 4.4×103 (板表面での最高温度約615℃に相
当) 5.7×103 (板表面での最高温度約785℃に相
当) に選んでいる。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).
【0046】縦軸は角度変形量(ラジアン)、横軸はζ
(熱源移動速度に対応)、βが大きいほど(表面温度が
高いほど)角変形量が大きいことがわかる。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.
【0047】図16は板の加熱線上長さ方向中央での横
断面における横方向の縮み量とパラメータの関係を表わ
している。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.
【0048】縦軸は縮み量、横軸は図15と同じであ
る。The vertical axis is the amount of shrinkage, and the horizontal axis is the same as in FIG.
【0049】図17は図16と同一横断面上の幅方向中
心位置における幅方向収縮歪とパラメータの関係を表わ
している。曲げ歪量については、板表面と板厚中央にお
ける塑性歪の差によって表現してある。図17は図14
と図15に示された傾向を統一して読みとれる図と考え
てよい。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.
【0050】図18は前述の実施例(A) と同じく図10
のような軸対称の加熱源を考え、その分布の集中度合い
κを変化させたときの角度変形量(ラジアン)と横収縮
(mm)の関係を表わしたものである。加熱を板表面から
の強制熱流束qとして与えると想定し、qを次のような
軸対称ガウス分布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】[0051]
【数2】 但し、r:熱源中心からの距離 qmax :熱源中心での熱流束 とした場合のκを横軸としてとっている。この場合は、
κはq(r)のひろがり加減を表わしκが大きいほど集
中し、小さいほど散漫となる。[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.
【0052】なお、qとQの関係は、 Q=πqmax /κ である。The relationship between q and Q is Q = πqmax / κ.
【0053】このグラフより入熱量も加熱速度も同じ場
合でも熱源の入熱分布パターンが異なると変形のおき方
が異なる。すなわち、曲げ加工の効率が大幅に変るとい
う重要な知見が与えられる。 (B) 生成固有歪から加熱条件を求める場合 ステップ4で求められた目的固有歪から加熱方法を策定
する例を示す。図6(ロ)に示したような面内の目的固
有歪が計算され、それに要素幅を掛けることによって与
えるべきY方向収縮量が求まる。この場合に、どのよう
な加熱条件(Q、v)で加熱したらよいかを知ることが
できる。板厚が16mmの場合に生成固有歪の特性値が、
Y方向収縮量δm =0.05mmに指定されたとする。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.
【0054】図15、図16において、角変形がなるべ
く小さく、収縮量が0.05mmとなるような位置を探
す。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.
【0055】図16を再掲した図21において、横収縮
量が0.05mmとなるような横軸に平行な線を引き、β
=5.7×103 とすればζ=0.9程度となる。図1
5を再掲した図20において、β=5.7×103 、ζ
=0.9の位置での角変形を見ると、0.001rad 程
度で十分に小さくなっており、ほぼ面内歪だけを与える
ことができることがわかる。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】[0056]
【数3】 よって、1340cal/sec の強さのガス炎で1.1mm/
sec の移動速度で線状加熱すれば、所要のδm =0.0
5mmが達成され、角変形φも十分小さくなっている。[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.
【0057】上記のようにしてステップ5、ステップ6
で求められた加熱方法での加熱による生成固有歪を、ス
テップ8で初期形状に付与させ、曲り形状の弾性シミュ
レーションを行い確認を行うようにして、金属板を曲げ
加工すると、求められた加熱方法で生成固有歪が与えら
れることによって目的形状に曲げ加工することができ
る。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】[0058]
【発明の効果】以上述べた如く、本発明の線状加熱によ
る金属板の曲げ加工方法によれば、次のような優れた効
果を奏し得る。 (i) 各要素内での目的固有歪分布を計算して面内成分と
曲げ成分とに分離し、面内の目的固有歪分布のみに着目
し、それらを複数の互いに直交する格子状の加熱線によ
って生成される生成固有歪で表現するようにしているの
で、曲げ成分がプレス又は小入熱の線状加熱によって付
与されたならば、残る面内成分は図1に示すフローに従
って曲げ加工方法を素人でも見つけ出せると共に、加熱
方向が直交する一定の2方向ですむため、作業が容易で
装置を単純化できるという効果を有し、又、要素内で与
えるべき生成固有歪の特性値が規定された場合には、図
15、図16で与えられたような加熱条件と生成固有歪
の関係を与えるデータバンクを用いて加熱条件を決定す
ることが可能になった。 (ii)上記(i) により、従来試行錯誤の要素を多く含んだ
複雑な現象であるために熟練した技術者に頼らざるを得
なかった線状加熱曲げ加工法について、装置化あるいは
最適加工法の選択が可能になった。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.
【図1】本発明の方法の実施例を示すフローチャートで
ある。1 is a flow chart showing an embodiment of the method of the present invention.
【図2】初期形状から目的形状への写像と強制変形を示
すもので、(イ)はFEMメッシュ分割の図、(ロ)は
目的形状の上に写像した状態図である。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.
【図3】実際の板を対象に実験を行う際に目的とした曲
面の形状を示す図である。FIG. 3 is a diagram showing the shape of a curved surface intended when an experiment is performed on an actual plate.
【図4】平板から曲面を成形するときに与えられる曲げ
歪分布を示すベクトル図である。FIG. 4 is a vector diagram showing a bending strain distribution given when a curved surface is molded from a flat plate.
【図5】平板から曲面を成形するときに与えられる面内
歪分布を示すベクトル図である。FIG. 5 is a vector diagram showing an in-plane strain distribution given when a curved surface is molded from a flat plate.
【図6】面内の固有歪を示すもので、(イ)は分布した
直交圧縮固有歪を与えた場合の図、(ロ)は格子状に集
約した直交圧縮固有歪を与えた場合の図、(ハ)は平行
線状に集約した直交圧縮固有歪を与えた場合の図であ
る。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.
【図7】応力分布を示すもので、(イ)は分布した直交
圧縮固有歪を与えたときに計算した応力分布の図、
(ロ)は格子状に集約した直交圧縮固有歪を与えたとき
に計算した応力分布の図、(ハ)は平行線状に集約した
直交圧縮固有歪を与えたときに計算した応力分布の図で
ある。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.
【図8】図6(イ)に示される面内歪と図5に示される
曲げ歪による確認形状を示す変形形状の等高線図であ
る。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.
【図9】図6(ロ)による確認形状を示す変形形状の等
高線図である。FIG. 9 is a contour diagram of a deformed shape showing the confirmation shape according to FIG.
【図10】相似則の適用例を示すもので、(イ)はモデ
ルM8の斜視図、(ロ)はモデルM16の斜視図であ
る。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.
【図11】パラメータζ=4.4の場合のモデルM8と
M16の対応する位置での温度履歴の比較を示す図であ
る。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.
【図12】パラメータζ=1.9の場合のモデルM8と
M16の対応する位置での温度履歴の比較を示す図であ
る。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.
【図13】モデルM8とM16の対応する位置での角変
形の時間的変化の比較を示す図である。FIG. 13 is a diagram showing a comparison of changes over time in angular deformation at corresponding positions of models M8 and M16.
【図14】モデルM8とM16の対応する断面での面内
横収縮量の時間的変化を示す図である。FIG. 14 is a diagram showing a temporal change in in-plane lateral contraction amount in corresponding cross sections of models M8 and M16.
【図15】パラメータβ、ζによる角変形量の変化を示
す図である。FIG. 15 is a diagram showing changes in the amount of angular deformation due to parameters β and ζ.
【図16】パラメータβ、ζによる面内横収縮量の変化
を示す図である。FIG. 16 is a diagram showing changes in in-plane lateral contraction amount due to parameters β and ζ.
【図17】中央断面における塑性歪のパラメータβ、ζ
による変化を示す図である。FIG. 17 shows parameters β and ζ of plastic strain in the central cross section.
It is a figure which shows the change by.
【図18】熱源の広がりが変形に及ぼす影響を示す図で
ある。FIG. 18 is a diagram showing the influence of the expansion of the heat source on the deformation.
【図19】最高温度のパラメータβ、ζによる変化を示
す図である。FIG. 19 is a diagram showing changes in maximum temperature due to parameters β and ζ.
【図20】角変形とパラメータζからのβの読みとりを
示す図である。FIG. 20 is a diagram showing angular distortion and reading of β from a parameter ζ.
【図21】熱収縮とパラメータζからのβの読みとりを
示す図である。FIG. 21 is a diagram showing thermal contraction and reading of β from a parameter ζ.
【図22】最近出願されている線状加熱による板の曲げ
加工方法の実施例を示すフローチャートである。FIG. 22 is a flowchart showing an example of a method of bending a plate by linear heating that has been recently applied.
【図23】初期形状から目的形状に強制変形させたとき
の面内歪成分を示すもので、(イ)は初期形状を示す
図、(ロ)は目的形状を示す図、(ハ)は面内主歪ベク
トル図である。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.
1 ステップ1 2 ステップ2 3 ステップ3 4 ステップ4 5 ステップ5 6 ステップ6 7 ステップ7 8 ステップ8 P 金属板 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
───────────────────────────────────────────────────── フロントページの続き (72)発明者 上田 幸雄 大阪府茨木市美穂ケ丘11−1 大阪大学溶 接工学研究所内 (72)発明者 村川 英一 大阪府茨木市美穂ケ丘11−1 大阪大学溶 接工学研究所内 (72)発明者 ラシュワン・アーメド・モハメド 大阪府茨木市美穂ケ丘11−1 大阪大学溶 接工学研究所内 ─────────────────────────────────────────────────── ─── 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)
曲げ加工するために、先ず、初期形状と目的形状の幾何
学情報をインプットし、初期形状に基づいて有限要素法
のメッシュ分割を行って、その分割形状を目的形状の上
に写像し、次いで、初期形状から目的形状まで強制的に
変形させて目的固有歪分布を計算し、得られた目的固有
歪分布を複数の互いに直交する格子状の加熱線によって
生成される生成固有歪で表現し、このとき加熱装置と被
加工材の組合わせに対する加熱条件と生成固有歪との定
量的関係を用い、次に、加熱条件が与えられたときに求
められた生成固有歪を初期形状に付与することによって
曲り形状の確認のための弾性シミュレーションを行った
上で、金属板の曲げ加工を行うことを特徴とする線状加
熱による金属板の曲げ加工方法。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.
Priority Applications (1)
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JP23216893A JP2626496B2 (en) | 1993-08-26 | 1993-08-26 | Method of bending metal plate by linear heating |
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