WO2012081717A1 - Method of designing material for cylinder formation process, and cylinder formation processed product - Google Patents
Method of designing material for cylinder formation process, and cylinder formation processed product Download PDFInfo
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- WO2012081717A1 WO2012081717A1 PCT/JP2011/079273 JP2011079273W WO2012081717A1 WO 2012081717 A1 WO2012081717 A1 WO 2012081717A1 JP 2011079273 W JP2011079273 W JP 2011079273W WO 2012081717 A1 WO2012081717 A1 WO 2012081717A1
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
- B21D—WORKING OR PROCESSING OF SHEET METAL OR METAL TUBES, RODS OR PROFILES WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
- B21D5/00—Bending sheet metal along straight lines, e.g. to form simple curves
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
- B21C—MANUFACTURE OF METAL SHEETS, WIRE, RODS, TUBES OR PROFILES, OTHERWISE THAN BY ROLLING; AUXILIARY OPERATIONS USED IN CONNECTION WITH METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL
- B21C37/00—Manufacture of metal sheets, bars, wire, tubes or like semi-manufactured products, not otherwise provided for; Manufacture of tubes of special shape
- B21C37/06—Manufacture of metal sheets, bars, wire, tubes or like semi-manufactured products, not otherwise provided for; Manufacture of tubes of special shape of tubes or metal hoses; Combined procedures for making tubes, e.g. for making multi-wall tubes
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
- B21D—WORKING OR PROCESSING OF SHEET METAL OR METAL TUBES, RODS OR PROFILES WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
- B21D5/00—Bending sheet metal along straight lines, e.g. to form simple curves
- B21D5/01—Bending sheet metal along straight lines, e.g. to form simple curves between rams and anvils or abutments
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
- B21D—WORKING OR PROCESSING OF SHEET METAL OR METAL TUBES, RODS OR PROFILES WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
- B21D5/00—Bending sheet metal along straight lines, e.g. to form simple curves
- B21D5/01—Bending sheet metal along straight lines, e.g. to form simple curves between rams and anvils or abutments
- B21D5/015—Bending sheet metal along straight lines, e.g. to form simple curves between rams and anvils or abutments for making tubes
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B21—MECHANICAL METAL-WORKING WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
- B21D—WORKING OR PROCESSING OF SHEET METAL OR METAL TUBES, RODS OR PROFILES WITHOUT ESSENTIALLY REMOVING MATERIAL; PUNCHING METAL
- B21D51/00—Making hollow objects
- B21D51/02—Making hollow objects characterised by the structure of the objects
- B21D51/10—Making hollow objects characterised by the structure of the objects conically or cylindrically shaped objects
Definitions
- the present invention relates to a metal material design method capable of setting a spring back angle during cylindrical molding to a predetermined value and a cylindrical molded product.
- cylindrical processed products manufactured by subjecting metal materials to cylindrical forming processing by bending are used.
- cylindrical forming processing For example, in a three-piece can composed of a lid, a trunk, and a bottom, a cylindrical processed product having a cylindrical portion subjected to a cylindrical molding process is used.
- a metal material metal plate
- the metal material causes a spring back due to elastic recovery, and as a result, the cylindrical shape changes. Therefore, when performing cylindrical forming, it is necessary to determine the processing conditions in consideration of this spring back in advance.
- the thickness of a metal material hereinafter, also referred to as “thinning”
- the springback angle is defined by the amount of change from the bending angle during loading to the bending angle after unloading in bending.
- the winding width is defined as a distance between one end of a metal plate that has been formed into a cylindrical shape by cylindrical forming processing and the opposite end, and a state in which both ends abut each other is 0.
- the open state is represented by a positive value, and the overlapping state is represented by a negative value.
- Non-Patent Document 2 proposes an empirical formula for stainless steel plates, but the metal materials are limited to stainless steel plates and cannot be said to be suitable for a wide variety of metal materials. The problem was left in terms of.
- the present invention has been made in view of the above circumstances, and has newly found a method for calculating a springback angle when a metal material having various mechanical properties and plate thicknesses is formed into a cylinder.
- the gist of the present invention is as follows. [1] In designing a metal material to be subjected to cylindrical forming by bending, the metal material was subjected to cylindrical forming under the conditions that the bending curvature radius r is 5 mm or more and the bending angle ⁇ is 90 degrees or more and 180 degrees or less.
- the yield strength YP, Young's modulus E, and sheet thickness t of the metal material are calculated based on the following formula (1) so that the spring back angle ⁇ at the time becomes a predetermined value, and the calculated yield strength YP and Young A method for designing a cylindrical molding material, wherein the metal material is designed to have a rate E.
- ⁇ / ⁇ ⁇ 5.52 [(YP ⁇ r) / (E ⁇ t)] 2 +4.13 (YP ⁇ r) / (E ⁇ t) (1)
- ⁇ springback angle (degree)
- ⁇ bending angle (degree)
- YP yield strength (MPa)
- E Young's modulus (MPa)
- t plate thickness (mm)
- r bending radius of curvature ( mm).
- a metal material capable of setting the springback angle to a predetermined value can be easily designed, which greatly contributes to productivity improvement and cost reduction in the cylindrical forming process.
- the present inventors first examined which of the factors affects the springback angle. As a result, it was confirmed that these factors were bending angle, bending radius of curvature, sheet thickness, yield strength and Young's modulus.
- the springback angle is measured by bending under various conditions, and the influence of each factor is quantitatively evaluated to give the relationship between the springback angle and these factors.
- the empirical formula was derived. Details will be described below. As described above, when the metal material is unloaded after being bent, the shape of the loaded state is slightly changed due to elastic recovery. This is called springback. If the bending angle ⁇ (degrees) is changed to ⁇ ′ (degrees) due to the springback, the springback angle ⁇ (degrees) is expressed by Expression (3). Also, in the bending process, assuming that the radius of curvature of the surface having no strain change in the circumferential direction is changed from r (mm) to r ′ (mm) by springback, the relationship represented by the following formula (4) is obtained.
- the range of factors that can determine ⁇ / ⁇ is narrow (0 ⁇ (YP ⁇ r) / (E ⁇ t) ⁇ 0.11) and lacks versatility.
- ⁇ / ⁇ 1.9 [(YP ⁇ r) / (E ⁇ t)] 0.62 (8) Therefore, the inventors measured the springback angle by actually performing bending under various metal materials (aluminum plate, copper plate, stainless steel plate, steel plate) and plate thickness conditions. At this time, the bending radius of curvature was in the range of 5 mm or more, and the bending angle was in the range of 90 to 180 degrees. Further, the plate thickness is in the range of 0.1 to 2.0 mm.
- FIG. 2 shows the results organized by the relationship between ⁇ / ⁇ and (YP ⁇ r) / (E ⁇ t).
- ⁇ is the result of this measurement.
- a regression equation that can be accurately reproduced from these measurement results was obtained, and the above equation (1) was obtained (see the solid line in the figure).
- This equation (1) can be used in a region where (YP ⁇ r) / (E ⁇ t) is 0.33 or less, and is much wider than the use range of Non-Patent Document 2.
- this equation (1) can be applied to a wide variety of metal materials, and from this equation, mechanical characteristics (YP, E) that give a predetermined springback angle at a desired plate thickness can be calculated.
- a metal material having the calculated mechanical characteristics may be designed. It is also possible to obtain a plate thickness that provides a predetermined spring back angle in a metal material having a predetermined mechanical property. Furthermore, it is possible to calculate the springback angle from the desired plate thickness and mechanical characteristics.
- the measurement data in Non-Patent Document 2 is indicated by ⁇
- the equation (8) is indicated by a dotted line
- the theoretical equation (2) is also indicated by a dotted line.
- the spring back angle ⁇ before changing the plate thickness is measured.
- a test piece having an arbitrary dimension is bent, for example, under conditions of a bending curvature radius of 12.7 mm and a bending angle of 180 degrees.
- the bending angle ⁇ ′ of the test piece after unloading is measured, and the springback angle ⁇ is calculated from the equation (3).
- this procedure may be omitted.
- a material satisfying the above-mentioned mechanical properties may be selected from a metal material database, and if it cannot be found from the database, a new material may be designed using YP and E as indices.
- YP and E as indices.
- the mechanical properties of a metal material subjected to cylindrical forming are changed.
- the metal material before changing the mechanical characteristics is bent in the same manner as described above, and the spring back angle is obtained.
- the plate thickness t is calculated from the formula (1) based on the springback angle, the yield strength YP and Young's modulus E determined in advance, and bending conditions (bending radius of curvature, bending angle). .
- a winding width equivalent to that before the mechanical properties are changed can be obtained.
- the springback angle of the metal material before the change is clarified, and then the condition that the formula (1) is satisfied is satisfied.
- a predetermined winding width can be secured after cylindrical molding.
- the material design was performed for the metal material that requires a winding width equivalent to that before the plate thickness reduction.
- the springback angle is made constant in order to obtain the same winding width as before the plate thickness reduction. Shows an example of studying optimization of yield strength YP.
- the pass / fail judgment of whether or not a winding width equivalent to that of the metal material before the reduction of the plate thickness has been obtained is acceptable if the average winding width of the current material is within ⁇ 10% in consideration of the variation of the winding width.
- the pass / fail judgment of whether or not a winding width equivalent to that of the metal material before the reduction of the plate thickness has been obtained is acceptable if the average winding width of the current material is within ⁇ 10% in consideration of the variation of the winding width.
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- Engineering & Computer Science (AREA)
- Mechanical Engineering (AREA)
- Bending Of Plates, Rods, And Pipes (AREA)
- Springs (AREA)
Abstract
Provided are a method of designing a material having mechanical characteristics such that a spring-back angle of a predetermined value can be obtained after a cylinder formation process of materials having various mechanical characteristics or thicknesses, and a processed product. A method of designing a material for a cylinder formation process, when designing a metal material subjected to a cylinder formation process involving bending, comprises: calculating a yield strength YP, a Young's modulus E, and a thickness t of the metal material such that a spring-back angle Δθ has a predetermined value after a cylinder formation process under the conditions of a bending radius of curvature r of 5 mm or more and a bending angle θ of 90° or more and 180° or less; and designing the metal material such that the metal material has the calculated yield strength YP and Young's modulus E.
Description
本発明は、円筒成形加工時のスプリングバック角を所定値とすることのできる金属材料の設計方法および円筒成形加工品に関する。
The present invention relates to a metal material design method capable of setting a spring back angle during cylindrical molding to a predetermined value and a cylindrical molded product.
食品容器、医療機器、金属容器、装置部品などでは、金属材料を曲げ加工による円筒成形加工（以下、円筒成形加工という）を施して製造した円筒状の加工品が使用される。例えば、蓋、胴、底からなるスリーピース缶では、胴部に円筒成形加工が施された円筒状の加工品が用いられる。
一般に、金属材料（金属板）に円筒成形加工を施し、その後に除荷すると、弾性的な回復により金属材料はスプリングバックを起こし、その結果円筒形状が変化する。従って、円筒成形加工を行なう場合は、予めこのスプリングバックを考慮して加工条件を決定する必要がある。
最近の傾向として、素材コストの低減を図るために金属材料の板厚を薄くすること（以下、薄肉化ともいう）が求められている。ところが、薄肉化するとスプリングバック角が大きくなって所定の円筒形状、すなわち所定の巻幅が確保できなくなるという問題がある。ここで、スプリングバック角とは、曲げ加工において、負荷時の曲げ角から除荷後の曲げ角への変化量で定義される。また、巻幅とは、図１に示すように、円筒成形加工により円筒状になった金属板の一端と反対側の端との間隔として定義されるもので、両端が突き合わさった状態を０とし、開いた状態をプラス、重なった状態をマイナスの値で表される。
薄肉化により巻幅が変化すると、その後の工程（例えば端部を溶接してスリーピース缶の胴部にする工程）を阻害するため、薄肉化しても巻幅が変化しないようにする必要がある。そのためには、円筒成形加工工程において、板厚が厚い金属材料から薄い金属材料に切り替わる場合、成形加工条件を設定しなおすかあるいは成形装置を改造するしかなく、生産性向上やコストダウンの妨げになっている。
そこで、板厚を低減した場合であっても所定の円筒形状（巻幅）が得られるような金属材料を設計することができれば、成形加工条件の再設定や成形装置の改造は不要となる。すなわち、板厚を変更しても板厚変更前と同等のスプリングバック角を得ることのできる金属材料を設計する必要がある。
ところで、加工に供する金属材料が加工硬化しない完全弾塑性体であると仮定すると、スプリングバック角は理論的に下記式（２）で算出することができる（非特許文献１参照）。
Δθ／θ＝３（ＹＰ・ｒ）／（Ｅ・ｔ）−４［（ＹＰ・ｒ）／（Ｅ・ｔ）］３ ・・・ （２）
ここで、Δθ：スプリングバック角（度）、θ：曲げ角（度）、ｒ：曲げ曲率半径（ｍｍ）、ｔ：板厚（ｍｍ）、ＹＰ：降伏強度（ＭＰａ）、Ｅ：ヤング率（ＭＰａ）である。
従って、式（２）を用いて目標とする板厚やスプリングバック角から金属材料に必要な機械特性（ヤング率、降伏強度）を算出し、この機械特性を有する金属材料を設計すればよい。
ところが、非特許文献２によると、上記式（２）で表される理論式は必ずしも実験事実を正確に再現しないと報告されている。更に、非特許文献２ではステンレス鋼板を対象とした実験式を提案しているが、金属材料がステンレス鋼板に限定されており、多種多様な金属材料に適しているものとは言えず、汎用性の点で課題を残していた。 For food containers, medical devices, metal containers, device parts, etc., cylindrical processed products manufactured by subjecting metal materials to cylindrical forming processing by bending (hereinafter referred to as cylindrical forming processing) are used. For example, in a three-piece can composed of a lid, a trunk, and a bottom, a cylindrical processed product having a cylindrical portion subjected to a cylindrical molding process is used.
In general, when a metal material (metal plate) is subjected to a cylindrical forming process and then unloaded, the metal material causes a spring back due to elastic recovery, and as a result, the cylindrical shape changes. Therefore, when performing cylindrical forming, it is necessary to determine the processing conditions in consideration of this spring back in advance.
As a recent trend, there is a demand for reducing the thickness of a metal material (hereinafter, also referred to as “thinning”) in order to reduce material costs. However, there is a problem that when the thickness is reduced, the springback angle becomes large and a predetermined cylindrical shape, that is, a predetermined winding width cannot be secured. Here, the springback angle is defined by the amount of change from the bending angle during loading to the bending angle after unloading in bending. Further, as shown in FIG. 1, the winding width is defined as a distance between one end of a metal plate that has been formed into a cylindrical shape by cylindrical forming processing and the opposite end, and a state in which both ends abut each other is 0. The open state is represented by a positive value, and the overlapping state is represented by a negative value.
If the winding width changes due to the thinning, the subsequent steps (for example, the step of welding the end portion to form the body of the three-piece can) are hindered, so that it is necessary to prevent the winding width from changing even if the thickness is reduced. To that end, when switching from a thick metal material to a thin metal material in a cylindrical molding process, it is only possible to reset the molding process conditions or remodel the molding equipment, which hinders productivity improvement and cost reduction. It has become.
Therefore, if a metal material capable of obtaining a predetermined cylindrical shape (winding width) can be designed even when the plate thickness is reduced, resetting of molding processing conditions and modification of the molding apparatus are unnecessary. That is, it is necessary to design a metal material that can obtain a springback angle equivalent to that before the plate thickness change even if the plate thickness is changed.
By the way, if it is assumed that the metal material to be processed is a complete elastoplastic material that does not work harden, the springback angle can be theoretically calculated by the following formula (2) (see Non-Patent Document 1).
Δθ / θ = 3 (YP · r) / (E · t) −4 [(YP · r) / (E · t)] 3 (2)
Where Δθ: springback angle (degree), θ: bending angle (degree), r: bending radius of curvature (mm), t: plate thickness (mm), YP: yield strength (MPa), E: Young's modulus ( MPa).
Therefore, the mechanical properties (Young's modulus and yield strength) necessary for the metal material are calculated from the target plate thickness and spring back angle using the formula (2), and the metal material having this mechanical property may be designed.
However, according to Non-Patent Document 2, it is reported that the theoretical formula represented by the above formula (2) does not necessarily accurately reproduce the experimental fact. Furthermore, Non-Patent Document 2 proposes an empirical formula for stainless steel plates, but the metal materials are limited to stainless steel plates and cannot be said to be suitable for a wide variety of metal materials. The problem was left in terms of.
一般に、金属材料（金属板）に円筒成形加工を施し、その後に除荷すると、弾性的な回復により金属材料はスプリングバックを起こし、その結果円筒形状が変化する。従って、円筒成形加工を行なう場合は、予めこのスプリングバックを考慮して加工条件を決定する必要がある。
最近の傾向として、素材コストの低減を図るために金属材料の板厚を薄くすること（以下、薄肉化ともいう）が求められている。ところが、薄肉化するとスプリングバック角が大きくなって所定の円筒形状、すなわち所定の巻幅が確保できなくなるという問題がある。ここで、スプリングバック角とは、曲げ加工において、負荷時の曲げ角から除荷後の曲げ角への変化量で定義される。また、巻幅とは、図１に示すように、円筒成形加工により円筒状になった金属板の一端と反対側の端との間隔として定義されるもので、両端が突き合わさった状態を０とし、開いた状態をプラス、重なった状態をマイナスの値で表される。
薄肉化により巻幅が変化すると、その後の工程（例えば端部を溶接してスリーピース缶の胴部にする工程）を阻害するため、薄肉化しても巻幅が変化しないようにする必要がある。そのためには、円筒成形加工工程において、板厚が厚い金属材料から薄い金属材料に切り替わる場合、成形加工条件を設定しなおすかあるいは成形装置を改造するしかなく、生産性向上やコストダウンの妨げになっている。
そこで、板厚を低減した場合であっても所定の円筒形状（巻幅）が得られるような金属材料を設計することができれば、成形加工条件の再設定や成形装置の改造は不要となる。すなわち、板厚を変更しても板厚変更前と同等のスプリングバック角を得ることのできる金属材料を設計する必要がある。
ところで、加工に供する金属材料が加工硬化しない完全弾塑性体であると仮定すると、スプリングバック角は理論的に下記式（２）で算出することができる（非特許文献１参照）。
Δθ／θ＝３（ＹＰ・ｒ）／（Ｅ・ｔ）−４［（ＹＰ・ｒ）／（Ｅ・ｔ）］３ ・・・ （２）
ここで、Δθ：スプリングバック角（度）、θ：曲げ角（度）、ｒ：曲げ曲率半径（ｍｍ）、ｔ：板厚（ｍｍ）、ＹＰ：降伏強度（ＭＰａ）、Ｅ：ヤング率（ＭＰａ）である。
従って、式（２）を用いて目標とする板厚やスプリングバック角から金属材料に必要な機械特性（ヤング率、降伏強度）を算出し、この機械特性を有する金属材料を設計すればよい。
ところが、非特許文献２によると、上記式（２）で表される理論式は必ずしも実験事実を正確に再現しないと報告されている。更に、非特許文献２ではステンレス鋼板を対象とした実験式を提案しているが、金属材料がステンレス鋼板に限定されており、多種多様な金属材料に適しているものとは言えず、汎用性の点で課題を残していた。 For food containers, medical devices, metal containers, device parts, etc., cylindrical processed products manufactured by subjecting metal materials to cylindrical forming processing by bending (hereinafter referred to as cylindrical forming processing) are used. For example, in a three-piece can composed of a lid, a trunk, and a bottom, a cylindrical processed product having a cylindrical portion subjected to a cylindrical molding process is used.
In general, when a metal material (metal plate) is subjected to a cylindrical forming process and then unloaded, the metal material causes a spring back due to elastic recovery, and as a result, the cylindrical shape changes. Therefore, when performing cylindrical forming, it is necessary to determine the processing conditions in consideration of this spring back in advance.
As a recent trend, there is a demand for reducing the thickness of a metal material (hereinafter, also referred to as “thinning”) in order to reduce material costs. However, there is a problem that when the thickness is reduced, the springback angle becomes large and a predetermined cylindrical shape, that is, a predetermined winding width cannot be secured. Here, the springback angle is defined by the amount of change from the bending angle during loading to the bending angle after unloading in bending. Further, as shown in FIG. 1, the winding width is defined as a distance between one end of a metal plate that has been formed into a cylindrical shape by cylindrical forming processing and the opposite end, and a state in which both ends abut each other is 0. The open state is represented by a positive value, and the overlapping state is represented by a negative value.
If the winding width changes due to the thinning, the subsequent steps (for example, the step of welding the end portion to form the body of the three-piece can) are hindered, so that it is necessary to prevent the winding width from changing even if the thickness is reduced. To that end, when switching from a thick metal material to a thin metal material in a cylindrical molding process, it is only possible to reset the molding process conditions or remodel the molding equipment, which hinders productivity improvement and cost reduction. It has become.
Therefore, if a metal material capable of obtaining a predetermined cylindrical shape (winding width) can be designed even when the plate thickness is reduced, resetting of molding processing conditions and modification of the molding apparatus are unnecessary. That is, it is necessary to design a metal material that can obtain a springback angle equivalent to that before the plate thickness change even if the plate thickness is changed.
By the way, if it is assumed that the metal material to be processed is a complete elastoplastic material that does not work harden, the springback angle can be theoretically calculated by the following formula (2) (see Non-Patent Document 1).
Δθ / θ = 3 (YP · r) / (E · t) −4 [(YP · r) / (E · t)] 3 (2)
Where Δθ: springback angle (degree), θ: bending angle (degree), r: bending radius of curvature (mm), t: plate thickness (mm), YP: yield strength (MPa), E: Young's modulus ( MPa).
Therefore, the mechanical properties (Young's modulus and yield strength) necessary for the metal material are calculated from the target plate thickness and spring back angle using the formula (2), and the metal material having this mechanical property may be designed.
However, according to Non-Patent Document 2, it is reported that the theoretical formula represented by the above formula (2) does not necessarily accurately reproduce the experimental fact. Furthermore, Non-Patent Document 2 proposes an empirical formula for stainless steel plates, but the metal materials are limited to stainless steel plates and cannot be said to be suitable for a wide variety of metal materials. The problem was left in terms of.
本発明は上記のような事情に鑑みてなされたもので、多種多様な機械特性や板厚を有する金属材料を円筒成形加工したときのスプリングバック角を算出する方法を新規に見出し、これを用いてスプリングバック角を所定値にすることのできる材質（機械特性）を有する金属材料を設計する方法およびこの方法で設計された金属材料に円筒成形加工を施して製造される加工品を提供することを目的とする。
The present invention has been made in view of the above circumstances, and has newly found a method for calculating a springback angle when a metal material having various mechanical properties and plate thicknesses is formed into a cylinder. To provide a method of designing a metal material having a material (mechanical characteristics) capable of setting the springback angle to a predetermined value, and a processed product manufactured by subjecting the metal material designed by this method to cylindrical forming With the goal.
本発明の要旨は以下の通りである。
［１］曲げ加工による円筒成形加工が施される金属材料を設計するにあたり、金属材料を曲げ曲率半径ｒが５ｍｍ以上、曲げ角θが９０度以上１８０度以下の条件で円筒成形加工を施したときのスプリングバック角Δθが所定値となるように、前記金属材料の降伏強度ＹＰ、ヤング率Ｅおよび板厚ｔを下記式（１）に基づいて算出し、該算出された降伏強度ＹＰおよびヤング率Ｅを有するように前記金属材料を設計することを特徴とする円筒成形加工用材料の設計方法。
Δθ／θ＝−５．５２［（ＹＰ・ｒ）／（Ｅ・ｔ）］２＋４．１３（ＹＰ・ｒ）／（Ｅ・ｔ） ・・・ （１）
ここで、Δθ：スプリングバック角（度）、θ：曲げ角（度）、ＹＰ：降伏強度（ＭＰａ）、Ｅ：ヤング率（ＭＰａ）、ｔ：板厚（ｍｍ）、ｒ：曲げ曲率半径（ｍｍ）である。
［２］前記［１］に記載の方法によって設計された金属材料に曲げ加工による円筒成形加工を施して製造されたことを特徴とする円筒成形加工品。 The gist of the present invention is as follows.
[1] In designing a metal material to be subjected to cylindrical forming by bending, the metal material was subjected to cylindrical forming under the conditions that the bending curvature radius r is 5 mm or more and the bending angle θ is 90 degrees or more and 180 degrees or less. The yield strength YP, Young's modulus E, and sheet thickness t of the metal material are calculated based on the following formula (1) so that the spring back angle Δθ at the time becomes a predetermined value, and the calculated yield strength YP and Young A method for designing a cylindrical molding material, wherein the metal material is designed to have a rate E.
Δθ / θ = −5.52 [(YP · r) / (E · t)] 2 +4.13 (YP · r) / (E · t) (1)
Here, Δθ: springback angle (degree), θ: bending angle (degree), YP: yield strength (MPa), E: Young's modulus (MPa), t: plate thickness (mm), r: bending radius of curvature ( mm).
[2] A cylindrical molded product manufactured by subjecting the metal material designed by the method described in [1] above to cylindrical molding by bending.
［１］曲げ加工による円筒成形加工が施される金属材料を設計するにあたり、金属材料を曲げ曲率半径ｒが５ｍｍ以上、曲げ角θが９０度以上１８０度以下の条件で円筒成形加工を施したときのスプリングバック角Δθが所定値となるように、前記金属材料の降伏強度ＹＰ、ヤング率Ｅおよび板厚ｔを下記式（１）に基づいて算出し、該算出された降伏強度ＹＰおよびヤング率Ｅを有するように前記金属材料を設計することを特徴とする円筒成形加工用材料の設計方法。
Δθ／θ＝−５．５２［（ＹＰ・ｒ）／（Ｅ・ｔ）］２＋４．１３（ＹＰ・ｒ）／（Ｅ・ｔ） ・・・ （１）
ここで、Δθ：スプリングバック角（度）、θ：曲げ角（度）、ＹＰ：降伏強度（ＭＰａ）、Ｅ：ヤング率（ＭＰａ）、ｔ：板厚（ｍｍ）、ｒ：曲げ曲率半径（ｍｍ）である。
［２］前記［１］に記載の方法によって設計された金属材料に曲げ加工による円筒成形加工を施して製造されたことを特徴とする円筒成形加工品。 The gist of the present invention is as follows.
[1] In designing a metal material to be subjected to cylindrical forming by bending, the metal material was subjected to cylindrical forming under the conditions that the bending curvature radius r is 5 mm or more and the bending angle θ is 90 degrees or more and 180 degrees or less. The yield strength YP, Young's modulus E, and sheet thickness t of the metal material are calculated based on the following formula (1) so that the spring back angle Δθ at the time becomes a predetermined value, and the calculated yield strength YP and Young A method for designing a cylindrical molding material, wherein the metal material is designed to have a rate E.
Δθ / θ = −5.52 [(YP · r) / (E · t)] 2 +4.13 (YP · r) / (E · t) (1)
Here, Δθ: springback angle (degree), θ: bending angle (degree), YP: yield strength (MPa), E: Young's modulus (MPa), t: plate thickness (mm), r: bending radius of curvature ( mm).
[2] A cylindrical molded product manufactured by subjecting the metal material designed by the method described in [1] above to cylindrical molding by bending.
本発明によれば、スプリングバック角を所定値にすることのできる金属材料を容易に設計することができ、円筒成形加工工程における生産性向上やコストダウンに大きく寄与する。
According to the present invention, a metal material capable of setting the springback angle to a predetermined value can be easily designed, which greatly contributes to productivity improvement and cost reduction in the cylindrical forming process.
同じ機械特性を有した板厚の異なる金属材料に、同一条件で円筒成形加工を施すと、板厚の違いによってスプリングバック角が異なってしまい、一定の巻幅（円筒形状）を得ることが困難である。そのため、生産現場で円筒成形加工を行なう場合には、板厚が変わる都度成形装置を改造するか、板厚に応じて加工条件を調整するしかなく、生産性等を阻害していた。この問題を解決するには、板厚に応じて機械特性が異なる別の金属材料に変更することが考えられる。すなわち、板厚をｔ１からｔ２に変更する場合、板厚ｔ１の金属材料のスプリングバック角と同等となるような機械特性を有する金属材料を使用すれば、円筒成形加工後の巻幅が変化しない加工品が得られることになる。
そのためには、金属材料の板厚、機械特性および成型加工条件などの各因子がスプリングバック角に及ぼす影響を明確にする必要がある。そこで、本発明者らはまず、各因子の中でどの因子がスプリングバック角に影響を及ぼすかについて検討した。その結果、これらの因子は、曲げ角、曲げ曲率半径、板厚、降伏強度およびヤング率であることを確認した。
次いで、これらの因子を様々に変化させた条件下で曲げ加工を行なってスプリングバック角を測定し、各因子の影響度を定量的に評価してスプリングバック角とこれらの因子との関係を与える実験式を導出した。以下、詳細に説明する。
前述したように、通常、金属材料に曲げ加工を加えた後に除荷すると、弾性的な回復により、負荷状態の形状から多少変化する。これをスプリングバックと呼ぶ。スプリングバックにより曲げ角θ（度）がθ’（度）に変化したとすれば、スプリングバック角Δθ（度）は、式（３）で表される。また曲げ加工において、円周方向のひずみ変化のない面の曲率半径がスプリングバックによってｒ（ｍｍ）からｒ’（ｍｍ）に変化したとすると、下記式（４）で表される関係が得られる。
Δθ＝θ−θ’ ・・・ （３）
Δθ／θ＝（１／ｒ−１／ｒ’）／（１／ｒ’） ・・・ （４）
除荷前後で上記ひずみ変化のない面が板厚の中央位置にあるとすると、除荷による曲率変化に対して上記式（４）を用いて下記式（５）が成り立つ。
Δθ／θ＝（Ｍ・ｒ）／（Ｅ・Ｉ） ・・・ （５）
ここで、Ｍは曲げモーメント（ＭＰａ・ｍｍ３）、Ｉは断面２次モーメント（ｍｍ４）である。
単純曲げ理論によれば、曲げモーメントＭは下記式（６）で表されるので、上記式（５）に式（６）を代入することによって、下記式（７）が得られる。なお、金属材料が加工硬化しない完全弾塑性体であると仮定すると、ｎ（加工硬化指数）＝０であるから、式（７）から前記の式（２）が得られる。しかし、実際の金属材料でｎ＝０とするのは妥当ではなく、ｎの値は金属材料によって異なる。
前述の非特許文献２では、ステンレス鋼板を対象にした実験から、Δθ／θと（ＹＰ・ｒ）／（Ｅ・ｔ）との間に相関があることを見出し、式（８）を導出している。しかし、対象がステンレス鋼板に限定されていることから、Δθ／θを決定できる因子の範囲が狭く（０＜（ＹＰ・ｒ）／（Ｅ・ｔ）≦０．１１）、汎用性に欠ける。
Δθ／θ＝１．９［（ＹＰ・ｒ）／（Ｅ・ｔ）］０．６２ ・・・ （８）
そこで、本発明者らは、多種多様な金属材料（アルミニウム板、銅板、ステンレス鋼板、鋼板）および板厚条件で、実際に曲げ加工を施してスプリングバック角を測定した。この際、曲げ曲率半径は５ｍｍ以上の範囲、曲げ角は９０~１８０度の範囲とした。さらに板厚については、０．１~２．０ｍｍの範囲としている。これらの範囲であれば、食品容器、医療機器、金属容器、装置部品等の分野では十分に実用に耐えることができ、汎用性を有しているためである。
Δθ／θと（ＹＰ・ｒ）／（Ｅ・ｔ）との関係で整理した結果を図２に示す。図中、○が本測定結果である。これらの測定結果から精度良く再現できる回帰式を求め、前記式（１）を得た（図中の実線参照）。この式（１）は、（ＹＰ・ｒ）／（Ｅ・ｔ）が０．３３以下の領域で使用でき、非特許文献２の使用範囲より格段に広くなっている。すなわち、この式（１）は多種多様な金属材料に適用でき、この式から、所望の板厚において所定のスプリングバック角となる機械特性（ＹＰ、Ｅ）を算出することができる。そしてこの算出された機械特性を有するような金属材料を設計すればよい。また、所定の機械特性を有する金属材料において所定のスプリングバック角となる板厚を求めることもできる。さらに、所望の板厚および機械特性からスプリングバック角を算出することも可能である。なお、図２において、非特許文献２での測定データを△、式（８）を点線で示すとともに、理論式である式（２）も点線で示している。
以下、円筒成形加工が施される金属材料の板厚を低減する場合、板厚が変化してもスプリングバック角を変化させない（巻幅を変化させない）ための金属材料を設計する手順について説明する。
まず、板厚変更前のスプリングバック角Δθを測定する。任意の寸法を有する試験片を、例えば曲げ曲率半径１２．７ｍｍおよび曲げ角１８０度の条件で曲げ加工を行なう。次に除荷後の試験片の曲げ角θ’を測定し、前記式（３）からスプリングバック角Δθを算出する。スプリングバック角Δθを既存データとして保有している場合は、この手順を省略してもよい。
上記のようにして得られたスプリングバック角Δθおよび曲げ角θ（＝１８０°）を式（１）に代入することで、右辺から、曲げ曲率半径ｒと板厚ｔは既知であるから、降伏強度とヤング率の比（ＹＰ／Ｅ）の取るべき値が定まる。次いで、円筒成形加工が施される金属材料の仕様を考慮しつつ、上記求められたＹＰ／Ｅから、降伏強度ＹＰ及びヤング率Ｅを決定し、この機械特性を有する金属材料を設計する。なお、材料の設計は、金属材料データベースから上記機械特性を満足するものを選定してもよいし、データベースから見つからない場合には、このＹＰおよびＥを指標として新規材料を設計すればよい。
別の実施形態として、円筒成形加工が施される金属材料の機械特性を変更する場合について説明する。まず、機械特性を変更する前の金属材料を上記と同様にして曲げ加工し、スプリングバック角を求めておく。次に、前記スプリングバック角と、予め決められている降伏強度ＹＰおよびヤング率Ｅと、曲げ加工条件（曲げ曲率半径、曲げ角）をもとに、式（１）から板厚ｔを計算する。この板厚および機械特性を有する金属材料を円筒成形加工すれば、機械特性を変更する前と同等の巻幅が得られることになる。
上述したように本発明では、金属材料の要求特性（板厚や機械特性）を変更する場合、まず変更以前の金属材料のスプリングバック角を明確にし、その後、式（１）を満たすという条件の下で金属材料の特性を順次決定していくことで、円筒成形後において所定の巻幅が確保できる。 If metal materials with the same mechanical properties and different plate thickness are subjected to cylindrical forming under the same conditions, the springback angle will differ depending on the plate thickness, making it difficult to obtain a constant winding width (cylindrical shape). It is. For this reason, when performing cylindrical forming at the production site, it is only possible to remodel the forming apparatus every time the plate thickness changes, or to adjust the processing conditions according to the plate thickness, which hinders productivity and the like. In order to solve this problem, it is conceivable to change to another metal material having different mechanical properties according to the plate thickness. That is, when the plate thickness is changed from t 1 to t 2 , if a metal material having a mechanical property equivalent to the spring back angle of the metal material of the plate thickness t 1 is used, the winding width after the cylindrical forming process A processed product that does not change is obtained.
For this purpose, it is necessary to clarify the influence of factors such as the thickness of the metal material, mechanical properties, and molding processing conditions on the springback angle. Therefore, the present inventors first examined which of the factors affects the springback angle. As a result, it was confirmed that these factors were bending angle, bending radius of curvature, sheet thickness, yield strength and Young's modulus.
Next, the springback angle is measured by bending under various conditions, and the influence of each factor is quantitatively evaluated to give the relationship between the springback angle and these factors. The empirical formula was derived. Details will be described below.
As described above, when the metal material is unloaded after being bent, the shape of the loaded state is slightly changed due to elastic recovery. This is called springback. If the bending angle θ (degrees) is changed to θ ′ (degrees) due to the springback, the springback angle Δθ (degrees) is expressed by Expression (3). Also, in the bending process, assuming that the radius of curvature of the surface having no strain change in the circumferential direction is changed from r (mm) to r ′ (mm) by springback, the relationship represented by the following formula (4) is obtained. .
Δθ = θ−θ ′ (3)
Δθ / θ = (1 / r−1 / r ′) / (1 / r ′) (4)
Assuming that the surface without the strain change before and after unloading is at the center of the plate thickness, the following formula (5) is established using the above formula (4) for the curvature change due to unloading.
Δθ / θ = (M · r) / (E · I) (5)
Here, M is a bending moment (MPa · mm 3 ), and I is a cross-sectional secondary moment (mm 4 ).
According to the simple bending theory, the bending moment M is expressed by the following formula (6). Therefore, the following formula (7) is obtained by substituting the formula (6) into the above formula (5). If it is assumed that the metal material is a complete elastoplastic material that does not work harden, n (work hardening index) = 0, and therefore, the above formula (2) is obtained from the formula (7). However, it is not appropriate to set n = 0 in an actual metal material, and the value of n varies depending on the metal material.
In the above-mentioned Non-Patent Document 2, it was found from an experiment on a stainless steel plate that there is a correlation between Δθ / θ and (YP · r) / (E · t), and Equation (8) was derived. ing. However, since the object is limited to the stainless steel plate, the range of factors that can determine Δθ / θ is narrow (0 <(YP · r) / (E · t) ≦ 0.11) and lacks versatility.
Δθ / θ = 1.9 [(YP · r) / (E · t)] 0.62 (8)
Therefore, the inventors measured the springback angle by actually performing bending under various metal materials (aluminum plate, copper plate, stainless steel plate, steel plate) and plate thickness conditions. At this time, the bending radius of curvature was in the range of 5 mm or more, and the bending angle was in the range of 90 to 180 degrees. Further, the plate thickness is in the range of 0.1 to 2.0 mm. Within these ranges, it is possible to withstand practical use in the fields of food containers, medical equipment, metal containers, device parts, etc., and it is versatile.
FIG. 2 shows the results organized by the relationship between Δθ / θ and (YP · r) / (E · t). In the figure, ○ is the result of this measurement. A regression equation that can be accurately reproduced from these measurement results was obtained, and the above equation (1) was obtained (see the solid line in the figure). This equation (1) can be used in a region where (YP · r) / (E · t) is 0.33 or less, and is much wider than the use range of Non-Patent Document 2. That is, this equation (1) can be applied to a wide variety of metal materials, and from this equation, mechanical characteristics (YP, E) that give a predetermined springback angle at a desired plate thickness can be calculated. A metal material having the calculated mechanical characteristics may be designed. It is also possible to obtain a plate thickness that provides a predetermined spring back angle in a metal material having a predetermined mechanical property. Furthermore, it is possible to calculate the springback angle from the desired plate thickness and mechanical characteristics. In FIG. 2, the measurement data in Non-Patent Document 2 is indicated by Δ, the equation (8) is indicated by a dotted line, and the theoretical equation (2) is also indicated by a dotted line.
Hereinafter, a procedure for designing a metal material for preventing the springback angle from changing even if the plate thickness is changed (not changing the winding width) when reducing the plate thickness of the metal material to be subjected to the cylindrical forming process will be described. .
First, the spring back angle Δθ before changing the plate thickness is measured. A test piece having an arbitrary dimension is bent, for example, under conditions of a bending curvature radius of 12.7 mm and a bending angle of 180 degrees. Next, the bending angle θ ′ of the test piece after unloading is measured, and the springback angle Δθ is calculated from the equation (3). When the springback angle Δθ is held as existing data, this procedure may be omitted.
By substituting the springback angle Δθ and the bending angle θ (= 180 °) obtained as described above into Equation (1), the bending radius of curvature r and the thickness t are known from the right side. The value to be taken of the ratio of strength to Young's modulus (YP / E) is determined. Next, the yield strength YP and Young's modulus E are determined from the obtained YP / E while taking into account the specifications of the metal material to be subjected to cylindrical forming, and a metal material having this mechanical property is designed. For material design, a material satisfying the above-mentioned mechanical properties may be selected from a metal material database, and if it cannot be found from the database, a new material may be designed using YP and E as indices.
As another embodiment, a case will be described in which the mechanical properties of a metal material subjected to cylindrical forming are changed. First, the metal material before changing the mechanical characteristics is bent in the same manner as described above, and the spring back angle is obtained. Next, the plate thickness t is calculated from the formula (1) based on the springback angle, the yield strength YP and Young's modulus E determined in advance, and bending conditions (bending radius of curvature, bending angle). . If the metal material having the plate thickness and the mechanical properties is subjected to cylindrical forming, a winding width equivalent to that before the mechanical properties are changed can be obtained.
As described above, in the present invention, when changing the required characteristics (plate thickness and mechanical characteristics) of the metal material, first, the springback angle of the metal material before the change is clarified, and then the condition that the formula (1) is satisfied is satisfied. By sequentially determining the characteristics of the metal material below, a predetermined winding width can be secured after cylindrical molding.
そのためには、金属材料の板厚、機械特性および成型加工条件などの各因子がスプリングバック角に及ぼす影響を明確にする必要がある。そこで、本発明者らはまず、各因子の中でどの因子がスプリングバック角に影響を及ぼすかについて検討した。その結果、これらの因子は、曲げ角、曲げ曲率半径、板厚、降伏強度およびヤング率であることを確認した。
次いで、これらの因子を様々に変化させた条件下で曲げ加工を行なってスプリングバック角を測定し、各因子の影響度を定量的に評価してスプリングバック角とこれらの因子との関係を与える実験式を導出した。以下、詳細に説明する。
前述したように、通常、金属材料に曲げ加工を加えた後に除荷すると、弾性的な回復により、負荷状態の形状から多少変化する。これをスプリングバックと呼ぶ。スプリングバックにより曲げ角θ（度）がθ’（度）に変化したとすれば、スプリングバック角Δθ（度）は、式（３）で表される。また曲げ加工において、円周方向のひずみ変化のない面の曲率半径がスプリングバックによってｒ（ｍｍ）からｒ’（ｍｍ）に変化したとすると、下記式（４）で表される関係が得られる。
Δθ＝θ−θ’ ・・・ （３）
Δθ／θ＝（１／ｒ−１／ｒ’）／（１／ｒ’） ・・・ （４）
除荷前後で上記ひずみ変化のない面が板厚の中央位置にあるとすると、除荷による曲率変化に対して上記式（４）を用いて下記式（５）が成り立つ。
Δθ／θ＝（Ｍ・ｒ）／（Ｅ・Ｉ） ・・・ （５）
ここで、Ｍは曲げモーメント（ＭＰａ・ｍｍ３）、Ｉは断面２次モーメント（ｍｍ４）である。
単純曲げ理論によれば、曲げモーメントＭは下記式（６）で表されるので、上記式（５）に式（６）を代入することによって、下記式（７）が得られる。なお、金属材料が加工硬化しない完全弾塑性体であると仮定すると、ｎ（加工硬化指数）＝０であるから、式（７）から前記の式（２）が得られる。しかし、実際の金属材料でｎ＝０とするのは妥当ではなく、ｎの値は金属材料によって異なる。
Δθ／θ＝１．９［（ＹＰ・ｒ）／（Ｅ・ｔ）］０．６２ ・・・ （８）
そこで、本発明者らは、多種多様な金属材料（アルミニウム板、銅板、ステンレス鋼板、鋼板）および板厚条件で、実際に曲げ加工を施してスプリングバック角を測定した。この際、曲げ曲率半径は５ｍｍ以上の範囲、曲げ角は９０~１８０度の範囲とした。さらに板厚については、０．１~２．０ｍｍの範囲としている。これらの範囲であれば、食品容器、医療機器、金属容器、装置部品等の分野では十分に実用に耐えることができ、汎用性を有しているためである。
Δθ／θと（ＹＰ・ｒ）／（Ｅ・ｔ）との関係で整理した結果を図２に示す。図中、○が本測定結果である。これらの測定結果から精度良く再現できる回帰式を求め、前記式（１）を得た（図中の実線参照）。この式（１）は、（ＹＰ・ｒ）／（Ｅ・ｔ）が０．３３以下の領域で使用でき、非特許文献２の使用範囲より格段に広くなっている。すなわち、この式（１）は多種多様な金属材料に適用でき、この式から、所望の板厚において所定のスプリングバック角となる機械特性（ＹＰ、Ｅ）を算出することができる。そしてこの算出された機械特性を有するような金属材料を設計すればよい。また、所定の機械特性を有する金属材料において所定のスプリングバック角となる板厚を求めることもできる。さらに、所望の板厚および機械特性からスプリングバック角を算出することも可能である。なお、図２において、非特許文献２での測定データを△、式（８）を点線で示すとともに、理論式である式（２）も点線で示している。
以下、円筒成形加工が施される金属材料の板厚を低減する場合、板厚が変化してもスプリングバック角を変化させない（巻幅を変化させない）ための金属材料を設計する手順について説明する。
まず、板厚変更前のスプリングバック角Δθを測定する。任意の寸法を有する試験片を、例えば曲げ曲率半径１２．７ｍｍおよび曲げ角１８０度の条件で曲げ加工を行なう。次に除荷後の試験片の曲げ角θ’を測定し、前記式（３）からスプリングバック角Δθを算出する。スプリングバック角Δθを既存データとして保有している場合は、この手順を省略してもよい。
上記のようにして得られたスプリングバック角Δθおよび曲げ角θ（＝１８０°）を式（１）に代入することで、右辺から、曲げ曲率半径ｒと板厚ｔは既知であるから、降伏強度とヤング率の比（ＹＰ／Ｅ）の取るべき値が定まる。次いで、円筒成形加工が施される金属材料の仕様を考慮しつつ、上記求められたＹＰ／Ｅから、降伏強度ＹＰ及びヤング率Ｅを決定し、この機械特性を有する金属材料を設計する。なお、材料の設計は、金属材料データベースから上記機械特性を満足するものを選定してもよいし、データベースから見つからない場合には、このＹＰおよびＥを指標として新規材料を設計すればよい。
別の実施形態として、円筒成形加工が施される金属材料の機械特性を変更する場合について説明する。まず、機械特性を変更する前の金属材料を上記と同様にして曲げ加工し、スプリングバック角を求めておく。次に、前記スプリングバック角と、予め決められている降伏強度ＹＰおよびヤング率Ｅと、曲げ加工条件（曲げ曲率半径、曲げ角）をもとに、式（１）から板厚ｔを計算する。この板厚および機械特性を有する金属材料を円筒成形加工すれば、機械特性を変更する前と同等の巻幅が得られることになる。
上述したように本発明では、金属材料の要求特性（板厚や機械特性）を変更する場合、まず変更以前の金属材料のスプリングバック角を明確にし、その後、式（１）を満たすという条件の下で金属材料の特性を順次決定していくことで、円筒成形後において所定の巻幅が確保できる。 If metal materials with the same mechanical properties and different plate thickness are subjected to cylindrical forming under the same conditions, the springback angle will differ depending on the plate thickness, making it difficult to obtain a constant winding width (cylindrical shape). It is. For this reason, when performing cylindrical forming at the production site, it is only possible to remodel the forming apparatus every time the plate thickness changes, or to adjust the processing conditions according to the plate thickness, which hinders productivity and the like. In order to solve this problem, it is conceivable to change to another metal material having different mechanical properties according to the plate thickness. That is, when the plate thickness is changed from t 1 to t 2 , if a metal material having a mechanical property equivalent to the spring back angle of the metal material of the plate thickness t 1 is used, the winding width after the cylindrical forming process A processed product that does not change is obtained.
For this purpose, it is necessary to clarify the influence of factors such as the thickness of the metal material, mechanical properties, and molding processing conditions on the springback angle. Therefore, the present inventors first examined which of the factors affects the springback angle. As a result, it was confirmed that these factors were bending angle, bending radius of curvature, sheet thickness, yield strength and Young's modulus.
Next, the springback angle is measured by bending under various conditions, and the influence of each factor is quantitatively evaluated to give the relationship between the springback angle and these factors. The empirical formula was derived. Details will be described below.
As described above, when the metal material is unloaded after being bent, the shape of the loaded state is slightly changed due to elastic recovery. This is called springback. If the bending angle θ (degrees) is changed to θ ′ (degrees) due to the springback, the springback angle Δθ (degrees) is expressed by Expression (3). Also, in the bending process, assuming that the radius of curvature of the surface having no strain change in the circumferential direction is changed from r (mm) to r ′ (mm) by springback, the relationship represented by the following formula (4) is obtained. .
Δθ = θ−θ ′ (3)
Δθ / θ = (1 / r−1 / r ′) / (1 / r ′) (4)
Assuming that the surface without the strain change before and after unloading is at the center of the plate thickness, the following formula (5) is established using the above formula (4) for the curvature change due to unloading.
Δθ / θ = (M · r) / (E · I) (5)
Here, M is a bending moment (MPa · mm 3 ), and I is a cross-sectional secondary moment (mm 4 ).
According to the simple bending theory, the bending moment M is expressed by the following formula (6). Therefore, the following formula (7) is obtained by substituting the formula (6) into the above formula (5). If it is assumed that the metal material is a complete elastoplastic material that does not work harden, n (work hardening index) = 0, and therefore, the above formula (2) is obtained from the formula (7). However, it is not appropriate to set n = 0 in an actual metal material, and the value of n varies depending on the metal material.
Δθ / θ = 1.9 [(YP · r) / (E · t)] 0.62 (8)
Therefore, the inventors measured the springback angle by actually performing bending under various metal materials (aluminum plate, copper plate, stainless steel plate, steel plate) and plate thickness conditions. At this time, the bending radius of curvature was in the range of 5 mm or more, and the bending angle was in the range of 90 to 180 degrees. Further, the plate thickness is in the range of 0.1 to 2.0 mm. Within these ranges, it is possible to withstand practical use in the fields of food containers, medical equipment, metal containers, device parts, etc., and it is versatile.
FIG. 2 shows the results organized by the relationship between Δθ / θ and (YP · r) / (E · t). In the figure, ○ is the result of this measurement. A regression equation that can be accurately reproduced from these measurement results was obtained, and the above equation (1) was obtained (see the solid line in the figure). This equation (1) can be used in a region where (YP · r) / (E · t) is 0.33 or less, and is much wider than the use range of Non-Patent Document 2. That is, this equation (1) can be applied to a wide variety of metal materials, and from this equation, mechanical characteristics (YP, E) that give a predetermined springback angle at a desired plate thickness can be calculated. A metal material having the calculated mechanical characteristics may be designed. It is also possible to obtain a plate thickness that provides a predetermined spring back angle in a metal material having a predetermined mechanical property. Furthermore, it is possible to calculate the springback angle from the desired plate thickness and mechanical characteristics. In FIG. 2, the measurement data in Non-Patent Document 2 is indicated by Δ, the equation (8) is indicated by a dotted line, and the theoretical equation (2) is also indicated by a dotted line.
Hereinafter, a procedure for designing a metal material for preventing the springback angle from changing even if the plate thickness is changed (not changing the winding width) when reducing the plate thickness of the metal material to be subjected to the cylindrical forming process will be described. .
First, the spring back angle Δθ before changing the plate thickness is measured. A test piece having an arbitrary dimension is bent, for example, under conditions of a bending curvature radius of 12.7 mm and a bending angle of 180 degrees. Next, the bending angle θ ′ of the test piece after unloading is measured, and the springback angle Δθ is calculated from the equation (3). When the springback angle Δθ is held as existing data, this procedure may be omitted.
By substituting the springback angle Δθ and the bending angle θ (= 180 °) obtained as described above into Equation (1), the bending radius of curvature r and the thickness t are known from the right side. The value to be taken of the ratio of strength to Young's modulus (YP / E) is determined. Next, the yield strength YP and Young's modulus E are determined from the obtained YP / E while taking into account the specifications of the metal material to be subjected to cylindrical forming, and a metal material having this mechanical property is designed. For material design, a material satisfying the above-mentioned mechanical properties may be selected from a metal material database, and if it cannot be found from the database, a new material may be designed using YP and E as indices.
As another embodiment, a case will be described in which the mechanical properties of a metal material subjected to cylindrical forming are changed. First, the metal material before changing the mechanical characteristics is bent in the same manner as described above, and the spring back angle is obtained. Next, the plate thickness t is calculated from the formula (1) based on the springback angle, the yield strength YP and Young's modulus E determined in advance, and bending conditions (bending radius of curvature, bending angle). . If the metal material having the plate thickness and the mechanical properties is subjected to cylindrical forming, a winding width equivalent to that before the mechanical properties are changed can be obtained.
As described above, in the present invention, when changing the required characteristics (plate thickness and mechanical characteristics) of the metal material, first, the springback angle of the metal material before the change is clarified, and then the condition that the formula (1) is satisfied is satisfied. By sequentially determining the characteristics of the metal material below, a predetermined winding width can be secured after cylindrical molding.
円筒成形加工が施される金属材料の板厚が低減された場合において、板厚低減以前と同等の巻幅が求められる金属材料について材質設計を行なった。まず、板厚低減前の金属材料の仕様が、ｔ＝０．１５３ｍｍ、ＹＰ＝４００ＭＰａ、Ｅ＝２０６０００ＭＰａ、Δθ＝９６度、θ＝１８０度、ｒ＝１２．７ｍｍ、巻幅＝−１０．５~−９．０ｍｍ（平均値：−９．６ｍｍ）の鋼板をｔ＝０．１１７ｍｍまで低減した場合において、板厚低減以前と同等の巻幅を得るために、スプリングバック角が一定となるように降伏強度ＹＰの最適化を検討した例を示す。式（１）において、Δθ＝９６度、Ｅ＝２０６０００ＭＰａ、ｔ＝０．１１７ｍｍを代入すると、ＹＰが３１０ＭＰａ程度であれば、目的を達成するとの結果を得た。
この結果をもとに、板厚が０．１１７ｍｍで降伏強度ＹＰが異なる鋼板２種類を作製し、各々寸法１６５．４ｍｍ×１３６．５ｍｍの試験片１０枚を切り出して板厚低減以前と同じ条件で円筒成形加工を行なった。円筒成形後の巻幅を測定した結果を表１に示す。板厚低減以前の金属材料と同等の巻幅を得られているかの合否判定は、巻幅のばらつきを考慮して現行材の平均巻幅±１０％以内にあれば合格とした。ＹＰ＝３００ＭＰａの鋼板（Ｎｏ．２）を用いた円筒成形後の巻幅は平均値で−１０．５ｍｍとなり、板厚低減以前の金属材料とばらつきを含めて同程度の巻幅を得ることができた。一方、ＹＰ＝３６２ＭＰａの鋼板（Ｎｏ．３）を用いた円筒成形後の巻幅は平均値で＋５．０ｍｍとなり、板厚低減以前の金属材料と同程度の巻幅を得ることはできなかった。
次に、板厚低減前の金属材料の仕様が、ｔ＝０．２４２ｍｍ、ＹＰ＝３１０ＭＰａ、Ｅ＝２０６０００ＭＰａ、Δθ＝５４．３度、θ＝１８０度、ｒ＝１２．７ｍｍ、巻幅＝−１２．０~−８．０ｍｍ（平均値：−１０．０ｍｍ）の鋼板をｔ＝０．２２６ｍｍまで低減した場合において、板厚低減以前と同等の巻幅を得るために、スプリングバック角が一定となるようにヤング率Ｅの最適化を検討した例を示す。式（１）において、Δθ＝５４．３、ＹＰ＝３１０~３２０ＭＰａ、ｔ＝０．２２６ｍｍを代入すると、Ｅが２３００００ＭＰａ程度であれば、目的を達するとの結果を得た。
この結果をもとに、板厚が０．２２６ｍｍでヤング率Ｅが異なる鋼板２種類を作製し、各々寸法１６５．４ｍｍ×１３６．５ｍｍの試験片１０枚を切り出して板厚低減以前の条件で円筒成形加工を行なった。それぞれの円筒成形後の巻幅を測定した結果を表２に示す。板厚低減以前の金属材料と同等の巻幅を得られているかの合否判定は、巻幅のばらつきを考慮して現行材の平均巻幅±１０％以内にあれば合格とした。Ｅ＝２３１０００ＭＰａの鋼板（Ｎｏ．２）を用いた円筒成形後の巻幅は平均値で−１０．５ｍｍとなり、板厚低減以前の金属材料とばらつきを含めて同程度の巻幅を得ることができた。一方、Ｅ＝２１４０００ＭＰａの鋼板（Ｎｏ．３）を用いた円筒成形後の巻幅は平均値で−２．４ｍｍとなり、板厚低減以前の金属材料と同程度の巻幅を得ることはできなかった。
上記の実施例では、板厚を低減する場合に、降伏強度およびヤング率のいずれか１つを固定して他方を最適化する例について説明したが、両方を変化させてもよい。また、上記実施例では、板厚を低減する場合に、スプリングバック角（巻幅）を板厚低減の前後で変化しないような降伏強度またはヤング率の最適化を行なう例について説明したが、スプリングバック角をある値に変化させるようにしてもよい。さらに、降伏強度およびヤング率を変えずに、板厚を変化させた場合のスプリングバック角を求めることもできる。あるいは、降伏強度およびヤング率を変えずに、所望のスプリングバック角となる板厚を求めることもできる。
In the case where the plate thickness of the metal material subjected to the cylindrical forming process is reduced, the material design was performed for the metal material that requires a winding width equivalent to that before the plate thickness reduction. First, the specification of the metal material before thickness reduction is t = 0.153 mm, YP = 400 MPa, E = 206000 MPa, Δθ = 96 degrees, θ = 180 degrees, r = 12.7 mm, winding width = −10.5. When a steel plate of ~ -9.0 mm (average value: -9.6 mm) is reduced to t = 0.117 mm, the springback angle is made constant in order to obtain the same winding width as before the plate thickness reduction. Shows an example of studying optimization of yield strength YP. Substituting Δθ = 96 degrees, E = 206000 MPa, and t = 0.117 mm in the formula (1), the result that the objective is achieved is obtained when YP is about 310 MPa.
Based on this result, two types of steel plates with a plate thickness of 0.117 mm and different yield strengths YP were produced, and 10 test pieces each having dimensions of 165.4 mm × 136.5 mm were cut out and the same conditions as before the plate thickness reduction. A cylindrical molding process was performed. Table 1 shows the results of measuring the winding width after cylindrical molding. The pass / fail judgment of whether or not a winding width equivalent to that of the metal material before the reduction of the plate thickness has been obtained is acceptable if the average winding width of the current material is within ± 10% in consideration of the variation of the winding width. The winding width after cylindrical forming using a steel plate (No. 2) of YP = 300 MPa is -10.5 mm on average, and it is possible to obtain the same winding width including variations from the metal material before thickness reduction. did it. On the other hand, the winding width after cylindrical molding using a steel plate (No. 3) of YP = 362 MPa was +5.0 mm on average, and it was not possible to obtain a winding width comparable to that of the metal material before the plate thickness reduction. .
Next, the specifications of the metal material before thickness reduction are t = 0.242 mm, YP = 310 MPa, E = 206000 MPa, Δθ = 54.3 degrees, θ = 180 degrees, r = 12.7 mm, winding width = − When a steel plate of 12.0 to -8.0 mm (average value: -10.0 mm) is reduced to t = 0.226 mm, the spring back angle is constant in order to obtain the same winding width as before the thickness reduction. An example in which the optimization of Young's modulus E is studied so that Substituting Δθ = 54.3, YP = 310 to 320 MPa, and t = 0.226 mm in the formula (1), the result that the objective is achieved is obtained when E is about 230000 MPa.
Based on this result, two types of steel plates with a plate thickness of 0.226 mm and different Young's modulus E were produced, and 10 test pieces each having a size of 165.4 mm × 136.5 mm were cut out under the conditions before the plate thickness reduction. Cylindrical molding was performed. Table 2 shows the results of measuring the winding width after each cylindrical molding. The pass / fail judgment of whether or not a winding width equivalent to that of the metal material before the reduction of the plate thickness has been obtained is acceptable if the average winding width of the current material is within ± 10% in consideration of the variation of the winding width. The winding width after cylindrical forming using a steel plate (No. 2) of E = 231000 MPa is -10.5 mm on average, and it is possible to obtain a winding width comparable to that of the metal material before thickness reduction. did it. On the other hand, the winding width after cylindrical molding using a steel plate (No. 3) with E = 21.4 MPa is an average value of −2.4 mm, and it is not possible to obtain a winding width comparable to that of the metal material before the plate thickness reduction. It was.
In the above embodiment, when reducing the plate thickness, an example is described in which one of yield strength and Young's modulus is fixed and the other is optimized, but both may be changed. In the above embodiment, an example in which the yield strength or Young's modulus is optimized so that the springback angle (winding width) does not change before and after the reduction of the plate thickness when the plate thickness is reduced has been described. The back angle may be changed to a certain value. Furthermore, the springback angle when the plate thickness is changed without changing the yield strength and Young's modulus can be obtained. Alternatively, it is also possible to obtain a plate thickness that provides a desired springback angle without changing the yield strength and Young's modulus.
この結果をもとに、板厚が０．１１７ｍｍで降伏強度ＹＰが異なる鋼板２種類を作製し、各々寸法１６５．４ｍｍ×１３６．５ｍｍの試験片１０枚を切り出して板厚低減以前と同じ条件で円筒成形加工を行なった。円筒成形後の巻幅を測定した結果を表１に示す。板厚低減以前の金属材料と同等の巻幅を得られているかの合否判定は、巻幅のばらつきを考慮して現行材の平均巻幅±１０％以内にあれば合格とした。ＹＰ＝３００ＭＰａの鋼板（Ｎｏ．２）を用いた円筒成形後の巻幅は平均値で−１０．５ｍｍとなり、板厚低減以前の金属材料とばらつきを含めて同程度の巻幅を得ることができた。一方、ＹＰ＝３６２ＭＰａの鋼板（Ｎｏ．３）を用いた円筒成形後の巻幅は平均値で＋５．０ｍｍとなり、板厚低減以前の金属材料と同程度の巻幅を得ることはできなかった。
この結果をもとに、板厚が０．２２６ｍｍでヤング率Ｅが異なる鋼板２種類を作製し、各々寸法１６５．４ｍｍ×１３６．５ｍｍの試験片１０枚を切り出して板厚低減以前の条件で円筒成形加工を行なった。それぞれの円筒成形後の巻幅を測定した結果を表２に示す。板厚低減以前の金属材料と同等の巻幅を得られているかの合否判定は、巻幅のばらつきを考慮して現行材の平均巻幅±１０％以内にあれば合格とした。Ｅ＝２３１０００ＭＰａの鋼板（Ｎｏ．２）を用いた円筒成形後の巻幅は平均値で−１０．５ｍｍとなり、板厚低減以前の金属材料とばらつきを含めて同程度の巻幅を得ることができた。一方、Ｅ＝２１４０００ＭＰａの鋼板（Ｎｏ．３）を用いた円筒成形後の巻幅は平均値で−２．４ｍｍとなり、板厚低減以前の金属材料と同程度の巻幅を得ることはできなかった。
Based on this result, two types of steel plates with a plate thickness of 0.117 mm and different yield strengths YP were produced, and 10 test pieces each having dimensions of 165.4 mm × 136.5 mm were cut out and the same conditions as before the plate thickness reduction. A cylindrical molding process was performed. Table 1 shows the results of measuring the winding width after cylindrical molding. The pass / fail judgment of whether or not a winding width equivalent to that of the metal material before the reduction of the plate thickness has been obtained is acceptable if the average winding width of the current material is within ± 10% in consideration of the variation of the winding width. The winding width after cylindrical forming using a steel plate (No. 2) of YP = 300 MPa is -10.5 mm on average, and it is possible to obtain the same winding width including variations from the metal material before thickness reduction. did it. On the other hand, the winding width after cylindrical molding using a steel plate (No. 3) of YP = 362 MPa was +5.0 mm on average, and it was not possible to obtain a winding width comparable to that of the metal material before the plate thickness reduction. .
Based on this result, two types of steel plates with a plate thickness of 0.226 mm and different Young's modulus E were produced, and 10 test pieces each having a size of 165.4 mm × 136.5 mm were cut out under the conditions before the plate thickness reduction. Cylindrical molding was performed. Table 2 shows the results of measuring the winding width after each cylindrical molding. The pass / fail judgment of whether or not a winding width equivalent to that of the metal material before the reduction of the plate thickness has been obtained is acceptable if the average winding width of the current material is within ± 10% in consideration of the variation of the winding width. The winding width after cylindrical forming using a steel plate (No. 2) of E = 231000 MPa is -10.5 mm on average, and it is possible to obtain a winding width comparable to that of the metal material before thickness reduction. did it. On the other hand, the winding width after cylindrical molding using a steel plate (No. 3) with E = 21.4 MPa is an average value of −2.4 mm, and it is not possible to obtain a winding width comparable to that of the metal material before the plate thickness reduction. It was.
Claims (2)
- 曲げ加工による円筒成形加工が施される金属材料を設計するにあたり、金属材料を曲げ曲率半径ｒが５ｍｍ以上、曲げ角θが９０度以上１８０度以下の条件で円筒成形加工を施したときのスプリングバック角Δθが所定値となるように、前記金属材料の降伏強度ＹＰ、ヤング率Ｅおよび板厚ｔを下記（１）式に基づいて算出し、該算出された降伏強度ＹＰおよびヤング率Ｅを有するように前記金属材料を設計することを特徴とする円筒成形加工用材料の設計方法。
Δθ／θ＝−５．５２［（ＹＰ・ｒ）／（Ｅ・ｔ）］２＋４．１３（ＹＰ・ｒ）／（Ｅ・ｔ） ・・・ （１）
ここで、Δθ：スプリングバック角（度）、θ：曲げ角（度）、ＹＰ：降伏強度（ＭＰａ）、Ｅ：ヤング率（ＭＰａ）、ｔ：板厚（ｍｍ）、ｒ：曲げ曲率半径（ｍｍ）である。 In designing a metal material to be subjected to cylindrical forming by bending, a spring when the metal material is subjected to cylindrical forming under the conditions that the bending radius r is 5 mm or more and the bending angle θ is 90 degrees or more and 180 degrees or less. The yield strength YP, Young's modulus E, and sheet thickness t of the metal material are calculated based on the following equation (1) so that the back angle Δθ becomes a predetermined value, and the calculated yield strength YP and Young's modulus E are calculated. A method for designing a material for cylindrical forming, wherein the metal material is designed to have a material.
Δθ / θ = −5.52 [(YP · r) / (E · t)] 2 +4.13 (YP · r) / (E · t) (1)
Here, Δθ: springback angle (degree), θ: bending angle (degree), YP: yield strength (MPa), E: Young's modulus (MPa), t: plate thickness (mm), r: bending radius of curvature ( mm). - 請求項１に記載の方法によって設計された金属材料に曲げ加工による円筒成形加工を施して製造されたことを特徴とする円筒成形加工品。 A cylindrical molded product manufactured by subjecting the metal material designed by the method according to claim 1 to cylindrical molding by bending.
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| KR1020137013764A KR101505340B1 (en) | 2010-12-14 | 2011-12-13 | Method for designing material to be subjected to cylinder forming |
| EP11849189.3A EP2638982B1 (en) | 2010-12-14 | 2011-12-13 | Method of designing material for cylinder formation process |
| CN201180059553.9A CN103260781B (en) | 2010-12-14 | 2011-12-13 | Method of designing material for cylinder formation process, and cylinder formation processed product |
| US13/994,103 US20130327116A1 (en) | 2010-12-14 | 2011-12-13 | Method for designing material to be subjected to cylinder forming and product formed by performing cylinder forming |
| CA2818716A CA2818716C (en) | 2010-12-14 | 2011-12-13 | Method for designing material to be subjected to cylinder forming and product formed by performing cylinder forming |
| ES11849189T ES2771482T3 (en) | 2010-12-14 | 2011-12-13 | Material design method for a cylinder shaping procedure |
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| JP2010277923A JP5803097B2 (en) | 2010-12-14 | 2010-12-14 | Cylindrical molding material design method and cylindrical molding product manufacturing method |
| JP2010-277923 | 2010-12-14 |
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| JP6439666B2 (en) * | 2015-12-09 | 2018-12-19 | Ｊｆｅスチール株式会社 | Steel plate for 3-piece can excellent in roll form workability and roundness after welding, manufacturing method thereof, and manufacturing method of 3-piece can |
| CN110403480A (en) * | 2019-08-28 | 2019-11-05 | 武汉安在厨具有限公司 | A kind of three layers of iron ferro-aluminum compound kitchen tools production technology |
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| US3352136A (en) * | 1965-03-22 | 1967-11-14 | Conrac Corp | Metal forming machine |
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| JPS59209425A (en) * | 1983-05-12 | 1984-11-28 | Nippon Kokan Kk <Nkk> | U press tool for uoe steel tube manufacturing process |
| JPS62124031A (en) * | 1985-11-22 | 1987-06-05 | Kobe Steel Ltd | Production of welded pipe |
| JP3169787B2 (en) * | 1995-03-13 | 2001-05-28 | 本田技研工業株式会社 | Press forming method for sheet material |
| JP3268163B2 (en) * | 1995-05-09 | 2002-03-25 | 三菱重工業株式会社 | Plate bending method |
| JPH0910850A (en) * | 1995-06-29 | 1997-01-14 | Kobe Steel Ltd | Steel tube forming with using spring back quantity |
| JPH10166059A (en) * | 1996-12-06 | 1998-06-23 | Mitsubishi Heavy Ind Ltd | Plate bending method |
| TW449509B (en) * | 1998-11-04 | 2001-08-11 | Kawasaki Steel Co | Bending rolls, and pipe formed thereby |
| JP2001252722A (en) * | 2000-03-09 | 2001-09-18 | Sumitomo Metal Ind Ltd | U press tool and manufacturing method of uoe steel tube |
| JP3565131B2 (en) * | 2000-03-30 | 2004-09-15 | Ｊｆｅスチール株式会社 | Steel sheet for 3-piece cans with excellent roll forming properties |
| JP4724626B2 (en) * | 2006-08-31 | 2011-07-13 | 新日本製鐵株式会社 | Springback occurrence cause identifying method, apparatus thereof, and program thereof |
| CN100493755C (en) * | 2007-08-15 | 2009-06-03 | 长春轨道客车股份有限公司 | Metal sheet molding process fro changing centre of circle |
| CN101109945A (en) * | 2007-08-17 | 2008-01-23 | 湖北鄂重重型机械有限公司 | Control method for horizontal down-regulation type 3-roller lapping machine |
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| EP2638982A1 (en) | 2013-09-18 |
| CN103260781B (en) | 2015-07-15 |
| JP2012125780A (en) | 2012-07-05 |
| EP2638982A4 (en) | 2018-01-10 |
| ES2771482T3 (en) | 2020-07-06 |
| CA2818716A1 (en) | 2012-06-21 |
| TWI453073B (en) | 2014-09-21 |
| KR20130083458A (en) | 2013-07-22 |
| JP5803097B2 (en) | 2015-11-04 |
| CN103260781A (en) | 2013-08-21 |
| US20130327116A1 (en) | 2013-12-12 |
| TW201244845A (en) | 2012-11-16 |
| CA2818716C (en) | 2016-03-15 |
| KR101505340B1 (en) | 2015-03-23 |
| EP2638982B1 (en) | 2020-01-15 |
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