JP2001286938A - Prediction method for dimensional accuracy defect quantity in press-forming metal plate - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method by which an engineer not having experience/ technical accumulation, before press-forming, easily, precisely predict a dimensional accuracy defect quantity in press-forming a metal plate even if in engineer has no special knowledge in a numerical simulation, mathematics, etc. SOLUTION: A method consists of five processes consisting of (A) stress/strain relation is set for a metal plate based on an elastic perfect plastic body having a fixed stress value after yielding, (B) a prediction formula of a dimensional accuracy defect quantity is derived with using the stress/strain relation based on the elastic perfect plastic body model, (C) concerning the metal plate, a value not larger than the tensile strength and exceeding the yield strength is set as apparent yield strength, (D) by replacing the yield strength in the prediction formula of the dimensional accuracy defect quantity with the apparent yield strength, the prediction formula of the dimensional accuracy defect quantity with work hardening added thereto is derived, (E) with using the prediction formula of the dimensional accuracy defect quantity with work hardening added thereto, the dimensional accuracy defect quantity is obtained.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for predicting an amount of dimensional accuracy defects generated when press-forming a metal plate such as a thin steel plate or an aluminum plate mainly applied to an automobile body.
In particular, it is possible to easily and accurately predict in advance the amount of defective dimensional accuracy (mainly the amount of wall warpage and the amount of angle change) of a molded product due to elastic recovery after release from press molding before press molding. It is about the method.

[0002]

2. Description of the Related Art Many parts of an automobile body are generally formed of parts formed by pressing a thin steel plate. However, when these parts are formed by press molding, the shape (dimensions) of the molded product depends on the elastic recovery behavior after release (removal from the mold after molding).
May change from the design value, and a problem may occur at the time of assembling and joining of molded products (mostly joining by spot welding). These defects are collectively referred to as dimensional accuracy defects, and various types of such dimensional accuracy defects such as wall warpage and angle change are known (for example,
"Press forming difficulty handbook" 2nd edition (1997),
175 pages, Nikkan Kogyo Shimbun).

[0003] In recent years, from the viewpoint of reducing the weight and stability of an automobile body, there are many occasions in which an automobile body is made of a thin steel sheet having higher strength or an aluminum sheet which is lighter but has a lower Young's modulus than a steel sheet. Therefore, the dimensional accuracy defect as described above has become a significant problem.

As means for solving these problems and further improving the dimensional accuracy, (A) development of a new technology, (B) adjustment by a prospective technology, and the like are mainly performed. As the technique (A), the present inventors have proposed a method of reducing the amount of wall warpage by increasing the wrinkle holding force at the end of the press to apply tension to the wall portion (Japanese Patent Application No. Hei 11 (1999)). -203751
issue). Also, as the technology of (B) above, the amount of elastic recovery after demolding is predicted, the mold dimensions are prepared by subtracting the predicted value of the amount of elastic recovery from the target product dimensions, and adjusted to the normal dimensions after demolding. There are known ways to do this.

Regardless of which of the above means is employed, it is extremely important to more accurately predict the dimensional accuracy defect after molding based on information such as the metal plate to be molded and molding conditions in advance.

[0006]

Until now, in estimating the amount of dimensional accuracy defect after press forming of a metal plate,
There are known (1) a method of making predictions based on the experience of a skilled worker and accumulation of past results, and (2) a method of making predictions by numerical simulation. However, it is pointed out that any of the methods has the following problems.

In the above method (1), it is difficult for a technician with little experience and accumulated technology to make an accurate prediction, and cannot be said to be a method suitable for actual operation. On the other hand, the above-mentioned method (2) has been described as “plasticity and processing” [for example, vo
l.36, no.410 (1995) p203-210, vol.37, no.410 (1996) p13
52-1366 etc.] are known, but there is a problem that specialized knowledge such as numerical simulation and mathematics is required and that simulation equipment such as a computer becomes large.

The present invention has been made under such a circumstance, and an object of the present invention is to make it possible for a technician who does not have experience and technical accumulation to obtain a metallurgy even if he does not have specialized knowledge such as numerical simulation and mathematics. It is an object of the present invention to provide a method capable of easily and accurately predicting a dimensional accuracy defect amount during press forming of a plate before press forming.

[0009]

The predicting method of the present invention, which has achieved the above object, is a method for predicting the amount of dimensional accuracy failure during press forming of a metal plate.
It has a gist in the point that it consists of the process of (E). (A) For a metal plate, a stress-strain relationship is set based on an elastic perfect plastic model having a constant stress value after yielding. (B) A stress based on the elastic perfect plastic model is set.
Deriving a formula for predicting the amount of dimensional accuracy failure using the strain relationship,
(C) For the metal plate, a value that is equal to or less than the tensile strength and exceeds the yield strength is set as an apparent yield strength. (D) By replacing the yield strength in the prediction formula of the dimensional accuracy defect amount with the apparent yield strength, (E) A dimensional accuracy defect amount is obtained using the dimensional accuracy defect amount prediction expression taking into account the work hardening.

[0010] As a specific configuration in the above method,
As the apparent yield strength, a value obtained by the following (1) may be used. σp ′ = k · YS + (1−k) TS (1) where σp ′: apparent yield strength (MPa), YS:
Yield strength (actual value; MPa), TS: tensile strength (actual value; MPa), k: internal division coefficient, respectively.

Further, the internal division coefficient k in the above equation (1) can be expressed as a function of the ratio (TS / t) between the tensile strength TS and the plate thickness t, and specifically, 0 <k <1. It takes a value in a range.

In the method of the present invention, when the dimensional accuracy defect amount to be predicted is the wall warpage amount at the time of press molding,
A formula for predicting the amount of dimensional accuracy failure taking into account the work hardening for obtaining the wall warpage amount may be set as in the following expression (2). ρ = [3σp ′ / (E · t)] · {1-D · [(σ _T /TS)−0.3] ² } −C · (rd-5) (2) where ρ: Wall warpage (curvature; 1 / mm), σp ': apparent yield strength (MPa), E: Young's modulus (MPa),
t: plate thickness (mm), TS: tensile strength (actual value; MP
a), σ _T : tension acting on a wall (MPa), rd: die shoulder radius (mm) of a press forming tool, C: positive constant (1 /
mm ² ) and D: a positive constant.

In the method of determining the amount of wall warpage at the time of press forming, the apparent yield strength σp ′ can be determined based on the following equation (3).
Can be obtained based on the following equation (4). σp ′ = k · YS + (1−k) TS (3) Here, YS: yield strength (actual side value; MPa), and k: internal division coefficient, respectively. k = A · (TS / t) + B (4) where, TS: the tensile strength (MPa), t: the plate thickness (mm), A: negative constant (mm / MPa), B: positive , Respectively.

On the other hand, in the method of the present invention, when the amount of dimensional accuracy defect to be predicted is the amount of angle change at the time of press molding, the amount of dimensional accuracy defect taking into account the work hardening for obtaining this angle change amount is determined. May be set as in the following equations (5) and (6). Δθ = −θ · (rp + t / 2) · Δρ (5) Δρ = [− 3σp ′ / (E · t)] · ｛1 + exp (−G · rp)] (6) , Δθ: angle change (degree), θ: bending angle (degree), rp: shoulder radius (mm) of the bending tool, t: plate thickness (mm), Δρ: curvature change (1 / mm), σp ′ : Apparent yield strength (MPa), E: Young's modulus (MPa),
G: Positive constant (mm).

In the method for determining the amount of angle change during press forming, the apparent yield strength σp ′ can be determined based on the following equation (7), and the internal division coefficient k
Can be obtained based on the following equation (8). σp ′ = k · YS + (1−k) TS (7) where YS: yield strength (actual value; MPa), TS: tensile strength (actual value; MPa), k: internal division coefficient Shown respectively. k = A · (TS / t) + B (8) where, TS: tensile strength (actually measured value; MPa), t: plate thickness (1 / mm), A: negative constant (mm / MPa), B: positive constant.

[0016]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The present inventors have studied from various angles in order to solve the above problems. As a result, it has been found that the above object can be achieved satisfactorily if the above configuration is adopted, and the present invention has been completed. Hereinafter, the operation and effect of the present invention will be described with reference to the drawings along the history of the present invention being completed. In the following description, for the sake of convenience, a case in which a hat channel member used frequently for parts of an automobile body is formed as a target member for predicting the amount of dimensional accuracy defect will be described. The member for estimating the amount is not limited to such a hat channel member.

FIG. 1 is an explanatory view showing an example of the outer shape of the hat channel member. As a main forming method of such a hat channel member, a drawing forming method as shown in FIG. 2 [FIG. ] And a bending method [FIG. 2 (b)].
There is. In these forming methods, dimensional accuracy defects that are particularly problematic are a “wall warpage” phenomenon that occurs mainly during drawing and an “angle change” phenomenon that occurs mainly during bending.

When the design (target) shape (shape perpendicular to the axis) of the hat channel member is as shown in FIG. 3A, the "wall warpage" phenomenon is indicated by a broken line in FIG. 3B. As shown, this is a phenomenon in which the wall between the R stops (R is the die shoulder radius of the press forming tool) is warped. "Angle change"
The phenomenon is a phenomenon in which the target angle of the bent portion is θ (FIG. 3A) and is formed at an angle θ ₁ that is larger than the angle, as indicated by the broken line in FIG. 3C. And
The wall warpage ρ is represented by the curvature (1 / mm) of the R,
The angle change amount Δθ is represented by the difference (θ ₁ −θ) between the target angle θ and the angle θ ₁ formed after molding. Next, a specific method for estimating the wall warpage amount ρ and the angle change amount Δθ will be described in detail below.

At the time of drawing, the metal sheet to be formed undergoes bending / unbending deformation when passing through the shoulder of the press-forming tool (die). For this reason, a stress difference (a difference between a tensile stress and a compressive stress) having a different sign is generated between the front and back of the wall portion in the thickness direction at the time of molding [see FIGS.
0]. A bending moment is generated in the plate thickness direction due to the stress difference having the different sign, but when the external force is unloaded at the time of release from the mold, the deformation somewhat returns due to the elasticity of the material (elastic recovery). It is known that this elastic recovery behavior is the cause of wall warpage (for example, “Press Forming Difficult Handbook”, 2nd edition (1997), p. 191, Nikkan Kogyo Shimbun). Note that the elastic recovery behavior occurs so that the bending moment becomes zero, and in the sheet thickness direction, FIGS. 11B and 11C described later.
Strain and stress remain.

It is known that the wall warpage ρ has the following tendency. FIG. 4 shows the relationship between the main influencing factors on the wall warpage and the wall warpage amount ρ.

As the strength (tensile strength TS) of the metal material increases, the wall warpage ρ also increases [FIG.
(A)]. As the thickness t of the metal plate decreases, the wall warpage amount ρ increases [FIG. 4B]. As the Young's modulus E of the metal material decreases, the wall warp amount ρ increases [FIG. 4 (c)]. As the die shoulder radius rd of the press forming tool increases, the wall warp amount ρ decreases (however, the die shoulder radius rd
(Excluding the region where the minimum is observed) [FIG. 4 (d)]. As the tension σ _T (wrinkle holding force) acting on the wall portion increases, the wall warp amount ρ decreases (however, a region where the tension is extremely small is excluded) (a broken line region in FIG. 4E).

Based on the above findings, the present inventors have studied from various angles with the aim of realizing a prediction formula that can accurately (quantitatively) predict these trends easily. And
First, the present inventors have considered the reason why complicated calculations such as numerical simulations are performed in the prior art for predicting the amount of wall warpage. As a result, one of the major reasons is that, in the prior art, the stress-strain relationship at the time of applying deformation (strain) is close to reality as shown in FIG. 5, that is, the stress increases as the plastic strain increases. It can be considered that work hardening in the plastic deformation region is also considered as a direct object of numerical simulation.

In order to further simplify the prediction formula, the present inventors suppose a stress-strain relationship which is different from the actual material behavior but does not cause work hardening of the metal material. An attempt was made to derive a simpler prediction formula. That is, as shown in FIG. 6, after yielding (yield strength σp), a stress is assumed to be a plastic body that does not work harden at a constant value (such a plastic body is generally called “elastic perfect plastic body”). An attempt was made to derive a prediction formula based on such a plastic body.

As a result, it can be understood that the amount of change in curvature due to elastic recovery after bending / unbending deformation (the amount of wall warp ρ when the tension is extremely small) can be expressed by a simple equation such as the following equation (I). Was. In addition, when a die having a die shoulder radius of about 3 to 20 mm is used, such as is often used during normal press molding, the formula (I) is a simplified formula such as the following formula (II). It can also be expressed by ρ = [3σp / (E · t)] · {1-7 / 3 · [[2σp / (E · t)] · rd] ² } (I) ρ {3σp / (E · t)} Where ρ: wall warpage (curvature; 1 / mm), σp: yield strength (MPa), E: Young's modulus (MPa), t: plate thickness (mm), rd: for press forming Die shoulder radius of tool (m
m), respectively.

The above equations (I) and (II) can be derived by analyzing the change in bending moment in the deformation step in press forming. This process will be described with reference to the drawings. FIG. 7 is a diagram for explaining a deformation history of a wall portion of a metal plate to be press-formed (particularly drawn). In this figure, the metal plate is shown in FIG.
Press forming is performed as shown in FIG. 7 (b) → FIG. 7 (c), and a portion where the wall warp occurs in the metal plate is indicated by a cross as a point of interest. 7A shows a stage before press forming, FIG. 7B shows a stage of bending, and FIG. 7C shows a stage of unbending.

On the other hand, FIG. 8 to FIG.
At each stage of press forming as shown in FIG. 7 (b) → FIG. 7 (c), the distribution of strain ε and stress σ acting in the thickness direction of the metal plate (the noted point x) and the inside of the metal plate FIG. 8 shows the distribution of the elastic region and the plastic region of FIG.
9A corresponds to the stage of FIG. 7B, and FIG. 10 corresponds to the stage of FIG. 7C. Also,
FIG. 11 shows the distribution of strain ε and stress σ acting in the thickness direction of the metal plate (the point of interest ×) after release, and the distribution of elastic and plastic regions in the metal plate. FIGS. 8A to 11A show the distribution of the elastic region and the plastic region in the metal plate, and FIGS.
The figure shows the distribution of strain ε, and each figure (c) shows the distribution of stress σ.

First, at the stage shown in FIG.
At the point of interest X, an elastic region is formed over the entire region in the thickness direction [FIG. 8A], and no distribution of strain ε and stress σ is generated [FIGS. 8B and 8C]. as a result,
At this stage, no bending moment is generated.
Therefore, the bending moment amount M acting on the center of the plate thickness t at this time is given by
It can be expressed as in equation (III).

[0028]

(Equation 1)

Next, in the stage shown in FIG. 7B (bending stage), at the point of interest x, both end surfaces in the thickness direction of the metal plate become a plastic region, and a central portion becomes an elastic region. [FIG. 9 (a)]. Then, the distribution of strain ε is such that the curvature is κ
When (= 1 / rd: rd is the die shoulder radius), a strain with a maximum strain of κ · (t / 2) is generated in a different direction [FIG. 9B]. In addition, the distribution of the stress σ at this time, when the amount of work hardening is neglected (FIG. 6),
A stress having a maximum stress σp (σp is the yield strength) is generated in different directions (compression stress and tensile stress) on the front surface side and the back surface side (FIG. 9C), and bending is performed by the stress distribution at this time. A moment will be generated. Then, the bending moment M acting on the center portion of the metal plate is obtained by taking the position η in the thickness direction as a variable and setting the distances from the center of the thickness to both ends of the elastic region to be + y ₁ and −y ₁ , respectively [FIG. c)],
Since y ₁ = σp / (E · κ) (where E: Young's modulus, κ: curvature), it can be expressed as the following equation (IV).

[0030]

(Equation 2)

Further, at the stage shown in FIG. 7 (c) (bending-back stage), after the entire region once returns to the elastic region at the point of interest x of the material, the stage shown in FIG. Yield occurs again in the opposite direction [FIG. 10 (a)], and no distribution of strain ε occurs [FIG. 10 (b)]. The stress σ at this time
Distribution is the maximum stress σ when the amount of work hardening is ignored.
Σp (σp is the yield stress) occurs in a different direction and in a direction opposite to that of FIG. 9C [FIG.
(C)]. At this time, the bending moment M acting on the central portion of the metal plate is obtained by taking the distance from the center of the thickness to both ends (elastic-plastic boundary) of the elastic region + y
₂ , −y ₂ [FIG. 10C], y ₂ = 2σ
Since p / (E · κ) (where E: Young's modulus, κ: curvature), it can be expressed as the following equation (V).

[0032]

(Equation 3)

When the mold is released, the external force is released, and the entire area of the metal sheet in the thickness direction becomes an elastic area.
(A)], elastic recovery (wall warp ρ) occurs so that the bending moment amount possessed by the elasticity of the material becomes zero. At this time, the strain and stress distribution generated in the thickness direction are shown in FIG.
1 (b) [Maximum strain ε = ρ · (t / 2)], FIG.
(C).

The bending moment e reduced by the elastic recovery can be expressed by the following formula (VI). The elastic recovery is obtained by the bending moment M generated by the stress distribution during molding. Is generated in such a manner as to cancel out, so that the wall warpage amount ρ is generated corresponding to the bending moment amount M satisfying the following equation (VII).

[0035]

(Equation 4)

[0036]

(Equation 5)

When the above equation (VII) is arranged with respect to the wall warpage amount ρ, the following equation (VIII) is derived.
By rearranging by substituting the relations of the equations, the above-mentioned equation (I) is derived. ρ = {12 / (E · t ³ )} · M (VIII)

By the way, in normal press molding,
7/3 in the second term on the right side of the above equation (I) [[2σp / (E
· T)] · rd] ^{2 is} a value much smaller than 1. For example, σp = 600 MPa, rd = 5 mm, E
= 205800MPa, t = 1.2mm, 7
/ 3 [[2σp / (E · t)] · rd] ^{2 has} the value of 1.
38 × 10 ⁻³ (≪1). Therefore, the second term on the right side of the above equation (I) ｛1-7 / 3 · [[2σp / (E · t)] · r
d] ² } is almost 1 and can be ignored, and the equation (I) can be further simplified as in the above equation (II).

The present inventors have compared the measured values of the wall warpage obtained by experiments with various material strengths and molding conditions with the above (II).
It was compared with the predicted value by the formula. The actual measurement values used at this time were taken in a region where the die shoulder radius is equal to or greater than the minimum region and the tension (wrinkle holding force) is relatively small [regions surrounded by broken lines in FIGS. 4D and 4E]. Value. As a result, it was found that work hardening must be added in order to accurately predict the wall warpage amount.

Therefore, the present inventors have further studied to reflect as much as possible the effect of work hardening. As a result, instead of the yield strength σp of the formula (II), as shown in FIG. 12, the value of the yield strength σp that is equal to or less than the tensile strength is changed to the apparent yield strength σp ′ obtained by correcting a work hardening amount different from the actual one. Based on the apparent yield strength σp ′, the following (II) ′
It has been found that the wall warpage ρ should be predicted by the equation. In addition, the apparent yield strength σp ′ may be an internal value obtained by the following equation (1) based on the actually measured yield strength YS and tensile strength TS, or the coefficient of the following equation (1) may be referred to as the tensile strength TS. A function of the ratio of the thickness t (TS / t) [k =
f (TS / t)], the measured value and the predicted value show relatively good agreement.

Here, as the above-mentioned yield strength YS and the above-mentioned tensile strength TS, values obtained by a normal tensile test or the like may be used. The reason that k is preferably a function of (TS / t) can be explained as follows. Generally, when a stress-strain diagram is measured by a tensile test or the like, a tendency of work hardening as shown in FIG. 21 is observed. The following table summarizes the degree of work hardening at the same strain value (processing with the same tool) for materials having different tensile strengths and plate thicknesses.

As the tensile strength increases, the strain value reaching the TS decreases (see FIG. 21 (a)), and the degree of work hardening at the same strain value [for example, evaluated by Y1 / Y2 in FIG. 21 (a)] I do. ] Becomes larger. as a result,
The yield strength after work hardening has a value closer to the tensile strength TS. The thinner the plate thickness, the smaller the strain value that reaches the tensile strength TS [see FIG. 21 (b)], and the greater the degree of work hardening at the same strain value. As a result, the yield strength after work hardening becomes a value closer to the tensile strength TS.

K, TS and t based on these trends
There are various possible forms of the relational expression relating to the above. Among them, it has been experimentally confirmed that when k is a function of TS / t, the measured value and the predicted value agree well. ρ = {3σp ′ / (E · t)} (II) ′ where ρ: wall warpage (curvature; 1 / mm), σp ′: apparent yield strength (MPa), E: Young's modulus ( MPa),
t: Plate thickness (mm) is shown. σp ′ = k · YS + (1−k) TS (1) where k is an internal division coefficient.

Incidentally, although the effect of the die shoulder radius rd is not fully expressed in the above equation (II) ′, the inventors of the present invention have studied according to the degree of change of the actually measured values by experiments, and found that II) ', the experimental correction term [-C ·
(Rd-5)], it was also found that the prediction accuracy could be further improved by performing correction so as to satisfy the following expression (II) ″. ρ = {3σp ′ / (E · t)} − C · (rd−5) (II) ″

However, even in the equation (II) ″, the effect of the tension (wrinkle holding force) cannot be sufficiently expressed. That is, the above (II) '' can be used only in a region where the tension is relatively small [region near the vertex in FIG. 4E]. Therefore, the present inventors have studied the correction when the tension is large according to the degree of change of the actually measured value by experiment. According to the present invention, the following equation (2) is obtained from the above equation (II) ″. It has been found that a good prediction accuracy can be obtained by making an appropriate correction. That is, while satisfying the following equation (2) obtained as described above, the following equation (3) is used as the apparent yield strength σp ′ based on the actually measured yield strength YS and tensile strength TS obtained by a tensile test. Same as equation (1)], and the internal coefficient k in equation (3) below is a function [k = f (TS / t) of the ratio (TS / t) between the tensile strength TS and the sheet thickness t. t)], the following equation (4) could be used to easily and accurately predict the wall warpage amount ρ. ρ = {3σp ′ / (E · t)} · {1-D · [(σ _T /TS)−0.3] ² } −C · (rd-5) (2) σp ′ = k · YS + (1−k) TS (3) k = A · (TS / t) + B (4) where ρ: wall warpage (curvature; 1 / mm), σp ′: apparent yield strength (MPa), E: Young's modulus (MPa),
t: plate thickness (mm), TS: tensile strength (actual value; MP
a), YS: yield strength (actual value; MPa), σ _T : tension acting on the wall (MPa), rd: die shoulder radius (mm) of the press forming tool, k: internal division coefficient, A: negative Constant (mm /
MPa), B: positive constant, C: positive constant (1 / mm ² )
Are shown respectively.

Next, a case where the angle change amount Δθ is predicted will be described. At the time of bending, the formed metal plate is
It is subjected to bending deformation at the shoulder of the punch as a press forming tool. For this reason, a stress difference (a difference between a tensile stress and a compressive stress) having a different sign occurs between the front and back sides in the thickness direction of the metal plate at the time of bending, as in the case of drawing. Even if the stress difference is balanced when the external force is released at the time of mold release and the bending moment becomes zero, a part of the stress remains, thereby causing the phenomenon of the angle change as described above. It has been known. Also,
It is known that the angle change amount Δθ has the following tendency.

As the strength (tensile strength TS) of the metal material increases, the angle change Δθ also increases [FIG.
(A)]. As the thickness t of the metal plate decreases, the angle change Δθ
Becomes larger [FIG. 13 (b)]. As the Young's modulus E of the metal material decreases, the angle change amount Δθ increases [FIG. 13 (c)]. As the shoulder radius rp of the bending tool (such as a punch) increases, the angle change amount Δθ increases [FIG. 13 (d)].

To make the prediction formula simpler, the present inventors, like the above-described prediction formula for the wall warpage amount ρ, differ from the actual material behavior but have a stress-
Assuming a distortion relationship [FIG. 6], an attempt was made to derive a simpler prediction formula in such a relationship. However, the angle change defect that occurs at the time of bending is generated in a portion that is subjected to only bending, such as a punch shoulder portion, and therefore, it is not necessary to consider the bending back phenomenon.

As a result, it was found that the angle change Δθ after bending deformation and elastic recovery can be expressed by a simple equation such as the following equations (5) and (IX). Δθ = −θ · (rp + t / 2) · Δρ (5) Δρ = {− 3σp / (E · t)} · ｛1-1 / 3 [[2σp ′ / (E · t)] · rp ] ² ] (IX) where Δθ: angle change (degree), θ: bending angle (degree), rp: shoulder radius (mm) of the bending tool, t: plate thickness (mm), Δρ: curvature The amount of change (1 / mm), σp ′: apparent yield strength (MPa), E: Young's modulus (MPa), respectively.

The above equations (5) and (IX) are obtained as follows. That is, the curvature change Δρ of the bent portion due to the elastic recovery after the bending is generated in such a manner as to cancel the bending moment M in the same manner as in the case of obtaining the above formula (VII), so that Δρ satisfies the following formula (X) Will occur.

[0051]

(Equation 6)

Therefore, the curvature variation Δρ is given by
It can be expressed as in equation (XI), and rearranging this equation leads to equation (IX). Δρ = ｛− 12 / (E · t ³ )｝ · M (XI) On the other hand, considering that the curvature change amount Δρ is geometrically converted, the length of the central portion of the sheet thickness after the curvature change is Since there is no change, the relationship of the following equation (XIII) holds, and this (XIII)
When the equation (III) is rearranged for the angle change amount Δθ, the above equation (5) is derived. θ / [1 / [rp + (t / 2)]] = (θ + Δθ) / [1 / [rp + (t / 2)] − Δρ] (XIII) where Δθ: angle change (degree), θ: bending angle (degree), rp: shoulder radius (mm) of bending tool, t: plate thickness (mm), Δρ: curvature change (1 / mm), respectively.

When a punch having a shoulder radius of about 3 to 20 mm, which is often used in ordinary press forming, is used, the above equation (IX) is as straightforward as in the case of the draw forming. For example, it can be expressed by a more simplified expression like the following expression (XII). Δρ = {− 3σp / (E · t)} (XII)

In the present invention, the value of the yield strength σp is different from the actually measured value, as in the case of the equation for predicting the amount of wall warpage, in order to simplify and consider the influence of work hardening. The apparent yield strength σp ′ obtained by correcting the work hardening defined by the equation is used. Also, in the above equation (XII), the influence of the shoulder radius of the bending tool (punch, etc.) cannot be fully expressed, so that it is necessary to judge based on the degree of change in the actually measured value and make a correction as in the following equation (6). It was found that good prediction accuracy could be obtained. Δρ = {− 3σp ′ / (E · t)} · {1 + exp (−G · rp)} (6)

That is, the apparent yield strength σp ′ together with the equations (5) and (6) obtained as described above is used as the apparent yield strength σp ′ based on the actually measured yield strength YS and tensile strength TS obtained by a tensile test. ) Formula [1]
Same as equation (3)], and the coefficient k in the following equation (7) is defined as the ratio of the tensile strength TS to the sheet thickness t (TS
/ T) as a function [k = f (TS / t)] (8)
If the equation is adopted, the angle change amount Δθ can be predicted relatively accurately. σp ′ = k · YS + (1−k) TS (7) k = A · (TS / t) + B (8) where σp ′: apparent yield strength (MPa), E: Young's modulus (MPa), YS: Yield strength (actual value; MP
a), TS: tensile strength (actually measured value; MPa), k: internal division coefficient, A: negative constant (mm / MPa), B: positive constant.

Hereinafter, the effects of the present invention will be described more specifically with reference to examples. However, the following examples do not limit the present invention, and any design change based on the above and following points is not limited to the present invention. It is included in the technical range of.

[0057]

Embodiment 1 First, a region where the tension is relatively small [see FIG. 4 (e)].
The accuracy of the prediction was confirmed. Using various steel plates having a yield strength YP, a tensile strength TS and a plate thickness t shown in Table 1 below, a forming experiment of a hat channel member was performed under the forming conditions (die shoulder radius rd) shown in Table 1. At this time, the ratio (σ _T / TS) between the tension σ _T and the tensile strength TS (σ _T / TS) is substantially constant so that the effect of the tension σ _T on the wall warpage amount is as small as possible [0.3: FIG. (Area near the vertex)].

[0058]

[Table 1]

Table 1 shows measured values (ρmes) of the wall warpage (curvature) ρ at that time. Using these measured values, the values of the constants A, B and C in the equations (2) to (4) were determined first. Here, since σ _T /TS=0.3, the value of D · [(σ _T /TS−0.3)] ² is 0 regardless of the value of D. Therefore, the value of D is ignored.
The method for determining the value of D will be described later. After that, the values of A, B and C between the actually measured values and the predicted values according to those formulas were determined. As a result, A = -9.708 × 10
^-4 (mm / MPa), B = 0.8161, C = 1.08
It was 2 × 10 ⁻⁷ (1 / mm ² ). A, B found
Table 1 also shows the values of C and C and the predicted value (ρcal) obtained using the equations (2) to (4). FIG. 14 shows a comparison between the measured value (ρmes) and the predicted value (ρcal). A high correlation is recognized between the two, and it can be seen that the wall warpage amount can be predicted with good accuracy.

Next, the formulas (2) to (4) and the values of A, B, and C obtained in the above experiment are applied to the formation of an aluminum plate having a Young's modulus that is significantly different from the steel plate used in the above experiment. I checked if I could. Yield strength Y shown in Table 2 below
P, tensile strength TS and thickness t of various aluminum plates (3000
7000 series) and σ _T /TS=0.3 under the molding conditions (die shoulder radius rd) shown in Table 2 [see FIG.
(E), a hat channel member forming experiment was performed, and in the same manner as described above, the measured value (ρmes) of the wall warpage (curvature) ρ and the predicted value (ρmes) based on the above equations (2) to (4) ρcal). The result is shown in FIG. 15, and a high correlation is recognized between the two, and it can be seen that the wall warpage amount can be predicted with good accuracy.

[0061]

[Table 2]

Next, the prediction accuracy in a region where the tension σ _T is relatively large was also confirmed. Here, the coefficient D was adjusted to correct the effect of the tension. At this time, No. 1 in Table 1 was used. For the specimen No. 2, the tension σ _T was adjusted to 200 MPa and 300 M by adjusting the BHF (wrinkle pressing force).
An actual measurement value (ρmes) was obtained for the amount of wall warpage when molding was performed while changing the pressure to Pa and 450 MPa.
These measured values and the constants A and B obtained in the above experiment
The value of D is determined using the Newton-Raphson method so that the sum of squares of the difference between the actually measured value and the predicted value (ρcal) according to the above equations (2) to (4) is minimized. did. As a result, D = 3.559. FIG. 16 shows a result of comparing the measured value (ρmes) with the predicted value (ρcal). There is a high correlation between the two,
It can be seen that the wall warpage can be predicted with good accuracy.

Example 2 The prediction accuracy of the prediction formula for the angle variation Δθ was evaluated by a basic bending experiment. First, an L-bending test was performed using various steel plates having a yield strength YP, a tensile strength TS and a plate thickness t shown in Table 3 below and under the forming conditions (punch shoulder radius rp) shown in Table 3. FIG. 17 schematically shows the state of the L-bending test.

[0064]

[Table 3]

Table 3 shows measured values (Δθmes) of the angle change Δθ at that time. Using these measured values,
Values were obtained for the respective constants of the above equations (5) to (8). Constant A,
B and C are constants for determining the apparent yield strength σp ′ in consideration of work hardening, similarly to the equation for predicting the amount of wall warpage ρ. Therefore, these values were set to the same values as the values obtained in the above-described experiment on the amount of wall warpage. Here, only for the coefficient G for correcting the influence of rp, the value was determined using the Newton-Raphson method so that the sum of squares of the difference between the actually measured value and the predicted value based on these formulas was minimized. . As a result, G = 0.012 (mm). Table 3 also shows the value of the obtained coefficient and the predicted value (Δθcal) obtained using the equations (5) to (8). FIG. 18 shows the result of comparing the measured value (Δθmes) with the predicted value (Δθcal). A high correlation is recognized between the two, and it can be seen that the angle change amount can be predicted with good accuracy.

Next, in order to confirm the prediction accuracy in a region where the punch shoulder radius rp is relatively large, a steel plate having a yield strength YP, a tensile strength TS and a plate thickness t shown in Table 4 below was used. A U-bend molding experiment was performed under the indicated molding conditions (punch shoulder radius rp). FIG. 19 schematically shows the state of the U-bending test.

[0067]

[Table 4]

The angle change Δθ was predicted using the values of A, B, C and G and the equations (5) to (8). FIG. 20 shows a comparison between the actually measured value (Δθmes) and the predicted value (Δθcal) based on the equations (5) to (8). A high correlation is recognized between the two, and it can be seen that the angle change amount can be predicted with good accuracy.

[0069]

The present invention is configured as described above, and a technician who does not have experience and accumulated technology can reduce the amount of dimensional accuracy defects during press molding without having specialized knowledge such as numerical simulation. This method makes it possible to easily and accurately predict, and this method makes it possible to quickly and effectively take measures for improving the dimensional accuracy, which is a particularly important problem in recent years, and its technical significance is extremely high. Expected to be large.

[Brief description of the drawings]

FIG. 1 is an explanatory diagram showing an example of an external shape of a hat channel member.

FIG. 2 is a schematic explanatory view showing a main method of forming a hat channel member.

FIG. 3 is a diagram for explaining a dimensional accuracy defect targeted by the present invention.

FIG. 4 is a graph showing a relationship between main influencing factors on wall warpage and wall warpage amount ρ.

FIG. 5 is a stress-strain diagram used in a conventional prediction method.

FIG. 6 is a stress-strain diagram assuming an elastic perfect plastic body (without consideration of work hardening).

FIG. 7 is a diagram for explaining a deformation history of a wall portion of a material to be press-formed.

8 (a) shows the distribution of strain ε and stress σ acting in the thickness direction of the material (the point of interest in FIG. 7) in the stage of FIG. 7 (a);
FIG. 4 is a diagram showing distribution of an elastic region and a plastic region in a material.

FIG. 9 shows the distribution of strain ε and stress σ acting in the thickness direction of the material (the point of interest in FIG. 7) in the stage of FIG.
FIG. 4 is a diagram showing distribution of an elastic region and a plastic region in a material.

FIG. 10 shows the distribution of strain ε and stress σ acting in the thickness direction of the material (the point of interest in FIG. 7) and the distribution of elastic and plastic regions in the material at the stage of FIG. FIG.

11 is a diagram showing the distribution of strain ε and stress σ acting in the thickness direction of the material after release from the material (the point of interest × in FIG. 7), and the distribution of elastic and plastic regions in the material. .

FIG. 12 is a stress-strain diagram used in the present invention.

FIG. 13 is a graph showing a relationship between a main influencing factor on an angle change and an angle change amount Δθ.

FIG. 14 shows the wall warpage (curvature) ρ of various steel plates shown in Table 1.
, The measured value (ρmes) and the above (2) to (4)
It is the graph which showed and compared the prediction value (pcal) based on a formula.

FIG. 15 shows measured values (ρmes) of the wall warpage (curvature) ρ of various aluminum plates shown in Table 2 and the values (2) to (2).
It is the graph which showed and compared the prediction value (pcal) based on Formula (4).

FIG. 16 shows the measured value (ρmes) of the wall warpage (curvature) ρ when the tension σ _T is relatively large, and the above (2) to
It is the graph which showed and compared the prediction value (pcal) based on Formula (4).

FIG. 17 is a schematic view showing a state of an L-bending test.

FIG. 18 is a graph showing a comparison between an actually measured value (Δθmes) and a predicted value (Δθcal) based on the formulas (5) to (8) for the angle change amount Δθ of various steel plates shown in Table 3. is there.

FIG. 19 is a schematic diagram showing a state of a U-bending experiment.

FIG. 20 is a graph showing a comparison between an actually measured value (Δθmes) and a predicted value (Δθcal) based on the equations (5) to (8) with respect to the angle change Δθ during the U-bending.

FIG. 21 is a graph showing the influence of tensile strength and plate thickness on work hardening.

Claims (9)

[Claims] 1. A method for predicting an amount of dimensional accuracy failure during press forming of a metal plate, comprising the following steps (A) to (E): Method for predicting the amount of dimensional accuracy defects in (A) For a metal plate, a stress-strain relationship is set based on an elastic perfect plastic model having a constant stress value after yielding. (B) A stress based on the elastic perfect plastic model is set.
Deriving a formula for predicting the amount of dimensional accuracy failure using the strain relationship,
(C) For the metal plate, a value that is equal to or less than the tensile strength and exceeds the yield strength is set as an apparent yield strength. (D) By replacing the yield strength in the prediction formula of the dimensional accuracy defect amount with the apparent yield strength, (E) A dimensional accuracy defect amount is obtained using the dimensional accuracy defect amount prediction expression taking into account the work hardening. 2. The prediction method according to claim 1, wherein a value obtained by the following equation (1) is used as the apparent yield strength. σp ′ = k · YS + (1−k) TS (1) where σp ′: apparent yield strength (MPa), YS:
Yield strength (actual value; MPa), TS: tensile strength (actual value; MPa), k: internal division coefficient, respectively. 3. The prediction method according to claim 2, wherein the internal division coefficient k is set as a function of the ratio (TS / t) between the tensile strength TS and the thickness t. 4. The method for predicting dimensional accuracy defects according to claim 1, wherein the amount of dimensional accuracy defects to be predicted is an amount of wall warpage at the time of press molding, and the work hardening for obtaining the amount of wall warpage is performed. The formula for predicting the amount of dimensional accuracy defects taking into account the following (2)
A prediction method that is an expression. ρ = [3σp ′ / (E · t)] · {1-D · [(σ _T /TS)−0.3] ² } −C · (rd-5) (2) where ρ: Wall warpage (curvature; 1 / mm), σp ': apparent yield strength (MPa), E: Young's modulus (MPa),
t: plate thickness (mm), TS: tensile strength (actual value; MP
a), σ _T : tension acting on the wall (MPa), rd: die shoulder radius (mm) of the press forming tool, C: positive constant (1 /
mm ² ) and D: a positive constant. 5. The prediction method according to claim 4, wherein the apparent yield strength σp ′ is obtained based on the following equation (3). σp ′ = k · YS + (1−k) TS (3) Here, YS: yield strength (actual side value; MPa), and k: internal division coefficient, respectively. 6. The prediction method according to claim 5, wherein the internal division coefficient k is obtained based on the following equation (4). k = A · (TS / t) + B (4) where, TS: the tensile strength (MPa), t: the plate thickness (mm), A: negative constant (mm / MPa), B: positive , Respectively. 7. The method for predicting a dimensional accuracy defect according to claim 1, wherein the amount of the dimensional accuracy defect to be predicted is an angle change amount, and the size considering the work hardening for obtaining the angle change amount. A prediction method in which the prediction formula of the accuracy failure amount is the following formulas (5) and (6). Δθ = −θ · (rp + t / 2) · Δρ (5) Δρ = [− 3σp ′ / (E · t)] · ｛1 + exp (−G · rp)] (6) Δθ: angle change (degree), θ: bending angle (degree), rp: shoulder radius (mm) of the bending tool, t: plate thickness (mm), Δρ: curvature change (1 / mm), σp ′: Apparent yield strength (MPa), E: Young's modulus (MPa),
G: Positive constant (mm). 8. The prediction method according to claim 7, wherein the apparent yield strength σp ′ is obtained based on the following equation (7). σp ′ = k · YS + (1−k) TS (7) where YS: yield strength (actual value; MPa), TS: tensile strength (actual value; MPa), k: internal division coefficient Shown respectively. 9. The prediction method according to claim 8, wherein the internal division coefficient is obtained based on the following equation (8). k = A · (TS / t) + B (8) where, TS: tensile strength (actually measured value; MPa), t: plate thickness (1 / mm), A: negative constant (mm / MPa), B: positive constant.