JPH11290961A - Method of designing draw bead for press working - Google Patents

Abstract

PROBLEM TO BE SOLVED: To enable the design of a draw bead without the need of a new experiment or the like even if conditions change such as a draw bead shape, lubrication and bead pressing force, by arranging, as a general design diagram, a relation among the strain of a material after draw bead passing, draw bead drawing resistance, and equivalent bending radius. SOLUTION: A first design diagram showing a relation between the strain of a material after draw bead passing and the drawing resistance of a draw bead is prepared, also a second design diagram showing a relation between the draw bead drawing resistance and an equivalent bending radius is prepared; on the basis of the first design diagram, under an arbitrary lubrication and a draw bead pressing force, a drawing resistance value is determined corresponding to the strain value of the material after the draw bead passing; on the basis of the second design diagram, an equivalent bending radius is determined for generating the drawing resistance; and, from the equivalent bending radius, determined is a draw bead shape for generating the prescribed drawing resistance and the strain of the material.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for designing a draw bead in a die for pressing a metal plate.

[0002]

2. Description of the Related Art Conventionally, bead passing resistance has been evaluated by an experimental method, numerical analysis, approximate calculation, or the like. Further, a bead shape and a bead holding force are designed based on the results (the relationship between the draw bead holding force and the pull-out resistance) for each bead.

[Outside 1]

[0003]

However, in the conventional method, the influence of the bead shape, lubrication conditions, bead holding force, etc. on the bead passing resistance, the amount of strain applied to the material, etc.
It was not organized and designed in a general form. For this reason, every time the conditions such as the bead shape, lubrication, and bead holding force change, it is necessary to know the bead passing resistance and the amount of strain through experiments and the like, which requires a lot of design costs.

[0004]

Means for Solving the Problems and Embodiments of the Invention The present inventors have studied the effects of the bead pressing force P and the lubrication conditions by assuming that the friction coefficient is μ and the friction per unit width is given by T ₀ = 2 μP. When the force is expressed and all of them act as the initial tension of the material before the bead flows, the strain ε applied to the material after the bead passes and the dimensionless tension value (T ₀₎ before and after the bead passes. / Ty),
During (T / Ty), a constant relationship determined for each material is approximately established regardless of the bead shape,
A diagram showing the relationship was created. Here, Ty is the yield sectional force of the material (= σy · t), where σy is the yield stress of the material, and t is the plate thickness. FIG. 1 shows the strain amount (thickness strain εt), (T ₀ / Ty), and (T / Ty) of a 5000 series aluminum alloy sheet material prepared based on the results of FEM analysis.
FIG. In FIG. 1, (T / T)
In other words, y) is referred to as dimensionless pullout resistance. Also,
When the dimensionless tension (T ₀ / Ty) on the bead inflow side (before passing) is constant, the present inventors consider the dimensionless tension (T / Ty) on the bead exit side (after passing) as described below. Dimensionless equivalent bending radius

(Equation 1) A constant relationship determined for each material was found to be approximately established between the two, and a diagram showing the relationship was created. Dimensionless equivalent bending radius

(Equation 2) For example, in the case of a draw bead as shown in FIG. 3, when the corner radii in contact with the material are r ₁ , r ₂ , r ₃ , the following equation is given.

[0005]

(Equation 3) FIG. 2 shows the relationship between (T / Ty) and the equivalent bending radius of the 5000-series aluminum alloy sheet material based on the results of the FEM analysis as a diagram with (T ₀ / Ty) kept constant. In FIG. 2, (T / Ty) is also referred to as a dimensionless pullout resistance.

Here, the design of the shape of the draw bead provided in the press-working die is determined by appropriately setting the pull-out resistance and the amount of strain received by the material (eg, plate thickness strain) under the conditions of a predetermined material, lubrication, and wrinkle holding force. It is assumed that this is performed as much as possible. Since the relationship shown in the diagram of FIG. 1 is established between the bead pull-out resistance and the plate thickness strain regardless of the draw bead shape, the plate thickness strain of the material generated when a certain bead pull-out force is assumed is calculated from the same diagram. Can be predicted. Therefore,
For example, it is possible to determine the presence or absence of breakage of the material under the pulling force, and thereby it is possible to set the maximum possible pulling resistance within a strain range allowable as a product, for example. Further, by using a diagram as shown in FIG. 2, it is possible to determine a draw bead equivalent bending radius for realizing the predetermined pull-out resistance. Then, by defining an arbitrary number of draw bead radii so as to be equal to the obtained equivalent bending radius, it is possible to obtain a draw bead shape that generates a required pulling resistance and a strain amount after pulling. Conversely, by using the diagram as shown in FIG. 2, it is possible to predict the value of the pull-out resistance corresponding to a certain lubrication and wrinkle holding force for a certain draw bead shape (an equivalent bending radius can be calculated from the shape). Since the thickness strain can be predicted from the value of the pull-out resistance based on FIG. 1, it is possible to determine whether molding conditions such as wrinkle holding and lubrication are appropriate. Further, this makes it possible to optimize the molding conditions.

The design diagram as shown in FIGS.
It can be determined from approximation by EM analysis or from experimental results, but can also be obtained only by calculation as described below. The deformation stress of the material is σf, the plate thickness is t, the yielding section force Tf for σf, and the total plastic moment Mf is Tf = σf ·
^{t, Mf = σft 2/4} , ρi bend radius at each corner of drawbead = ri + t / 2 (i is a number indicating the drawbead R, in the case of drawbead shape of FIG. 3 1
を 取 る 3), and it is assumed that a rigid-plastic approximation that ignores elastic deformation of the material holds. When subjected to bending with a bending radius ρ under dimensionless tension (T / Ty), the amount of strain △ ε generated at the center of the plate thickness is

(Equation 4) Given by Also from the moment balance in the draw bead R part

(Equation 5) Holds approximately. Here, ΔT represents an increase in tension before and after the bending radius ρ. In the following, the deformation behavior of the material during the passage of the draw bead is approximated by a series of discrete plastic bending. From the equation (2), the strain amount ε _{3 at the} center of the sheet thickness after passing through the draw bead in FIG. 3 can be approximated by the following equation since each bead R undergoes two plastic deformations of bending and unbending.

(Equation 6) Here, Ti represents the tension after passing through the i-th bead R. On the other hand, from equation (3),

(Equation 7) Which is substituted into equation (4) to obtain the following equation.

(Equation 8) Here, T ₀ represents the initial tension, and is approximated by the following equation using the draw bead pressing force P and the friction coefficient μ.

(Equation 9) Also, from equation (3),

(Equation 10) Is obtained. From the equation (6), the relationship between the strain amount ε of the material after passing through the draw bead and the tensions T ₀ and T ₃ before and after the draw bead can be obtained. Since the tension T ₃ after passing through the draw bead becomes the pullout resistance T, FIG. Can be obtained as an approximate solution only by calculation. Further, the relationship between the draw bead shape and the draw bead pull-out resistance can be obtained from equation (8).
Can be obtained as an approximate solution only by calculation. Note that the yield force Tf and the total plastic moment Mf
Is not a so-called initial yield stress, but an appropriate value determined in consideration of strain hardening due to deformation in a draw bead.

[0008]

Next, a specific description will be given of a method of determining a bead shape that generates the maximum drawing resistance within an allowable range of a reduction in thickness. Here, the design diagram for the 5000 series aluminum plate material shown in FIGS. 1 and 2 is used, and the friction coefficient μ = 0.
1. Under the wrinkle pressing force P / Ty = 3 per bead unit width, a bead shape that generates the maximum drawing tension with which the thickness reduction is within 20% is determined. In this case, 2 μP /
Ty (= T ₀ /Ty)=0.6 and 2 μm in FIG.
From the curve of P / Ty = 0.6, the bead pull-out force for the plate thickness strain ε = 0.2 can be obtained as T / Ty = 1.25. Next, from FIG. 2, the draw bead equivalent bending radius that generates T / Ty is 1 / Σ (t / ρi) = 1.7.
5 is obtained. When the thickness of the material used is 1 mm,
For example, in a draw bead shape as shown in FIG. 3, if a bending radius of each draw bead R = 4.75 is selected as shown in FIG.

[Equation 11] Thus, a draw bead shape having a predetermined function can be determined.

[0009]

According to the present invention, the relationship between the strain of the material after the draw bead has passed, the draw bead pull-out resistance, and the equivalent bending radius is arranged as a general design diagram, so that the draw bead shape, lubrication, bead holding force, etc. Even if the above conditions change, it is possible to design a draw bead without needing a new experiment or the like. Specifically, based on a design diagram prepared in advance for a predetermined material, under the conditions of predetermined lubrication and wrinkle holding force, the strain received by the material after passing the bead corresponding to an arbitrary bead pull-out resistance is obtained. Predictable, and conversely, bead pull-out resistance corresponding to the strain the material experiences after passing through. Furthermore, a draw bead equivalent bending radius corresponding to a predetermined pull-out resistance can be determined, and a draw bead shape can be obtained by determining the draw bead radius so as to be equal to the draw bead equivalent bending radius.

[Brief description of the drawings]

FIG. 1 is an example of a design diagram showing a relationship between a strain of a material after passing a draw bead and a draw bead withdrawal resistance.

FIG. 2 is a design diagram showing a relationship between draw bead pull-out resistance and draw bead equivalent bending radius.

FIG. 3 is an example of a draw bead shape to which the present invention is applied.

FIG. 4 shows a draw bead shape obtained in an example.

Claims (3)

[Claims] 1. A drawing diagram representing the relationship between the strain of a material after passing through a draw bead and the drawing bead withdrawal resistance is created, and the drawing resistance and draw bead under arbitrary lubrication, draw bead holding force are created based on the design diagram. A method for designing a draw bead for press working, wherein a value of strain of a material after passing is determined. 2. A design diagram representing the relationship between the draw bead pull-out resistance and the draw bead equivalent bending radius is created, and the required pull-out resistance is generated under any lubrication and bead holding force based on the design diagram. A method for designing a draw bead for press working, characterized in that an equivalent bending radius to be determined is determined. 3. A design diagram representing the relationship between the strain of the material after passing through the draw bead and the draw bead pull-out resistance and a design diagram representing the relationship between the draw bead pull-out resistance and the equivalent bending radius are prepared, and based on both design diagrams. And determining the shape of the draw bead that generates a predetermined pulling resistance and material strain under an arbitrary lubrication and bead holding force.