KR20210017803A - Curvature area prediction for the deep drawing-ironing process of a cylindrical cup using finite element method and regression analysis - Google Patents

Abstract

The present invention relates to a cylindrical cup using a finite element method and regression analysis to perform curvature area prediction for a deep drawing-ironing process, in which a product including a side wall having a long cylindrical or rectangular can shape is manufactured by using the deep drawing-ironing (DDI) process. Accordingly, a volume of a typical cylindrical axisymmetric product after the DDI process is broadly divided into a bottom, a curvature, and a side wall. In partial sheet metal molding, a volume of a product before and after the molding is easily calculated from law of volume constancy. Since axisymmetric multiplication of a cylinder is expressed as a two-dimensional axisymmetric problem, a two-dimensional area is calculated by using a volume calculation method. A curvature area of the axisymmetric multiplication corresponds to a formula obtained by subtracting an area of a circle from an area of an ellipse. However, a geometrical curvature area, which is the above formula, is different from a curvature area of an actual product, so that finite element analysis is performed under the same condition as the actual product to which the DDI process is applied, and validity of the analysis is verified by performing the regression analysis on data obtained finally from the finite element analysis to compare the curvature area with data related to an actual component by the proposed method.

Description

Curvature area prediction for the deep drawing-ironing process of a cylindrical cup using finite element method and regression analysis}

The present invention relates to a cylindrical cup using a finite element method and regression analysis for predicting a curvature area of a deep drawing ironing process. More specifically, a deep drawing that reduces the number of processes and sequentially performs a guaranteed quality, drawing and ironing process. The present invention relates to a cylindrical cup using finite element method and regression analysis for predicting the area of curvature in the ironing process.

In general, many products are produced through drawing. Used in automotive parts in the process daily life of kitchen utensils and home appliances.

These products are divided into asymmetric drawing products, and the axially symmetric container and the central column part of the car. In the case of cylindrical containers, large diameter products and shallow heights are produced in only one process.

A multi-step deep drawing process is required to narrow down products with narrow diameter and high height. The diameter and height can be increased through multiple drawings.

When the multi-step deep drawing process is completed, the ironing process, which is a sprinkling process, is completed. The number of product processes is reduced while the required wall thickness is reduced while the wall height is increased to match the target height, and guaranteed quality, drawing and ironing processes are sequentially performed.This process is called a deep drawing ironing (DDI) process.

1 shows the steps related to the DDI process. Cost reduction methods, product usage, and related constraints in consideration of Ramirez, etc. are disclosed. The drawing of surplus ratios for the DDI process can reduce and improve production costs.

In the case of mold die design through the DDI process, the life of the mold for making a CNG pressure vessel is proposed as well as an experiment.

Studies on the determination of the DDI pull-out holder force, sidewall height or initial blank specifications observed in the DDI process, and curvature design are still insufficient.

Volume After the DDI process, the volume corresponding to the bottom, curvature, and sidewall of the product is described as shown in FIG. 2(a); (a) volume classification; (b) The difference can be calculated as a real and a solution.

In a simple drawing or ironing process, the formula for subtracting the circular area from the simple elliptical area is used as the design formula for the curvature volume.

However, the formula for the area of curvature has the following differences compared to the actual product.

As shown in Fig. 2(b), this causes an accumulated interval during prediction of the curve. It predicts the area of curvature of the product and, consequently, the height of the sidewalls.

The blanking refers to sheet metal processing in various forms using a punch and a die.

The drawing is a method of deforming metal to make a wire rod or a thin tube, and it is also called drawing. It is pulled out to the side and pulled into a wire rod having a cross-sectional shape according to the shape of the hole drilled in the die. The most common drawing materials are steel wire and copper wire, and various other materials are used.

When the punch or die is worn out in the process of extrusion processing of hollow parts, the ironing is not processed to the exact dimensions of the molded product's outer or inner diameter. It is a processing method that must be modified.

The present invention was invented in consideration of the above points, and a cylindrical shape using finite element method and regression analysis for predicting the curvature area of a deep drawing ironing process in which the number of processes is reduced and guaranteed quality, drawing and ironing processes are sequentially performed. Its purpose is to provide a cup.

According to a preferred embodiment for achieving the object of the present invention described above, a cylindrical cup using a finite element method and regression analysis for predicting a region of curvature in a deep drawing ironing process according to the present invention selects a spacing function using the difference between , Mentor analysis and regression analysis as an objective function of the structure of the actual product and the area of finite elements, finite elements are applied through a new curvature area prediction formula that minimizes this gap function, and AFDEX-3D analysis (FEA) program And, through sensitivity analysis based on FEA and influence of each design variable on the curvature area, select data and various designs to perform regression analysis, select design variables and infer prediction formulas, Curvature area Finally, it is possible to measure the pre-products and areas used in the actual process for production.

According to the cylindrical cup using the finite element method and regression analysis for predicting the curvature area of the deep drawing ironing process according to the present invention, it can be effectively used for designing the cross-sectional area and accurate shape of an actual product through the DDI process.

1 is a characteristic diagram of a DDI process.
Fig. 2 is a diagram showing a region description: (a) volume classification: (b) difference.
3 is a diagram showing a shape variable and a design variable of a curvature region.
4 shows a method for finite element analysis.
5 is a diagram showing an experimental punch.
6 shows the definition of the wrinkle index (WI) in the forming limit diagram.
Fig. 7 is a diagram showing selection of major variables that affect the curvature area.
8 is a diagram showing a comparison of curvature areas.
9 is a diagram showing verification of prediction of a curvature region.

Hereinafter, an embodiment of a cylindrical cup using a finite element method for predicting a curvature area and a regression analysis in a deep drawing ironing process according to the present invention will be described with reference to the accompanying drawings. At this time, the present invention is not limited or limited by the examples. In addition, in describing the present invention, detailed descriptions of known functions or configurations may be omitted to clarify the gist of the present invention.

In describing the drawing, ironing and DDI according to the present invention, a cylinder drawing die is provided with a punch, a die and a blank, and drawing is performed by pressing the blank holder.

The material on the die and the punch are placed, and at this point the material is uniaxial. Through the tension of the flange pressed by the blank holder the wall is subjected to a complex plane strain stress state. By designing the die to prevent nearby tearing, the wall is adjusted for punch due to plane deformation.

The twin ironing process of die and punch requires free space through inserting to reduce the wall thickness or through a cylindrical cup-shaped container punch that evenly penetrates the die. It is larger than the thickness of the material. In contrast, a negative margin is given to the wall during the ironing process, and uniform thickness can be maintained while obtaining a height greater than the original wall height.

The ironing thickness before and after the process is t 0 and t 1, and the ironing ratio is calculated as an average t 0 / t 1. It is the reduction ratio of the cylindrical part to the wall thickness.

In DDI, the drawing and ironing process processes are performed simultaneously. DDI is advantageous in reducing the required number of processes. Complex design skills are required.

As in Fig. 1, the thickness reduction, the stretching speed and the ironing speed are considered simultaneously. During DDI, the diameter of the cylindrical drawing part is d 0 and d 1, and the blank diameter is D, so the calculation is simple.

The thickness reduction amount after the ironing process increases the height of this part (h 0) equally. In addition, since there is no reduction in the floor thickness, the floor area can be conveniently measured geometrically.

However, when calculating the curvature area after DDI, the curvature is as shown in FIG. 2(b) because the thickness changes along the height punch obtained by using the design and the actual height of the product.

In addition, the existing geometric calculation of the cross section in the curvature region using the geometric method is the initial thickness (t 0) and the thickness after ironing (tf ), for convenience, while calculating a consistent change according to the curvature, as shown in FIG. The curve is expressed as a quarter circle equation with a punch radius (R p ), the bottom curve is t 0 of the elliptic equation R 0 + which becomes the 1/4 major axis radius, and the minor axis diameter is R 0 + tf.

If the curvature area is a branched ellipse area 1 and the branching circle area is A 2, the curvature area can be obtained as a difference, and is a side surface of 1 and 2 shapes between the areas.

The simple formula for calculating the area of curvature is as follows.

Expressed using the equation,

As described above, the thickness of the curvature region is further measured, instead of the reduction ratio from wall to floor as in the rim, when the thickness of the actual DDI process is not the same. It is affected by ironing thicker in the bottom area than in the area near the wall, and as a result, the design spacing of the curvature area has a difference in the height of the final product.

So, to sign a more accurate DDI process, you need something new. There is a need for a curvature calculation method that can accurately calculate the DDI curvature area.

In addition, finite element analysis is performed in the DDI procedure. In order to design and verify the newly proposed curvature calculation method, a multi-stage deep drawing product is produced.

To do this, axial symmetry and a total of 6 drawing steps. And ironing-drawing begins with the second step in a process of up to six steps. Step 1 is the normal drawing procedure, determine the shape of the cylindrical cup, and Step 2 starts the DDI process. AFDEX-3D S/W finite element analysis, and an elastomeric plastic model are used.

Two-dimensional analysis is possible considering the axial symmetry of the product, and the FEA curve obtained when the friction coefficient is 0.05 is the same as the experiment.

The coefficient of friction is considered to be 0.05, and the change load-distance curve changes the maximum element size, number of elements, and is 4000, 7000 and 8000 respectively.

If the number of elements is more than 4000, the load-distance curve is constantly connected, and the initial thickness t 0 is 0.4 mm.

The curve obtained from the true stress-true strain tensile test is applied to the equation (3).

Where σeq is the effective stress and K is the strength factor.

n is the work hardening index, ε0 is the initial strain, and εeq is the effective strain.

[Table 1] shows the mechanical properties.

AISI 1010 relationship. 4 shows the finite element analysis.

The production process modeled based on actual mass conditions is the thickness (t 0 is the used sheet).

After the DDI process, the wall is 0.4 mm and the thickness (t f) is 0.3 mm, and the punch radius (P DDI process of R) is 2.8 mm. As can be seen from the FE analysis, the curvature is not proportional to the same thickness reduction ratio.

6 shows the comparison result of Fi-Fi.

When comparing the area analysis and the actual product through the program after the DDI process to confirm the accuracy of the element analysis data and the height analysis of the actual product, a very low gap of 2.8% appears in the DDI process.

Considering that the actual area and the twin curvature of the analysis result, and the DDI is a complex process, when the stretching and ironing processes are combined, the result can be regarded as a fairly accurate analysis.

In order to further reduce the gap in the analysis, the rot of the plastic anisotropic plate, friction between the material and the die, and the mold condition can be understood as follows.

In addition, the independent variable through the design of related factors by performing the sensitivity analysis is an experiment through the combination of all factories level.The factor used in the sensitivity analysis is the design variable used in the analysis, the practical applicability of the finite element analysis is have.

The product is Sec. 2.3 Various design variables and sheet metal forming processes have ambient noise, but only design variables that affect the curvature area have been selected for the study, and the variables can be quantified through the effect and sensitivity analysis of these designs.

The design variables that affect the post curvature area include the initial material thickness after the DDI process.

In the case of the punch radius, thickness after formation and coefficient of friction, if the initial material thickness is t 0, then the punch radius is R p, the thickness after formation is tf, the thickness ratio is m = tf / t 0, t 0, R p and m can be set as follows.

Each independent variable and experimental level els can be set to maximum and minimum. In order to analyze the sensitivity, [Table 2] shows the results obtained from a total of 8 finite cases.

Elemental analysis. Compare by defining:

The existing curvature area is A (0) and the curvature area is analyzed by A (FEM), and equation (1) Sec. 2.1 is the Mula for calculating A (0), A (FEM) is the acquired data through the area measurement provided in 3D in NX 8.0, CAD software Figure 7 shows the Pareto chart.

The bar graph shows the importance of conditional factors according to the order of the greatest influence of the data values.

Thus, Figure 7 shows that each design variable (FEM) analysis for the region of curvature shows a sensitivity of 60%, t 0, P of 35% row R, and 5% m. Thus, t 0 and R p have a dominant effect. Contract for the curvature area, the intensity ratio m is weak, and the sensitivity is about 5% in the curvature area.

In addition, regression analysis is a mathematical relationship between a dependent variable and an independent variable, and regression analysis assumes that there is a prediction equation Y for the curvature domain, the dependent variable X 0,1,... , k is an independent variable.

β 0,1,... , k is a regression coefficient and a regression formula, and can be expressed through a linear combination such as an equation. (4)

The default values obtained through regression are coefficients and constants. It is an independent variable about the dependent variable.

The data listed in Table 3 are used for regression analysis.

The prediction equation DDI for the area of curvature afterwards. The equation is as follows.

From the results of the sensitivity analysis, it was found that Sec.2.2, the design variable affects the dependent variable. Possible A (FEM), thus A (predicted), represents the obtained area in Table 3.

As shown in Fig.8, the area A (0) cal area calculation equation obtained using the geometry and the area A (FEM) tween 7.9% to 12.3% through finite element analysis. As mentioned in Fig. 6, the results obtained with FEA are of 97.2% of simulated experiments with accuracy and thus the prediction equation is very accurate. The area of curvature A (predicted) obtained using 99.7% A can be compared.

The prediction formula and the region of curvature (FEM) shown in Fig. 8 can be obtained using finite element analysis.

That is, to check the curvature area of the actual product, the area calculated using regression analysis is as follows.

Scan the cross section of the actual product and measure the area accordingly, and the thickness ratio of the product used for the area measurement is m, the initial thickness is 0.75mm (t1 of 0.4mm and post) ironing thickness (t2) of 0.3mm, The punch radius is 2.8mm.

After the DDI process, the cross-sectional curvature of the final product is measured as shown in FIG. 9.

Measure up to half of the cross section, and the measured value use shows that the actual area of curvature is 1.8086 mm2. The area obtained through the proposed regression analysis is 1.803 mm2.

The difference between the two is about 0.3%, so it can be neglected by comparing the values.

Therefore, it can be considered a valid calculation method.

That is, when calculating the curvature area of a cylindrical cup, a difference occurs when the geometric calculation method is applied to an actual product while going through the DDI process.

Reviewing the results of this study using regression analysis,

(1) In order to check the accuracy of the FEA software, the actual height of the product in consideration of DDI differs by up to 2.8% through the analysis process and FE analysis data.

(2) The sensitivity test result shows the sensitivity for the area of curvature in the analysis data. They are found in the following order (highest to lowest).

Initial material thickness (to), punch radius (Rp) and thickness ratio (m)

(3) The curvature prediction equation can be neglected because the regression analysis of the related variable and the estimated curvature area are about 0.3% different from FEA.

This result is also valid for cross comparison.

The DDI process is the actual product cross-sectional area. Therefore, the proposed method can be effectively used for accurate shape design.

Above, the present invention has been shown and described in connection with a preferred embodiment for illustrating the principle of the present invention, but the present invention is not limited to the configuration and operation as shown and described as such. Rather, it will be well understood by those skilled in the art that a number of changes and modifications to the present invention can be made without departing from the spirit and scope of the appended claims.

Claims (1)

Select the spacing function that uses the difference between, conduct mentor analysis and regression analysis as an objective function of the structure of the actual product and the area of the finite element, and calculate the finite element through a new curvature area prediction formula that minimizes this gap function. Apply, use the AFDEX-3D analysis (FEA) program,
Regression analysis is performed by selecting data and various designs through sensitivity analysis based on FEA and influence of each design variable on the curvature area.
After selecting the design variables and inferring the prediction formula, the curvature area of the DDI process. Finally, the curvature area prediction of the deep drawing ironing process, which measures the pre-product and area used in the actual process for production, using finite element method and regression analysis. Cylindrical cup.

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