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The process and characteristics of bending deformation

Bending deformation process

In this chapter, V-shaped bending is taken as an example to illustrate the bending deformation process, as shown in Fig. 1-1. At the beginning of bending, the inner bending radius of the blank is greater than the radius of the punch fillet. As the punch is pressed down, the straight edge of the blank is gradually closer to the V-shaped surface of the die, and the radius inside the bending is gradually reduced, i.e

R₀＞r₁＞r₂＞r

At the same time, the bending moment arm is gradually reduced, i.e

l₀＞l₁＞l₂＞l_k

Wann the punch, the blank, and the die are completely pressed together, the bending radius and the bending arm inside the blank reach the minimum, and the bending process ends.

Bending is divided into free bending and correction bending. Free bending means that when the bending ends, the punch, the die, and the blank are consistent, the punch is no longer pressed down. Correction bending refers to the punch, concave die, and blank three consistent, punch continues to press down, so that the blank has further plastic deformation, so as to correct the bending parts.

Bending deformation characteristics

In order to observe the metal flow when the sheet is bent and to analyze the deformation characteristics of the material, a square grid can be set on the side surface of the sheet before bending. The mesh is usually made by mechanical engraving or photographic etching, and then the size and shape changes of the mesh before and after bending are observed and measured using a tool microscope, as shown in Fig. 1-2.

Before bending, the sidelines of the material are all straight lines, forming a small square lattice of uniform size, and the length of the longitudinal grid line aa=bb. After bending, it can be seen that the bending deformation has the following characteristics by observing the changes of the mesh shape.

1. The curved fillet part is the main area of bending deformation.

After bending, the bending part is divided into two parts: the rounded corner and the straight edge. The deformation mainly occurs in the range of the center Angle of bending α, and there is basically no deformation outside the center Angle.

2. In the deformation zone, the blank has deformation in the three directions of length, width, and thickness, but the deformation is not uniform.

• Length direction

The grid is changed from square to fan, the length of the side close to the die (outer area) is extended, the length of the side close to the punch (inner area) is shortened, that is, arc bb＞ line segment bb, arc aa ＜ line segment aa. From the inner and outer surfaces to the center of the blank, the degree of shortening and elongation decreases gradually. Between the two deformation zones of shortening and elongation, there must be a layer whose length does not change before and after deformation. This layer is called the strain neutral layer.

• Thickness direction

The thickness of the inner area increases and the thickness of the outer area decreases, but because the inner area punch compacts the blank, the thickness direction deformation is more difficult, so the increase of the inner thickness is less than the thinning of the outer thickness, so the thickness of the material in the bending deformation area will become thinner so that the neutral layer of the blank occurs inward shift.

• The width direction

There are two cases: one is the bending of the narrow plate (b/t≤3), and the deformation in the width direction is not constrained, and the section becomes a fan shape with a width inside and a width outside; the other is the bending of the wide plate (the ratio of the blank width to the thickness b/t＞3), and the deformation of the material in the width direction is limited by the adjacent metal, and the cross-section is almost unchanged and basically remains a rectangle, as shown in Fig. 1-3 (a) and (b) show the changes of the section under two conditions.

Because the deformation zone section of the narrow plate is distorted when bending, it is necessary to add subsequent auxiliary procedures when the side size of the bending part is required or it is required to cooperate with other parts. Most of the bending in actual production belongs to wide plate bending.

Quality analysis of bending parts

Bending crack

1.Minimum bending radius

Bending radius refers to the radius of curvature inside the bending part, r as shown in Fig. 1-3. It can be seen from the bending deformation that the outside of the sheet material is stretched when bending. When the tensile stress on the outside exceeds the tensile strength of the material, a crack will occur on the outside of the sheet material. This phenomenon is called bending crack.

Under the condition of the same sheet thickness, whether the bending part is bent and cracked is mainly related to the bending radius r. The smaller r is, the greater the bending deformation degree is. Therefore, there is a minimum bending radius r_Mindest that can ensure that the outer fiber does not produce bending crack. In other words, the minimum fillet radius that can be bent into the inner surface of the part under the condition that the sheet material does not destroy is called the minimum bending radius r_Mindest, and it is used to express the forming limit during bending.

The minimum bending radius r_Mindest is affected by the mechanical properties of the material, the surface quality and section quality of the sheet, the thickness of the sheet, the width of the sheet, the bending center Angle and the direction of the bending line. Because the influence of the above factors is very complex, the value of the minimum bending radius is generally determined by the experimental method. The minimum bending radius values of various metal materials in different states are shown in Table 1-1.

Notiz:

• This table is used for plate thickness less than 10 mm, bending Angle greater than 90°, good shear section;
• In the bending after blanking or cutting but no annealed blank, should be used as a hardened metal selection;
• When the bending line is at a certain angle to the fiber direction, the middle value between the vertical and parallel fiber directions can be used;
• Table t is the thickness of sheet metal.

2. Measures to control bending and cracking.

• To choose good surface quality, no defects of the material to do blank. If the blank has defects, it should be removed before bending, otherwise bending will crack at the defect.
  For more brittle materials, thick materials, and cold hardening materials, can use the heating bending method, or the use of annealing to increase the material plasticity and then bending method.

• When the bending radius of the workpiece is small, the burr should be removed in advance, and the hardening layer of the blank should be eliminated by the annealing method.

• If the burr is small, you can also put the burr side toward the curved punch surface to avoid stress concentration and cracking of the workpiece.

• Under normal circumstances, the minimum bending radius should not be used in the design. If the bending radius of the workpiece is less than the value shown in Table 1-1, it should be bent two or more times, that is, the first bending into a larger radius of the fillet (greater than r_Mindest), after intermediate annealing. Then the required bending radius is bent by the calibration procedure. This allows the deformation area to be enlarged and the elongation of the outer material to be reduced.

• For the bending of thicker materials, if the structure allows, the inside of the bending fillet can be slotted first, and then bent, as shown in Fig. 1-4.

Bend and rebound

Plastic bending at room temperature, like other plastic deformation, is always accompanied by elastic deformation. When bending ends, the external force is removed, the plastic deformation is retained, and the elastic deformation is completely disappeared, making the shape and size of the bending parts change and inconsistent with the size of the mold, this phenomenon is called bending resilience, referred to as resilience.

1. Biegen resilience phenomenon.

As the tangential stress-strain properties of the bending deformation zone and the outer side are opposite, the outer side is shortened due to elastic recovery while the inner side is elongated due to elastic recovery during unloading, and the resilience direction is opposite to the direction of bending deformation. In addition, for the whole billet, the proportion of the non-deformation zone is much larger than that of the deformation zone, and the inertia action of a large area of the non-deformation zone will also increase the resilience of the deformation zone, which is another reason that the resilience of bending is more serious than that of other forming processes.

The resilience phenomenon of bending parts is usually manifested in two forms, as shown in Fig. 1-5.

• Curvature reduction. Before unloading, the radius of the bending neutral layer is ρ, and after unloading, the radius of the bending neutral layer is increased to ρ’. The curvature decreases from 1/ρ before unloading to  1/ρ’ after unloading. If ∆K represents the reduction in curvature, then

• The bending center angle decreases. Before unloading, the central Angle of the bending deformation zone is α; after unloading, the central Angle of the bending deformation zone decreases to α’. If ∆α represents the reduction of the bending central Angle, then

∆α = α – α’

The bending Angle β ( the included angle between two straight edges of the bending part, the relation between it and the bending center Angle α is: β = 180°- α ) is increased by

∆β = β – β’

The calculated ∆K、∆α ( ∆β ) is the resilience amount of bending parts but compared with the resilience amount of actual stamping production, there is a certain difference, the reason is that there are many factors affecting the resilience amount of bending.

2. Factors affecting resilience

• Mechanical properties of materials. The larger the yield strength σ_s A is, the smaller the elastic modulus E is, and the greater the resilience of bending deformation is. Because the higher the yield point σ_s of the material is, the greater the stress in the section of the deformation area of the material is under a certain degree of deformation, and thus the greater the elastic deformation can be caused, and the greater the rebound value is. The larger the elastic modulus E is, the stronger the ability of the material to resist elastic deformation is, so the smaller the rebound value is. 

• Relative bending radius r/t. The smaller the relative bending radius r/t is, the smaller the rebound value is. The smaller the relative bending radius r/t, the greater the degree of bending deformation, the greater the total tangential deformation degree of the deformation area, the greater the proportion of plastic deformation in the total deformation, and the corresponding proportion of elastic deformation decreases so that the rebound value decreases. On the contrary, the greater the relative bending radius r/t, the greater the rebound value. This is also the reason why the workpiece with large r/t is not easy to bend and form.

• The center Angle of bending α. The greater the bending center Angle α, the greater the rebound Angle. Because with the increase of α, the length of the deformation section increases, so does the cumulative value of rebound, but it does not affect the rebound of the curvature radius.

• Bending mode. The resilience value is large when the bending is free, but small when the bending is corrected. When bending freely in the bottomless concave die, the rebound is the largest; The rebound is minimal when correcting bending in a bottom die.

• The shape of bending parts. In general, the more complex the shape of the bending parts, the more the number of a bending forming Angle, the greater the interaction between the bending parts, the greater the tensile deformation of the bending components, the smaller the amount of rebound. Therefore, in the process of primary bending, the resilience amount of concave-shaped parts is smaller than that of U-shaped parts, and the resilience amount of U-shaped parts is smaller than that of V-shaped parts.

• Mold clearance. In bending U-shaped parts, the clearance between convex and concave dies has a great effect on the rebound Angle. The larger the clearance, the larger the rebound Angle, as shown in Fig. 1-6. When negative clearance is used, the rebound Angle can be reduced to the minimum value, or even zero or negative value, due to the extrusion effect of the die on the material.

3. Determination of rebound value

Since resilience directly affects the shape and size of bending parts, the resilience of materials must be considered in advance when designing and manufacturing molds. Usually, the size of the working part of the mold is preliminary determined according to the empirical value and simple calculation, and then the shape and size of the corresponding part of the mold are corrected by trying the mold.

The determination methods of rebound value include the theoretical formula calculation method and empirical value lookup table method.

• The resilience of free bending can be divided into the following situations.

The resilience value of free bending when the relative bending radius is large. When the relative bending radius r/t ＞10, the resilience is relatively large. As shown in Fig. 1-7, the radius and Angle of the bending fillet of the bending parts changed greatly after unloading. In this case, the change of the material thickness and the movement of the stress-strain neutral layer can be ignored to simplify the calculation. In this case, the punch fillet radius r_schlagen and the punch fillet part center Angle α_schlagen can be calculated according to the following formula.

In the formula, r_schlagen — the radius of the punch fillet, mm;
α_punc —— center Angle of punch fillet;
r —— the fillet radius of bending parts, mm;
α —— the center Angle of the rounded corner of the bending part;
σ_s —— the yield limit of the bending material, MPa;
E —— elastic modulus of bending material, Mpa;
t —— material thickness of bending parts, mm.

The resilience value of free bending when the bending radius is small. When the relative bending radius r/t of the bending part is less than 5, due to the large degree of deformation, the change of the bending fillet radius is small after unloading, so it can not be considered, but only the change of the bending center Angle is considered.
When the bending center Angle of the bending part is not 90°, the resilience angle can be calculated according to the following formula.

∆α =α/90x∆α₉₀

In the formula, ∆α —— the resilience Angle when the bending center Angle of the bending part is α;
∆α₉₀ —— the resilience Angle when the bending center Angle is 90°, as shown in Table 1-2;
α —— the bending center Angle of the bending part.

• Correct the resilience when bending. The resilience value of bending correction can be calculated by the formula obtained from the test, the symbol is shown in Fig. 1-8, and the formula is shown in Table 1-3.

4. measures to control the rebound

When designing the mould, the resilience should be minimized. The common methods are compensation method and correction method.

• Compensation method. The compensation method is to estimate or test the amount of resilience after the workpiece is bent in advance. When designing the mold, the deformation of the bending workpiece exceeds the original design deformation, and the shape of the workpiece is obtained after the resilience. Fig. 1-9 (a) shows the compensation of single angle resilience. According to the determined resilience angle, when designing a punch and concave dies, reduce the angle of the die to make compensation. 

In the case shown in Fig. 1-9 (b), two measures can be taken: first, the punch is tilted inward to form a compensation angle of ∆θ; The other is to make the convex and concave die unilateral clearance is less than the thickness of the material, the punch will be pressed into the concave die, the use of the blank outside and the concave die friction force on both sides of the blank are inwards attached to the punch, so as to achieve the compensation of rebound. 

The compensation method as shown in Fig. 1-9 (c) is to form a circular arc bending at the bottom of the workpiece. After the separation of the convex and concave dies, the circular arc part of the workpiece has the trend of resilience as a straight line, which drives the two sides of the plate to tilt inward, so that the resilience is compensated.

• Correction method. The correction method is to take measures in the mold structure, so that the correct pressure is concentrated in the corner, so that it produces a certain plastic deformation, to overcome the rebound. Fig. 1-10 shows that the bending correction force is concentrated on the curved fillet.

The offset

In the bending process of sheet metal, the sides are moved along the length of the workpiece by the unequal resistance at the concave die fillet, resulting in the height of the straight edge of the workpiece does not meet the requirements of the drawing, this phenomenon is called migration.

1. Ursachen of deviation

• The shape of the blank is not symmetrical, as shown in Fig. 1-11 (a) and (b).
• The workpiece structure is asymmetrical, as shown in Fig. 1-11 (c).
• The angles on both sides of the die are not symmetrical, as shown in Fig. 1-11 (d).
• convex and concave die rounded corners, gap asymmetry so that the resistance is not equal.

2. Measures to control the coding

• The use of a pressing device. The blank is gradually bent and formed under the pressing state, so as to prevent the slide of the blank, and a relatively smooth workpiece can be obtained, as shown in Fig. 1-12.

• Bending after positioning. The positioning plate should be properly designed for shape positioning, as shown in Fig. 1-13 (a), or the positioning pin should be inserted into the hole by using the hole on the blank or the design process hole. For some bending parts, the process hole and the press plate can be used together, as shown in Fig. 1-13 (b). Due to the positioning of the roof and the locating pin, the deflection of the blank can be prevented during bending. The effect of the reverse pressure is to balance the horizontal lateral force generated by the left bending.

• Bending in pairs. The asymmetrical bending parts are combined into symmetrical bending parts, and then cut, so that the sheet material in the bending force is uniform, to prevent the generation of offset.
• Accurate Schimmel Herstellung. The gap is adjusted symmetrically, so that the resistance is distributed symmetrically, so as to prevent the generation of offset.