Bending of Sheets - Procedure Description

Bending is the technological operation used to modify the shape and dimensions of semi-finished products without removing material. In other words, it involves changing the shape of a semi-finished product by bending it around a straight edge.

Bending is a deformation processing method where a flat sheet is curved with a certain bending radius "R." During the bending process of a material with a thickness "g," only the neutral fiber maintains its original dimension (remains undeformed). The outer fiber is stretched due to tensile stresses that appear on the outer surface of the sheet in the bent area, while the inner fiber is compressed due to compressive stresses that occur on the inner side of the curve.

Fig. 1: Diagram of the Bending Process

Understanding the undeformed fiber in the bent area "B" (Fig. 1) is very useful for dimensioning the semi-finished product that will undergo bending. If we assume that the neutral fiber (Rfn) has a curvature radius $Rfn = R + 0.45g$ Rfn=R+0.45g, where $R$ R is the bending radius and $g$ g is the thickness of the material, then the length of the neutral fiber in the bent area is given by the following relationship:

$B=\left (R+0.45\times \mathit{g} \right )\frac{2\pi \alpha }{360}$

In this context, $\alpha$ α represents the bending angle, and $g$ g refers to the material thickness.

In reality, the deformations in the bent area are much more complex. However, if the ratio between the width and thickness of the sheet is greater than 8, it can be assumed that only the longitudinal fibers (parallel to the neutral axis) undergo deformation. This simplification makes it easier to model and calculate the bending process for practical applications, particularly when the material has a high width-to-thickness ratio, such as in sheets with large surface areas.

Because the deformations increase significantly as the ratio G/R $\frac{g}{r}$ (thickness to bending radius) becomes larger, care must be taken to avoid cracks on the stretched surface of the material. For this reason, the bending radius is expressed as multiples of the sheet thickness. To prevent cracking of the sheet and damage to the forming tools, it is recommended that the bending radius be at least 0.8 mm, even in the case of high-plasticity sheet materials.

The minimum bending radius can be determined with considerable accuracy, taking into account the value of the "necking" $Z$ Z obtained from a tensile test of the material, using one of the following relations:

$R_{min.}=\mathit{g}\left (\frac{1}{2Z}-1 \right )$ , where Z < 0.2

$R_{min.}=\mathit{g}\left (\frac{1-Z^{2}}{2Z-Z^{2}}\right )$ , where Z > 0.2

Plastic deformation of sheets is accompanied by elastic deformation (due to the law of coexistence of elastic and plastic deformation). This elastic deformation causes the material, after the bending process, to relax and return to a different bending radius $R_f$ Rf compared to the original bending radius $R_0$ R0 of the material under load (Fig. 2).

Fig. 2: Elastic relaxation of the material after bending (ao - bending angle; ax - bending angle after material relaxation)

There are several calculation formulas for elastic relaxation, but none of them provide exact values. For this reason, experimental determinations of relaxation are necessary. However, to reduce the number of experimental determinations, the use of such calculation relations is recommended. For example, for bending sheets made of refractory alloys, the following relation is recommended:

$\frac{R_{0}}{R_{f}} = 4\left (\frac{R_{0}\sigma _{c}}{E \times g} \right )^{3}-3\frac{R_{0}\sigma _{c}}{E\times g}+1$

In this case:

$\sigma_c$ - σc is the yield strength of the material
$E$ - E is the modulus of elasticity

Compensation of Elastic Relaxation

Elastic relaxation is compensated by properly dimensioning the tools, meaning they should be constructed with a bending radius $R_{ef}$ Ref that is smaller than the radius $R_0$ R0 specified for the part in the engineering drawing.

Bending at Large Bending Radii

Bending with large bending radii is performed using roll devices or by using specific templates.

Bending in the 3-Roller Device (Roll Bending)

Bending in a 3-roller device involves introducing the sheet between rollers 1, 2, and 5 (Fig. 3). The displacement of the sheet between these rollers, in both directions, is done by roller 1, which can be rotated manually or mechanically. The force required for the bending process is applied through roller 2. The bending radius is modified by adjusting the position of rollers 2 and 5.

Fig. 3: Bending in the 3-Roller Device (Roll Bending)

CC – Bending cylinders
SF – Semi-finished product
PC – Curved product

With this device, various bending angles and radii can be achieved, including the formation of a cylinder, where the ends of the sheet meet. Bending at large angles or smaller bending radii is performed gradually.

Bending with One Roller (Fig. 4)

Bending with a single roller is performed only at the roller's radius.

Fig. 4: Bending with One Roller

In this process, the sheet (3) is clamped onto roller (6) using a clamping system (4) (such as bolts, clamps, etc.). The sheet is bent by rotating roller (6), while the sheet is kept in contact with it by the tensile force $F_j$ Fj. The bending radius can be small, within the technological limits of the roller processing. The bending angle can be nearly 180°, allowing for the formation of large bends or even circular shapes.

Bending with a Roller Segment

Fig. 5: Bending with a Roller Segment

This operation is similar to bending in a roller device. In this situation, the sheet (3) is brought into contact with the bending roller through the secondary roller (2), which is pressed with a force $F$ F. The bending angle is limited by the angle of the roller segment.

Bending with Small Bending Radii

For bending parts with large dimensions and small bending radii, a manual bending machine is most commonly used (Fig. 6). In this case, the sheet (4) is clamped between jaws (1) and (2), which also serve as the edges around which the bending occurs. A movable jaw (3), which can rotate around an axis parallel to the clamping edges and passes through their tips, bends the material to the desired angle. The possibilities for bending are limited by the angle values, bending radius, and combinations of bends.

Fig. 6: Manual Bending Machine

Bending on mechanically operated sheet metal bending machines (Fig. 7) is done using a die, ensuring higher bending precision and increased productivity.

On the bending machine table (4), the die (2) is mounted. The sheet (1) (the workpiece) is bent with the help of the punch (3), upon which a bending force $F$ F is applied. This force is calculated using the following relation:

$F=K\frac{b \times g^{2}}{L}\sigma _{r}$

where:

$K$ K is a stability coefficient depending on the ratio of the distance between the supports ( $K = 1.25 \to 1.6$ K=1.25→1.6 for $l = (15 \to 5)g$ l=(15→5)g), where $l$ l is the distance between the supports, and $g$ g is the thickness of the material.
$L$ L is the distance between the supports (the length of the sheet that is clamped between the machine's supports).
$b$ b is the width of the semi-finished product (the sheet).
$\sigma_r$ σr is the tensile strength (breaking strength) of the material.

Fig. 7: Mechanically Operated Sheet Metal Bending Machine (Abkant)

Rotary Bending

The punch is a cylinder with a channel that has the desired bending angle. The sheet is placed on the die, with the area to be bent positioned on the edge of the die. No devices are used to secure the sheet in place. The force is transmitted to the punch, which forces the sheet to bend. The channel on the cylinder has two surfaces: one that makes contact with the sheet, transmitting pressure, and another that holds the sheet in position on the die.

Fig. 8: Rotary Bending

Bending in Die

In this situation, the process takes place on mechanically operated bending machines using dies of greater complexity, which lead to increased productivity. This method is used to obtain profiles with various configurations, whether functional or for strength purposes, in large series and of superior quality.

To produce the part (Fig. 9), the material (1), cut to the necessary dimensions, is placed in the die (2) and positioned properly in relation to its cavity. The punch (3), driven by force $F$ F, will bend the sheet according to the geometry of the die cavity. After the bending process is completed, due to the elastic relaxation of the sheet material, the part is held in the die and is removed with the help of the extractor (4), which applies the extraction force $F_s$ Fs to release the part.

Fig. 9: Bending in Die

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