1

Bending

Reference: Schulder, MetalForming Handbook, Springer,1998, chapter 4.

Bending Radius

On principle, the should assume the valuesrecommended by DIN 6935, i.e. they shouldbe selected from the following series(preferably using the values in bold type):

1 1,2 1,6 2 2,5 3 4 5 6 8 10 12 16 20 25 2832 36 40 45 50 63 80 100 etc.

2

Rolling direction

When bending sheet metal, particularattention should also be paid to therolling direction.

The most suitable direction for bendingis transverse to the direction of rolling.

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

3

FIGURE 7.15 (a) Bending terminology. The bend radius is measured to the inner surface of the bend. Notethat the length of the bend is the width of the sheet. Also note that the bend angle and the bend radius(sharpness of the bend) are two different variables. (b) Relationship between the ratio of bend radius tosheet thickness and tensile reduction of area for various materials. Note that sheet metal with a reductionof area of about 50% can be bent and flattened over itself without crackling. Source: After J. Datsko and C.T. Yang.

Bending

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

An approximate formula for the bend allowance, Lb, is given by

ktRLb

knessSheet thicconstant

radiusBendangleBend

tkR

Bending Allowance

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

4

1/21

0

tRee i

Theoretically, the strains at the outer and inner fibers are equal in magnitude and aregiven by the equation

(7.5)

The true strain at fracture in tension is

rAA

ef

f 100100lnln 0 sheettheofareaofReductionr

Minimum Bend Radii

Assume natural line is at R+0.5t

2/ln

1/211ln1ln 00 tR

tRtR

e

From Section 2.2.2, true-strain is

(7.6)

The true strain Equating the two expressions and simplifying,we obtain

150Minimum rt

R

The curve that best fits the data shown in the figure to theright is

160Minimum rt

R (7.7)

Minimum Bend Radii

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

5

TABLE 7.2 Minimum bend radii for various materials at room temperature.

MATERIAL CONDITIONMATERIALSOFT HARD

Aluminum alloysBeryllium copperBrass, low-leadedMagnesiumSteels

austenitic stainlesslow-carbon, low-alloy, and HSLA

TitaniumTitanium alloys

000

5T

0.5T0.5T0.7T2.6T

6T4T2T

13T

6T4T3T4T

Minimum Bend Radii

Springback The angle ratio is the so-called springback factor kR,

which depends on the material characteristics andthe ratio between the bending radius and sheetmetal thickness (r/s):

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

6

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

Springback

7

Residual stress

Bending causes residual stresses in theworkpiece.

The smaller the bending radius relative to thesheet metal thickness, the greater thesestresses are.

When a subsequent heat treatment is used toreduce residual stresses in the workpiece, it isimportant to remember that heat treatmentalters the workpiece radii and the angles.

Deformation of the crosssection during bending

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

8

Determining the blank length forbent workpieces (I) The blank length of the part to be bent is not equal to the

fiber length located at the center of the cross section afterbending.

The extended length of bent components 1 [mm] iscalculated as

whereby a [mm] and b [mm] stand for the lengths of the twobent legs, and v [mm] is a compensation factor which can beeither positive or negative

Geometry of bent legsRef: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

Determining the blank length forbent workpieces (II)

9

FIGURE 7.16 The effect of lengthof bend and edge condition on theratio of bend radius to thickness of7075-T aluminum. Source: After G.Sachs and G. Espey.

Length of Bend And EdgeCondition/Ratio of Bend Radius

FIGURE 7.17 (a) and (b) Theeffect of elongated inclusions(stringers) on cracking as afunction of the direction ofbending with respect to theoriginal rolling direction of thesheet. This example shows theimportance of the direction ofcutting from large sheets inworkpieces that aresubsequently bent to make aproduct. (c) Cracks on theouter radius of an aluminumstrip bent to an angle of 90 .̊

The Effect of ElongatedInclusions

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

10

FIGURE 7.18 Terminology for springbackin bending. Springback is caused by theelastic recovery of the material uponunloading. In this example, the materialtends to recover toward its originally flatshape. However, there are situationswhere the material bends farther uponunloading (negative springback), asshown in Fig. 7.20.

ffiitRtR

22allowanceBend radiibendfinalandInitial, fi RR

The springback factor is defined as 1/2

1/2

tRtR

Kf

i

i

fs

(7.9)

Springback in Bending

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

FIGURE 7.19 Springback factor K, forvarious materials: (a) 2024-0 and 7075-0aluminum; (b) austenitic stainless steels; (c)2024-T aluminum; (d) 1/4- hard austeniticstainless steels; (e) 1/2-hard to full-hardaustenitic stainless steels. Source: After G.Sachs.

An approximate formula for estimating spring back is

1343

EtYR

EtYR

RR ii

f

i (7.10)

Springback in Bending

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

11

FIGURE 7.20 Schematic illustration of the stages in bending round wire in a V-die.This type of bending can lead to negative springback, which does not occur in airbending (shown in Fig. 7.26a). Source: After K. S. Turke and S. Kalpakjian.

Negative Springback

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

FIGURE 7.21 Methods of reducing or eliminating springback in bendingoperations. Source: V. Cupka, T. Nakagawa, and H. Tyamoto.

Methods of Reducing orEliminating Springback

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

12

Roll forming: roll bending inseveral stages

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

Rolling and Folding

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

13

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

14

Roll bend radius

Strain=(R+0.5s)/RReL=Strain*E

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

15

Start-stop roll forming line

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

Roll stands

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

16

Width adjustable telescopicroll set

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

Roll stand for exchange ofsection rolls

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

17

Stand for a complete standexchange

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

Roller straightening with 13rollers

Bending and counter bending must each take place within theplastic range of the material in order to ensure that the bendingdirection is retained following elastic recovery, i. e. the yieldstrength of the material must be exceeded.

On the other hand, care must be taken to ensure that thestraightened material does not sustain damage.

If bending is too pronounced, brittle materials can develop slightcracks at the surface.

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

18

Reduction of residual stress

The reduction of residual stress is highlybeneficial for further processing.

The larger the number of rollers used, thelower is the residual stress in the sheet metalafter straightening.

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

Residual stresses in the sheetmetal

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

19

The feed value

The feed value zw for therollers is limited by thegeometry of the straighteningmachine

with the roller radius Rw [mm],sheet metal thickness s [mm]and roller pitch tw [mm].

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.

Roller straightening machine forlarger sheet metal thickness rangefrom 0.5 to 20 mm in thickness

Ref: Schulder, Metal Forming Handbook, Springer, 1998, chapter 4.