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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.