Bending  Course:Technique of working sheet metals, pipes and sections. Trainees' handbook of lessons (Institut für Berufliche Entwicklung, 33 p.) 

When a workpiece is being bent, its original length may alter by a certain measure.
Therefore, the workpiece has to be cut to size very exactly before being bent The required blank length is called “stretched length” and is to be calculated from the length of the neutral axis.
Figure 20 Dimensions on parts to be
bent 1 stretched length, 2 leg lengths, 3 bending radius, 4 workpiece
thickness
If the bending radius is bigger than five times the workpiece thickness, the neutral axis runs in the middle of the workpiece. Hence, the neutral axis bending radius is to be calculated with the following formula:
With R_{B} > 5 · S 
R_{N} = radius of neutral axis 
_{} 
R_{B} = bending radius 

S = workpiece thickness 
If the bending radius is smaller than five times the workpiece thickness, the neutral axis is displaced to the bending internal side during the bending process.
Then the bending radius of the neutral axis can be calculated with the following formula:
With R_{B} < 5 · S
_{}
If workpieces are bent by 360°, the length of bend is calculated with the formula for calculating the circumference:
L_{B} 
= 
U 
= 
D · p 
or L_{B} 
= 
U 
= 
2 · R_{N} · p 
L_{B} 
= 
length of bend  
U 
= 
length of circumference  
D 
= 
circle diameter  
p 
= 
constant with the value of 3.14 
Hence, the following formula is used for a 180° bending:
_{}or L_{B} = R_{N} · p
Hence, the following formula is used for a 90° bending:
_{}
_{}
For any optional bending, the formula of the bending angle is to be considered:
_{}
_{}
What does the term "stretched length"
mean?
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How does the position of the neutral axis change when a
workpiece is bent around a bending radius smaller than five times the workpiece
thickness?
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Calculation example:
A flat section is to be bent for several times. Its dimensions are to be seen from the following illustration.
Figure 21 Example for dimensioning a
part to be bent
For calculation, the total length is subdivided into 4 partial lengths:
Total length  sum of all partial lengths 
L = L1 + L2 + L3 + L4 
Figure 22 Subdividing the piece to be
bent into partial lengths 1 partial length L_{1}, 2 partial length
L_{2}, 3 partial length L_{3}, 4 partial length
L_{4}
The neutral axis of partial length L_{1} is calculated as follows:
L_{1} 
= 
40 mm  S  R_{B1} 
L_{1} 
= 
40 mm  6 mm  10 mm 
L_{1} 
= 
24 mm 
The neutral axis of partial length L_{2} is calculated with the formula derived from that to calculate the circumference for a 90° bending:
_{}
Since the bending radius R_{B1} is smaller than five times the section thickness, therefore R_{N1} is:
_{}
R_{N1} = 10 mm + 2 mm
R_{N1} = 12 mm
This means for partial length L_{2}:
_{}
_{}
L_{2} = 18.84 mm
The neutral axis of partial length L_{3} is to be calculated as follows:
L_{3} = 120 mm  2 · S  R_{B1}  R_{B2}
L_{3} = 120 mm  12 mm  10 mm  35 mm
L_{3} = 63 mm
The neutral axis of partial length L4 is calculated with the formula derived from that to calculate the circumference for a 180° bending:
L_{4} = R_{N2} · p
Since the bending radius R_{B2} is bigger than five times the section thickness, therefore R_{N2} is:
_{}
R_{N2} = 35 mm + 3 mm
R_{N2} = 38 mm
Now, the neutral axis of partial length L4 can be calculated as follows:
L_{4} = R_{N2} · p
L_{4} = 38 mm · 3.14
L_{4} = 119.32 mm
With the help of die partial lengths so calculated, the total stretched length of the flat section can be calculated now:
L 
= 
L_{1} + L_{2} + L_{3} + L_{4} 
L 
= 
24 mm + 18.84 mm + 63 mm + 119.32 mm 
L 
= 
225.16 mm 
The calculated value is always brought up to a round millimetre figure, thus the stretched length of the flat profile is 226 mm.
How is the stretched length of a workpiece calculated, if
several different bends are to be
made?
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