This document provides information on bending theory and design principles for bending operations. It discusses the following key points in 3 sentences: Types of bending covered include V-bending, edge bending, and flanging. Springback occurs as the bent part partially recovers its original shape after bending forces are removed. The document outlines methods to compensate for springback like overbending and bottoming, and provides formulas to estimate springback and calculate bending allowance and force.

1. TOOL DESIGN
UNIT 4
THEORY OF BENDING
BY
PURNESH ALONI
ROLL NO. 11
MTECH(PRODUCTION ENGG)
DEPARTMENT OF
MECHANICAL ENGINEERING
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2. CONTENTS
• Introduction
• Types of bending
• Spring back in bending
• Compensation for spring back
• Variations in bending operations
• Design principles
2

3. INTRODUCTION
• BENDING :- Bending is defined as the straining
of metal around a straight axis. The metal on
the inside of the neutral axis is compressed.
The metal on the outside of the neutral axis is
stretched.
3

4. V-bending :
• In V-bending the sheet metal blank is bent between a V-shaped
punch and die
• The figure below shows a front view and isometric view of a V-
bending setup with the arrows indicating the direction of the applied
force
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TYPES OF BENDING
Figure courtesy of Engineering Research Center for Net Shape Manufacturing

5. Edge or wipe bending:
• Edge or wipe bending involves cantilever loading of the
material
• A pressure pad is used to apply a Force to hold the blank
against the die, while the punch forces the workpiece to yield
and bend over the edge of the die
TYPES OF BENDING

6. 6
Spring back in bending
• Spring back is defined as the increase in included angle of the
bent part relative to the included angle of the forming tool
after the tool is removed.
• When the bending stress is removed at the end of the
deformation process, elastic energy remains in the bent part
causing it to partially recover to its original shape. In bending,
this elastic recovery is called springback.
• It increases with decreasing the modulus of elasticity, E, and
increasing the yield strength, Y, of a material.

7. Spring back in bending
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αi: bend angle before springback
αf: bend angle after springback
Ri: bend radius before springback
Rf: bend radius after springback

8. Spring back in bending
In order to estimate springback, the following formula
can be used:
Manufacturing processes by S. Kalpakjian and S. Schmid
where:
Ri, Rf: initial and final bend radii respectively
Y: Yield strength
E: Young’s modulus
t: Sheet thickness
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9. 9
Compensation for Springback
Overbending
• When overbending is used in V-bending (for example), the
punch angle and radius are fabricated slightly smaller than the
specified angle and raduis of the final part. This way the
material can “springback” to the desired value.
Bottoming (coining)
• Bottoming involves squeezing the part at the end of the stroke,
thus plastically deforming it in the bend region.

10. Variation in Bending Operations
• Flanging is a bending operation in which the edge of a sheet
metal is bent at a 90° angle to form a rim or flange. It is often
used to strengthen or stiffen sheet metal. The flange can be
straight, or it can involve stretching or shrinking as shown in
the figure below:
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(a)Straight flanging
(b)Stretch flanging
(c)Shrink flanging

11. Variation in Flanging
In stretch flanging the curvature of
the bending line is concave and the
metal is circumferentially stretched,
i.e., A > B. The flange undergoes
thinning in stretch flanging.
In shrink flanging the curvature of
the bending line is convex and the
material is circumferentially
compressed, i.e., A < B. The material
undergoes thickening in shrink
flanging.
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12. Variations in Bending Operation
•Hemming involves bending the edge of the sheet over
onto itself in more than one bending step. This process is
used to eliminate sharp edges, increase stiffness, and
improve appearance, such as the edges in car doors.
•Seaming is a bending operation in which two sheet metal
edges are joined together.
•Curling (or beading) forms the edges of the part into a roll.
Curling is also used for safety, strength, and aesthetics.
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(a)Hemming
(b)Seaming
(c)Curling

13. Design Principles
BEND RADIUS: It is defined as the radius of curvature on the
inside or concave surface of bend
When bending to an angle of 900 ,the minimum bend radius
= 2 to 5t for C-steel
= 1t for stainless steel
= 2 to 3.5t for Ti alloys
= 0.3 to 0.5 t for brass
= 0.35t for Al
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14. Design Principles
BENDING ALLOWANCE: To calculate the blank length for bending ,the
length of material in the curved section or bend area has to be
calculated. This length in the bend area which will be more than
corresponding length before bending is call Bending Allowance.
B.A=
2πθ (𝑟+𝑘𝑡)
360
,mm
B.A = Bending allowance along neutral axis, mm
θ = Bend angle in degree
r = inside radius of bend, mm
k = Distance of neutral axis from the inside surface of
bend.
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15. Design Principles
STOCK MATERIAL Where r<2t Where r>2t
1.MILD STEEL
(i)Edge Bending
(ii) V-bending, U-bending
0.2t
0.33t
0.33t
0.5t
2.SOFT COPPER, SOFT BRASS,SOFT TO
HALF HARD ALUMINIUM
0.33t 0.5t
3. HALF HARD COPPER ,HALF HARD
BRASS, HALF HARD ALUMINIUM
0.4t 0.5t
4.HARD COPPER, HARD BRASS , HARD
STEEL
0.5t 0.5t
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Values of k:-

16. Design Principles
WIDTH OF DIE OPENING :- The width of die opening controls
spanking area, the amount of press exertion and the length off
effective press stroke.
w= R1+R2+c – V-bending
w=R1+R2+c+t -Edge bending
R1 - Punch edge radius
R2 - Die edge radius
c - Clearance=t
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17. Design Principles
BENDING FORCE : Bending force depends upon the thickness of
the stock, the length of the bend , the width of die operation and
the type of bend.
F=
𝐾∗𝐿∗𝑆𝑈𝑇 𝑡2
𝑤
, N
L=Total length of bend
𝑆 𝑈𝑇= Ultimate tensile strength of material ,MPA
w= Width of die opening, mm
t=m Thickness of blank, mm
K= Die-opening factor
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18. Design Principles
VALUES OF DIE-OPENING FACTOR
• For V-bending
K=1.20 for w=16t
=1.33 for w=8t
• For U-bending
K=0.67
• For Edge bending
K=0.33
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