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How to Calculate Bending Springback?

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Key takeaways:

1. The article emphasizes the importance of accounting for springback when designing bending dies, highlighting that a one-size-fits-all approach to adjusting the die radius based on material hardness is inadequate for precision bending, especially in cases involving large radii and thin materials.

2. A universal formula for calculating springback is introduced, which considers various factors including the workpiece and punch radii, the central angles of their arc lengths, material thickness, and material properties such as elastic modulus and yield point, thereby providing a more reliable method for die design that can reduce the trial-and-error process.

3. To facilitate more accurate and efficient die design, the article suggests the creation of a material database that includes essential physical parameters like elastic modulus and yield strength, which can be sourced from suppliers, underscoring the necessity of precise material data for predicting bending outcomes and springback.

When designing a bending die with an internal arc, many people either choose to use the same R value as the original product and do not consider the springback, or directly reduce the R value by a certain factor.

For example, if the original product has an R value of 1 and the material is relatively hard, they would choose 0.8 times the R value for the convex mold, which would be 0.8.

If the material is relatively soft, they would choose 0.9 times the R value, which would be 0.9.

If there is any deviation, they modify the mold several times based on experience to achieve tolerance within the range.

However, if this method is used to design a product with a thickness of 0.5 and an internal R value of 200mm, it may be difficult to accurately predict the amount of springback.

Therefore, a universal formula for springback is introduced below, which can be used to calculate the springback value based on numerical input.

In the formula:

  • r – workpiece fillet radius (mm):
  • r1 – punch radius (mm);
  • a – the central angle of the arc length of the workpiece fillet;
  • a1 – the central angle of the arc length of the punch fillet;
  • t – material thickness;
  • E – elastic modulus of material;
  • σs – yield point of the material.

Assuming 3σs/E=A as the simplification coefficient, with values listed in Table 2-27. The calculation formula for the convex die corner radius during the bending of circular section bars is as follows:

The value of A is shown in the table below.

Material ScienceStateAMaterial ScienceStateA
1035(L4) 
8A06(L6)
annealing0.0012QBe2soft0.0064
Cold hardness0.0041hard0.0265
2A11(LY11)soft0.0064QA15hard0.0047
hard0.017508, 10, Q215 0.0032
2A12(LY12)soft0.00720, Q235 0.005
hard0.02630, 35, Q255 0.0068
T1, T2, T3soft0.001950 0.015
hard0.0088T8annealing0.0076
H62soft0.0033cold hardness 
semi-hard0.008ICr18N9Tiannealing0.0044
hard0.015cold hardness0.018
H68soft  0.002665Mnannealing0.0076
hard0.0148cold hardness0.015
QSn6.5-0.1hard0.01560Si2MnAannealing0.125

If the necessary materials are not available above, you can also refer to the table below to find the modulus of elasticity and yield strength of the material, and then substitute them into the formula above for calculation.

Material name Material grade Material StatusUltimate StrengthRate of elongation(%)Yield strength/MPaElastic modulusE/MPa
resisting shear/MPatensile/MPa
Carbon structural steel30Normalized440-580550-7301430822000
55550≥67014390
60550≥70013410208000
65600≥73012420
70600≥76011430210000
Carbon structural steelT7~T12
T7A-T12A
Annealed60075010
T8ACold hardened600-950750-1200
High quality carbon steel10Mn2Annealed320-460400-58022230211000
65M60075018400211000
Alloy structural steel25CrMnSiA
25CrMnSi
Low-temperature annealed400-560500-70018950
30CrMnSiA
30CrMnSi
440-600550-750161450850
High-quality spring steel60Si2Mn
60Si2MnA
65Si2WA
Low-temperature annealed720900101200200000
Cold hardened640-960800-12001014001600
Stainless steel1Cr13Annealed320-380400-17021420210000
2Cr13320-400400~50020450210000
3Cr13400-480500~60018480210000
4Cr13400-480500-50015500210000
1Cr18Ni9
2Cr18Ni9
Heat treated460~520580-61035200200000
Cold-hardened800-880100-110038220200000
1Cr18Ni9TiHeat treated softened430~55054-70040240200000

It is best to establish a commonly used material database and obtain missing physical parameters from suppliers. If the parameters for elastic modulus and yield strength are correct, the bending and rebound of general spring terminals, appearance parts, and profiles are more precise.

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