When designing an internal arc bending die, many people choose to use the same R value as the original product and do not consider 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 reach the 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 200 mm, it may be difficult to accurately predict the amount of springback.
Therefore, a universal formula for springback is presented below, which can be used to calculate the springback value based on numerical input.
In the formula:
- r – part fillet radius (mm):
- r1 – punch radius (mm);
- a – the central angle of the arc length of the fillet of the part;
- a1 – central angle of the arc length of the punch fillet;
- t – material thickness;
- E – elastic modulus of the material;
- σ is – yield limit of the material.
Assuming 3σ is /E=A as the simplification coefficient, with values listed in Table 2-27. The calculation formula for the corner radius of the convex matrix during bending of circular section bars is as follows:
The value of A is shown in the table below.
| Materials science | state | A | Materials science | state | A |
| 1035（L4） 8A06（L6） |
girdling | 0.0012 | QBe2 | soft | 0.0064 |
| Cold hardness | 0.0041 | hard | 0.0265 | ||
| 2A11（LY11） | soft | 0.0064 | QA15 | hard | 0.0047 |
| hard | 0.0175 | 08, 10, Q215 | 0.0032 | ||
| 2A12（LY12） | soft | 0.007 | 20, Q235 | 0.005 | |
| hard | 0.026 | 30, 35, Q255 | 0.0068 | ||
| T1, T2, T3 | soft | 0.0019 | 50 | 0.015 | |
| hard | 0.0088 | T8 | girdling | 0.0076 | |
| H62 | soft | 0.0033 | cold hardness | ||
| semi-hard | 0.008 | ICr18N9Ti | girdling | 0.0044 | |
| hard | 0.015 | cold hardness | 0.018 | ||
| H68 | soft | 0.0026 | 65 minutes | girdling | 0.0076 |
| hard | 0.0148 | cold hardness | 0.015 | ||
| QSn6.5-0.1 | hard | 0.015 | 60Si2MnA | girdling | 0.125 |
If the required 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 above formula for calculation.
| Material name | Material Grade | Condition of the material | Maximum force | Elongation rate（%） | Yield limit/MPa | Modulus of elasticityE/MPa | |
| shear strength/MPa | traction/MPa | ||||||
| Carbon Structural Steel | 30 | Standardized | 440-580 | 550-730 | 14 | 308 | 22,000 |
| 55 | 550 | ≥670 | 14 | 390 | – | ||
| 60 | 550 | ≥700 | 13 | 410 | 208,000 | ||
| 65 | 600 | ≥730 | 12 | 420 | – | ||
| 70 | 600 | ≥760 | 11 | 430 | 210,000 | ||
| Carbon Structural Steel | T7~T12 T7A-T12A |
Annealed | 600 | 750 | 10 | – | – |
| T8A | Cold hardened | 600-950 | 750-1200 | – | – | – | |
| High quality carbon steel | 10Mn2 | Annealed | 320-460 | 400-580 | 22 | 230 | 211,000 |
| 65 million | 600 | 750 | 18 | 400 | 211,000 | ||
| Structural Alloy Steel | 25CrMnSiA 25CrMnSi |
Annealed at low temperature | 400-560 | 500-700 | 18 | 950 | – |
| 30CrMnSiA 30CrMnSi |
440-600 | 550-750 | 16 | 1450850 | – | ||
| High quality spring steel | 60Si2Mn 60Si2MnA 65Si2WA |
Annealed at low temperature | 720 | 900 | 10 | 1200 | 200,000 |
| Cold hardened | 640-960 | 800-1200 | 10 | 14001600 | – | ||
| Stainless steel | 1Ch13 | Annealed | 320-380 | 400-170 | 21 | 420 | 210,000 |
| 2Ch13 | 320-400 | 400~500 | 20 | 450 | 210,000 | ||
| 3Ch13 | 400-480 | 500~600 | 18 | 480 | 210,000 | ||
| 4Ch13 | 400-480 | 500-500 | 15 | 500 | 210,000 | ||
| 1Cr18Ni9 2Cr18Ni9 |
heat treated | 460~520 | 580-610 | 35 | 200 | 200,000 | |
| Cold hardened | 800-880 | 100-1100 | 38 | 220 | 200,000 | ||
| 1Cr18Ni9Ti | Softened with heat treatment | 430~550 | 54-700 | 40 | 240 | 200,000 | |
It is best to establish a database of commonly used materials and obtain the missing physical parameters from suppliers. If the modulus of elasticity and yield strength parameters are correct, the deflection and rebound of general spring terminals, appearance parts and profiles are more accurate.
