Key takeaways:1. The precision of sheet metal fabrication hinges on the accurate calculation of the unfolding coefficient, which is determined by the neutral layer's position—affected by factors such as bending radius and plate thickness—and is critical for maintaining product dimensional integrity after bending. 2. With the advent of 3D software, the process of calculating sheet metal unfolding has become more standardized and efficient, allowing for more accurate simulations that take into account various material thicknesses, angles, and radii, ultimately leading to the development of empirical K-factor values that guide the unfolding process. 3. The sheet metal unfolding process varies depending on the specific bending scenario, with different formulas and considerations for compensation values based on the bending radius, angle, and material thickness, ensuring that the final unfolded length accommodates the physical changes that occur during bending.

The first step in the sheet metal fabrication process is the unfoldment of the geometries and the coherent body. The accuracy and correctness of the sample unfoldment directly impacts the quality of the final part.

In the past, due to the limitations of calculation tools, people would use the projection method to enlarge the sample on a plane with a 1:1 ratio and measure the real length of the required plan line.

However, this method is complicated and inefficient, and cannot meet the current demands of production.

With the advancements in calculation tools, such as electronic calculators and widespread use of computers, sheet metal unfolding can now be performed using calculation methods.

To standardize the calculation method of sheet metal unfolding coefficient by technicians, minimize dimensional deviations of products after bending, and facilitate self-inspection by workshop personnel and re-inspection by quality inspectors, there is a unified standard and basis for the unfolding coefficient.

As a result, the calculation standard for the sheet metal unfolding coefficient has become increasingly standardized.

**Neutral Layer Unfolding Method**

In the bending process, the outer layer undergoes tensile stress, while the inner layer experiences compressive stress. The transition layer between tensile and compressive stress is referred to as the neutral layer. The length of the neutral layer during bending remains the same as before bending, making it the benchmark for determining the unfolded length of the bent part.

The location of the neutral layer is dependent on the degree of deformation.

The position of the neutral layer is not only related to the bending radius, plate thickness, inward shift coefficient, etc., but also to factors such as processing method, sheet metal shape, and size.

Therefore, the position of the neutral layer can only be approximately determined, and in practical applications, approximate values are generally used for calculation.

The calculation formula for the length dimension L of the neutral layer is:

*L=L1+L2+Π(180°-β)(r+tk)/180°*

Among them,

- L1, L2 – Length of straight sections (mm);
- β – Bending angle (°);
- r – Inner radius of bent plate (mm);
- t – Thickness of steel plate (mm);
- k – Neutral layer coefficient.

By using 3D software to perform simulations and calculations of various thicknesses, angles, and radii, along with on-site fabrication practices, we have compiled a set of K-factor values. Please refer to Table 1 for the specific values.

Table 1: Neutral Layer Coefficient K-Values

r/t | ≤05 | 0.6 | 0.8 | 1 | 1.2 | 1.3 | 1.5 | 2 | 2.5 | 3.0 | 4.0 | 5.0 | 6.0 | ≥8 |

k | 026 | 0.28 | 0.30 | 0.32 | 0.33 | 0.34 | 0.36 | 0.38 | 0.39 | 0.4 | 0.42 | 0.44 | 0.46 | 0.5 |

**Rapid Unfolding Calculation for 90° Bends**

The unfolding diagram for a 90° bend is shown in Figure 9. In recent years, we have used 3D software like CATIA and SOLIDWORKS for sheet metal modeling to calculate unfolding dimensions.

Through repeated verification, it has been observed that when the cold bending angle of flat steel products is 90°, the formula for calculating the unfolded length L is:

*L = L1 + L2 – A*

Where,

- L1, L2 – Lengths of the straight segments (mm);
- A – Compensation value (mm), i.e., the deduction value for one bend, see Table 2.

Table 2 90 ° Bending Parameters Table

Thickness t/mm | Beding radius r/mm | |||||||||||

1 | 1.2 | 16 | 2 | 25 | 3 | 4 | 5 | 6 | 8 | 10 | 12 | |

Compensation value A mm | ||||||||||||

1 | -1.92 | -1.97 | -2.10 | -2.23 | -2.41 | -2.59 | -2.97 | -3.36 | -3.79 | -4.65 | -5.51 | -6.37 |

1.5 | -2.90 | -3.02 | -3.18 | -3.34 | -3.70 | -4.07 | -4.45 | -5.26 | -6.11 | -6.97 | ||

2 | -3.84 | -3.98 | -4.13 | -4.46 | -4.81 | -5.18 | -5.94 | -6.72 | -7.58 | |||

2.5 | -4.80 | -4.93 | -5.24 | -5.57 | -5.93 | -6.66 | -7.42 | -8.21 | ||||

3 | -5.76 | 6.04 | -6.35 | -6.69 | -7.40 | -8.14 | -8.91 | |||||

4 | -7.7 | -7.95 | -8.26 | -8.92 | -9.62 | -10.36 | ||||||

5 | -9.6 | -9.87 | -10.48 | -11.15 | -11.85 | |||||||

6 | -11.5 | -12.08 | -12.71 | -13.38 | ||||||||

8 | -15.4 | -15.9 | -16.51 | |||||||||

10 | -19.2 | -19.73 | ||||||||||

12 | 23.01 |

When the bending radius is large and the bending angle is small, the degree of deformation is low and the neutral layer is close to the center of the sheet thickness.

However, when the bending radius (R) becomes smaller and the bending angle (θ) increases, the degree of deformation also increases and the neutral layer moves towards the inner side of the bending center. The distance from the neutral layer to the inner side of the sheet is denoted by λ, and the material thickness is denoted by T.

**The basic formula for calculating the unfold length: **

Unfolding length = inner size of material + inner size of material + amount of compensation.

You can also use the following calculator to calculate sheet metal unfold length:

The following describes the unfolding algorithms of various bend features one by one.

**General bending I**

R = 0mm, θ = 90° (Note: When R ≤ 1.0mm, it is treated as R = 0mm).

**L = A + B + K**

- When 0 < T ≤ 3mm, K = 0
- When 0.3mm < T ≤ 5T, K = 0.4T

In actual production, the bending upper die may wear an R angle, or there may be an R angle less than 1mm, or the choice of the lower die‘s V slot may be large, among other reasons, resulting in a small bending coefficient. As a result, the bending coefficient of each material plate thickness is presented in Table 1 based on actual empirical values.

Fig. 1 Schematic diagram of general bending I

**General bending II**

R ≠ 0mm and θ = 90°

**L = A + B + K (K is the arc length of neutral layer )**

- When 0 < T ≤ 1.6mm, λ = 0.5T
- When 0 < T ≤ 1.6mm, λ = 0.5T
- When T > 1.6mm, λ = 0.4T

Fig. 2 Schematic diagram of general bending II

**General bending III**

R = 0mm, θ ≠ 90°

**L = A + B + K’**

- When T ≤ 0.3mm, K’ = 0
- When T > 0.3mm, K’ = (θ/90° )×K

Note: K is the compensation amount at 90°.

**General bending I****V**

R ≠ 0mm, θ ≠ 90°

**L = A + B + K**

(K takes the neutral layer arc length)

Fig. 4 General bending IV bending diagram

The Unfolding Method is equivalent to the Parallel Straight-Edge Z-Fold Method, and the measurement for height is demonstrated in Figure 6.

The angle θ is considered a 90° unfolding.

For 0 < T ≤ 1.6mm, λ equals 0.5T.

When T is greater than 1.6mm, λ equals 0.4T.

**Z-****bend**

Z-Fold, also referred to as Offset Bending, is differentiated into Straight-Edge Offset Bending and Bevel-Edge Offset Bending based on the forming angle, and the method of processing is determined by the offset height.

When the offset height, h, is less than 3.5 times the thickness of the material, offset dies or changeable dies are used for forming.

If the offset height exceeds 3.5 times the material thickness, normal positive and negative forming is employed.

When the length of the beveled edge is less than 3.5 times the material thickness, offset dies or changeable dies are used for forming.

If the length of the beveled edge exceeds 3.5 times the material thickness, normal one-positive and one-negative folding is applied.

**Z-fold 1 (straight edge ****offset****)**

(1) When H < 3.5T, only then can be processed by offset bending.

**L = A + B + H**

(if H ≤ T, then compensate 0.2mm)

Fig. 5 Schematic diagram of straight edge offset

(2) Non-parallel straight-edge offset

The expansion method is the same as the parallel straight-edge Z-fold method, and the height value is shown in Figure 6.

Angle θ can be considered as 90 ° unfold.

Fig. 6 Schematic diagram of non-parallel straight edge offset

(3) Straight edge offset – the transition segment is tangent to two arcs

When the Straight-Edge Offset is unfolded at the tangent point of two circular arcs, a vertical line is created at the tangent point of the two circular arcs on the outer surface of the substrate. The material is then offset by one material thickness inward, as depicted in Figure 7, for processing and unfolded using the Z-Fold 1 (Straight-Edge Offset) method.

Fig. 7 Straight edge offset diagram – transition segment is tangent to two circular arcs

**Z-fold 2 (bevel ****offset****)**

When H < 2T, the unfolding algorithm is as follows according to the offset processing.

- When θ ≤ 70°, L = A + B + C + 0.2
- When θ > 70°, unfold according to Z-fold 1 (straight edge offset)

Fig. 8 Diagram of beveled edge offset

**Reverse folding and flattening**

**L = A + B – K**

(1) When flattening, consider pressing the line prior to bending based on the actual conditions.

The line pressing location is in the center of the bending deformation area.

Fig. 9 Schematic diagram of reverse folding and flattening

The Reverse Folding and Flattening processes are usually performed in two steps: first, the material is bent to 30° using the insertion die, followed by flattening.

Therefore, when creating the bending line on the expanded drawing, it is essential to illustrate the bending line based on the 150° bending, as demonstrated in Figure 9.

Table 1 bending coefficient of plates with different thicknesses under different bending angles

Angle | Thickness/mm | ||||
---|---|---|---|---|---|

1 | 1.2 | 1.5 | 1.8 | 2.5 | |

45° | 5.3 | 6.3 | 7.8 | 9.5 | 13 |

50° | 4.5 | 5.4 | 6.8 | 8.1 | 11.25 |

55° | 4 | 4.7 | 5.8 | 7.05 | 9.75 |

60° | 3.4 | 4.1 | 5.1 | 6.15 | 8.5 |

65° | 3 | 3.6 | 4.5 | 5.4 | 7.5 |

70° | 2.65 | 3.2 | 4 | 4.75 | 6.6 |

75° | 2.35 | 2.8 | 3.5 | 4.25 | 5.9 |

80° | 2.1 | 2.5 | 3.1 | 3.75 | 5.25 |

85° | 1.9 | 2.25 | 2.8 | 3.35 | 4.65 |

90° | 1.7 | 2 | 2.5 | 3 | 4.15 |

95° | 1.5 | 1.8 | 2.2 | 2.7 | 3.75 |

100° | 1.35 | 1.6 | 2 | 2.4 | 3.35 |

105° | 1.2 | 1.4 | 1.75 | 2.15 | 3 |

110° | 1.1 | 1.3 | 1.6 | 2 | 2.65 |

115° | 1 | 1.25 | 1.4 | 1.7 | 2.35 |

120° | 0.85 | 1 | 1.25 | 1.5 | 2.1 |

125° | 0.75 | 0.9 | 1.1 | 1.35 | 1.85 |

130° | 0.65 | 0.8 | 1 | 1.18 | 1.65 |

135° | 0.55 | 0.7 | 0.85 | 1.05 | 1.45 |

140° | 0.5 | 0.6 | 0.75 | 0.9 | 1.25 |

145° | 0.43 | 0.5 | 0.65 | 0.77 | 1.05 |

150° | 0.35 | 0.43 | 0.55 | 0.65 | 0.9 |

155° | 0.3 | 0.35 | 0.45 | 0.53 | 0.75 |

160° | 0.23 | 0.27 | 0.35 | 0.4 | 0.6 |

165° | 0.17 | 0.2 | 0.25 | 0.3 | 0.45 |

**N****–****fold**

The N-fold processing method involves both reshaping and flattening, and the algorithm for unfolding is:

**L = ****A + B + K**

(K takes the neutral layer arc length).

λ = 0.5T

Fig.10 N-fold diagram

**Arc (including straight edge on one side)**

(1) The arc expansion is directly K, and the arc length of the neutral layer is taken. λ＝ 0.5T

(2) Expansion with the straight edge on one side.

**L = ****A**** + K**

(k is the arc length of the neutral layer)

Fig. 11 Schematic diagram of arc bending

**Conclusion**

Sheet metal parts are utilized extensively in the electromechanical, light industry, and automotive industries.

The unfolded form of sheet metal parts is the primary determining factor for blank size, which in turn affects the size and shape of the blank.

However, traditional methods of unfolding sheet metal parts have become increasingly inadequate in meeting modern design needs due to their long cycles, low efficiency, and poor quality.

To address these shortcomings, the use of advanced CAD systems has become increasingly prevalent in recent years.

These specialized sheet metal part design systems boast robust functionality and can greatly reduce the amount of time and effort required for the preliminary design and deployment of sheet metal parts.

Boris.WHi

Formula for General bending II is missing :)

ShaneThe formula is L = A + B + K (K is the arc length of neutral layer ), updated.