1. Unfolding Calculation Principle
During the bending process, the outer layer of the sheet metal is subjected to tensile stress, while the inner layer experiences compressive stress. Theoretically, there is a neutral layer between the inner and outer layers that is neither under tension nor compression. This neutral layer is a hypothetical layer assumed to remain unchanged in length during the bending process, serving as the reference for calculating the length of the bent part. The position of the neutral layer depends on the degree of deformation. When the bending radius is larger and the bending angle is smaller, the deformation is minimal, and the neutral layer is closer to the center of the sheet metal thickness. As the bending radius decreases and the bending angle increases, the degree of deformation increases, and the neutral layer gradually moves towards the inner side of the bending center. The distance from the neutral layer to the inner side of the sheet metal is denoted as A.
2. Determination of Bending Methods
There are two methods for bending: single-stroke punch bending and bending with a bending machine. In single-stroke punch bending, the method and accuracy are achieved through the use of specific dies. Therefore, as long as qualified dies are produced, satisfactory bent products can be manufactured. On the other hand, when using a bending machine, not only the appropriate bending die needs to be selected, but also the bending parameters must be adjusted. Therefore, when using a bending machine for bending, the bending method of the machine must be considered when calculating the unfolding dimensions.
1. Single-bend method: This method is accomplished using general-purpose bending dies. It includes bending right angles, obtuse angles, and acute angles.
2. Double-bend method - Coining: This bending method requires special dedicated dies and is more challenging than general bending.
3. Hemming: This bending method also requires special dies to complete.
4. Large R-radius bending: For this type of bending, if the R-value falls within a certain range, it can be achieved using dedicated R-dies. However, if the R-value is too large, it requires multiple pressing with smaller R-dies to achieve the desired shape.
The unfolding calculation for these four bending methods is different. The choice of bending method depends on the bending dimensions of the part. The V-groove width of the general-purpose bending die matched with the bending machine is typically 5-6 times the applicable plate thickness. If the single-bend method is used, the width of the V-groove (W1) and the distance from one side of the V-groove to the outer edge of the die (L1) must be taken into account.
The empirical value of the bending height (H) depends on the shape of the product and can be categorized into the following three types (using 90 degrees as an example, similar to obtuse angles and acute angles):
1. Simple 90-degree single-sided bending.
1. 90-Degree Bending (General Bending):
The length of the unfolding is calculated as: L = LL + LS - 2t + coefficient a.
The empirical values for coefficient a are shown in the table below:
2. Hemming:
Hemming is a bending shape where two layers overlap, usually used for reinforcement purposes. Hemming is rarely seen on plates thicker than 2.0mm as it requires special bending dies and multiple steps to form. The calculation formula for the unfolding length of hemming bending is:
3. Flanging:
1) Inclined Flanging:
In this type of flanging, the H value is usually small. The calculation formula for the unfolding length is:
L = A + B + C + 0.2 (Note: A, B, C = internal dimensions, 0.2 = compensation value).
2) Right-angle Flanging:
The flanging edge is vertical, and the C value is generally larger. The calculation formula for the unfolding length is:
L = A + B + C - 4T + 2a + 0.5 (Note: A, B = external dimensions, C = height including two layers of plate thickness, a = coefficient for 90-degree bending, 0.5 = compensation value).
3) Parallel Flanging:
The maximum height of the flanging is H = 2t. The calculation formula for the unfolding length is:
L = A + B + H + 0.2 (Note: A, B = internal dimensions; H = flanging height; 0.2 = compensation value).
Since the height of the flanging mainly depends on the adjustment of the flanging die's adjustment pieces, and each operator's experience may vary, sometimes there may be cases where the overall unfolding size is too large or too small even if the height meets the requirements. In such cases, adjustments should be made based on the actual deviations.
4. Sharp Angle Bending:
The empirical formula is an inner diameter algorithm, where the inner diameter refers to the distance from the imaginary intersection point on the inner side of the bending edge to the other end. The calculation formula for the unfolding coefficient is as follows: K = 0.4txδ/90° (t < 2.5). However, when t ≥ 2.5, the following formula should be used: K = 0.5txδ/90° (t ≥ 2.5). Therefore, the unfolding calculation formula is: L = L1 + L2 + K (Note: L = unfolding length, L1, L2 = inner diameter dimensions, K = unfolding coefficient).
5. Obtuse Angle Bending:
The external dimension b is actually equal to the internal dimension a plus a parallel distance l from the inner corner vertex to the outer vertex.
According to trigonometry, the calculation formula for l is: l = tθ/2xt. Therefore, the external diameter is: b = a + l. The calculation formula for the unfolding coefficient K is as follows: Inner diameter: K = θ/90°x0.4t (t < 2.5), Outer diameter: K = δ/90°x0.4t (t < 2.5). However, when t ≥ 2.5, the following formulas should be used: Inner diameter K = θ/90°x0.5t (t ≥ 2.5), Outer diameter K = δ/90°x0.5t (t ≥ 2.5).
6. Arc R Bending:
For the three shapes of R bending, the calculation formula for the unfolding coefficient K is as follows: K = (2R·tanθ/2) - [лθ·(2R-t)/360°] (Note: R = bending outer diameter (outer radius), θ = outer angle (180° - bending angle), л = pi (approximately 3.14), t = plate thickness).
When θ = 90°, tanθ/2 = l, so the above formula can be simplified as follows: K = 2R - л(2R-t)/4. After obtaining the unfolding coefficient K, the calculation formula for the unfolding length L of the arc bending is: L = L1 + L2 + (L3 + L4 + ...) - K (Note: L1, L2, L3, L4 = outer diameter (distance to the imaginary intersection point on the outer side, the distance from the tangent point to the intersection point can be calculated using the law of triangles)).
There is a type of U-shaped bending within the R bending, which can be seen as a combination of two 90° R bendings. Therefore, the calculation formula for the unfolding length L of U-shaped bending is: L = L1 + L2 - 2K (Note: The calculation formula for R bending is only applicable to iron plates).
During the bending process, the outer layer of the sheet metal is subjected to tensile stress, while the inner layer experiences compressive stress. Theoretically, there is a neutral layer between the inner and outer layers that is neither under tension nor compression. This neutral layer is a hypothetical layer assumed to remain unchanged in length during the bending process, serving as the reference for calculating the length of the bent part. The position of the neutral layer depends on the degree of deformation. When the bending radius is larger and the bending angle is smaller, the deformation is minimal, and the neutral layer is closer to the center of the sheet metal thickness. As the bending radius decreases and the bending angle increases, the degree of deformation increases, and the neutral layer gradually moves towards the inner side of the bending center. The distance from the neutral layer to the inner side of the sheet metal is denoted as A.
2. Determination of Bending Methods
There are two methods for bending: single-stroke punch bending and bending with a bending machine. In single-stroke punch bending, the method and accuracy are achieved through the use of specific dies. Therefore, as long as qualified dies are produced, satisfactory bent products can be manufactured. On the other hand, when using a bending machine, not only the appropriate bending die needs to be selected, but also the bending parameters must be adjusted. Therefore, when using a bending machine for bending, the bending method of the machine must be considered when calculating the unfolding dimensions.
1. Single-bend method: This method is accomplished using general-purpose bending dies. It includes bending right angles, obtuse angles, and acute angles.
2. Double-bend method - Coining: This bending method requires special dedicated dies and is more challenging than general bending.
3. Hemming: This bending method also requires special dies to complete.
4. Large R-radius bending: For this type of bending, if the R-value falls within a certain range, it can be achieved using dedicated R-dies. However, if the R-value is too large, it requires multiple pressing with smaller R-dies to achieve the desired shape.
The unfolding calculation for these four bending methods is different. The choice of bending method depends on the bending dimensions of the part. The V-groove width of the general-purpose bending die matched with the bending machine is typically 5-6 times the applicable plate thickness. If the single-bend method is used, the width of the V-groove (W1) and the distance from one side of the V-groove to the outer edge of the die (L1) must be taken into account.
The empirical value of the bending height (H) depends on the shape of the product and can be categorized into the following three types (using 90 degrees as an example, similar to obtuse angles and acute angles):
1. Simple 90-degree single-sided bending.
1. 90-Degree Bending (General Bending):
The length of the unfolding is calculated as: L = LL + LS - 2t + coefficient a.
The empirical values for coefficient a are shown in the table below:
2. Hemming:
Hemming is a bending shape where two layers overlap, usually used for reinforcement purposes. Hemming is rarely seen on plates thicker than 2.0mm as it requires special bending dies and multiple steps to form. The calculation formula for the unfolding length of hemming bending is:
3. Flanging:
1) Inclined Flanging:
In this type of flanging, the H value is usually small. The calculation formula for the unfolding length is:
L = A + B + C + 0.2 (Note: A, B, C = internal dimensions, 0.2 = compensation value).
2) Right-angle Flanging:
The flanging edge is vertical, and the C value is generally larger. The calculation formula for the unfolding length is:
L = A + B + C - 4T + 2a + 0.5 (Note: A, B = external dimensions, C = height including two layers of plate thickness, a = coefficient for 90-degree bending, 0.5 = compensation value).
3) Parallel Flanging:
The maximum height of the flanging is H = 2t. The calculation formula for the unfolding length is:
L = A + B + H + 0.2 (Note: A, B = internal dimensions; H = flanging height; 0.2 = compensation value).
Since the height of the flanging mainly depends on the adjustment of the flanging die's adjustment pieces, and each operator's experience may vary, sometimes there may be cases where the overall unfolding size is too large or too small even if the height meets the requirements. In such cases, adjustments should be made based on the actual deviations.
4. Sharp Angle Bending:
The empirical formula is an inner diameter algorithm, where the inner diameter refers to the distance from the imaginary intersection point on the inner side of the bending edge to the other end. The calculation formula for the unfolding coefficient is as follows: K = 0.4txδ/90° (t < 2.5). However, when t ≥ 2.5, the following formula should be used: K = 0.5txδ/90° (t ≥ 2.5). Therefore, the unfolding calculation formula is: L = L1 + L2 + K (Note: L = unfolding length, L1, L2 = inner diameter dimensions, K = unfolding coefficient).
5. Obtuse Angle Bending:
The external dimension b is actually equal to the internal dimension a plus a parallel distance l from the inner corner vertex to the outer vertex.
According to trigonometry, the calculation formula for l is: l = tθ/2xt. Therefore, the external diameter is: b = a + l. The calculation formula for the unfolding coefficient K is as follows: Inner diameter: K = θ/90°x0.4t (t < 2.5), Outer diameter: K = δ/90°x0.4t (t < 2.5). However, when t ≥ 2.5, the following formulas should be used: Inner diameter K = θ/90°x0.5t (t ≥ 2.5), Outer diameter K = δ/90°x0.5t (t ≥ 2.5).
6. Arc R Bending:
For the three shapes of R bending, the calculation formula for the unfolding coefficient K is as follows: K = (2R·tanθ/2) - [лθ·(2R-t)/360°] (Note: R = bending outer diameter (outer radius), θ = outer angle (180° - bending angle), л = pi (approximately 3.14), t = plate thickness).
When θ = 90°, tanθ/2 = l, so the above formula can be simplified as follows: K = 2R - л(2R-t)/4. After obtaining the unfolding coefficient K, the calculation formula for the unfolding length L of the arc bending is: L = L1 + L2 + (L3 + L4 + ...) - K (Note: L1, L2, L3, L4 = outer diameter (distance to the imaginary intersection point on the outer side, the distance from the tangent point to the intersection point can be calculated using the law of triangles)).
There is a type of U-shaped bending within the R bending, which can be seen as a combination of two 90° R bendings. Therefore, the calculation formula for the unfolding length L of U-shaped bending is: L = L1 + L2 - 2K (Note: The calculation formula for R bending is only applicable to iron plates).
