As depicted in figure 1, a grooving machine is needed to bend 20×20 square tubes of 1 mm thickness.

The remaining groove thickness depends on the size of the bend of the rectangular arch and the thickness of the sheet (t). In general, if the sheet thickness is no more than 1 mm or equal to it, a=0.4 mm. If the thickness exceeds 1 mm, a=t/2.

L = 2 × (L1 + L2) = 2x ((side length-1xa-0.2) + (side length-2xa))= 2x ((20-1 × 0.4-0.2) + (20-2 × 0.4)) = 77.2 mm.

It should be noted that one side of L1 is cut off, regardless of the thickness of the sheet, all should be minus 0.2 mm.

The following is a comparison of the calculation of bending expansion in groove bends and without groove bends.

The entire length calculation for groove bends is as the following:

L = 20-0.4 + 20-2X0.4 + 20-0.4 = 58.4 mm.

Here is the calculation formula of the entire length of bends without grooving:

L = (20-1xt + k) + (20-2xt + 2xk) + (20-1xt + 1xk) = (20-1 + 0.2) + (20-2 + 2 × 0.2) + (20-1 + 0.2) = 56.8 mm

T is the sheet thickness, k is the coefficient, the size of which depends on the sheet thickness, mostly within 0.2-0.25 mm. The thicker the sheet, the larger the k. In the example offered, 0.2 is selected.

Next, the developed bending length is calculated by combining the Z-shaped groove and without the groove.

For sheets with a thickness of 2 mm, the remaining thickness of the groove (a) is t / 2 = 1 mm (if the client requires a smaller arch, the value of a should be less than 1 mm). Thus, the unfolded length will be L = 15-1 + 20-2×1 + 15-1 = 46 mm.

For plates 2 mm thick without groove bending, the coefficient k is 0.25, so the length in the expanded state is:

L = (15-2 + 0.25) + (20-2 × 2 + 2 × 0.25) + (15-2 + 0.25) = 43 mm.

The following scheme depicts the method of calculating multi-bend work pieces with and without grooving.

For sheets with a thickness of 3 mm, if a client requires a smaller rectangular arch, the remaining sheet thickness is 0.5 mm. Thus, the extension length L = (40-0.5) + (30-2 × 0.5) + (30-2 × 0.5) + (10-0.5) = 107 mm.

For sheets 3 mm thick, the coefficient k is chosen equal to 0.25, so the extension length is L = (40-3 + 0.25) + (30-6 + 2 × 0.25) + (30-6 + 2 × 0.25) + (10-3 + 0.25) = 93.5 mm.

The following describes a method for expansion calculation of reverse bending after a groove.

For reverse bending after a groove as depicted in figure 5, the expansion length calculation will be L = (20-2 + 0.2) + (30-2 × 2 + 2 × 0.2) + (20-2 + 0.2) = 62.8 mm.