The bending test of t-2 red copper plate was carried out with u-shaped bending die, and the springback of bending angle after unloading was measured. The results showed that the springback of bending angle decreased gradually with the increase of plate thickness in the range of 0.15ー2.0 mm. In order to describe the relationship between the springback of Bending Angle and the thickness of the plate accurately, the functional relationship between the springback of bending angle and the thickness of the plate was obtained by least squares fitting and Joseph-Louis Lagrange interpolation, respectively, the accuracy of the two methods is verified by a set of measured values of the springback of the bending angle. The results show that the calculated values of the function relations obtained by the least squares method have smaller root mean square error, it can be used to predict the springback of the bending angle of the T2 Red Copper Plate, and it is helpful to analyze the bending deformation of the T2 red copper plate and to work out the bending process reasonably. Keywords: T2 Copper Plate; u-bend; Bending Angle Rebound; least squares fitting; Joseph-Louis Lagrange interpolation

1. Bending is a typical sheet metal forming method, which is one of the most widely used and mature forming methods in the world at present, many structural parts are made of beams, plates, tubes and profiles by bending. The material is accompanied with elastic deformation during plastic bending. When the bending part is unloaded, the plastic deformation is retained and the elastic deformation is recovered. The result is that the bending angle and the bending radius of the bending part are not consistent with the die size, this phenomenon is called bending rebound. Bending springback is different from common springback, because the plate produces bending deformation in the process of loading, the stress and strain of its inner layer and outer layer are opposite, so the springback direction of inner and outer layer is opposite when unloading, and the springback of bending parts is increased. SPRINGBACK is one of the most common factors affecting the quality of bending process, and the springback control is also one of the technical difficulties in bending process. U-BENDING is a common form of bending. The u-bending die can be used to bend the sheet into a U-SHAPE. As shown in Fig. 1, the shape of the sheet after unloading deviates from the U-SHAPE because of the springback, that is, the springback of the bending angle is produced.

2. Test materials and methods 2.1 the clearance between the Bending Punch and the female die for the test materials is 2 mm, in order to ensure that the specimen is subjected to pure bending deformation in the bending die, in the range of 0.15ー2.0 mm thickness, 7 kinds of T2 copper bending specimens were selected. The specimens are 75 mm in length, 35 mm in width and 0.15 mm, 0.20 mm, 0.40 mm, 0.60 mm, 1.0 mm, 1.5 mm and 2.0 mm in thickness, respectively. Its chemical composition is shown in Table 1. The test equipment is YL41-40T single-arm hydraulic press with u-shaped bending die, in which the bending punch is installed on the press head and the bending die is fixed on the worktable.

2.2 in the test scheme, seven specimens are bent in turn on a u-shaped bending die, the pressure head is lowered by operating a hydraulic press, and the bending deformation begins after the bending punch contacts the specimen, when the punch presses the sample completely into the die and the bending ends because the resistance stops dropping, the hydraulic press is operated to make the indenter go back and take out the bending sample. 3. The test results and analysis were used to measure the springback of Bending Angle of 7 samples. According to the measured values, the changing trend of springback was plotted as shown in Fig. 2.

As can be seen from Fig. 2, the springback of the bending angle of the T2 copper sample decreases as the thickness of the plate increases, the functional relationship between the two can be worked out mathematically, usually by least squares fitting and Joseph-Louis Lagrange interpolation. First of all, the least squares fitting is used, and the number of fitting polynomials is given before the fitting. When the number of fitting polynomials is 4, the fitting polynomials with the highest precision can be obtained, that is: = 96.3499 t 4-472.9223 t 3 + 818.7734 t 2-606.2848 t + 189.4369(1) and then using Joseph-Louis Lagrange interpolation to find the relationship between the thickness of the plate and the springback of the bending angle is a six-degree polynomial, nAMELY: = 636.409 T 6-3843.31 t 5 + 9039.32 t 4-10587.8 t 3 + 6551.78 t 2-2093.39 t + 319.036(2) in the formula, the thickness of t plate and the springback of the bending angle are mm fo fo, the springback of bending angle of three T2 copper plates with different thickness and length of 7535 mm was measured, and then the springback of bending angle of the three copper plates was calculated by least squares fitting and Joseph-Louis Lagrange interpolation respectively, the measured and calculated values of the springback of the bending angle are shown in table 2. The RMS error between the calculated values and the measured values of the two methods is then calculated. The RMS error of the least squares is calculated to be 4.1681, and the RMS error of the Joseph-Louis Lagrange interpolation is calculated to be 5.4775, is greater than the root mean square error of the least squares.

After the above analysis, it is determined that the fitting polynomial of the least squares is a function of the springback of the bending angle and the thickness of the plate. This formula can be used to predict the springback of the bending angle of a certain plate, which is useful for analyzing the springback of the t-2 red copper plate u-shaped bending parts and establishing the bending process reasonably. 4. Conclusion (1) in the range of 0.15ー2.0 mm of plate thickness, the springback of bending angle decreases with the increase of plate thickness. (2) the functional relationship between the plate thickness and the springback of the bending angle can be obtained by both least squares fitting and Joseph-Louis Lagrange interpolation. (3) the calculated value of the least squares fitting formula has smaller root mean square error, which can be used to predict the springback of the bending angle of T2 copper plate, it can be used to analyze the bending deformation of T2 red copper plate and to work out a reasonable bending process. 

Source: Die Making