Spring-back effect during multi-pass bending of sheet blanks

A significant factor, which leads to the discrepancy of the final sizes of the bent sheet parts to their drawings is the springing of the sheet blank during bending. At the same time, the springing during multi-pass bending is not sufficiently studied. The purpose of the work is to obtain the graphical and mathematical dependencies for descriptions of the resultative spring-back angle of the blanks at the multi-pass bending, taking into account the width of the blank, number of passes, and pre-bending angle at each preliminary pass. The paper describes the basic information about the difference between the spring-back angle for one-pass or multi-pass bending. In the course of the study it is shown that during calculations of forming and preventive prediction of the geometric quality of bending shapes it is necessary to take into account properties of the blank material, as well as the angles of the prebends and the width to thickness ratio of the blank. A methodology of experimental research was developed for determining the spring-back angle during multi-pass bending in three bending dies with 109o, 91o and 72o pass-by-pass reducing angles.


Introduction
Steel sheet products and products from it are the most common product of metallurgical and machine-building enterprises [1][2][3], also, very stringent requirements are imposed of the geometric accuracy of these products [4][5][6][7]. Steel reinforcing cold-formed shapes are common products manufactured by enterprises specializing in the metal forming processes. Initial material for cold-formed shapes is galvanized cold-rolled flat steel with a thickness of 0,65 mm. to 2,0 mm. Issues of the development of a special of cold-formed dising and their production are constantly pay attention because of the effectiveness of their application [8][9][10]. Cold-formed shape is obtained during the blank forming process in the multi-roll roll-profiling mills. However, the bent parts after load relief elastically unbend and change the bending angle, which is characterized by the spring-back effect [11][12][13]. The influence of the strengthening effect on the geometric parameters and the magnitude of the parts springing formed in the die and various roll-systems was considered in works [14,15]. It is also known that the sheet blank is prone to springing at bending on multi-roll rollforming mills [8,15]. The spring-back angle can be determined based on experimental analysis of the measuring experiments [1][2][3][4][5][6][7].
To date, there is no reliable information about the difference of the spring-back angle, which occurs when the flat blank is bending to a certain final angle for one or several passes. Also, the value of the initial blank width is not taken into account, although such oscillations essentially affect the energy parameters of bending. Failure is to not consider that the springing leads to inconsistency of the finite size of the shapes and defect formation between the roller space of the roll-forming mill stands. There are also no mathematical dependences for determining the value of the spring-back angle at passes and at the end of the multi-pass bending, which complicates the performance of the preventive prediction of the quality of cold-formed shapes.

Matherials and Methods
Investigations of bending at the bending of Steel 3 grade (0.14-0.22% C; 0.15-0.3% Si; 0.4-0.65% Mn; ≤ 0.3% Ni; ≤ 0.05% S; ≤ 0.04% P; ~ 97% Fe) blanks were carried out on the crank-press model K116G (Fig. 1). As a working tool, were used bending die of U8 grade tool steel (0.76-0.83% C; 0.17-0.33% Si; 0.17-0.33% Mn; ≤ 0.25%C Ni; ≤ 0.027% S; ≤ 0.03% P; ~ 97% Fe) with heat-treated to hardness HRC 40-44. They were made for different angles of bending: 72°, 91° and 109° (Fig. 2). Radii : (i)for die with a bending angle of 72°: upper die r in = 3 mm, lower die r out = 4,0 mm; (ii)for die with a bending angle of 91°: upper die r in = 4 mm, lower die r out = 5,0 mm; (iii)for die with a bending angle of 109°: upper die r in = 4 mm, lower die r out = 5,0 mm. The lower and the apper dies were fixed in the die block, which was installed on the specified press. Measurement of the shape parameters of the blanks was carried out by an angle-meter and a caliper, which has undergone metrological checking in due time. The length of the blanks were used is L = 60 m (Fig. 3).   The first group of blanks was exposed to one-pass bending. Bending of the blank was carried out in a die at a predetermined bending angle of 72°, 91°, and 109°, and the springback angle Δα = (α / -α) was measured (see Fig. 3).
The second group of blanks with same geometric sizes was subjected to a multi-pass bending (Fig. 4). That is, the blanks were first bent in a die with an angle of 109° and measured the bending angle. Further, bending upper and lower dies were changed, and the preformed bends were doped in a die with a 91° angle and measured the bending angle. Then they again changed the bending lower and apper dies, and the preformed bends were duplicated in a die at an angle of 72°, and measured the bending angle.
The measurements were carried out after each bend, which was carried out separated by passes, according to the developed method. Each experiment included at least five measurements. The processing of these experiments was carried out on the basis of the generally accepted method of dispersion analysis of the factor experiment in accordance with standard. The standard methods based on the positions of probability theory and mathematical statistics are given in the specialized literature, the experimental values of the basic parameters of forming are considered as random variables characterized by the normal distribution law and obtained as a result of measurements of equal accuracy.

Results of Research
After the processing of the experimental information, dependence of the main parameters of the form change, which characterizes change of the spring-back angle during forming in the dies, was developed. The graphic dependences show the change of the spring-back angle -Δα, depending on the width to thickness ratio (B/S) and the relative angle of the blank (β): Examples of experimental graphics are shown in Fig. 5-10.  Analyzing the change of the spring-back angle, it is should be noted its overall growth with the thickness and width of the samples increasing.
As it is established, during deformation of blanks with thickness S = 2 mm, springing occurs more intensively. It should also be noted for the blank with a width B = 60 mm. Bending of the blank S = 1 mm is accompanied by less intensive springing, compared with the blanks S = 1.5 mm, S = 2 mm. It should also be noted for blanks with a width B = 20 mm.

Discussion
Experiments data are shown in Figs. 5-10 were processed in the MS Exсel package using the "Analysis ToolPak" macros and using a linear, logarithmic and exponential regression model. As a result of the data processing of the experiment it was found that the linear model does not give adequate results for any of the cases, because the calculation on it gives a big difference between experiment and calculation.
For the case when only the data of one-pass bending (n = 1) are taken into account, the logarithmic model has been found to be the most adequate and correct: for which the correlation coefficient is equal to 0.77744; coefficient of linear determination is equal to 0,5969; the adapted determination coefficient is 0.5663; standard error is 0.7111. For the case of multi-pass bending (n = 1, 2, 3), the logarithmic model was also found to be the most adequate and correct.
for which the correlation coefficient is 0.8702; the linear determination coefficient is 0.77573; the adapted determination coefficient is 0.7256; standard error is 0.6290. For the case when the data of one-pass and multy-pass bending (n = 1, 2, 3) are taken into account, it is found that the result is the most adequately and correctly describes the exponential model: