Influence of the electromagnetic field pressure on the free bending of the straight side

Bending is the operation of forming or changing the angles between the parts of the workpiece or giving it a curved shape and in the mean time is the most difficult and timeconsuming operation of the technological process of manufacturing parts from profiles. Aircraft bending parts of the following nomenclature are obtained as profiles: frames, ribs, stringers, linings and brackets. Profile parts are responsible for their intended purpose; therefore, high requirements are placed on the accuracy of their dimensions and the preservation of the crosssection shape. The process of bending profiles has its own characteristics, which are due to the shape of the profile section; the first feature is the presence of vertical shelves, significantly loaded and deformed due to large distances from the neutral axis of the bent section, the second is the mismatch of the bending plane with the main axes of inertia of the section, which causes oblique bending and twisting of the part. When analyzing the bending process of extruded profiles, it should be borne in mind that the neutral layer of the workpiece coincides with the line that passes through the centers of gravity of the sections. When using the hypothesis of planar sections of the plot of deformations and stresses in the stretched and compressed zones do not have a mutually reflected form. It is very important how the profile is oriented in the bending plane. Different orientation of the profile, even the simplest cross-section (for example, angular), gives a qualitatively different picture of the deformed state.


Introduction
With an arbitrary load distribution, the straight-side of the part has a deviation from the shape of the specified profile, which is expressed in non-lying. Therefore, it is necessary to search for the optimal distribution of the pressure of the pulsed-magnetic field (PMF), at which the forming side will be rectilinear during deformation that will allow us to get accurate details [1][2][3]. Authors recommend a new bending method by using a free straight bending without a die and different from bending traditional methods with determining the bending radius   5 . The equation of the dynamic equilibrium of the workpiece elements under large deformations has the form: In the flat case, in equations (1) According to the thickness, the board of the flat blank is divided into discrete layers that can perceive normal stresses [2][3][4]. It is assumed that these layers are separated by layers of material of infinitely small thickness, in which there are no normal stresses, which have infinite shear stiffness [5,6]. The time process is also divided into intervals

Mathematical calculation for free bending of the straight-side
System (2) is supplemented by equations for the relationship between displacements and deformations, deformations with stresses, stresses with forces and moments, as well as equations for the initial and boundary conditions. For the time step increments 1 + j we do have the next equations [8,9]: . sin sin cos cos , 1 . ,..., 1 , cos cos sin sin

Impact contact of a stamped sheet metal part with a free shaping
The production of sheet metal parts requires the development of efficient technological processes that can significantly improve both operational performance and efficiency in production. In many ways, modern requirements are met by processes using high-speed loading when forming parts. One of these methods is magnetic-pulsed pressure, which allows high-energy of PMF to be applied to parts made of electrically conductive materials. The duration of a stamped side edge contact with a free shaping is significantly affected by dynamic yield strength w Y 0 of the workpiece material, upon impact at constant velocity [6]. If w Y 0 is increased indefinitely, then for a constant impact speed can achieve such a value of w Y 0 at which a plastic compression wave does not arise in the workpiece. With a decrease of w Y 0 , the acoustic wave appears and if its intensity becomes higher, the dynamic yield strength of the workpiece material is getting lower. The electromagnetic coil is decisive for electromagnetic forming and must be designed to be positioned under the metal sheet as shown in figure 3 to generate electromagnetic forces equally.  Figure 3. Grid scheme of the straight side free bend on a sheet metal by electromagnetic field pressure. 1single turn coil; 2blank; 3hard boundary plate.

Results of the numerical simulation analysis
Plastic strain during the free straight-side bending process showed that the greatest deformation is concentrated in the bending zone, where also a significant thinning of the part wall occurs (figure 4).

Results and Analysis
Thus, the conducted research allows us to draw the following conclusions: