Plastic Folding of Bar Stocks of Round and Barrel-Shaped Sections

. Research has been carried out on the process of plastic folding of bar stocks with round and barrel-shaped cross-sections. The dependence of the movement of the movable tool on the bending angle has been established. The force parameters of the deformation process and the stress-strain state in the bending workpiece are determined based on the results of finite element modeling of plastic bending.


Introduction
Rod products formed using plastic bending operations are widely used in various industries, railway transport, construction, etc. In particular, spring clips are widely used in modern railway track structures [1,2], bent reinforcing wire in the form of clamps is used in reinforced concrete structures [3], and bent welded links are used in lifting devices for various purposes [4].
Either standard presses with special technological equipment in the form of bending dies or special bending machines and mechanisms are used to implement the bending processes.
Plastic bending is a shaping operation in which there is a change in the curvature of the bar axis of the workpiece [5,6]. In the process of bending, only a part of the workpiece in the form of a deformation zone is subject to plastic deformation. The rest of the bar of the workpiece either does not deform or deform elastically. Uneven stresses and deformations occur along the section of the deformation zone. Linear deformation along the workpiece axis is practically absent.

Materials and Methods
Folding finds wide application among the variety of plastic bending methods [7][8][9][10]. In fig. 1 shows a diagram of plastic folding of a bar stock. The original workpiece 1 with a section radius r is fixed on the supporting surface of the stationary tool 2, the working cylindrical surface of which has a radius R1. Deformation of the workpiece is carried out by a movable working tool 3, the working surface of which is made in the form of a cylinder with a radius of R2. The original length of the deformable section of the workpiece is l. When moving the working tool by the value h, the workpiece is bent through an angle α.
Based on the analysis of the geometric relationships of the sizes and parameters of the bending process, the dependence of the movement of the working tool h on the angle α was established where l is the initial length of the deformable section of the workpiece; R1 is the radius of the bearing surface of the stationary tool; R2 is the radius of the working surface of the movable tool; r is the radius of the cross section of the original workpiece.

Fig. 1. Folding scheme
Computer modeling of the process of folding of bar stocks with round and barrel-shaped sections using the finite element method based on the widely used DEFORM-3D software package [11][12][13][14][15][16] has been performed. The workpiece material is steel 40S2A (GOST 14959-2016), which is used in the manufacture of spring clips for fastening rails. The mechanical properties and the hardening curve of 40S2A steel were determined from the results of tensile tests [3]. Fig. 3 shows the position of the workpiece and the tool at the intermediate stage of the cantilever bending process and the stress intensity distribution field σi in the deformation zone.

Fig. 3. The position of the workpiece and the tool at the intermediate stage of deformation and the stress intensity distribution field σi in the plastic zones: a -round section; b -barrel-shaped section in bending about the x-axis; c -barrel-shaped in bending about the y-axis
The graphs of the dependence of the bending force P on the movement of the movable tool h were built, which are shown in Fig. 4 based on the results of the calculations. Curve a is bending of a round section, curve b is bending of a barrel-shaped section about the x-axis, curve c is bending of a barrel-shaped section about the y-axis. The polynomial of the 6th degree was used to describe the nature of the change in deformation forces depending on the movement of the movable tool. P = a1h 6 + a2h 5 + a3h 4 + a4h 3 + a5h 2 + a6h. (2) Equation (2) quite accurately describes the nature of the change in the bending force P from the movement of the movable tool h, since the coefficients of determination have a high value (R² = 0.995…0.998). The values of the coefficients of the polynomial (2) are presented in the table 1.

Conclusion
Based on the research results, the following conclusions can be drawn. 1. Based on the results of the analysis of the geometric relationships of the sizes and parameters of the bending process, the dependence of the movement of the working tool h on the bending angle α was established.
2. Finite element modeling of the process of plastic folding of bar stocks with round and barrelshaped sections has been carried out. It was found that when bending the barrel-shaped section relative to the x-axis with a minimum moment of inertia, the maximum bending force is 2.4 times less than when bending the round section and 1.88 times less than when bending a barrel-shaped section relative to the y-axis with a maximum moment of inertia.
3. The obtained research results are recommended to be used when choosing equipment for plastic bending of rod products, when designing a bending tool and assessing its service life.