The assessment of the process of drawing a cylindrical workpiece without pressing with alternating strain of the workpiece flange

The development of a method for drawing cylindrical parts without pressing the workpiece flange, which allows reducing the cost of production due to the use of dies without a fit ring and single-acting presses. The performed research revealed that this method results in obtaining cylindrical parts with drawing ratios typical for pressing drawing. In this case, the different thickness of the finished product is several times less compared with the same type of semi-finished products obtained by drawing with a fit ring. Steel, aluminum and copper workpieces were researched. The best results were shown by more plastic materials. This method is not applicable for materials with the less than 0.25 mm thickness.


Introduction
The method of manufacturing cylindrical parts by drawing in the cold state is used at almost all mechanical engineering enterprises, which include forging and workpiece-preparation workshops and sections. In largescale production, rather productive drawing methods are mainly used, such as drawing with pressing the flange, with pulling ribs and sills, drawing on sheet stamping machines, drawing out from a tape, drawing out with thinning the wall, etc. [1-3]. In the medium and small batch production, the above methods are used. Other methods include stamping with elastic media, liquid and gas, soft metals, explosion stamping, package drawing, pulsating drawing, stamping with a profile tool, drawing with heating and local cooling, drawing on sheet punching hammers and hydraulic presses, drawing on hydraulic presses, rotary drawing, stamping with workpiece end support, non-pressing drawing [4][5][6]. In single and smallscale production, the use of most of the above methods is impractical due to the high costs and the duration of the die tooling manufacture, the use of multi-operation, which makes it difficult or almost impossible to switch to the production and development of products new types. The decisive role here will be played by partially universal or universal equipment, which can be used at any stage of manufacturing a new product [7][8][9].
From this point of view, the application of the nonpressing method in single and small-scale production is promising and low cost, since there is no need to complicate the equipment by the fit ring and use doubleand triple-action presses. Therefore, the purpose of the work consists in the experimental research of the possibilities of the drawing method with alternating strain of the flange and the development of recommendations for production.

Material and methods
Drawing without a fold holder for flangeless parts is only possible with a low drawing coefficient m = d/D ≥ 0.75 ÷ 0.85 [10,11]. To implement this process, simple equipment is used, where the stamped part is mainly pulled to dip. It is difficult to turn a flat part into a hollow one. The process is accompanied by the formation of an insignificant amount of folds and their smoothing when pulling the cup through the gap between the die and the punch. Moreover, parts made of plastic metals and alloys with a large flange can be drawn without noticeable signs of corrugation without pressing only to a shallow depth of h ≈ (3 ÷ 6) s. High values of h correspond to workpieces with big thickness. Drawing without pressing parts with big flange is only possible before the start of decreasing the size of the initial workpiece [5, 13,14].
To test the possibility of obtaining high-quality cylindrical parts by drawing without pressing the flange, experimental research was carried out on round workpieces of various diameters and thicknesses. The workpieces dimensions exceeded the ultimate ones, but they were corrected according to the L.I. Shofman condition of the stability loss [11,17]. Workpieces made of 08 kp steel, aluminum A2 and copper M4 were subjected to drawing without pressing. The diameters of workpieces made of 08 kp steel were 77, 80, 83 mm, thickness -1.2 mm, punch diameter -46.8 mm. For aluminum the diameters of the workpieces were 83, 86, 89 mm, thickness -1.4 mm, the punch diameter -46.4 mm. For copper -58, 61, 64 mm, workpiece thickness -0.25 mm, the punch diameter -49 mm. For all sizes of workpieces, the diameter of the inlet of the die was 50 mm. The radius of curvature of the die for all experiments was chosen the same and equal to 5 mm, the radius of curvature of the punch for all experiments was 4 mm.
The process of drawing without a fold holder is accompanied by the difficulty of centering the workpiece on the die and, as a result, unilateral tightening of the semi-finished product, the appearance of premature folds and destruction at the location of strains, and these processes are aggravated when using the same die for workpieces of different diameters. Therefore, to conduct these experiments, a universal die with movable centering elements was designed, with the help of which the workpiece was accurately aligned with the hole of the die and punch. Here, the clamps move along the radial grooves simultaneously and synchronously with each other to the center or from the center of the die, which ensures self-centering of the workpieces (Fig. 1). The ultimate diameters for drawing is performed without fold formation are: for steel -D = 76 mm, for copper -D = 56 mm, for aluminum -D = 80 mm [15][16][17].

Calculation
At the first stage of drawing the punch stroke was limited according to the leap in effort at the stroke-effort diagram of the tensile machine. So the corrugations formed on the flange prevent the workpiece from being pulled into the die hole. It was noted that for different thicknesses of the workpieces, the value of the stroke of the punch, at which the leap in effort was observed, was also unequal. An empirical dependence was proposed for calculating the length of the penetration of the punch into the workpiece. It accurately described this process component where s -the workpiece thickness; r d -the radius of the die rounding; r p -the radius of the punch rounding.
After the first stage of drawing passed, the semifinished product with corrugations was removed from the die, turned by 180° and reinstalled. It was centered with the use of moving elements. The stroke of the punch was turned on and the semi-finished product was deformed until the corrugations on the flange were smoothed out. Then the punch was stopped and it was given a precisely calculated stroke until a new formation of folds of the inverse curvature on the flange. The length of the reverse stroke of the punch was calculated by mathematical dependence where l 1 -the length of the punch stroke at the first step; Δh -the addition to the reverse stroke calculated by the G. Backhaus model taking into account the Bauschinger effect [14,[18][19][20][22][23][24][25].
Then the semi-finished product was removed from the die, turned over by 180º and the process was repeated until the desired product height was obtained. Thus, all batches of workpieces were drawn, and their final height exceeded the standard height of the products obtained by drawing without pressing the flange and corresponded to the height of the drawn parts with the use of pressing. So, e.g. the drawing coefficient for the aluminum part with the workpiece diameter D = 80 mm was m = d/D = 0.58, the workpiece height -h = 24.5 mm (according to the tables of Romanovskyi V.P. [17,21,[26][27][28]). It is recommended to perform this drawing with pressing, cutting allowance -about 3.5 mm according to the data of Skvortsov G.D. [17,29,31]. I.e. the final height of the finished part is 21 mm. It is impossible to obtain such a part by drawing without pressing the flange.

Results
However, the experiment result revealed that the use of When conducting experiments on drawing workpieces without pressing the flange, the thicknesses of the obtained parts were also measured [30,34,35]. To do this, we used a micrometer thickness gauge with a measuring range of 0-25 mm and a division value of 0.01 mm to determine the strain mechanism and to formulate recommendations on the application of this process to production. The question of the legitimacy of determining the additional stroke of the punch by theoretical dependences based on the Bauschinger effect [32,33] and recommended for use in this drawing method also remained open. Some results of the performed experimental research are presented in Table 1, which shows the dimensions of the workpieces and the drawn parts, their thickness in the characteristic zones of the profile, the material, the number of turnings to obtain the given height, the variants of the loss of stability and destruction, as well as the size of the first stroke of the punch and the addition at the reverse of the stroke load. However, it was noted that this process does not go smoothly and there are difficulties and shortcomings in the size of the stroke of the punch, as well as alignment of the workpiece after turning, which results in its destruction in the form of the separation of the bottom (Fig. 5).  These phenomena's leaded to an increase in the number of rejected parts and the instability of the drawing process, which is unacceptable in the current production. Therefore, during the course of this experiment, some improvements in the die design were made and the methodology for calculating the additional stroke of the punch was improved taking into account the results of the experimental research.

Discussion
The table demonstrates that it is possible to obtain the aluminum and steel parts after at least six turnings. The number of turnings depends on the workpiece diameter and the drawing coefficient. With the larger diameter and the smaller the drawing coefficient, the greater number of the turnings is necessary to obtain a normal part. Aluminum is a more ductile metal in this case; in comparison with steel it requires a smaller number of steps with the same initial parameters and drawing coefficient. However, the thickness of the workpiece is higher for aluminum than for steel, which may explain the better stability of the workpiece flange and the possibility to obtain increased strains during one step. Drawing of thin metals by this method is difficult, because when the workpiece approaches the shape of the finished part, the corrugations are not completely smoothed out and remain on the product, which is unacceptable. Besides, the turning of thin workpieces and their strain results in a loss of bottom stability in the form of local buckling of metal. It is shown in the table for copper workpieces whose thickness is 0.25 mm.
The results of the measurements of the thicknesses of the characteristic zones of the semi-finished product allow us to conclude that the nature of the strain of the workpiece by this method is radically different from the method of the strain by drawing with a fit ring. The data in column 6 shows that the workpiece deforms along its entire perimeter. This is not characteristic of the classical drawing method, where the bottom of the part is practically not deformed, and mainly the workpiece flange is subjected to plastic strains [36,39]. When turning, during shaping, the zone of transition of the wall to the bottom of the part and the workpiece flange are subjected to the greatest strains. Moreover, the main difference is the thinning of the flange, and not it's thickening as in the classic drawing. Plastic strain covers all zones of the workpiece and the end face of the workpiece receives compressive deformations in thickness, which indicates the large tensile stresses acting here, comparable with their value at the transition of the wall to the bottom. Based on the experimental data, the ratio of thicknesses in these zones is practically of the same order: steel -0.83/0.81; 0.79/0.79; 0.77/0.76; aluminum -0.79/0.77; 0.77/0.76; 0.76/0.75.
However, the experimental result revealed that the use of drawing with step-by-step stretching of the workpiece.

Conclusions
Thus, the conducted experiments confirmed the possibility of manufacturing cylindrical parts by drawing without pressing the workpiece flange with its step-bystep stretching. It will allow applying the method to a single and small batch production using simple presses and mold tools without a fold holder. However, one question remains open. It is the problem of the maximum diameter of the workpiece for this method, more precisely, the ratio of the diameter of the workpiece to the diameter of the part. Also the possibilities of stamping workpieces that are outside the range of sizes given in this research have not been analyzed.