Experimental research of the frictional condition in the pipes extrusion process

The article demonstrated the results of an experimental study of the pipe extrusion process using the method of coordinate grids. The estimation of the influence of separate conditions of friction on the contact surfaces of the deformable material and the pressing tool on metal flow pattern. The calculation of the forming operation is made for extrusion process stages. It is shown that the deformation proceeds non-uniformly. At the same time, due to the creation of favorable conditions on the contact surfaces with the use of the lubricant, the deformable sample differs uniformly in the distribution of the coordinate grid along the wall thickness of the tube’s sample. The boundary stagnation zones are identifying. It has been demonstrated that the front portion of the sample tubes is not fully worked through the wall thickness. While, the rear section is characterized by a dense grid structure. This in combination allows us to indirectly judge the possible anisotropy of the properties along the body of extruded pipes. It is proved that the using of lubricants on the contact surface: the press needle – inner surface of the sleeve will not have a significant effect on the extrusion force, and can be used mainly to ensure the durability of the press tool and to perform the quality characteristics of the inner surface of the extruded tubes. It was concluded that, first of all, the requirements for thermo-technical properties: heat capacity and thermal conductivity, and, secondarily, frictional, must be imposed on lubricants used for coating the inner surface of the sleeve and, accordingly, providing a separation layer between the press needle and the sleeve.


Introduction
As it is shown in works [1,2], qualitative characteristics of extruded pipes depend on a number of technological parameters. Among them, a strain capacity of a work material [3][4][5][6] and friction conditions on contact surfaces, i.e. a deformed metal -a pressing tool [7] should be singled out. The studies in the first area are successfully realized due to upsetting tests of cylindrical specimens using a multifunctional complex Gleeble [3,5,6,8].
The rationale for choosing a lubricant on the external and internal surfaces of a deformable material raises an unconventional problem. However, friction conditions specify not only qualitative characteristics of pipes of a finished size but also the maximum load on a deforming instrument of a pipe extrusion press. Thus, an experimental study of the influence of friction conditions on the pattern of metal flow when pressing pattern pipes can ensure in the initial approximation the formation of a scientific and technology-based approach to the selection of lubricants during the pipe extrusion. At 2

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International Conference on Materials Engineering and Science IOP Publishing IOP Conf. Series: Materials Science and Engineering 454 (2018) 012008 doi: 10.1088/1757-899X/454/1/012008 the same time, the coordinate grid method (CGM) [9,10] can help justify the choice of boundaries of plastic deformation applied in case of the mathematical description of the pipe extrusion process. Besides, the choice in favor of CGM is also justified by the fact that when using it is possible to consider each element of the coordinate grid as an element of the metal flow nucleus undergoing homogeneous strain during the deformation process [11].

Research method
12 lead billets (С1 grade), 45 mm in diameter, 40 mm long and with a through hole of 9 mm in diameter were used for physical simulation. The billets were preliminary cut along the centerline in two halves. The coordinate grid consisting of square cells with a way of nearly 5 mm was applied to each cut surface with the help of the EDM machine (see Figure 1).  Subsequently, the billet parts were put together according to a parting plane, previously covered by automobile oil, which protects them from thermal bonding during the extrusion and joined together. Using the testing machine by the maximum deformation force of 1.25 MN and corresponding pressing equipment (see Table 2) pattern sleeves were exposed to extrusion in case of production of pattern pipes 25×18 mm in size according to the following schemes: without lubrication (scheme No. 1); lubrication on the contact surface: a mandrel -an internal surface of the sleeve (scheme No. 2); lubrication on the contact surface: a two-part container liner -an external surface of the sleeve (scheme No. 3); lubrication on all contact surfaces (scheme No. 4). To reduce a time interval and consequently improve the reliability of experimental data, used for quantitative assessment of a strained condition, we evaluated three positions of the coordinate grid (see Tables 3 -5), which correspond to well-known stages [12] of the extrusion process: pressing out (see Figure 2); steady state (see Figure 3); extrusion process end (see Figures 4 -7).     -A hypothesis about the flow non-uniformity in case of correct pressing; -The maximum speed differential of longitudinal movements is observed in the area before an exit from the deformation zone. When the metal moves towards the exit from the deformation zone, the deformation speed becomes balanced.
-Near the contact surface of the deformed metal with the mandrel grids are deformed for a smaller value, as compared to the zone of a matrix funnel, where deformation has a larger value; -In the matrix funnel zone, where deformation has a larger value, the quality of the coordinate grid is unsatisfactory and difficult to replicate. In case of large values of deformation degrees, the use of CGM is unacceptable.   It is commonly known [13] that the stress of contact friction ( К τ ) is defined by Siebel's formula: The work of deformation can be defined as: Where S σ is a value of metal resistance to plastic shear strain; И ε is a strain intensity; V is the volume of metal where deformation happens.
The strain intensity ( И ε ) is calculated according to the formula [14]: Where ρ ε , ϕ ε , Z ε is a normal component of the strain intensity; γ is a tangential component of the strain intensity. During extrusion, there is a non-uniform plastic flow and a value of the strain intensity is different at different points of the deformation zone. Thus, for determination of deformation work we should specify the strain intensity (7), as a function, the volume integral of which, can be used for calculation of deformation work. The analytical determination of the deformation field is not a trivial task. That's why in this case the CGM is applied to determine the deformation strain. To find the strain intensity the components of a deformation tensor should be specified. Therefore, from the plasticity theory [14,15] it is known: Where u is displacement of elementary volume.

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International Conference on Materials Engineering and Science IOP Publishing IOP Conf. Series: Materials Science and Engineering 454 (2018) 012008 doi:10.1088/1757-899X/454/1/012008 The metal doesn't flow in a circular motion around an axis of pressing, i.e. displacement: As the process is axially symmetrical, the displacement of points and deformation doesn't depend on the ϕ coordinate. As for derivative determination, a derivative of the constant value is equal to 0 [16] To specify the components of strain intensity coordinates of all points before ( нач ij z , нач ρ ij ) and after deformation ( ij z , ij ρ ) should be defined. After that it is not difficult to determine the average values of height, width and radius of cells, respectively: For each cell we define the values of four angles ( The diagram for determination of values reflected in the formulas (11)(12)(13)(14) is shown in Figure 8. According to Figure 8, the cell height can be specified using the formula: Where Whereupon, using the dependency (7), the stain intensity ( И ε ) is specified.
As a result, having the information about the strain intensity, it is possible to define the deformation work in each cell:

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International Where i,j max ρ is a maximum cell radius: Using the results of coordinate measuring of the coordinate grid nodes, given in Tables 1, 3 -5, we performed calculation of deformation work when manufacturing pattern pipes 25×18 mm in size in accordance to the following schemes: without lubrication (scheme No. 1, see Figure 4); with lubrication on the contact surface: a mandrel -an internal surface of the sleeve (scheme No. 2, see Figure 5); with lubrication on the contact surface: a two-part container liner -an external surface of the sleeve (scheme No. 3, see Figure 6); with lubrication on all contact surfaces (scheme No. 4, see Figure 7). The calculation results are shown in Table 6.  9. Macrostructure of a press residue template made of 10Х13Н3 steel

Conclusions
The conducted experimental study of pipe extrusion process using the CGM under different friction conditions on the contact surfaces of the deformed metal and the pressing tool has enabled us to draw the following conclusions: