Study and Computer-aided Design of Flux-cored Wire Rolling in Round Gauges

: The mathematical model of the stress-strain state during flux-cored wire rolling in round gauges has been developed. Simulation was based on dividing the deformation zone into elementary volumes and simultaneous solution of the plasticity condition for porous materials and power static equilibrium equation inside the elementary volume. A distinctive feature of this model is taking into account the porous medium strain in the deformation zone. The experiments have confirmed the validity of the mathematical model for predicting the powder density and the energy-power characteristics of the process. Based on the developed mathematical model, the criteria and conditions for optimization were formulated, and the algorithm was developed for the automated design of technology for flux-cored wire rolling in round gauges. As an example of the obtained solutions implementation, the calculation of sintered copper flux-cored wire rolling technology was given.


Introduction 2.1 Actuality of research
Despite the number of papers devoted to the flux-cored electrodes production, the problem of determining the stress-strain state during rolling flux-cored wire in round gauges has not been solved.Known solutions in the field of rolling wire rod and drawing in roller dies are devoted to the continuum deformation.Recently, the most common method for the powder materials forming processes is the finite element method, but its use hampers performing automated calculations due to a specific implementation method.All this generates a need for developing a mathematical model of the rolling flux-cored wire in round gauges, based on the joint solution of the plasticity conditions for porous bodies and the equilibrium equations of the elementary volume in the deformation zone.

Aims and scopes
The aim of this work is to study the effect of reducing on the final relative density of flux-cored wire when rolling it in round gauges and to determine rational reduction modes based on the creation of a computer-aided design system for this technology.To achieve this goal, the following tasks were set and solved: a mathematical model of the material stress-strain state was developed and experimental studies of the rolling flux-cored wire in round passes were carried out.

Prime novelty statement
The main contribution to this area is the study of the rolling flux-cored wire in round gauges.The proposed model expands the understanding of the process and evaluates the influence of the initial characteristics on the finished wire.
Theoretically, for the first time, a mathematical model for rolling flux-cored wire in round gauges has been developed.The model is based on the joint solution of the conditions for static equilibrium of the deformation zone isolated elementary volume of a flux-cored wire.The model takes into account the real distribution of mechanical properties and friction conditions along the length of the deformation zone.A distinctive feature of the model is taking into account the deformation of the powder material in the round gauges.
In the experimental technique, for the first time, experimental studies of rolling flux-cored wire in round gauges were carried out, which revealed the influence of the initial parameters on the formation of the process power characteristics and the final density of the wire.
In industrial applications, the results are interesting for developers of equipment for the production of flux-cored electrodes and technologists in the development of technology for the flux-cored wire production by rolling methods.The developed model allows us to determine the maximum values of the force, rolling torque and rolling power.The model helps to solve the problems of computer-aided design for flux-cored wire rolling modes by choosing optimal initial parameters, such as powder density and initial wire diameter.

Theoretical research 3.1 Mathematical model
In accordance with the above-mentioned and similar to the methods of paper [33; 34], the considered numerical one-dimensional mathematical model of the pressed flux-cored wire rolling process was based on the numerical recurrent solution of the finite-difference form of the static equilibrium condition of the deformation zone selected elementary volume.The design diagram of the integral deformation zone included the seal zone Lpl (Fig. 1a).Speaking from the perspective of the kinematic relations, the seal zone Lpl was subdivided into the backward slip zone Llag and the forward slip zone Ladv.
Directly left AB and right CD boundary sections of the deformation zone in the framework of the considered mathematical model were taken parallel to the plane passing through the axes of the working rolls.The seal zone sections, including neutral sections, which are the backward and forward zones sections on the corresponding working rolls, were taken as parallel to this plane.
Besides the above-mentioned, when developing a one-dimensional mathematical model, a number of assumptions were used, the main of them are the following: mechanical properties values, standard axial stresses σх, standard contact stresses рx, and rolling kinematic parameters change only along the length of the deformation zone, while their value remains constant along the thickness of each separate section; current values of the contact angle αх along the length of each individual selected elementary volume do not change, while the changes in the standard рх and tangential τх contact stresses are linear (Fig. 1b); tangential contact stresses in the deformation zone are subjected the Coulomb-Amonton friction law, τх = fхPх, while the analytical descriptions of the external friction coefficients distributions for both the backward zone and forward zones can be represented by power dependences of the following form: ]  1 (2) at Ladv1(2)  х  Lpl; (1) where x is a geometric coordinate originating in the plane of the seal zone coupling with the elastic recovery zone (Fig. 1a As an analytical description of the composition thickness value current along the deformation zone length dx, the power approximation of contact arcs was used: where d1 is the final thickness of the resulting wire (Fig. 1a); аhpower characteristic of the deformation zone shape, the quantitative assessment of which with the cylindrical working rolls can be taken equal to аh = 2.0; d0is the initial thickness of the pressed flux-cored wire in the section at the input to the deformation zone (Fig. 1a).
Having carried out, taking into account the above-mentioned, the division of the deformation site seal zone into a finite aggregate (KR) of elementary volumes and expressions, based on the nature of the assumptions made, the geometric characteristics, and the stresses σх, τх and pх in finite-difference form, as shown in Fig. 1b, let's consider the condition of static equilibrium of the selected i-th elementary volume: where positive values of standard stresses σх correspond to compression stresses, and the opposite direction of tangential contact stresses in backward and forward slip zones (Fig. 1a) is taken into account by signs in the analytical description ( 1 where: Besides the static equilibrium condition (4), normal σх and normal contact рх stresses are functionally related to each other by the plasticity condition, its analytical description, taking into account the assumption of the powder medium axisymmetric stress-strain state, has the following form [22]: where αх, βх -coefficients values current along the deformation zone length, taking into account the specifics of the powder medium deformation; σsx is the current value of the yield strength for the solid phase of this powder composition.
The current values of the coefficients αх and βх, according to the recommendations of the paper [22], can be determined as: where γх =ρх/ρ0is the rolled material relative density value current along the deformation zone length; ρх/ρ0current density and the given powder composition solid phase density; a, m, ninvariables for each coefficient value specific content, characterizing the intensity of αх and βх changes depending on the change in the relative density indicator γх.
Let us express from the equation ( 7) the value of normal stresses σx: Substituting the Coulomb-Amonton friction law and the plasticity condition (9) into equation ( 5), we determine the normal contact stresses px2: where ; index 1 indicates that this or that parameter belongs to the initial one, and index 2 belongs to the final section of the selected elementary volume of the deformable medium (Fig. 1b).
Taking into account the known values of рх2, proceeding from the plasticity condition (7), i.e. by analogy with (9), the value of normal stresses σx2 can also be determined: in this case, the tangential contact stresses  2 : To determine the deformation parameters, using the dependencies between the main plastic deformation rates ε1, ε3 and the main stresses σ1, σ2, σ3, provided by the theory of porous materials flow [22]: speed ratio, and at the same time the corresponding deformation indices ratio ε1 and ε2 can be defined as: where λ -Lagrangian coefficient.
Taking into account that in relation to the considered technological scheme (Fig. 1a), by virtue of the accepted assumptions, the following ratios are fulfilled:  2 =  3 =   ;  1 =   , and the strains in the plane-strain condition should correspond to [22]: required value of the strain ratio εlx / εdx can be defined as: Proceeding to the selected elementary volume stress-strain state indicators (Fig. 1b): according to the mass conservation condition and taking into account the billet length before rolling L0 and after rolling L1: ; (19) the resulting value of the powder medium relative density within a given volume can be determined as: It should be pointed out that in a strict setting, the joint solution of equations ( 1) -( 20) is rather lengthy.Therefore, within the framework of this mathematical model based on a numerical recurrent solution, when calculating the coefficients αх2 and βх2, we used the value of the relative density corresponding to the initial section of each individual selected elementary volume, i.e.: ) Similar to (20), (21), i.e., depending on the current indicators of the strain degree   ,   , and the current indicator of the relative density  , the current value of the yield strength solid phase   can be determined, taking into account the strain change of which is necessary when analyzing the rolling process of sintered powder materials [22].In this case, the following dependences obtained by the author of the paper [22] for sintered copper powder can be used directly as an analytical description of the functional relationship between the yield strength   and the equivalent strain index  х : = 522.2( + 0.007) 0.427 at εex <0.23;   = 431.4( − 0.011) 0.279 at εex >0.23.( 22) Actually, the current value of the equivalent strain  ех for the i-th elementary volume can be determined on the basis of the dependences of the paper [22] by numerically integrating the corresponding increments  е in all the previous identified elementary volumes: The direction corresponding to the direction of the rolled composition motion was taken as the vector direction of the used recursive decision scheme, and the following conditions were used as the connection conditions in the transition from the i-th to (i + 1) elementary volume: where the initial conditions, i.e. geometric and power characteristics for the first elementary volume, corresponded to: where ρ0powder density.Speaking from the perspective of the initial conditions, the calculated values of stresses σх, in turn, should be equal to the known stresses of the front tension or support σ1 (Fig. 1a).The achievement of this condition was ensured by a directed iterative change in the relative length of the forward slip zone on the control work roll Sl=Ladv/Lpl:  (+1) =   +    (  −  1 ), (26) where k is the ordinal number of the next iteration cycle; AS is the step of changing the forward slip zone relative length, its value depending on the degree of approach to the desired result, was taken as a variable; sign{σxCDk-σ1}gradient estimate of the increment direction, corresponding numerically to: In general, the set of analytical descriptions presented in this paper, combined with the organization of subsequent numerical integration, made a complete algorithm for one-dimensional mathematical simulation of the pressed flux-cored wire rolling process.The software was developed for the automated calculation of technological modes for the pressed flux-cored wire rolling in a round gauge.Programming is carried out in the linguistic environment MS Visual Studio.

Calculation results
As an example of the obtained mathematical model implementation, Fig. 2

Technique of experimental research
Experimental studies of the rolling process were carried out in order to clarify the initial data for the mathematical model numerical implementation and assess the degree of its reliability, as well as to assess the efficiency of the reduction degree in the rolling process to the structure and basic properties of pressed flux-cored wire.
The pressed flux-cored wire rolling is implemented on a unit including a laboratory mini-mill 100x100 DSEA (Fig. 3) and an analog-to-digital converter ADC SDI-ADC 16-32 connected to the mill using a computer.Experimental studies of energy-power parameters and accuracy of geometric characteristics obtained when rolling a pressed fluxcored wire were carried out on this equipment.The work rolls themselves are made of steel 40X for eight gauges with a gauge surface hardness of 30… 40 HS and roughness corresponding to √1.25.The diameter of the work rolls is Dr = 100 mm, the length of the barrel is Lb = 100 mm.The roll drafting was made according to the method [46] used to calibrate the rolls of wire mills, based on the condition that the average stretch per pass does not exceed 1.2: where d0initial value of the pressed flux-cored wire diameter; d1the value of the diameter after deformation, respectively.The dimensions of the round gauge dr, taking into account the plus and minus allowances (Fig. 4), made: where  1 = 0.02 0 ;  2 = 0.03 0plus and minus diameter allowance.The roll-to-roll distance was changed using a mechanical-type screw-down gear.When conducting experimental studies, the following technological parameters were recorded:  the value of the rolling power at each gauge, which was measured by means of measuring cells installed under the mill screws;  the rolling torque on the driven rolls, which was recorded by resistance strain sensors glued to the bodies of each of the universal spindles in a bridge circuit;  the original diameter of the pressed flux-cored wire d0 and the diameter after each pass (strain) d1;  the original length of pressed flux-cored wire and drawing after each pass.
In the course of rolling, in each gauge, the reduction was carried out with different relative deformations, which varied in the range ε = 0.15-0.75.The process proceeded without the use of rolling lubricant.For each subsequent gauge and corresponding reduction, the rolling force P and the moments on the upper and lower rolls were measured.
All recorded parameters, current in time, were recorded using an analog-to-digital converter ADC SDI-ADC 16-32 with a computer.The power source was a storage battery with the 12 V nominal voltage.The use of this sixteenbit analog-to-digital converter allowed to digitize the input signal with a frequency of 100 kHz, with a hundredfold amplification of the signal.
To interpret the obtained oscillograms by force and by the moment of rolling, calibration charts were built, and the calibration constant was determined.Calibration of the force and rolling moment meters was performed before and after the rolling process.Measuring cells installed on the mill between the mill screws and the journal boxes of the work rolls were calibrated using a hydraulic press, on which they were loaded with a force P, the value of which was known based on the working fluid pressure in the system recorded by the pressure gauge.The calibration of the spindles with strain gauges glued to them was carried out using a lever, which was loaded with a known load.
After each pass by the obtained pressed flux-cored wire, the geometric characteristics were measured, they are: the values of the diameter d0 (d1) were measured at three points using a micrometer (with a scale division of 0.01 mm), and drawing λ was measured using a ruler (with a scale division of 1.0 mm) Also, after each pass, the relative density of the pressed flux-cored wire was measured.Determination of the density of molded powder materials is regulated by GOST 18898-83 and provides for the use of calculation and hydrostatic methods.
Determination of the obtained pressed flux-cored wire samples density by the calculation method: the essence of the method is to measure the volume and mass of the sample.The following equipment was used for the tests: electronic weigher AR 3130 (Ohaus, USA) with an accurate within 0.001 g; measuring tool -micrometers with a scale division of 0.01 mm (GOST 6507-90); vernier caliper with a scale division of 0.1 mm.
To determine the density, the sample was weighed in air with an accuracy within 0.001 g, and its main dimensions were measured, by which the volume was calculated.
The sample density γ in g/cm 3 was calculated by the formula: where msample weight, g; Vsample volume, cm 3  The relative density of the samples in percent was determined by the formula: where γмtheoretical density of a non-porous material given composition (copper M1 -γм=8.3g/сm 3 ) Determination of the obtained pressed flux-cored wire samples density by the calculation method: the essence of the method is to measure the mass of the product in air and in distilled water.This method was used to control the measurement of the pressed flux-cored wire samples density by the calculation method.
A specially designed unit was used for the measurement (Fig. 5).The use of the AR 3130 electronic analytical balance (Ohaus, USA) in this unit allows weighing with an accuracy of 0.001 g.Before each weighing, the zero point of the balance was checked.The sample was suspended to the special balance pickup on a thin (0.1 mm) monofilament.The length of the monofilament was chosen so that the sample, when lifting the measuring cylinder with distilled water, was freely immersed to a depth of at least 10 mm from the surface of the liquid.To measure the density, the distilled water (GOST 6709-72) was used with the addition of 1-2 drops of triethanolamine, a substance that reduces the surface tension of a liquid, that protects the samples from the settling of air bubbles on them.
The tests were carried out in the following way.Samples of pressed flux-cored wire after each gauge with a length of l = 20 mm were weighed in air.After that, the surface pores were closed by covering the surface with a thin layer of petroleum jelly (GOST 3582-84).Petroleum jelly was applied to the surface of the product, in a thin layer, followed by rubbing.After processing, the sample was weighed in air and in water.When weighing in water, the formation of air bubbles on the surface of the samples is not permissible.When bubbles appeared, the samples were removed from the water, dried, processed to close the pores, and weighed again in air and water.
The density ρ of the pressed flux-cored wire samples was calculated by the formula: where m is the mass of the sample, g; ma is the mass of the coated sample, weighed in air, g; mw is the mass of the sample suspended in water, g; mwire is the weight of the wire during weighing, g; ρw is the density of water, g/cm 3 (see Table 1).The density of petroleum jelly was taken equal to 0.830 g/cm 3 , the density of the samples was calculated with an accuracy of 0.001 g/cm 3 .When determining the density of the pressed flux-cored wire, the error between the calculated and hydrostatic methods was not more than 5%.

Results of experimental studies
The results of pressed flux-cored wire rolling process study are presented in Table 2. Graphical interpretation of experimental pressed flux-cored wire rolling process study, supplemented with calculated dependencies, obtained using a mathematical model, is shown in Figure 6.Fig. 6a shows the experimental and calculated distributions of the relative density γ over the passes.From the analysis of the obtained experimental data, it can be seen that as the diameter decreases, i.e. the degree of reduction increases, the relative density increases from 0.86 to 0.93 and approaches the density of the monometal.The error in comparing the calculated and experimental distributions of the relative density along the passes is within the acceptable range from 0.5% to 5%.
Fig. 6b shows the experimental and calculated distributions of the drawing λ over the passes.From the analysis of the obtained experimental data, it can be seen that with an increase in the degree of reduction, there is an increase in the drawing along the length of the pressed flux-cored wire and makes 3.23.In this case, the error in comparing the calculated and experimental distributions of the drawings along the length was from -4% to 9%.The drawing incrementation along the passes is increased the most significantly after reaching the reduction strain of 45%, which is associated with the achievement of the relative density maximum value due to plastic strain and partial slipping of particles relative to each other.Ultimately, the volume equality condition and analysis of the obtained calculated and experimental distributions of the relative density and the pressed flux-cored wire drawing along the passes, shown in Fig. 6a, b, resulted in the fact that the elongation strain   was 77%, and the seal strain   was 23%.Such a ratio of strain is possible in the case of strain in metal grits volume with the plastic flow of the metal for its shell, that affected the location of the pressed flux-cored wire non-metallic component.
Fig. 6c depicts the experimental distributions of the pressed flux-cored wire rolling force over the passes.Comparison of the obtained experimental and calculated distributions shows that the discrepancy between them is in the range from 0% to 5%.
The above-mentioned confirms the reliability of the developed mathematical model and the possibility of its use to solve optimization problems for the development of technological modes for the manufacture of pressed flux-cored wire.The main task in the design of the pressed flux-cored wire rolling technological modes is to obtain the required diameter with a given density, which is achieved due to the optimal calibration of the work rolls.When solving this problem, it is necessary to know the number of passes and reduction in each of them, that is, it is necessary to know the main integral characteristics of the process, such as the final relative density of the powder, wire elongation and energy-power parameters.Since these parameters depend on the conditions for the process implementation, the problem comes down to solving the optimization plan issue.
To determine the optimal calibration of the rolls, an automated design of technological modes for rolling pressed flux-cored wire in a round gauge was carried out.As design criteria, we used the required wire diameter [d1], the average drawing along the passes λ, or the uniform distribution of technological loads P along the passes.The relative deformation ε in each pass was used as a design parameter.The previously considered mathematical model of the rolling flux-cored wire in a round gauge was used as the target functions.
The solution was an iterative procedure to determine the reduction in each pass depending on the required technological parameters.When determining the reductions from the condition of uniform loading according to rolling force: where kthe ordinal number of the iterative solution procedure next cycle;   опthe step of changing the relative length of the forward slip zone, the value of which was taken as a variable, depending on the degree of approach to the desired result:   = 10 −5 − 10 −3 ;   = 10 −5 − 10 −3 ; { п2 | =  −  п1 }sign function corresponding to: Determination of reductions from the of uniform drawing along the passes allows uniform strain of the pressed flux-cored wire, thereby reducing the likelihood of its destruction during rolling.Analytically, the optimization condition for this criterion can be expressed as follows: 1(+1) =  1  +   {[] − }  , (38) where { п2 | =  −  п1 }sign function corresponding to: When determining the optimal rolling modes, the method of targeted enumeration was used.The enlarged block diagram of this solution algorithm is shown in Fig. 7. On its basis, software was developed in the MS Visual Studio environment for the automated design of pressed flux-cored wire rolling technological modes.
As an example, the Table 3 shows the calculated values of technological parameters, which allow to determine the necessary calibration of the rolls from the condition of uniform drawing along the passes, which allows uniform strain of the pressed flux-cored wire, thereby increasing the relative density and reducing the likelihood of its destruction during rolling.Table 4 shows the reduction modes calculated from the conditions of the equipment uniform loading, which allows, for example, with the same rolling force, to reduce the elastic strain of the rolling mill working stand, thereby reducing the opening of the gauge and increasing the quality of the obtained pressed flux-cored wire.

Discussion
The analysis of the developed mathematical model implementation resulted in the following.The growth of the process integral characteristics, such as force, moment, maximum contact stresses, drawing, relative density, increase with the reduction degree addition (Fig. 3).So, with the pressed flux-cored wire reduction degree increase from ε = 10% to ε = 75%, the rolling power P increases by 75%, and the maximum contact stresses рmax increase by 54% (Figure 2a).The relative density increased by 10%, and the drawing increased by 71% (Figure 2b).These dependencies can be used to select the most rational rolling modes, on conditions that the required parameters of the finished wire are provided with a minimum level of energy costs.
The presented results of the calculated distributions of the pressed flux-cored wire rolling integral indicators are of a rather complex non-monotonic nature.This fact, in turn, confirms the need for a more complete consideration of the whole set of factors inherent in this technological scheme, that, in particular, was carried out on the basis of the presented mathematical model applied to the pressed flux-cored wire manufacturing.
The adequacy of the developed mathematical model was verified by experiment on the mill 100, at the laboratory of the Department of AMM DSEA.The analysis of the obtained results showed that the error in theoretical density calculations did not exceed 10%.This confirms the possibility of using a mathematical model in the design of technology and equipment for the implementation of the pressed flux-cored wire rolling in round gauges.Rolling was performed at the following initial values: the initial diameter of the pressed flux-cored wire was 8.0 mm, the initial relative density was γ0 = 0.88, and the radius of the rolls was R = 50 mm.
From the analysis of these distributions, it is clear that the solving optimization problem resulted in a uniform distribution of the drawing over the passes, that will allow the process to be carried out with a uniform deformation intensity and reduce the probability of wire fracture during rolling.On the other hand, with such a process, a decrease in the rolling power is observed, which, if the rigidity of the system is insufficient, can lead to the ridges formation along the edges of the billet in the first passes.Rational option in the latter case is the use of a generalized optimality criterion.
Thus, using the developed software, it is possible to solve the problems of the optimization plan for various requirements for the production technology.For example, to determine the required initial wire diameter depending on the number of passes, to determine the required initial powder density at a given final density, to determine the modes of pressed flux-cored wire production at a given final diameter, etc. Conclusions 1.A one-dimensional mathematical model of the pressed flux-cored wire rolling process is developed.It is based on the numerical recurrent solution of the static equilibrium condition of the selected elementary metal volume in the zone of its plastic strain, that allows calculating local and integral indicators.
2. The error of the calculated data and experimental studies is not more than 10%, that indicates the adequacy of the developed mathematical model for the pressed flux-cored wire rolling and the possibility of its use for solving optimization problems in computer-aided design of both equipment and technological modes.
3. Computer-aided design of the pressed flux-cored wire rolling in a round gauge was carried out and resulted in the optimal technological modes of pressed flux-cored wire rolling with diameters from 8 mm to 4.2 mm to be determined on the basis of drawings equality along the passes and the increased quality of pressed flux-cored wire.
4. From a practical point of view, the results of rolling technological modes automated design allow to determine all the initial parameters of the process to obtain a given standard size of pressed flux-cored wire.General view of roll mill stand 100 with rolls for rolling ux-cored wire rolling   The enlarged block diagram of the algorithm for solving the automation process when rolling pressed ux-cored wire

Figure 1 :
); flog, fadvreference values of the friction coefficients corresponding to the values of these coefficients in the section at the input (x = Lpl) and in the section at the output (x = 0) -from the seal zone; аfpower value characterizing the diagram shape of the friction coefficients distribution along the length of the contact surfaces on the leading and driven working rolls, respectively, аf = 0.2-0.5;Ladv, Llogrespectively the length of the forward and backward zones, on the contact surfaces of the working rolls.a) b) Design diagram of the integral deformation zone (a) and the selected elementary volume (b) during the implementation of the pressed flux-cored wire rolling process

Figure 2 :
shows the calculated distributions of local and integral characteristics of the pressed flux-cored wire rolling process.The calculation was performed with the following values: the initial diameter of the pressed flux-cored wire was D0 = 8.0 mm, the initial relative density was  н = 0.86, the radius of the rolls was R = 50 mm, a = 0.633, m = 1.017, n = 1.94.a b Calculated distributions of the flux-cored wire rolling integral characteristics depending on the degree of reduction: rolling force (a) and relative density (b)

Figure 3 :
Figure 3: General view of roll mill stand 100 with rolls for rolling flux-cored wire rolling The working stand of the mini-mill includes the following equipment: lower and upper working rolls, their value of the nominal diameter and barrel length are 100 mm.The work rolls are fixed in journal boxes with angular contact bearings.To balance the upper work roll, between journal boxes rubber packings are installed.The journal boxes of the lower and upper work rolls, in turn, are placed in the window guides of the stands unit and are fixed in the vertical and horizontal planes.The journal boxes of the upper work roll are fixed by means of measuring cells, which are annular elastic elements with strain sensors glued to them.Measuring cells, in turn, are associated with spherical rolling bodies, which are supported by the screw-down gear.The work rolls themselves are made of steel 40X for eight gauges with a gauge surface hardness of 30… 40 HS and roughness corresponding to √1.25.The diameter of the work rolls is Dr = 100 mm, the length of the barrel is Lb = 100 mm.The roll drafting was made according to the method[46] used to calibrate the rolls of wire mills, based on the condition that the average stretch per pass does not exceed 1.2:  =

Figure 4 :
Figure 4: Construction of a finishing gauge for rolling pressed flux-cored wire In order to ensure a developed high-quality profile, the gauge was made with an allowance (with a discrepancy) on the side walls, based on this, the width of the gauge bg:   = ( 0 +  1 )(1.012. ..1.015);(30) the hollow space S between the rolls made: S = (0.08…0.15) dr; (31) the sides were rounded with a radius: r = 0,1 dg; (32) Work rolls were made with gauges dg= 8.0; 7.3; 6.7; 6.1; 5.6; 5.1; 4.6; 4.2; (mm).The roll-to-roll distance was changed using a mechanical-type screw-down gear.When conducting experimental studies, the following technological parameters were recorded: the value of the rolling power at each gauge, which was measured by means of measuring cells installed under the mill screws;  the rolling torque on the driven rolls, which was recorded by resistance strain sensors glued to the bodies of each of the universal spindles in a bridge circuit;  the original diameter of the pressed flux-cored wire d0 and the diameter after each pass (strain) d1;  the original length of pressed flux-cored wire and drawing after each pass.

Figure 6 :
Theoretical and experimental distributions of the integral characteristics for the flux-cored wire rolling through passes: relative density (a), drawing (b), rolling force (c) 5 Pressed flux-cored wire production optimization

Figure 7 :
Figure 7: The enlarged block diagram of the algorithm for solving the automation process when rolling pressed flux-cored wire

Figure 4 Construction
Figure 4

Figure 5 Unit
Figure 5

Table 2
Results of experimental and theoretical studies of rolling flux-cored wire in round gauges

Table 3
Results of computer-aided design for rolling pressed flux-cored wire rolling technological modes from the condition of uniform drawing along the passes