The Finite Element Modulation of Thermostressed State of Coating Formation at Electric Contact Surfacing of “ Shaft ” Type Parts

.e finite element modulation of forming of coating at electric contact surfacing is provided. .is model considers distribution of thermal properties and geometric parameters along the thermal deformation zone during the process of electric contact surfacing by tapes. It is found that the change of the value of the speed asymmetry factor leads to increasing of the friction coefficient in the zone of surfacing which is caused by the increasing of the tangential contact stresses in the zone of contact of the electrode tape with the surface of the part. .is leads to the forming of the coating with higher adhesion strength, and thereby the higher quality of the restored part under the lower operating regimes such as current pulse, force of the roller electrode, and duration of the current pulse is achieved. Mentioned above allows to decrease the thermal influence on the structure of the material.


Introduction
In the case of electrocontact surfacing, the bond between the welded and the base metals is formed by their joint compression as a result of heating by the transmitted electric current under conditions of the welded metal plastic deformation.In this connection, the main advantage of the electrocontact surfacing in comparison with the arc surfacing methods is a bond between the welded and the base metals without melting them. is helps to prevent mixing of the welded and the base metals, to reduce the thermal influence zone size, and to avoid defects in the cast structure [1][2][3].e electrocontact surfacing method is characterized by high productivity and low energy consumption of coatings [4]; minimum zone of thermal influence on a part; and absence of necessity to use protective atmosphere and absence of radiation and gas evolution.e process of electrocontact surfacing is characterized by short-term highspeed heating (800-1000 °/sec) of welded material and base metal to temperatures of 1400-1600 °S and the force action of roller electrodes.Heating occurs by passing a pulsed current through the welded material, which is under pressure from the deformation force between the base metal and the roller electrode.Electrocontact surfacing refers to the number of processes with pronounced force and temperature activation.e magnitude of the force action is by 2-3 times higher than in the case of the centrifugal induction and vibrational and other technological options for obtaining coatings.Electrocontact surfacing occurs under the action of two activating factors: forces on the roller electrode and current strength.is allows significantly speeding up the coating on the surface of parts [5][6][7].At the same time, the physical and mechanical properties of the layer obtained on the surface of the restored product (wear resistance, hardness, porosity, etc.) depend on the technological parameters of the process, which must be selected taking into account the influence of activating factors such as force and temperature activation.Considering the short-term course of the electrocontact surfacing process, there are certain difficulties in predicting the quality of the obtained coating and its compliance with the main operational properties.
erefore, there is a necessity to use a mathematical apparatus for analytical modeling of electrocontact surfacing in order to optimize the main parameters of the process to obtain a coating that best meets the specified requirements.
Regardless of the welded metal type (metal tape, wire, powder materials, or their compositions) [8,9], the nature of the bond formation with the base metal remains unchanged, which is explained by the generality of the main regularities of the welded bond formation in the metals surfacing by pressure [10][11][12].Dubrovskiy and Bulychev [13] developed a theoretical model of the formation of the welding areas of homogeneous metals during electrocontact welding.Dependences are obtained for the calculation of the size of the welding areas under electrocontact welding on different modes.It has been established that, with the electrocontact welding of iron-based alloys, the formation of welding areas with high bonding strength is possible when heated to critical temperatures [13].
It is noted in the work [14] that, in the case of wire electrocontact surfacing, its plastic deformation leads to a shift in the welded metal volumes on the surface of the part both in the radial (across the welded metal seam) and in the axial (along the welded metal seam) directions.According to the work [14], experimental data indicate an increase in the strength of the bond between the deposited wire and the part with increasing axial deformation.However, the axial deformation in this work was controlled by changing the temperature parameters of the surfacing conditions and this complicates the assessment of the deformation processes impact on the increase in strength of the resulting welded layer.Bulychev and Zezyulya [15] proposed a mathematical model of the process of forming a layer on the surface of cylindrical parts during electrocontact surfacing with wire.
e study is aimed at solving the problem of increasing the adhesion strength between the wire being deposited and the part without increasing the heat input and, accordingly, with minimizing the thermal effect on the part. is problem, according to [15], can be solved by developing methods for controlling the axial deformation of the wire without changing the strength and duration of the surfacing current pulses.According to the mathematical model of the electrocontact surfacing process presented in the work [15], the values of the roller electrode rotation delay factor should be selected in the range 0.54-0.64.e results of the experimental studies given in the work [15] confirm the possibility of a significant increase in the strength of the adhesion of the wire to the part by increasing only the axial strain of the wire.Because of this, the wire axial deformation can be represented as one more controlling parameter of the surfacing conditions.However, in order to apply the welded method with delayed rollers-electrodes in practice, it is necessary to develop a method of effective control of the deposited wire axial deformation.
In the work [16], there is a mathematical model of a sintered tape formation by reinforced metal lath for increasing mechanical characteristics using the method of electrocontact surfacing.e normal contact stresses in the center of deformation are determined.It is noted that the proposed method for calculating the sintering zone during the manufacture of reinforced powder tape can also be used to estimate the parameters of the electrocontact surfacing process.
In the case of electrocontact surfacing to obtain a quality weld joint, it is important to know the nature of the heat distribution in the joint zone of the base and the welded metal.e main difficulty in surfacing the working layers is obtaining the required temperature distribution over the whole contact area due to uncontrolled and uneven surfacing current density in various areas of electrical contact, with different conditions for heat removal.
Gulakov et al. [17] show the solution of the problem by obtaining a data array with their subsequent processing and finding the optimal parameters for the surfacing regime.However, to optimize the process parameters, dozens of experiments must be carried out.It is a labor-intensive process and takes a large number of machine resources.In consideration of the electrocontact surfacing real process short duration, making a fraction of a second, it is difficult to produce such a volume of calculations in real time.Lavrentik and Pavlova [18] proposed a simplified calculation model for estimating the influence of factors on the heat distribution over the weld joint contact area according to various criteria.Mathematical description of temperature distribution allows us to simplify the modeling, building, and predicting real dependencies processes for various parameters of a real experiment.To describe the data, the regression equations were obtained on the basis of the density function of the normal probability distribution for one-dimensional and two-dimensional models of temperature distribution in the contact zone.Statistical analysis allows determining the influence degree of a factor on the temperature distribution and, depending on this, optimising the process parameters to obtain a qualitative weld joint.It was established in the work [19] that gravity surfacing is performed with tangential force, which leads to the tangential stress appearance in the contact zone of the joined metals that requires taking this factor into account in modeling the electrocontact surfacing process.In the works [20,21], the effect of strain rate on the grain size of rolled steel was simulated and the effect of an energy pulse on the structure of the coating material was also investigated.However, the technology proposed in the works under consideration involves the modification of the surface layers without coating, which does not quite coincide with the purpose of this study.
With the development of coating technologies by the electrocontact method, the empirical approaches in the choice of coating design and process schemes ran their course.
is provides analysis of the electrode material stress-strain state in the process of electrocontact surfacing, taking into account the real nature distribution of the physicomechanical properties under the influence of thermal and mechanical loads at the stage of designing the technological process.In view of the physicochemical processes complexity occurring during the coating by electrocontact methods, the existing analytical dependencies do not provide an opportunity for comprehensive study of the welded layer formation.is makes it necessary to use 2 Advances in Materials Science and Engineering finite element simulation methods for analyzing the distribution of energy-force parameters and thermal fields over the cross-sectional layer for the purpose of optimizing the modes of electrocontact surfacing.In the work [22], based on a theoretical analysis of the electrocontact surfacing by tapes conditions using the finite difference method, the influence of the kinematic asymmetry coefficient magnitude on the change in the local energy-force characteristics of the process was established.e kinematic asymmetry coefficient is determined by the ratio of the linear velocities on the roller electrode and the remanufactured part.It is shown that, with the kinematic asymmetry coefficient increase to 1.015, the amount of tangential contact stresses in the surfacing zone increases too, which must be taken into account when designing the technological process.On the basis of experimental studies of the electrocontact surfacing by tapes, the adequacy of the developed finite difference model was confirmed.According to the results of the experimental verification, the error in calculating the force on the roller electrode and the current impulse strength does not exceed 10%.On the basis of electrocontact surfacing by tapes technological modes automated design, the tasks of ensuring the necessary geometric parameters of the coating are solved.However, in view of the thermal field distribution experimental verification complexity and also taking into account the one dimensionality of the proposed mathematical model, it is necessary to develop a two-dimensional model for more accurate account of all factors and for obtaining more reliable picture of the stress-strain and thermal state.
e construction of such two-dimensional models should be performed by the finite element method to make the most efficient use of them.

Prime Novelty Statement
e formation of coating at electric contact surfacing of "shaft" type parts is investigated.
e effect of the kinematic asymmetry coefficient of the electrocontact surfacing, which is determined by the ratio of the velocities of the roller electrode and the cylindrical part, on the change in the thermal and energy-force local characteristics of the process is investigated.e optimum value of the kinematic asymmetry coefficient is established, which makes it possible to increase the tangential contact stresses in the contact zone of the tape with the surface of the part.In the zone of contact of the tape with the roller electrode, tangential contact stresses remain unchanged, which must be taken into account during the development of the technological process.
On the basis of finite element modeling, it is established that, when the kinematic asymmetry of the electrocontact surfacing process with the value of the coefficient K v � 1.015 is established, the bond strength of the reduced samples increases by 24.3-26.8%.

Theoretical Studies
For the purpose of carrying out the research, the changes in the local characteristics of the electrocontact surfacing process by tapes of cylindrical parts, taking into account the actual conditions of the process, and also for testing the adequacy of the proposed mathematical model, the finite element modulation of the process was carried out.Finite element modulation of the electrocontact surfacing by tapes of cylindrical parts is realized on the basis of the Abaqus software complex using the Abaqus/Standard solver and provides a joint solution of the electrical heating and plastic deformation problems, including the surfacing of the electrode tape to a cylindrical surface.In the modulation, the design model, shown in Figure 1(a), was used.
is model, in order to simplify and reduce the amount of calculations, taking into account the plane symmetry XY (Figure 1), represents the half of the task.It consists of deformable element, modeling the electrode tape, two absolutely rigid, nondeformable bodies modeling the part being restored, and roller electrode.Besides, to ensure the clamping of the roller electrode with the force necessary for carrying out the electrocontact surfacing, the elastic element is included in the model.e contact interaction between the roller electrode 3 and the electrode tape 1 is described by Coulomb's Friction Law through the coefficient of friction, represented in the temperature function in accordance with the data of Grudev [23].
In the zone of contact interaction between the cylindrical surface of the part and the electrode tape, in order to simulate the adhesion process, the "closing" of the contacted surface of the tape with the part is additionally realized.Actually the process simulation is realized in several stages: (i) First, the roller electrode is pressed against the tape along the upper line of the front end face, which is realized by shifting the upper fixing point of the elastic element 4 by an amount capable of providing the required pressing force of the roller electrode.(ii) Next, after ensuring the pressing force, the part 2 and the roller electrode 3 are rotated, and the electric heating of the electrode tape is initiated.
Taking into account the impulse (periodic) nature of the electric load application and the relatively short time of influence, the electric current to the tape is implemented on the upper area of the surface, represented in the diagram (Figure 2) in the form of grid with the length that the tape passes during the period of the electric load.It includes a heating cycle up to the surfacing temperature and a pause (disconnection of the electric current).e electric potential is applied to the lower surface, which is shown in Figure 2 in the form of points along the surface area of the tape of the same length.e heat removal from the tape surface is realized on its surface, excluding the front and back end surface of the tape, the surface passing through the symmetry plane, and also the upper surface to which the electric load is applied.e roller electrode in the process of electrocontact surfacing is forcedly cooled by the water, which is supplied through the cooling channel.After the first period of heating the tape (Figure 2), the transition to the next section of the same length occurs, in order to carry out further electrical heating of the tape.

Results
As an example, Figures 3-5 show the temperature eld of the electrode steel tape in the time interval of the surfacing current impulse: the rotation speed of the part V part 0.4 sec −1 and the speed of rotation of the roller electrode V r 0.203 sec −1 .According to the obtained data, the electrode material heating is initiated in the area of its contact with the surface of the part.At the same area of the tape, in the thermodeformation hearth, there are the maximum temperatures during the whole heating period.Such a nonuniform distribution of the space-time temperature eld over the electrode material thickness indicates the melting of the tape in the contact zone with the surface of the part.
e main part of the electrode material in the thermal deformation source in the tough-plastic state is caused by heating up to 911-1010 °S.Comparatively low values of temperature indices in the contact zone of the electromagnetic tape with the roller electrode are caused by the intensive removal of heat from it, which is released in the electrode tape material during the electrocontact surfacing.us, there is no sticking of the electrode metal with the roller electrode.
Comparison of the modeling results of spatiotemporal heat elds for di erent durations of electric current impulse  Advances in Materials Science and Engineering behavior (Figures 4 and 5) testifies to the leveling of the temperature gradient in the thermal deformation hearth both along the length and width of the tape with increasing current impulse running time.
With a duration of the electric current impulse, t imp � 0.04 sec, a local temperature increase is observed in the thermodeformation hearth with a preferential displacement of the thermal spot into the alloying zone of the tape with the surface of the part (Figure 4).e maximum of temperature indices with a value of 1200 °C in the zone of contact of the tape with the surface of the product ensure the alloying in this area with a cast zone formation, which contributes to the creation of a coating with the necessary strength of adhesion to the base metal.
In the zone of contact with the roller electrode, the thermal spot is characterized by lower temperatures, which is explained by the significant heat removal into the copper water-cooled roller electrode.In all the considered cases, heating of the surfacing zone is accompanied by the insignificant heat removal in adjacent to the thermal deformation hearth areas of the electrode material.e increase in the duration of the current impulse during the electrocontact surfacing, with the other constant process parameters (current strength and stress at the roller electrode) according to the obtained results (Figure 5), provides heating over the whole thickness of the tape in the thermal deformation zone to the temperature T �1200 °C. is with a further increase in the time of the current impulse can lead to burn through or splash of the molten electrode material, adversely affecting the quality of the deposited layer and restoring the whole product.
In order to study the effect of the electric current impulse duration on the change in the picture of the stress-strain state of the electrode tape in the thermal deformation zone, a modeling of the process at K v � 1.015 and K v � 1.0 was carried out.show the results of the finite element modulation of the stress-strain state of the tape in the thermal deformation center, depending on the duration of     According to the obtained data (Figures 6-8), the maximum equivalent stresses during the whole time of the current impulse occur in the thermal deformation hearth in the zone of contact of the electrode tape with the surface of the part. is is agreed with the calculated data of the developed finite difference mathematical model [20] and normal contact stresses.
e increase in the time of the surfacing current impulse helps to reduce the value of the equivalent stresses.us, at the time of the current impulse, t imp � 0.03 sec, the maximum value of the equivalent stresses is 115 MPa.And, this value is observed over the whole thickness of the electrode tape in the thermal deformation hearth (Figure 6).With an increase in the time of the current impulse to 0.04 sec, the maximum values of equivalent stresses decrease to 110 MPa and move mainly to the contact zone of the electrode tape with the surface of the part (Figure 7). is is caused by the process of electrode strip metal relaxation, which is in a tough-plastic state.With an increase in the time of the electric current impulse, the overall heating temperature of the metal increases over the thickness of the electric tape, which reduces the value of the equivalent stresses.
High values of equivalent stresses up to 110 MPa in the alloyage zone, which has the highest temperature in the thermal deformation zone (about 1200 °C), are caused by the frictional forces.ey are caused by the kinematic asymmetry of the electrocontact surfacing process.
Further increase in the duration of the current impulse to 0.05 sec results in a shift of the maximum values of the equivalent deformation to the side of the contact zone of the tape with the roller electrode and to a general decrease in their value (Figure 8).us, a further increase in the overall heating temperature of the electrode material, which with the duration of the electric current impulse t imp � 0.05 sec will be 1200 °C along the whole thickness of the electrode strip (Figure 5), will lead to a decrease in the value of the equivalent stresses in the fusion zone, even with a kinematic asymmetry of the electrocontact surfacing process due to the expansion of the heating region and increase in the residence time of the thermodeformation focus in the heated state.is is due to the fact that design of the roller electrode of the contact machine for electrocontact surfacing provides the cooling of the roller electrode.
is avoids welding the tape to the surface of the roller electrode.An increase in the duration of the current pulse leads to an increase in the temperature of the tape in the surfacing zone as a whole.However, in the zone of contact of the tape with the roller electrode, it is forcibly cooled, and in the zone of contact with the surface of the part, its temperature rises significantly.
is helps to increase the equivalent stresses in the zone of contact of the tape with the roller electrode.
At the same time, equivalent stresses in the contact zone of the tape with the surface of the part will be 60-70 MPa,  Advances in Materials Science and Engineering and in the contact zone with the roller electrode, it will be 100-110 MPa, which is related to the less plastic state of the tape in the area of its contact with the roller electrode due to the removal from its surface a certain amount of heat.
According to the results of the presented finite element modulation (Figures 9-11), in the contact zone of the electrode tape with the roller electrode surface, the deformation processes practically do not occur which is caused       when the impulse width of the surfacing current is increased and correlated very accurately with the data of the developed mathematic finite difference model of the electrocontact surfacing on the tape.Besides, higher values of equivalent deformations in the contact zone of the electrode tape with the surface of the part are explained by an increase in the temperature in the thermal deformation zone, which contributes to the intensification of deformation processes and to the qualitative formation of the coating.e contact zone of the electrode tape with the roller electrode is characterized by lower temperatures (T � 911 °C) than the contact zone of the tape with the surface of the part (T �1200 °C) (Figure 3(b)), which causes a decrease in the value of the equivalent deformation up to 0.093, as compared with 0.186 in the fusion zone (Figure 9).With the duration of the current impulse t imp � 0.03 sec, equivalent stresses are 115 MPa and are distributed over the whole thickness of the tape in the thermal deformation zone (Figure 6).In the fusion zone, the area of equivalent stresses increases, according to the results of finite element analysis (Figure 6), which together with the influence of temperature contributes to double the equivalent deformations in this area (Figure 9).e increase in the time for the surfacing current impulse up to 0.04 sec causes an increase in the maximum value of the equivalent deformations in the thermodeformation hearth to 0.203 (Figure 10).According to the initial conditions for the development of a finite element model of the electrocontact surfacing, the heat removal from the surface of the electrode tape to the water-cooled roller electrode in the contact zone was taken into account.
is affected the simulation results in the calculation of equivalent deformations: in the contact zone with a roller electrode with an increase in the duration of the electric current to 0.04 sec, they practically do not change and amount to 0.101 (Figure 10).Moreover, the decrease in the value of the equivalent stresses at t imp � 0.04 sec to 110 MPa in the fusion zone (Figure 7) does not affect the level of equivalent deformations in this section.is is caused by the predominant effect on the deformation processes of the expansion of the metal heating zone of the electrode strip to 1200 °C in the thermodeformation hearth (Figure 4), that is, with the increase in the amount of material in the plastic state.is also allows expanding the area of the deformable metal in the zone of the tape contact with the surface of the part, which increases the adhesion strength of the coating to the surface of the part (Figure 10) and correlated with data [24][25][26].
With an increase in the time of the surfacing current impulse to 0.05 sec, the value of equivalent deformations is doubled (Figure 11).Moreover, such an increase is observed both in the zone of contact with the surface of the electrode tape products (equivalent strain is 0.399) and the tape contact zone of the roller electrode (equivalent strain is 0.190).is is due to the overall increase in temperature over the thickness of the electrode strip.us, the temperature in the zone of contact with the roller electrode will be 1100 °C and the contact with the component surface area will be 1200 °C (Figure 5).Moreover, in the contact area of the tape and parts' surface, equivalent strains increase due to the high temperatures, and in the zone of contact with the roller electrode, they have maximum values (110 MPa) due to combined influence of heating and equivalent stresses at t imp � 0.05 sec (Figure 8).Such an increase in the equivalent deformations along the cross section of the electrode strip in the thermal deformation zone indicates that further increase in the duration of the surfacing current impulse at K v � 1.015 can lead to considerable deformations of the electrode strip and it is unreasonable.
e results of the finite element analysis at K v � 1.0 indicate a decrease in the value of equivalent stresses along the cross section of the electrode tape in the thermal deformation zone from 100 MPa at t imp � 0.03 sec (Figure 12) to 90 MPa at t imp � 0.04 sec (Figure 13).In the first case, the maximum values of equivalent stresses are observed over the whole thickness of the electrode tape, and in the second case, the largest equivalent stresses are concentrated mainly in the zone of contact of the tape with the roller electrode and in the fusion zone. is type of distribution is caused by the heating time of the electrode material, as in the cases with K v � 1.015 (Figures 6-8) and is explained by the fact that, in some areas, the material becomes more plastic, and in some cases, it remains elastic due to the maldistribution of temperature fields.
e increase in the duration of the current impulse to t imp � 0.05 sec, as in the case with K v � 1.015 (Figure 8), helps to reduce the equivalent stresses in the zone of contact of the tape with the surface of the part due to the increase in the area of the material with a temperature of 1200 °C (Figure 14).e value of equivalent stresses is reduced to 60-75 MPa.In all three cases, regardless the duration of the surfacing current impulse, the area of equivalent stresses activity in the zone of contact of the tape with the roller electrode is equal to the area of their activity in the zone of contact of the tape with the surface of the part (Figures 12-14).However, at K v � 1.015, there is the increase in the area of equivalent stresses activity from the contact zone with the roller electrode toward the fusion zone, which is most noticeable with a moderate heating of the electrode material t imp � 0.03 sec (Figure 6).
When studying the effect of the current impulse duration on the variation of equivalent deformations, the same pattern is observed, as in the case of electrocontact surfacing with K v � 1.015.e difference is in decreasing the value of the equivalent strains at K v � 1.0, in comparison with K v � 1.015 for the same values of the surfacing current pulse duration (Figure 15).e general regularity of the increase in equivalent deformations is the same in both symmetrical and asymmetrical processes, with an increase in temperature, that is, with an increase in the amount of material heating to 1200 °C.At K v � 1.0 and t imp � 0.05 sec, the maximum value of the equivalent strain is 0.280 (Figure 15), while at K v � 1.015 and t imp � 0.05 sec, it reaches 0.380 (Figure 11).In the contact zone of the electrode tape with the roller electrode at K v � 1.0 and t imp � 0.05 sec, the equivalent deformations do not exceed 0.187 (at K v � 1.015 and t imp � 0.05 sec, the equivalent deformations in this area are 0.190).is confirms the hypothesis about the effect of the Advances in Materials Science and Engineering electrocontact surfacing kinematic asymmetry coe cient on the deformation processes during the coating by the electrochemical method, and, consequently, on the formation of the interconnection as a whole and its bonding strength.us, one of the methods of increasing the adhesion strength due to the intensi cation of deformation processes in the fusion zone is the increase in the time of the electric current impulse.But both with the kinematic asymmetry of the electrocontact surfacing process and without it, this method causes a rapid change in the stress-strain state, which is di cult to control under the transient nature of the coating process.erefore, it is advisable to control the process of electrocontact surfacing by using tapes by the construction of the kinematic asymmetry of the process.
e kinematic asymmetry coe cient K v e ect on the change in tangential contact stresses in the contact area of the electrode material with the surface of the roller electrode and the part to be reconstructed was analyzed (Figures 16-19).According to the calculated data, the minimum values of tangential contact stresses are observed at the value of the kinematic asymmetry coe cient K v 1.0, that is, without the asymmetry of electrocontact surfacing by using tapes.
eir value under such conditions of the electrocontact surfacing process is 25 MPa.Moreover, the spread areas in the contact zone of the electrode with the roller electrode and in the contact zone with the part's surface are equivalent (Figure 16).
It is established that an increase in K v to 1.015 leads to an increase in the tangential contact stresses in the contact area of the electrode material with the surface of the remanufactured part (τ xi1 38 MPa), while in the contact zone with the roller electrode, these stresses practically do not change (τ xi2 26 MPa), which is consistent with the calculated data of the developed mathematical model [22].
e area of distribution of tangential contact stresses also changes: in the zone of contact of the electrode tape with the surface of the part, they occupy a much larger area than in the contact zone of the tape with the roller electrode (Figure 17).
With an increase in K v to 1.025, τ xi1 increases to 45 MPa in the contact area of the electrode tape with the surface of the part.In the contact zone of the tape with the roller electrode, there is also an increase in tangential contact stresses: τ xi2 is 35 MPa (Figure 18).However, there is also an increase in the area of distribution of τ xi2 in the contact zone of the electrode material with the roller electrode.
Further increase in the kinematic asymmetry coe cient is unreasonable since even at K v 1.075, the tangential contact stresses in the contact zone of the electrode material with the roller electrode occupy a considerable area, which can hinder the qualitative formation of the deposited layer

Comparison
According to the obtained data (Figure 20), the error in calculating the nite di erence model when compared with the results of the nite element model does not exceed 10.2%, which indicates the adequacy of the proposed models.
e adhesion strength of the deposited layer was determined by breaking o the pin by a normally applied force on Sta ens samples with the length of 20 mm and diameter of 4 mm on a tensile-testing machine R-20 GOST 7855-74.
e results of the experiment (Figure 21), carried out on the welded samples at R z 50 mm, I 6.5 kA, and P 1.5 kN, showed that, at K v 1.015, the adhesion strength of the welded layer to the base metal is maximal.
A further increase in the kinematic asymmetry coe cient leads to an increase in the tangential contact stresses    Advances in Materials Science and Engineering in the zone of contact of the electrode tape with the roller electrode.is can contribute to the sticking of the tape on the roller electrode, reducing of the adhesion strength of the coating with part's surface and prevent the formation of high-quality coating.
us, in the course of nite element modeling, the data of the nite di erence model on the kinematic asymmetry coe cient in uence on the change in the local energy-force characteristics of the electrocontact surfacing process by tapes of cylindrical parts are con rmed.It is established that an increase in the adhesion strength of the welded surface is possible due to an increase in the friction coe cient in the zone of their contact, which corresponds with data [24][25][26].According to the obtained data, the optimal value of the kinematic asymmetry coe cient is 1.015 with the invariability of the other parameters of the regime.is allows us to increase the adhesion strength of the welded layer and simultaneously avoid the increase of the mechanical and thermal action on the metal of the welded layer and to prevent an increase in the friction coe cient in the contact zone of the electrode material with a roller electrode, which increases the operational stability of the tool.

Discussion
According to the data obtained, the heating of the electrode material is initiated in the area of its contact with the surface of the detail.At the same section of the tape, the maximum thermal temperatures are observed in the thermal deformation zone during the whole heating period.e main part of the electrode material in the thermal deformation zone is in the viscous-plastic state caused by heating up to   911-1010 °C.Comparison of the modeling results of spatiotemporal thermal fields for different durations of electric current pulse flow indicates the leveling of the temperature gradient in the thermal deformation center, both along the length and width of the tape with increasing time of the current pulse.
In order to study the effect of the electric current pulse duration on the change in the picture of the electrode strip stress-strain state in the thermal deformation zone, a modeling of the process flow was carried out at K v � 1.015 and K v � 1.0.It is established that the maximum equivalent stresses (about 115 MPa) during the whole time of the surfacing current pulse in the thermal deformation heath occur in the zone of electrode tape contact with the surface of the part.High values of equivalent stresses in the deposition zone, which has the highest temperature (1200 °C) in the thermal deformation zone, are caused by frictional forces conditioned by the kinematic asymmetry of the electrocontact surfacing process.
A short-term impulse of electric current of 6000 A promotes almost instantaneous heating of the electrode tape in the surfacing zone.e frictional force in the zone of contact of the tape with the surface of the part acting as a result of the kinematic asymmetry does not have a significant effect on the heating of the tape.However, the presence of friction improves the adhesion of the tape to the surface of the part. is contributes to high-quality coating formation.
According to the results of the presented finite element modeling, the deformation processes practically do not occur in the contact zone of the electrode tape with the roller electrode surface: they practically do not change in this contact zone and amount to 0.101. is is caused by the low values of tangential contact stresses (25-26 MPa) typical for this section of the tape thickness and also the relatively low temperature of the material in this zone (900 °C).On the contrary, equivalent deformations are characterized by maximum values in the contact zone of the steel tape with the surface of the part (45 MPa).Such a picture is observed with increasing duration of the surfacing current pulse and agrees well with the data of the developed finite element mathematical model of the electrocontact surfacing by tapes [22].
e effect of the kinematic asymmetry coefficient magnitude on the change in tangential contact stresses in the contact area of the electrode material with the surface of the roller electrode and the remanufactured part is analyzed.It is established that an increase in the kinematic asymmetry coefficient up to K v � 1.015 leads to an increase in tangential contact stresses in the contact zone of the electrode material with the surface of the remanufactured part up to 38 MPa. e area of tangential contact stresses also changes: in the zone of the electrode tape contact with the part surface, they occupy a larger area than in the contact zone of the tape with the roller electrode (Figures [16][17][18][19].
Experimental studies of the adhesion strength of the parts' surface coated with different values of the kinematic asymmetry coefficient were carried out.e results of the experiments indicate an increase in the adhesion strength of the applied layer up to 217 MPa with an increase in the kinematic asymmetry coefficient up to 1.015.

Conclusion
Based on the theoretical analysis of the conditions of the process of electrocontact surfacing with tapes using the finite element method, the influence of the value of the kinematic asymmetry coefficient K v , determined by the ratio of the linear velocities of the roller electrode and the product, on the local energy-force parameters of the process is investigated.It is shown that, at K v � 1.015, the distribution area and the magnitude of the tangential contact stresses in the fusion zone up to 30 MPa are increased, while the tangential contact stresses in the contact zone with the roller electrode are unchanged, which must be taken into account when designing the technological process of restoring the parts.e effect of K v on the strength of adhesion of the deposited layer and the surface of the part σ ad is experimentally established: at K v � 1.015, strength of adhesion strength increases by 1.54 times to 217 MPa.

Finite
element modulation of the electrocontact surfacing by tape was performed for the following initial parameters: (i) Diameter of the roller electrode: 100 mm (ii) Tape width: 3.2 mm (iii) Tape thickness: 0.5 mm (iv) Force on the roller electrode: 2 kN (v) Surfacing current: 6 kA Material and mechanical properties of the tape are given in Tables 1-4.

Figure 1 :Figure 2 :
Figure 1: Design model of the nite element modulation of the electrocontact surfacing of cylindrical parts by the tape. 1, electrode tape; 2, cylindrical part; 3, roller electrode; 4, elastic element simulating the clamping force of the roller electrode.

Figure 3 :
Figure 3: Distribution of temperature elds in the process of electrocontact surfacing during an electric current impulse t imp 0.04 sec: in 0.02 sec of the current pulse behavior (a); in 0.03 sec of the current pulse behavior (b); at the exit from the thermal deformation hearth (c).

Figure 4 :
Figure 4: e general form of the temperature eld of a steel strip in a thermal deformation hearth (a, b) and the distribution of thermal elds in the zone of the tape contact with the surface of the component (c) in the process of electrocontact surfacing at the outlet from the thermal deformation hearth t imp 0.04 sec.

Figure 5 :
Figure 5: General view of the temperature field of a steel tape in the thermal deformation hearth (a, b) and the distribution of thermal fields in the zone of tape contact with the surface of the part (c) in the electrocontact surfacing at t imp � 0.05 sec.

Figure 7 :
Figure 7: e distribution of equivalent stresses in the thermodeformation hearth (a, b) and in the zone of contact of the tape with the surface of the part (c) in the case of electrocontact surfacing with steel tape at K v � 1.015 and the duration of the current pulse t imp � 0.04 sec.

Figure 6 :
Figure 6: e distribution of equivalent stresses in the thermodeformation hearth (a, b) and in the contact zone of the tape with the surface of the part (c) during the electrocontact surfacing of the steel tape at K v � 1.015 and the duration of the current impulse t imp � 0.03 sec.

Figure 8 :Figure 9 :Figure 10 :Figure 11 :
Figure 8: e distribution of equivalent stresses in the thermodeformation hearth (a, b) and in the zone of contact of the tape with the surface of the part (c) in the case of electrocontact surfacing with steel tape at K v 1.015 and the duration of the current pulse t imp 0.05 sec.

Figure 12 :
Figure 12: e distribution of equivalent stresses in the thermal deformation hearth (a, b) and in the zone of contact of the tape with the surface of the part (c) in the case of electrocontact surfacing with a steel tape at K v 1.0 and the pulse duration of the current t imp 0.03 sec.

Figure 14 :
Figure 14: e distribution of equivalent stresses in the thermal deformation hearth (a, b) and in the contact zone of the tapes with the surface of the part (c) in the case of electrocontact surfacing of the steel tape at K v 1.0 and the impulse width of the current t imp 0.05 sec.

Figure 13 :
Figure 13: e distribution of equivalent stresses in the thermal deformation hearth (a, b) and in the zone of tape contact with the surface of the part (c) in the electrocontact surfacing of the steel strip at K v 1.0 and the impulse width of the current t imp 0.04 sec.

Figure 15 :
Figure 15: e distribution of equivalent deformations in the thermal deformation hearth in electrocontact surfacing of a steel tape at K v 1.015 and the duration of a current impulse: t imp 0.03 sec (a), t imp 0.04 sec (b), and t imp 0.05 sec (c).

Figure 16 :
Figure 16: Distribution of tangential contact stresses in a thermal deformation hearth at K v 1.0.

Figure 17 :
Figure 17: e distribution of the tangential contact stresses in the thermal deformation hearth at K v 1.015.

Figure 18 :
Figure 18: e distribution of tangential contact stresses in a thermal deformation hearth at K v 1.025.

Figure 19 :
Figure 19: e distribution of tangential contact stresses in a thermal deformation hearth at K v 1.075.

Figure 20 :Figure 21 :
Figure 20: Comparative analysis of the calculated values of tangential contact stresses obtained using the proposed nite di erence and nite element models.

Table 1 :
e chemical composition of the material of the electrode tape.

Table 2 :
Mechanical properties of the electrode tape at T � 20

Table 3 :
Physical properties of the electrode tape depending on the heating temperature.

Table 4 :
Yield strength σ T depending on plastic deformation δ and heating temperature T.