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The forming of coating at electric contact surfacing is considered. The mathematical model of the coating formation is developed. The method of numerical recurrent solution of the finite-difference form of static equilibrium conditions of the selected elementary volume of coating is used. This model considers distribution of thermal properties and geometric parameters along the thermal deformation zone during the process of electric contact surfacing by compact material. It is found that the change of value of speed asymmetry factor leads to increasing of the friction coefficient in zone of surfacing. This provides the forming of the coating of higher quality. The limitation of the technological capabilities of equipment for electric contact surfacing is related to the size of recoverable parts and application of high electromechanical powers. The regulation of the speed asymmetry factor allows for expanding the technological capabilities of equipment for electric contact surfacing. The nomograms for determination of the stress on the roller electrode and the finite thickness of the coating as the function of the initial thickness of the compact material and the deformation degree are shown.

The creation of a coating with the necessary operating characteristics is a perspective direction in the reconditioning of worn parts as well as improvement of their service life [

One of the most common technological processes of the reconditioning of the worn parts is arc welding, which achieves the desired working layer on the surface of the product but has a number of disadvantages too. Those include a significant change in the initial phase state of coating material and substantial thermal effect in material of a part [

This method is a combination of short-term thermal and mechanical effects on the surfaced material located on the surface of a renewed rotating axisymmetric part, which allows for providing a tough coating. The conjoint plastic deformation of a renewed part together with adding material results in combination of the coating with the base metal. Currently, there are a lot of studies on the selection of the recommended composition of the compact material, providing the desired performance characteristics of the coating. However, because of the short duration of the electric contact surfacing, there are some difficulties in predicting the quality of the coating and its compliance with basic operation characteristics. That is why it is necessary to use the mathematical apparatus for analytical design of electric contact surfacing in order to optimize the basic parameters of this process to obtain the coating that best meets the specified requirements.

Authors in [

The short-term thermomechanical exposure during the electric contact surfacing allows decreasing thermal influence on the coating and part material on the one hand and decreases the quality forecasting accuracy of the coating on the other hand. The adhesive strength of the coating to the part surface during the electric contact surfacing is an important quality indicator; thus, the task of developing technological methods to improve the adhesive strength is an actual problem.

The formation of coating at electric contact surfacing of “shaft” type parts is investigated. The influence of the thermomechanic operating parameters on the coating formation on the surface of cylindrical part with predicted geometric parameters is investigated.

Based on the numerical recurrent solution of the finite-difference form of the static equilibrium conditions of selected elementary volume of the coating, mathematical model of coating formation was developed. Its peculiarity is the proper record of actual distribution of the thermal properties and geometric parameters on the length of thermal deformation zone during the process of electric contact surfacing by compact material. The problem of automated design of technological modes of electric contact surfacing is formulated and solved by using the developed mathematical model.

The method to improve the adhesive strength of the coating to the part surface by creation of the speed asymmetry during the electric contact surfacing by the compact material is proposed.

The influence of the speed asymmetry factor on the friction coefficient changing in thermal deformation zone in the zone of contact of part with compact material is investigated.

The impact of the speed asymmetry factor on the energy-power and thermal operating parameters’ changing is proved.

Results of research can be used in the designing of equipment for electric contact surfacing, as well as in selection of optimal operating parameters of surfacing process.

The mathematical model of electric contact surfacing of “shaft” type parts is developed on the basis of the numerical recurrence solution of the finite-difference form of static equilibrium conditions of selected elementary volumes [

Design model for process of “shaft” type parts surfacing (1: part to be surfaced, 2: compact material, and 3: roller electrode).

Due to the specific realization conditions of considered technology, we should point out that the circumferential speed of part 1 and compact material 2 at the outlet from the plastic deformation zone are equal; that is, _{2} is a bit lower than surface speed

In addition to the abovementioned, a number of assumptions were adopted. The most important of them are the following.

(i) Deformation of compact material 2 (see Figure

(ii) On the length of each selected

Design diagrams of elementary volumes of mathematical modeling of stress-strain state of the compact material.

(iii) Analytical descriptions of tangential contact stresses

The value of double shift resistance of the compact material is determined with considering current values of degree, speed, and temperature of deformation. The current value of the plastic friction coefficients depends on the geometric coordinate

(iv) We neglect the presence of an elastic compression zone of surfaced compact material in sections at the inlet of the deformation zone, as well as the presence of the inertial components of the equilibrium conditions, due to their very low influence.

(v) Analytical description of the current thicknesses value

(vi) The total length of zone of the plastic deformation

Given the nature of the assumptions and finite-difference record forms of the main components of the stress-strain state (see Figure

The current levels of double shift resistance

Equation (

As the directions of recurrent circuit of solutions, the direction of the compact material is used. Taking this into account, the initial conditions for the first

With the calculation of local characteristics for stress-strain state within zones of the plastic deformation of the compact material by numerical integration, there were certain forces

Modeling of thermal state of compact material in thermal deformation zone at electric contact surfacing is performed with considering of the compact material as unlimited plate [

With considering that

Equations (

The differential equation of heat conductivity with considering of initial condition (

The solution of (

According to symmetry condition (

Boundary condition (

With considering

Then, constant

Thus, the solution for the image is

Solution (

The decomposition theorem can be presented as

If

According to the decomposition theorem,

The substitution of other roots

Thus, the solution can be presented as

Equation (

If

Then, the solution can be presented as

Thus, the relative temperature in any point of compact material in thermal deformation zone is the function of nondimensional values Fo, Bi, and

In this point, the temperature of compact material is minimal.

Knowing the distribution of temperature fields along the length of compact material in thermal deformation zone, required current pulse can be calculated as

Presented set of analytical descriptions made the complete algorithm for the numerical one-dimensional mathematical modeling of electric contact surfacing for parts such as bodies of rotation by a compact material. The aggregated block diagram of this solutions algorithm is shown in Figure

The aggregated block diagram of the algorithm for electric contact surfacing by the compact material.

The calculated distributions of normal contact stresses along the zone of the surfacing, depending on the speed asymmetry coefficient (the initial thickness of compact material is 0.5 mm).

The calculated distributions of tangential contact stresses on the roller electrode along the zone of the surfacing, depending on the speed asymmetry coefficient (the initial thickness of the compact material is 0.5 mm).

The calculated distributions of tangential contact stresses on the detail along the zone of surfacing, depending on the speed asymmetry coefficient (the initial thickness of the compact material is 0.5 mm).

The calculated distributions of forces on the roller electrode, depending on the reduce and the speed asymmetry coefficient (the initial thickness of the compact material is 0.5 mm).

The calculated distributions of the moment on the detail, depending on the reduce and the speed asymmetry coefficient (the initial thickness of compact material is 0.5 mm).

The calculated distributions of the moment on the roller electrode, depending on the reduce and the speed asymmetry coefficient (the initial thickness of compact material is 0.5 mm).

The calculated distributions of the current pulse, depending on the reduce and the speed asymmetry coefficient (the initial thickness of compact material is 0.5 mm).

The peculiarity of the proposed mathematical model is the correct consideration of distribution of the thermal characteristics of the compact material along the thermal deformation zone, which significantly affects the forming of welded joint during the surfacing process. The adhesive strength, structural homogeneity, and the geometric parameters of the coating are the quality indicators of the surface layer. The durability of the restored part directly depends on the adhesive strength of the coating to the part. Because of the low adhesive strength, there is exfoliation of the deposited layer during operation. Therefore, the development of the technological scheme to improve the adhesive strength of the coating is the actual task, which allows providing the forming of the high quality coating.

The important characteristic of electric contact surfacing is the short duration of the heat process. Therefore, the desired thickness of the deposited layer and the high adhesive strength of bond by controlling the technological modes of electric-welding process are very important. One of the widely known methods of the bond strength of the coating improving is intensification of the electric contact surfacing by increasing the friction coefficient in the zone of contact of part with compact material due to creation of opposite torque under a current pulse [

The theoretical researches were conducted at various values of the speed asymmetry factor (

So, the most rational in terms of the quality of the coating is the asymmetrical electric contact surfacing process with speed asymmetry of not more than 1.015. This allows providing the increase of the friction coefficient in the surfacing zone without the increase of the energy and power parameters. Reduction of the integral characteristics of the process allows repairing big sized parts with the lowest thermal and mechanical impact. This minimizes the structure changes of the functional coating and the surface layer of main metal. On the basis of the developed software, the calculation of the main technological process parameters was made (Figures

The results of automated design of the efforts on the roller electrode, depending on reduce. ^{2};

The results of automated design of the final thickness of the coating, depending on the reduce._{1} = 0.124;_{2} = 0.052;_{3} = −3.70; ^{2};

The check of the adequacy of the obtained analytical descriptions of electric contact surfacing was done during restoring of the parts of “shaft” type made of steel St45 by continuous ribbon St45 on the electric machine of the seam type welding MSHP-150 with a rated power of the surfacing current 20 kA and a maximum compression force of 8 kN (Figure

General view of the installation for experimental investigation (a, b), the basic scheme of equipment for electric contact surfacing (c) (1: bottom bracket, 2: cantilever, 3: roller electrode, 4: intermediate plate, 5: slider for drive efforts, 6: articulated shaft, 7: casing wall, and 8: the rotary drive).

Force measurement on the roller electrode was done with the help of load cells; also the measurement of the moments on the roller electrode and the detail was provided with the help of tensiometric sensor of resistance. Using the sliding strings of current collectors, the electrical signal from the rotating universal spindles was read. The calibration of the measuring instruments was performed by simulation of loading with the use of the cantilever arm and a set of cargos. Recording of registered parameters was produced by means of a PC with built-in analog-to-digital converter, providing the measuring ability at 16 differential channels. Input in this case is digitized by 16-bit analog-digital converter with a frequency of 100 kHz and a gain opportunity in the range of 1 to 1000. The oscillograms were recorded by a converter of voltage measuring E14-140 (Figure

The control of geometric parameters of the initial compact materials and the received coating was carried out by a micrometer and caliper. The results of comparison of the calculated and experimental distributions of the efforts on the roller electrode are presented in the form of graphic dependence (Figures

The calculated and the experimental distributions of the efforts on the roller electrode during the electric contact surfacing by the compact material._{1} = 0.124;_{2} = 0.052;_{3} = −3.70; ^{2};

The calculated and the experimental distributions of the current pulse during the electric contact surfacing by the compact material._{1} = 0.124;_{2} = 0.052;_{3} = −3.70; ^{2};

The integral characteristics of the process of electric contact surfacing by compact materials are determined in investigation. This allows making conclusion about sufficient convergence of experimental results and theoretical assumptions concerning process laws. The change of speed asymmetry factor is the perspective direction for control of the stress-strained state of compact material, which allows regulating the plastic deformation of the material process. The optimum conditions for forming of wearproof coating without lack of fusion can be obtained by changing the speed asymmetry factor which depends on rotational speed ratio of roller electrode and “shaft” type parts.

The heavy operating conditions lead to fast deterioration of details durability. Increasing of technical and economic parameters of equipment is inextricably linked with increasing of service life of parts working in conditions of intense abrasive deterioration. Restoration of operability of worn equipment can be achieved by two ways: either changing of worn parts by new ones or building up of metal on worn surface until reaching the nominal sizes. The first way is less profitable from economic point of view because the expenses on spare parts can achieve 80% of initial cost of equipment. The electric contact surfacing by compact materials allows applying on the worn surface a coating of the specified thickness with the required operating characteristics. Use of this method allows solving effectively the problem of prolonging of service term of technological unit. The method of electric contact surfacing is characterized by transience of intensely thermomechanical impact on the surfacing compact material. This allows obtaining coating on the surface of part without significant thermal influence on the base metal of part. This peculiarity of the process allows avoiding the structural changes of the base metal and preventing decreasing of its mechanical properties. However, the transience of current pulse confines the precision of quality prediction of the coating. The adhesive strength of the deposited coating is the most important quality indicator because at the low value of this parameter there is exfoliation of the coating during operation. The intensification of the surfacing process at the expense of increasing of the friction coefficient in zone of contact of part with compact material is an effective method to improve the adhesive strength of the coating. The speed asymmetry factor has a great influence on increasing of friction coefficient in surfacing zone. The change of this parameter has a significant impact on stress-strain state of compact material in thermal deformation zone.

The influence of speed asymmetry factor on the local and integral characteristics of the process is considered in present work (Figures

Increase of the speed asymmetry factor leads to change of stress-strain state of the compact material in thermal deformation zone. Increase of

The calculation of the main technological parameters of the process is received with application of developed software. Via developed software, the value of speed asymmetry factor was calculated, which allows increasing friction coefficient in thermal deformation zone. The nomograms for determination of the stress on the roller electrode (Figure

Generally, the obtained results confirm that the variation of initial parameters of electric contact surfacing process of cylindrical parts is very important during the formation of power parameters, as well as during preparation of measures aimed at ensuring the stability of the surfacing process and improving the quality of the deposited layer with specified geometrical characteristics.

A mathematical model, which allows optimizing the technological parameters of electric contact surfacing by compact material of the “shaft” type parts, was developed. As a result of numerical implementation of the developed model, it was found that a significant effect on the change of power parameters of the process was made by the ratio of roller electrode and the “shaft” type parts speeds. It is established that the change of the speed asymmetry factor has a significant influence on the forming of the coating because of the increasing of the friction coefficient. It is proved that the application of the asymmetric process of electric contact surfacing allows decreasing the thermomechanical impact on the compact material in surfacing zone. This considerably expanded the capabilities of the equipment and allows reducing the thermomechanical influence on the base metal of the parts. Obtained graphic dependences allow determining the initial parameters of the process such as the amperage, stress on the roller electrode, and the initial thickness of the compact material, depending on the required characteristics of the coating before the beginning of the process of electric contact surfacing.

Geometric coordinates of initial and finite boundary section of selected elementary volume

Rotational speed of roller electrode and part

Radius of roller electrode and part

Length of the zone of the plastic deformation

Length of the mixed zone

Length of the zone of the lag on the roller electrode

The value of the partition step of the plastic deformation zone

Current value of the double shift resistance of the compact material along the length of thermal deformation zone defined with considering of the current values of degree, velocity, and temperature of deformation

Normal contact stresses on the roller electrode and on the part

Current values of thickness of the coating along the length of selected elementary volume

Initial thickness of the compact material

Final thickness of the coating

Thickness of the compact material in the neutral section

Exponent indicator of the real convex shape of the roller electrode

Width of the roller electrode

Stress on the roller electrode

Moment on the part and on the roller electrode

The environment temperature

The material temperature

Coefficient of temperature conductivity

The half of the thickness of compact material

The exponent characterizing the distribution of the plastic friction coefficients on the contact surfaces of the part and the roller electrode

Biot criterion

Fourier criterion

Predvoditelev criterion

The current pulse.

Tangential contact stresses on the roller electrode and on the part

Rear tension stress of the compact material

Normal axial stresses in the outlet of thermal deformation zone

Current value of plastic friction coefficient

Coefficient of thermal conductivity

Heat transfer coefficient.

The current ordinal number of the selected elementary volume along the length of the thermal deformation zone

The number of partitions along the length of thermal deformation zone

The value at the entrance to the elementary volume of thermal deformation zone

The value at the output from an elementary volume of thermal deformation zone.

The submission of the authors’ paper implies that it has not been previously published, that it is not under consideration for publication elsewhere, and that it will not be published elsewhere in the same form without the written permission of the editors.

The authors Olena V. Berezshnaya, Eduard P. Gribkov, and Valeriy D. Kuznetsov declare that there is no conflict of interests regarding the publication of this paper.

All authors participated in the design of this work equally. All authors read and approved the final manuscript.

_{2}–SiC protective coatings