Yu. Korobov, M. Shalimov, V. Shymiakov
Ural State Technical University, Ekaterinburg, Russia
A BSTRACT. At usage of cored wires, designed with reference to welding and surfacing, is established, that the received arc metallization coatings have no sufficient adhesive and cohesive strength. It is connected with heightened oxidation of drops of sputtered metal and with uncompleted fusion of a charge core. Here model of propagation of heat in cored wire from exposure of electric arc is introduced.
Obtained results can be utilized both for forecast of temperature of drops, and as input data for description of physicochemical interactions on designed before model of
EAM processes. Propagation of heat is described by differential heat conduction equation, which was numerically solved. Heat transfer on borders "shell of cored wire
– transporting gas" and "shell - charge core" was taken into account. Analysis of calculation results has shown, that shell is melted approximately in 100 times faster, than solid wire, temperature of core can be considerably heightened at increase of its heat conduction, temperature gradient on border" shell - gas" is insignificant.
Industrial use of economically profitable process of electro arc metallization
(EAM) have met with a problem of unreliable reception of solid wires of necessary structure and properties. It is connected with difficulties in manufacturing of wires of high hardness in case of wear-resistant coatings and with unacceptable elongation of manufacturing cycle if updating of elemental compositions of wire is necessary. Usage of core wires (CW) allows deciding this problem. CW represents a continuous electrode of tubular design with a powdery filling material - charge. The shell is usually made from low carbon steel of 0,3 - 0,5 mm thickness. The charge consists of a mixture of minerals, ferroalloys, and other ingredients. The features of EAM do not allow ensuring quality of coatings at usage CW, designed with reference to welding and surfacing. EAM process is shown in fig. 1. The continuously feeding wires are melted in arc, which is burning between them. The molten stuff, under effect of a gas stream, is blown from arc burning zone. In comparison with welding here specific surface of drops is by an order of magnitude greater, and the dwell-time of metal in liquid state is an order of magnitude less.
The former feature easies receipt of oxygen into metal, and the latter one reduces efficiency of measures on deoxidation because of restricted time of interaction in system "gas – CW components" and of possible uncompleted fusion of charge. In known CW, which are designed for EAM (1), these features are not taken into account. It results in no sufficient adhesive and cohesive strength. The scientifically reasonable analysis of the causes of these lacks now misses.
For solution of this problem we developed mathematical model of EAM processes depicting fusion and separation of a sputtered stuff from electrode end face (2), field of speeds and temperatures in a diphase flow (3), and also kinetics of interphase interaction with reference to a system "gas - drop of sputtered metal" (4). However it suits with reference to usage of solid wires only. CW differ by irregularity of
2 - 40

+
R r N z r s
- i s i d m l
Fig. 1 . Scheme of electro arc metallization process thermo-physical properties on cross-section, that changes character of thermal and physicochemical processes at end face sharply. So, for example, the results of investigation of coating obtained at CW metallizing, has shown, that the charge can be adjoined from end face in an infused state (5).
In the present study the model of propagation of heat through CW from exposure of electric arc is offered. The data, obtained as a result of simulation, can be utilized as independently, for forecast of temperature of drops, which are generated at wire fusion, and as input data for description of physicochemical interactions. The analysis of passing processes at sputtering CW will allow to reduce volume of researches of CW developing, and to optimize CW both in design, and in charge composition.
Distribution of heat in area of end face of electrode is considered as axially symmetric problem and is depicted by differential equation of heat transferring:


T t
 с

 





2 x
T
2



2 y
T
2

 , [1]
Where Т - temperature, K; t - time, s;

- thermal conductivity, W / (m

K); c - specific heat, J / (kg

K);

- density, kg / m
3
; x, y - coordinates on cross-section and through CW generating, accordingly.
The following assumptions were accepted. As electrical conductivity of shell is by a factor of 10
2
, than charge one; active arc spots are localized at ends faces of shells. According to our scheme of formation of drops at EAM (3), temperature on a surface of end face of a metallic shell reaches 2900 K. Charge composition corresponds standard CW, intended for spraying wear-resistant coating by EAM: 20 % of carbon ferrochromium, 4 % of aluminum, 3 % of a titanium (6). At calculation the heat propagation during 4.7

10 -4 s is reviewed, according to data of oscillography measurement of drops dwell-time at end face before separation in case of solid wire
2 - 41

metallization (7). 6 mm depth section of heat propagation area is reviewed. That depth is selected on calculation of bed depth of molten metal according to the solution of a problem of a melting of non-warmed-up body of the restricted sizes at continuous removal of forming melt subjected to enthalpy of a melting [8] with reference to a solid wire.
The surface of charge receives heat from arc column by radiation and is heated thus up to 1300 K. Shell is heated up with an arc, returns heat to transporting gas and to charge.
At calculation of heat exchange "shell - gas " the factor of convective surface heat exchange is determined by Nusselt cryteria, which one is calculated by equation used for cross-flow of tubes (9):
Nu

0 , 245

Re
0 .
6
[2]
According to our calculations, at cross air flowing of electrode (2 mm dia, air speed
300 m\s, air temperature 300 K) a heat-transfer coefficient on border"gas - shell" constitutes

1
= 2070 W / (m constitutes

2
2
= 1400 W / (m

K). Heat-transfer coefficient on border "shell - charge"
2 
K) (10).
On the given research stage taken at calculations values of thermo-physics quantities of components were averaged over temperature range reference for liquid state. Besides the exothermal effects were ignored at oxidation of components (Al, Cr,
Fe, Ti).
Equation [1] was numerically solved by explicit difference method. The considered area was divided on radius (r) by coordinate lines j = const with step
 r = r/11 and on depth (s) by coordinate lines i = const with a step
 s = s/10. Within borders of element temperature is considered as constant and is related to its middle.
For these elements of a grid we accept:

T
 t


T
 t


T i k
, j

1 
 t
T i , k j

,
It is possible to express a differential, for example through (r), as:

T
 r
 
T
 r ,
[3]
 r
2

 2
T
1
 r





T r i k

1 , j

T
 r


T i k
, j

 r

T i , k j

T
 r


T i k

1 ,
1 j
 r





T
 r
T i k

1 , j



2 T i , k j

T
 r




T i k

1 , j

 r
[4]
 r
2
The differential on (s) is expressed similarly. Then for considered grid area the equation, which approximate differential equation [1], may be represented as follows:
T i k
, j

1 
T i k
, j
 с

 

B
 r
1
2

B
 s
2
2
  t , [5]
Where B
1

T i k

1 , j

2 T i , k j

T step on time;
 t - step on time. i k

1 , j
; B
2

T i , k j

1

2 T i , k j

T i , k j

1
; k - number of a
At the solution of equation (5) the constraint, which is followed from a condition of convergence at selected method is imposed:
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с

 


1 r
2

1
 s
2

1
2
(6)
Temperature on outer surface of electrode shell was calculated on a condition of heat exchange at cross-flow of electrode by gas:

1


T i k
, j
 r

T i k

1 , j

 
1


T i k

1 , j

T g

(7)
Temperature on border "shell - charge core" was calculated on a condition of heat exchange:

1


T i k

1 ,
 r j

T i k
, j

 
2


T i , k j

T i k

1 , j

(8)
The values of the thermal characteristics, taken in calculations, of stuffs are shown in table.
T able. Values of the thermal characteristics of stuffs taken in calculations
Stuff с, J/(кg  К)  , кg/m 3 
, W/(m
 К) 
, W/(m
2  К)
Shell-gas Shellcharge
2070 1400 Shell, steel
08кп
Charge
806 7300 20
806 4500 5
The analysis of results of calculations, in particular, has shown:
1) Shell temperature reaches level of 2000 K during 4

10 -6 s (fig. 2). It is approximately in 100 times faster, than in case of a solid wire. It is possible to explain
2500

= 20 W/(m

K)
2000
1500
1000

= 5 W/(m

K)
500 r,mm
0
0,0 0,2 0,4 0,6 0,8 1,0
Fig. 2 . Distribution of temperatures in cross-section of cored wire on depth 6 mkm from surface of electrode end face after 4.7

10
-6
s
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such result by heightened density of a thermal energy allocated in active arc spot: according to adopted assumption all heat is evolved only in steel shell and is not consumed for charge heating;
2) Charge temperature can be considerably heightened at increase of its heat conduction (fig. 2). It will increase probability of simultaneous fusion of shell and core. It will allow, in turn, providing more favorable conditions for alloying elements transition in drops of sputtered metal and their effective protection against undesirable interaction with components of transporting gas;
3) Temperature gradient on border of transition "shell - gas " is insignificant owing to high heat conduction of shell (fig. 3).

= 5 W/(m

K); s = 6 mkm; t = 4

10
-6
s
2040
2030
2020
2010 r,mm
2000
0,8 0,9 1,0
Fig . 3 . A decrease of temperature of shell owing to cross-flow of electrode by gas.
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