ELECTRO ARC METALLIZATION - LIQUID METAL LAYER BEHAVIOR
AT ELECTRODE END FACES.
Yu. Korobov, O. Ogorodnikova, D. Maltsev
Urals State Technical University – УПИ, Russia
Electro arc metallization (EAM) is more preferable spraying process in
comparison with flame spraying and plasma spraying by its heat efficiency. It is 3 –
10 times higher than that one of the latter. But it's difficult to form narrow metal flow
in spite of high velocity and rate of gas flow. It leads to low material efficiency, so
EAM expansion is restrained.
Coating quality is strongly depended by processes at arc burning zone. Our
calculations showed that 70 – 90 % of common oxygen reception takes place here [1].
At EAM electrode metal is fused at arc burning zone and transporting gas flow sprays
it, fig. 1.
F
Fig. 1. Scheme of Electro Arc Metallization process.
"Liquid metal – electric arc" interaction is considering widely at arc welding.
But these investigations are not able to explain liquid metal behavior adequately at
EAM It differs from arc welding by gas flow velocity, 250 – 1500 m/s at EAM
against 10 – 30 m/s at arc welding. Besides, mutual location of cathode and anode is
another. So process parameters are altering abruptly from EAM to arc welding:
- at EAM drop is detached from electrode face at less period, it's size is
decreased also. Detaching period  = (10-1 – 10-2) s, drop size d = (1 –
3) mm at arc welding [2]. At EAM  = (10-3 – 10-4) s, drop size d =
(10 – 300)10-6 mm, our experimental data.
- mutual electrode inclination causes special interaction of magnetic and
electric fields of running current.
- both cathode and anode are electrodes at EAM. It means that detaching
drops from one electrode don't achieve another
Liquid metal behavior at electrode face is determined by following:
2 - 88
1. EAM electric arc distinctive features.
Arc column compression takes place because of pinch – effect. It leads to longitudinal
pressure gradient. So plasma flows occur from less diameter places. According to
solution of Navie-Stocks equation for that case, maximal plasma flow velocity is
determined by following equation [3]:
v max 
I j

2
  I2
2  2  r 2  
(1)
1
3
+
15Å
here:  - permeability of medium; I – current; j = 6.4107 A/m2 – current density; r –
arc column radius. Such current density is specified at diameters of electrode and of
arc column as subjects to the equality. According to equation (1) it corresponds to
vmax = 140 m/s. This is of short distance to experimental data from [5, 6], where high
–speed photography was used. That value lies between plasma flow velocity v = 78
m/s at arc welding, where j = 2107 A/m2 [2], and plasma flow velocity v = 393 m/s at
plasmatron, where j = 5108 A/m2 [4]. Equation structure shows that gas flow velocity
increase causes compression of plasma flows around arc column. It strengthens arc
stability in interelectrode gap.
We accepted scheme according to [3], where arc column stays cylindrical
despite of gas flow exposure. At the same time plasma flows are attached to arc spots
and are drifted by joint influence of Ampere force and gas-dynamic head, fig.2.
+
5
Ãàç
-
2
4
1
3
Ãàç
-
5
2
4
a)
b)
Fig. 2. Arc form at joint air – magnetic blast
a) in interelectrode gap; b) at face edge. 1, 2 – electrodes; 3, 4 – plasma
flows; 5 - arc column
It's possible to evaluate arc column velocity vпс by drop detaching period:
v пс  2  10 3 sin 15   5.7  10 4   12м / с
(2)
-3
here: 210 m – electrode diameter; slope angle is 15; drop detaching period is
5.710-4 s.
2. Liquid layer thickness at electrode face.
Evaluation of liquid layer thickness was done by means of heat balance equation:
Qэ = Qток + Qт - Qконв
(3)
here: Qэ – summary received heat; Qток – Joule heat; Qконв – convective heat
When equation is opened:
с    v п (Tk  T)
 с    v п L  L x    4T  Tg  
dT

(4)
с    vп
 j2  
exp  
  
dL
L  Lx

d

 

2 - 89
here:  - specific resistance;  - electrode material density; vп – electrode feed
rate; L – electrode extension; Lx – running extension; Тк = 2500 К – taken drop
temperature on electrode face; Тg – gas temperature, d – electrode diameter.
Electrode heating by arc heat was calculated according to equation of
propagation a continuous flat heat source, which is drifted uniformly. Convective heat
transfer coefficient  was calculated according to criteria dependences:
Nu   g
(5)

d
Nu  0.032  Re 0.8
(6)
Re  v g  d   g / 
(7)
here: g, vg, g,  – thermal conductivity, velocity, density, dynamic viscosity of gas.
Temperature dependences of specific resistance, specific heat were
approximated by equation of the form y  A1  T 2  A2  T  A3 according to [11, 12].
In interval of (300 - 1184) K these characteristics change abruptly according to phase
transformations. So, taking value averaged over this interval leads to excessive error.
Equation (4) was numerically calculated for typical EAM initial data. It shows that
average thickness of liquid layer on steel face is about 1110-6 m, fig. 3.
2500
T, K
2000
1500
1000
500
h,mm
0
0,00
0,04
0,08
0,12
0,16
0,20
Fig. 3. Liquid face temperature change. EAM taken parameters: I = 200 A,
wire - Св08Г2С  2 mm, vg = 300 m/s.
We can also evaluate thickness of detaching layer and gas flow velocity in
interelectrode gap.
Thickness of detaching layer is calculated from condition of value equilibrium
between detaching layer and drop per detaching period. According to oscillogram
([13], for example) data processing, drop detaching period is 5.710-4 s. It means that
drop mass m = 6.410-7 at electrode feed rate 0.05 m/s. If detaching layer thickness is
assumed uniform, then:
m

 6.4  10 6 м
(8)
  Sпов
Calculation of gas flow velocity.
Gas flow over face surface causes friction tensions  in liquid metal layer. Its viscosity
determines them. It leads to detaching of some liquid metal portion. Tension is
2 - 90
determined by Newton equation:
dv

(9)
dx
In cause of thin liquid layers, which are entrained by gas flow, decision of equation
(9) is following [4]:
0. 5
  

 0  
(10)
3 


v
0 

here:   - density, surface tension coefficient of liquid metal;     - kinematics
viscosity; v0 – gas velocity above boundary layer.
Approximately temperature dependence of surface tension coefficient in interval of
temperatures "melting point Tпл – boiling point Tкип" is following [15]:
2
  3
(T )   пл  B   Me   Tкип  Т 
(11)
 M 
here:  пл - surface tension coefficient at Tпл, Ме , M - density and molecular mass
of liquid metal; В  2  10 7 kg  m 2 / с 2  К .
According to calculations from equations (8 - 11), gas velocity in gap is about
1.5 m/s.
Gap velocity comparison, see table 1, shows, that most likely form of arc
column in gap is cylindrical. Besides, its drifting is caused by electromagnetic forces
mainly.
Table 1. Gap velocities
Velocity type
Plasma flows around arc column
Column drifting along electrode faces
Transporting gas flow
Equation
(1)
(2)
(10)
Value, m/s
140
12
1.5
Liquid metal is exposed by gas–dynamic head. So, it is detached from
electrode faces and it is extended into "tongue", which is contained by surface tension
force. Following equation expresses it:
2
0.5  Сd  S   г  v u  v p     d п  
(12)
here: Cd – aerodynamic resistance coefficient; S    d 2 / 4 - midship section square,
dп – break away necking diameter.
Calculation according to equation (12) gives us detached drop diameter d = (600 900)10-6 m. The same result was obtained by arc current oscillogram data processing.
Critical drop diameter was evaluated by Weber criteria:
2
d к   g  v p  v g 
(13)
We 

Calculation showed that for the most possible We = (10 - 12), according to [16], drop
break down is unlikely at flight, fig. 4.
But our size grading (spraying into water) showed that drop diameter is of (10
- 350)10-6 m, fraction up to 12510-6 m are about (70 – 80) mass %. Jointly with V.
Boronenkov we offered way of small diameter drops forming at EAM. Processes of
large drop detaching by means of gas-dynamic head and it's break down in arc take
place simultaneously [1].
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According to classic scheme, gas flow breaks down liquid metal jet in
neckings, which are formed by differential pressure in local perturbation places [14].
Running current increases necking heating greatly by means of higher ohm resistance.
That leads to break down at neckings, which became micro-arc jumpers also.
Explosion type expanding of metal and gas vapour takes place in micro-arc jumpers.
10000
1
2
dкр ,mkm
1000
100
10
s,mm
1
0
20
40
60
80
100
Fig. 4. Critical drop diameter along spraying distance.
1 – according to equation (13); 2 – drop size grading
It's possible to evaluate expanding gas front velocity, when necking diameter d
is taken equal to detaching layer thickness from equation (8):
16  Cd  
= 1520 м/с
(14)
vф 
d  г
Gas expanding with such velocity causes sudden gas volume increase and strike wave
propagation as well. According to [17], strike wave pressure on its front is following:
2   0г 2
pф 
 vф
(15)
к 1
Force Fф, which is caused by strike wave:
Fф  Pф  2  rп  h
(16)
here:  0г - initial gas density, k – adiabatic constant; h – necking length.
Besides gas-dynamic forces, electromagnetic forces expose necking. They are
conditioned by current run in electrodes and in "tongue", fig. 5.
Three main directions of running current, respectively gas flow axis, are
permitted to single out: through electrode extension of length L at the angle ;
through liquid metal layer; through arc column of length x.
Magnetic induction B1 of electrode extension at point A (center of necking) is
calculated from linear conductor magnetic field equation:
I
В1 
 cos  2  cos 1 
(17)
4    r1
2 - 92
here: r1 – the shortest distance from point A to electrode; 1, 2 – angles between
conductor current density vector and radiuses – vectors, which are passed from
beginning and end points of conductor.
Fig. 5. Electromagnetic forces at arc burning zone.
As seen from fig. 6:
r1  h  sin  ;
cos  2 
dэ
 h1 ;
2  sin 
L  h  cos 
h
h  sin  
2
cos 1  cos(180  )   cos  ;
 L  h  cos  
2
;
Finally equation (17) is reduced to following form:


I
L  h  cos 
B1 

 cos  

4    h  sin   h  sin  2  L  h  cos  2


(18)
Fig. 6. Scheme for calculation electromagnetic forces at arc burning zone.
Ampere force F1 on necking of length h is caused by interaction of magnetic
field B1 and necking running current:
(19)
F1  I  B1  h
Force F2 is caused by local conductor constriction at necking (pinch-effect):
2 - 93
r
  I2
(20)
 ln c
4
rп
Numerical value of magnetic induction B3 at point A is likely B1 from equation (17):
I
I 
x 
(21)
В3 
 cos 2  cos 1  
 1  
4    r2
4    h2  h2 
F2 
here: 1, 2 - angles between current density vector at arc column and radiuses –
vectors, which are passed from beginning and end points of arc column, 2 = 90
according to accepted admission concerning vertical location of arc column
respectively gas flow axis.
Interaction " arc column magnetic field - necking current " causes force F3:
(22)
F3  I  B3  h
Above-mentioned drop detaching forces were calculated, see table 2.
Table 2. Evaluation of forces at arc burning zone area.
Forces
Aerodynamic
Strike wave pressure
Ampere (electrode extension magnetic field – necking
current)
Ampere (pinch-effect)
Ampere (arc column magnetic field – necking current)
Equations
(12)
(16)
(19)
Value,
105 N
7.1
5.6
5.2
(20)
(22)
9.4
0.03
Following admissions were taken:
- "tongue" is divided to equal drops of 10010-6 m dia, its thickness is
710-7 m, necking thickness is 6.510-7 m.
- permeability of medium is corresponded to vacuum one
- initial gas flow velocity is 300 m/s
- necking extend h = 110-6 m
Calculation shows that forces of electromagnetic nature are of the same order of
magnitude with aerodynamic ones. Values and directions of these forces determine
drops flight tracks nearby electrode faces, and difficulties in forming narrow spraying
torch. These forces are to be taken into account at EAM spraying head developing.
Influence on magnetic flows at arc burning zone has good perspective also. Now we
are occupied with obtaining experimental data with reference to various types of
EAM spraying heads.
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