Biuletyn Instytutu Spawalnictwa No. 01/2012

No. 01/2012

No. 01/2012 

BIMONTHLY 

Volume 56 

CONTENTS 

• J. Dworak - Impact of laser beam shape on YAG pulsed laser welding..................... 5 

• A. Sawicki - Modified Habedank and TWV hybrid models of the arc with variable 

length for simulating processes in electrical devices ..................................................... 15 

• E. Turyk, A. Żydzik-Białek, M. Bormann, A. Jastrzębiowski, 

M. Kościelniak, T. Kuzio, B. Czwórnóg - Repair welding of elements 

of the sign “ARBEIT MACHT FREI” of the main gate to the former German Nazi 

concentration and extermination camp Auschwitz I....................................................... 23 

• A. Kiszka, T. Pfeifer - Variable polarity MAG welding of thin protective-coated 

steel plates...................................................................................................................... 33 

• M. St. Węglowski - Testing electromagnetic radiation of welding arcin TIG 

method from welding process monitoring point of view................................................ 40 

INSTITUTE OF WELDING 

The International Institute of Welding 

and The European Federation for Welding, 

Joining and Cutting member

Summaries of the articles 

J. Dworak - Impact of laser beam shape 

on YAG pulsed laser welding 

The study presents the general characteristic 

of laser welding with a radiation beam emitted 

in the pulsed mode and explains the characteristics 

of the energy-related parameters of 

a pulsed radiation beam. The text indicates the 

shape of a pulse (specific course of power changes 

within the duration of a pulse) as one of 

the parameters of a laser beam influencing the 

process of welding, particularly of thin precise 

elements. Examples of penetrations and welded 

joints were used to illustrate the possibility of 

changing the shape of a weld and the manner 

of weld metal crystallisation by applying laser 

beam pulses of diversified shapes. 

A. Sawicki - Modified Habedank and 

TWV hybrid models of the arc with 

variable length for simulating processes 

in electrical devices 

The paper indicates main difficulties in determination 

of characteristics and mathematical 

modelling of the electric arc. Limitations 

in practical use of the simplified and combined 

models of discharge with constant plasma column 

length have been pointed out. New plasma 

column models with variable arc length 

have been presented. The models consist of 

series or parallel connected elements corresponding 

to the modified Cassie-Berger and 

Mayr-Kulakov ones. 

E. Turyk, A. Żydzik-Białek, M. Bormann, 

A. Jastrzębiowski, M. Kościelniak, 

T. Kuzio, B. Czwórnóg -Repair 

welding of elements of the sign “ARBE- 

IT MACHT FREI” of the main gate to 

the former German Nazi concentration 

and extermination camp Auschwitz I 

The article presents theft-accompanying 

damage to the sign “ARBEIT MACHT FREI” 

and discusses the requirements of the Conservation 

Section of the Auschwitz-Birkenau 

State Museum related to the joining of the sign 

elements and the extent of conservation performed. 

The study also covers the process and 

results of the work regarding the technology 

of the repair welding of the sign carried out at 

Instytut Spawalnictwa and addresses the issue 

of welding-related technological supervision. 

A. Kiszka, T. Pfeifer - Variable polarity 

MAG welding of thin protectivecoated 

steel plates 

The study presents results of research on the 

application and usability of variable polarity 

MAG welding of thin protective-coated sheets 

in automotive industry. The research-related 

process was carried out using OTC Daihen DW 

300 and Cloos Qineo Champ welding devices. 

The study also discusses the influence of EN 

ratio in the course of current and voltage on 

the stability of process, quality of joints, and 

the degree of damage to protective coating. 

M. St. Węglowski - Testing electromagnetic 

radiation of welding arc in TIG 

method from welding process monitoring 

point of view 

The study presents the results of tests of 

welding arc electromagnetic radiation in TIG 

method. Within the research it was necessary 

to carry out an extensive overview of reference 

publications about arc radiation and applied 

testing methods. Taking advantage of an arc 

model in TIG method described in reference 

publications it was possible to determine a 

dependence of welding current intensity and 

welding arc length on the intensity of welding 

NR 01/2012 

BIULETYN INSTYTUTU SPAWALNICTWA 

3

arc visible radiation. The research-related tests 

made it possible to determine new parameter 

values in the generalised arc model for a 2÷5- 

mm range of welding arc length, which resulted 

in better matching of a model. It was also 

possible to demonstrate that an increase in 

welding current intensity for a constant length 

of a welding arc causes an increase in the intensity 

of arc visible radiation and that the 

same effect can be obtained by increasing an 

arc length at constant welding current intensity. 

The research also led to a conclusion that 

the monitoring of welding arc visible radiation 

in TIG method can be used for controlling an 

arc length. 

Biuletyn Instytutu Spawalnictwa 

PL ISSN 0867-583X 

Publisher: 

Instytut Spawalnictwa (The Institute of Welding) 

Editor-in-chief: Prof. Jan Pilarczyk 

Managing editor: Alojzy Kajzerek 

Address: 

ul. Bł. Czesława 16-18, 44-100 Gliwice, Poland 

tel: +48 32 335 82 01(02); fax: +48 32 231 46 52 

E-mail: biuletyn@is.gliwice.pl; 

Alojzy.Kajzerek@is.gliwice.pl; 

Marek.Dragan@is.gliwice.pl 

www.bis.is.gliwice.pl 

Biuletyn Scientific Council: 

Akademik Borys E. Paton - Institut Elektrosvarki im. E.O. 

Patona, Kiev, Ukraine; Nacionalnaia Akademiia Nauk Ukrainy 

(Chairman) 

Prof. Luisa Countinho - European Federation for Welding, 

Joining and Cutting, Lisbon, Portugal 

Dr Mike J. Russel - The Welding Institute (TWI), Cambridge, 

England 

Prof. Andrzej Klimpel - Silesian University of Technology, 

Welding Department, Gliwice, Poland 

Prof. Jan Pilarczyk - Instytut Spawalnictwa, Gliwice, Poland 

Biuletyn Program Council: 

External members: 

Prof. Andrzej Ambroziak - Wrocław University 

of Technology, 

Prof. Andrzej Gruszczyk - Silesian University of Technology, 

Prof. Andrzej Kolasa - Warsaw University of Technology, 

Prof. Jerzy Łabanowski - Gdańsk University of Technology, 

Prof. Zbigniew Mirski - Wrocław University of Technology, 

Prof. Jerzy Nowacki - The West Pomeranian University 


Dr inż. Jan Plewniak - Częstochowa University 


Prof. Jacek Senkara - Warsaw University of Technology, 

Prof. Edmund Tasak - AGH University of Science 

and Technology, 

International members: 

Prof. Peter Bernasovsky - Výskumný ústav zváračský - 

Priemyselný institút SR, Bratislava, Slovakia 

Prof. Alan Cocks - University of Oxford, England 

Dr Luca Costa - Istituto Italiano della Saldatura, Genoa, Italy 

Prof. Petar Darjanow - Technical University of Sofia, 

Bulgaria 

Prof. Dorin Dehelean - Romanian Welding Society, 

Timisoara, Romania 

Prof. Hongbiao Dong - University of Leicester, England 

Dr Lars Johansson - Swedish Welding Commission, 

Stockholm, Sweden 

Prof. Steffen Keitel - Gesellschaft für Schweißtechnik 

International mbH, Duisburg, Halle, Germany 

Ing. Peter Klamo - Výskumný ústav zváračský - 

Priemyselný institút SR, Bratislava, Slovakia 

Prof. Slobodan Kralj - Faculty of Mechanical Engineering 

and Naval Architecture, University of Zagreb, Croatia 

Akademik Leonid M. Łobanow - Institut Elektrosvarki 

im. E.O. Patona, Kiev, Ukraine; 

Dr Cécile Mayer - International Institute of Welding, 

Paris, France 

Prof. Dr.-Ing. Hardy Mohrbacher - NiobelCon bvba, Belgium 

Prof. Ian Richardson - Delft University of Technology, 

Netherlands 

Mr Michel Rousseau - Institut de Soudure, Paris, France 

Prof. dr Aleksander Zhelew - Schweisstechnische Lehr- und 

Versuchsanstalt SLV-München Bulgarien GmbH, Sofia 

Instytut Spawalnictwa members: 

dr inż. Bogusław Czwórnóg; 

dr hab. inż. Mirosław Łomozik, prof. I.S.; 

dr inż. Adam Pietras; dr inż. Piotr Sędek; 

dr hab. inż. Jacek Słania, prof. I.S.; 

dr hab. inż. Eugeniusz Turyk, prof. I.S. 

4 BIULETYN INSTYTUTU SPAWALNICTWA 

NR 01/2012

Jerzy Dworak 

Research 

Impact of laser beam shape on YAG pulsed laser welding 

Introduction 

Laser radiation beams are utilised in a variety 

of technological processes, having become 

nowadays an almost universal heat source. 

Typical applications such as cutting, welding 

and marking are being supplemented by such 

processes as surface hardening, surfacing by 

welding, re-melting, micro-machining and 

others. These technological processes can be 

carried out using various sources of laser radiation 

e.g. CO 2 

lasers, YAG lasers or HPDL 

lasers. YAG lasers are, at present, becoming 

increasingly popular, resulting from the significant 

power of a radiation beam (more than 

ten kilowatts) reached by the latest generation 

of devices available on the market and due 

to the efficient absorption of radiation, particularly 

by strongly reflective metals, when 

compared to e.g. CO 2 

lasers, This fact makes 

it possible to apply the YAG solution to an increasing 

number of industries, including areas 

which have not been available for these lasers 

until today. 

YAG lasers of power in excess of ten kilowatts 

constitute one of the two groups of lasers 

of this type. The other is composed of low-power 

YAG lasers (of power up to 1kW), applied 

mainly in precision engineering, where their 

position is particularly strong due to, among 

others, the high quality of the radiation beam. 

One of the characteristics of YAG lasers is 

the possibility of the emission of a radiation 

beam in a pulsed mode. High-power YAG lasers 

may be applied in such a mode, whereas 

low-power YAG lasers are usually applied in 

this mode. 

In the case of many technological processes, 

welding in particular, considerable importance 

is attached to the possibility of shaping 

individual radiation beam pulses through defining 

various courses of power changes within 

the duration of a pulse. The combination of the 

repetition frequency and the possibility of shaping 

a pulse within a significant pulse duration 

enables precise control of the heat supplied to 

the material being processed, which is of particular 

importance during the welding of precision 

elements using a low-power radiation 

beam. 

Power parameters of laser radiation 

emitted in pulsed mode 

The emission of YAG laser radiation in pulsed 

mode results from the pulsed excitation of 

the laser resonator. This excitation is implemented 

through optical pumping (the illumination 

of a resonator with radiation pulses of 

laser diodes grouped into so-called packages 

i.e. modules consisting of a specific number of 

diodes). A characteristic feature of the operation 

of YAG crystalline lasers is the generation 

of significant amounts of heat by these pumping 

modules, which constitutes the limitation 

of the maximum value of the average power 

and energy of a radiation beam pulse (basic 

parameters of the operation of pulsed lasers). 

The energy of a pulse depends upon the com- 

mgr inż. Jerzy Dworak - Instytut Spawalnictwa, Welding Technologies Department 



5

ination of its power and width (duration). 

Therefore, these radiation beam parameters 

cannot be shaped freely, as one cannot freely 

define the duration and emission frequency of 

a pulse for the assumed value of the average 

power of a radiation beam. The energy of a 

pulse cannot exceed the maximum value defined 

for a given resonator. 

The average power of laser radiation in pulsed 

mode is defined as the product of the average 

power of the radiation of one pulse P i 

, 

the duration of this pulse t i 

and the number 

of pulses per a second expressed through the 

frequency of emission f. For a given average 

power there is a number of combinations of 

the selection of pulse energy and pulse repetition 

frequency. 

P śr 

= P i 

× t i 

× f = E i 

× F (1) 

The frequency of a pulse emission is a parameter 

closely related to the period of their occurrence 

expressed in the following relation: 

A weld produced by a laser beam emitted in 

pulsed mode is composed of a number of overlapping 

spot welds. The degree of overlapping 

of individual pulses expressed in percentage, 

i.e. the so-called overlap, represents the degree 

at which the area of a material molten by 

a single pulse overlaps a similar area produced 

by the previous pulse. By means of a specific 

overlap one can control the amount of heat 

supplied to a material being welded, as well as 

influence the homogeneity of the structure of 

a weld. 

The overlap is defined by the rate of the 

welding process appropriately selected in relation 

to the frequency of pulses. In turn, the 

frequency of pulses depends on the pre-defined 

power of a pulse and its duration. If an 

area molten by a single pulse of a laser beam 

takes an elliptic shape (as a result of the pro- 

1 ⎡ 1 ⎤ 

T = 

f ⎢ 

s = 

⎣ Hz ⎥ ⎦ 

(2) 

The average energy of laser radiation for 

the pulsed operation mode is defined as the 

product of the average radiation power and radiation 

beam action time. 

E śr 

=P śr 

× t [J] (3) 

In the case of single pulse spot welding, an 

important parameter is the density of pulse power. 

GP 

i 

Pi 

Ei 

= = 

A t × A 

i 

⎡ J 

⎢ 

⎣s 

⋅ m 

(4) 

where A represents the focusing area of a 

radiation beam. 

In the case of a pre-defined average power 

of a radiation beam P śr 

, the density of the power 

supplied to the area unit, i.e. the average 

2 

⎤ 

⎥ 

⎦ 

area power density, is determined by means of 

the following quotient: 

GP 

śr 

= 

P 

śr 

A 

⎡ W 

⎢ 

⎣m 

2 

⎤ 

⎥ 

⎦ 

(5) 

The quotient of the area power density GP śr 

and radiation beam action time determines the 

average area power density: 

GEśr = GPśr 

× t 

⎡ J 

⎢ 

⎣m 

(6) 

The quantities defined above are presented 

in Figure 1. 

Fig. 1. Graphic interpretation of average power of pulse 

P i 

, average power of radiation beam P śr 

, pulse energy E i 

, 

pulse duration t i 

, pause time t p 

pulse period T 

2 

⎤ 

⎥ 

⎦ 



cess being carried out at a specific rate), the 

longer axis of the ellipse is designated as the 

dimension S, whereas the shorter one as the 

dimension D (Fig. 2,3) 

Fig. 2. Scheme of process of laser welding with radiation 

beam emitted in pulsed mode 

Degree of overlapping of pulses is defined 

by the following relation: 

[ ] 

% 

' 

S − S 

Z = × 100 

(7) 

S 

where: 

S = D + v × t (8) 

i 

S’ = v× T (9) 

After transformation of relations 7, 8, 9, the 

overlap Z is the following: 

⎡ v × T ⎤ 

Z = ⎢1 − ⎥ ×100% 

(10) 

⎣ D + v × t i ⎦ 

Effective penetration depth is conditioned 

by the overlap Z (Fig. 3). 

Welding with laser radiation beam emitted 

in pulsed mode 

The miniaturisation in many areas of technique 

has almost become a trend, stimulating 

the development of micro-machining (including 

micro-joining) of various structural materials. 

In relation to miniature structural elements 

and modules, as well as a variety of 

miniature components and devices, today’s 

manufacturing techniques and classical joining 

technologies in particular meet technical limitations 

preventing the efficient use of the former. 

In many applications the only solution is 

the laser, regarded as one of the most innovative 

tools of modern industry. 

Operating a laser in pulsed mode enables 

the precise production of welded joints of elements 

made of technologically advanced materials 

and having minute dimensions. A joint of 

this type is obtained through the melting of a 

very small amount of metal by a single pulse of 

a laser beam and its immediate crystallisation. 

A continuous weld is formed as a result of the 

proper selection of welding rate and pulse repetition 

frequency. 

Pulsed laser welding is applied where one 

needs to join ready-made electronic components 

in a tight housing, thin-walled elements 

(membranes) with massive cases, thin-walled 

housings, medical equipment elements (housings 

of cardiac pacemakers, endoscopes, medical 

implants, surgical instruments and others). 

Fig. 3. Graphic interpretation of overlap of pulses of laser radiation beam: v – welding rate, 

t i 

– pulse duration, D – diameter of area of focusing of radiation beam, T – pulse period [1,3] 



7

In the pulsed laser welding process the most 

important issue is to ensure a slight heat impact 

unaccompanied by damage to the elements being 

joined yet accompanied by a metal-melting 

process. The requirements in question are met 

by the pulsed mode of laser operation, where 

relatively low average power of a radiation 

beam is accompanied by significant values of 

pulse power obtained for a very short (pulse) 

time. The action of a pulsed beam lasts only a 

few milliseconds. The molten material undergoes 

crystallisation before the occurrence of 

the next pulse. In this welding process a material 

is exposed to a number of pulses which 

melt a minimum volume of metal. 

The short duration of a laser radiation beam 

pulse in the process of welding of such materials 

as medical steels (some austenitic acid resistant 

steels e.g. X15CrNiSi20-12 (1.4828)), 

titanium alloys (particularly Ti6Al4V applied 

in medicine), dispersion-hardened aluminium 

alloys, and galvanised steel, may be the reason 

for the formation of specific imperfections in 

welds and of the occurrence of some technological 

problems (medical steels and dispersion-hardened 

aluminium alloys – hot cracks, 

titanium alloys – hardening of the joint area, 

galvanised steels – evaporation of zinc, impeding 

the process of welding) [2]. 

It is emphasized [3,4,5] that the production 

of imperfection-free welds by means of a laser 

beam emitted in pulsed mode, particularly 

in the process of welding of precision elements, 

when, as a rule, the process of welding 

is carried out without adding a filler metal, is 

conditioned by the accurate selection of laser 

beam parameters. The production of a good 

quality weld depends on the power of the pulse 

(beam pulse action force) and its duration, 

the frequency of pulses and welding rate, the 

determination of the degree of overlap of the 

single welds formed by individual pulses of a 

laser beam, as well as the size of the area of 

a focused beam (active area), the location of 

the focus of the radiation beam in relation to 

the surface of material being welded, and the 

shape of a pulse. 

On this occasion, one should also mention 

the significant impact of the shape of the pulse 

of a laser beam emitted in pulsed mode on the 

elimination of welding imperfections, in particular, 

hot cracks [3,4,5]. 

The focusing area is the active area of a 

laser beam in contact with the surface of an 

element being welded and is decisive for penetration 

depth and the width of the face of a 

weld. The power of a pulse represents the force 

with which a laser beam affects the inside 

of the focusing area. The higher the power of a 

pulse, the faster the heating of the material in 

the active area, though unfortunately also an 

increased risk of crack formation in the weld. 

The duration of a pulse represents the time of 

the action of an active radiation beam on a material, 

and thus is decisive for the volume of 

molten metal. The greater the amount of molten 

metal, the longer the heating and post-weld 

cooling times and the lower the tendency of 

crack formation in a weld. 

An important parameter is the shape of a 

pulse, determining the time-related course of 

power changes within the area of a single pulse 

(Fig. 4). Many devices enable the emission of 

Fig. 4. Example of complex shape of laser radiation beam 

pulse 



pulses up to several dozen milliseconds 

long, enabling simultaneous, 

almost steady, shaping of the course 

of power within the duration of 

a pulse i.e. shaping the division of 

pulse duration into time sub-areas 

(sectors) with very big density. 

The complex shape of a pulse is 

the result of the division of the basic 

(rectangular) pulse into sectors of specific 

height and width. The length of each sector can 

be contained within the range of 0.3ms÷50ms 

with an increment of 0.1ms in the case of many 

precise laser welding machines. The height of 

rectangular pulse, P i max 

=2250 W 

penetration depth h=1.52 mm 

face width s=1.36 mm 

shaped pulse, P i max 

=5556 W 




=5556 W 



Fig. 6. Geometry of penetrations of steel X15CrNiSi20-12 made with laser 

beam emitted in pulsed mode with various pulse shapes; 

diameter of focusing area 0.8 mm, emission frequency 5 Hz, 

pulse energy 18 J, pulse duration 8 ms, welding rate 1.6 mm/s [2] 

Fig. 5. Typical shapes of laser radiation beam pulse 

each sector can adopt values from the range 

0%÷100% of the specific power of a pulse. 

The shape of a pulse should be optimised in 

relation to the basic physicochemical properties 

of the material being welded, in particular 

to the absorptivity of surfaces being processed. 

The most commonly applied shapes 

are simple rectangular pulses (Fig. 

5a), rectangular pulses with a very 

short phase of high power and a long 

phase of low power (Fig. 5b) (applied 

while welding materials which strongly 

reflect radiation), and pulses with 

the gentle edge of radiation beam power 

decrease (Fig. 5c) (applied when 

the limitation of the dynamics of a 

welding thermal cycle is required e.g. 

in the case of materials susceptible to 

hot cracking). 

Appropriate shaping of a pulse 

through the composition of several 

phases adopting the form of a rectangular 

pulse and a pulse of edges 

of rising and falling power of a radiation 

beam can make it possible to 

produce proper joints without imperfections 

occurring in typical welding 

conditions. 

In the majority of typical cases it is 

the application of a rectangular pulse 

that makes it possible to obtain desirable 

results. As regards testing the 

impact of the parameters of YAG pul- 



9

sed laser welding of various metals 

on the course of a welding process, 

research publications usually contain 

information about laser radiation 

beam pulses of a simple, rectangular 

shape. There are cases, however, 

when the application of a specific 

pulse shape improves the result of 

a welding process (enhanced seam 

appearance, elimination of welding 

imperfections). One may thus assume 

that the greater the density of the 

division of pulse duration into time 

sub-areas, the more effective the selection 

of an appropriate pulse shape 

(Fig. 4). The foregoing assumption 

allows more precise shaping of “the 

welding part of a pulse” and of “the 

control part of weld crystallisation” 

i.e. the function of the precise adjustment 

of the thermal effect of a radiation 

beam. 

Through the application of a specific 

laser radiation beam shape one 

can modify the geometry of a weld. 

Figures 6, 7 and 8 present the penetrations 

of the steel X15CrNiSi20-12 

acc. to PN-EN 10088-1 (mat. no. 

1.4828, acc. to AISI – 309) made with a rectangular 

pulse laser beam at the Laboratory of 

Laser Technologies of Instytut Spawalnictwa. 

In addition to the penetrations, the previously 

mentioned figures also contain examples of 

pulses shaped by means of a device TruLaser 

Stadion 5004 equipped with an Nd-YAG laser 

of the maximum average power of a radiation 

beam of 95 W and the maximum power of a 

beam pulse of 6 kW [2]. The same welding 

parameters (pulse power, pulse duration, emission 

frequency and welding rate) were applied 

for both shaped and rectangular pulses. 



=1314 W 




=3210 W 

penetration depth h=1.72 mm, 



=3210 W 



Fig. 7. Geometry of penetrations of steel X15CrNiSi20-12 made with laser 

beam emitted in pulsed mode with various pulse shapes; 


pulse energy 10.5 J, pulse duration 8 ms, welding rate 1.9 mm/s [2] 

For a specific value of power and duration 

of a laser beam pulse having a basic rectangular 

shape, the average power of a pulse is 

similar to its maximum power, whereas in 

the case of a shaped pulse of the same energy 

(and average power), the value of the maximum 

power of a pulse is higher (Fig. 6), 

thus affecting the course of the formation of 

a weld. 

The replacement of a rectangular pulse with 

a shaped pulse of a prolonged edge of decreasing 

power resulted in a greater penetration 

depth and led to the advantageous modifica- 


ectangular pulse, P i max 

=702 W, 




=1584 W, 




=1584 W, 


face width s=0.79 mm. 


=1422 W, 


face width s=1.30 mm. 

Fig. 8. Geometry of penetrations of steel X15CrNiSi20-12 made with 

laser beam emitted in pulsed mode with various pulse shapes; 


pulse energy 4.20 J, pulse duration 6 ms, welding rate 1.8 mm/s [2] 

tion of the shape factor (Fig. 6). Impulses of a 

different shape having the same energy were 

responsible for the formation of incompletely 

filled grooves despite the fact that the power 

of the pulse was lower [2]. 

It should be noted that in conditions 

of high density of energy 

and high power of a pulse, only the 

modification of the direction of power 

increase or decrease at the beginning 

of a pulse may significantly 

modify welding conditions. 

A pulse with an initial holding 

phase and an increase in power at 

the final phase is responsible for the 

gouging of the material, whereas an 

increase in power of the same value 

at the beginning of a pulse and further 

holding phase make it possible 

to obtain a properly-shaped weld. 

These relations are different in the 

case of a radiation beam of different 

power density and pulse energy (Fig. 

7, 8). 

The appropriate shaping of a laser 

beam pulse may have a favourable 

effect on the geometry of a weld as 

well as positively affect the crystallisation 

of a weld. The foregoing 

is well exemplified by the melting 

(welding) of the aluminium alloy 

EN AW-5754 (EN AW-AlMg3). The 

penetrations (welds) made with a laser 

beam of a rectangular shape were 

characterised by the presence of clearly 

visible hot cracks (Fig. 9). The 

modification of the shape of a pulse 

enabled a significant reduction of 

these cracks (Fig. 10) [2]. 

The laser welding of thin plates is often 

used to produce overlapping joints, ensuring 

high tolerance of the placing of elements being 

welded [6]. 



11

The gas-dynamic passage (capillary) 

formed during laser welding should 

be stable enough to form a vent 

for zinc vapours being formed. The 

pressure of these vapours, however, 

is so high that it significantly hinders 

the formation of a proper weld. If in 

the structure of the joints of galvanised 

plates (i.e. proper projections) no 

special gaps for the removal of zinc 

vapours were provided, the weld interface 

between plates being joined 

becomes deformed and covered with 

imperfections in the form of gas 

pores, i.e. zinc vapours confined in 

the weld (Fig. 11). Zinc evaporates 

not only in the area of molten metal 

where metal is being molten but also 

in the heat affected zone heated as 

a result of a welding thermal cycle. 

For this reason, the intensity of the 

evaporation depends not only on the 

thickness of the coating of plates being 

joined but also on a welding thermal 

cycle. 

In the process of laser welding 

using a radiation beam emitted in 

pulsed mode, the phenomena described 

above occurs with less intensity. 

A weld is formed by overlapping spot 

welds. The volume of liquid metal is 

smaller than in the case of laser welrectangular 

pulse, P i max 

=1752 W 

penetration depth h=0,2 mm 

face width s=0,9 mm 

Fig. 9. Geometry of penetration 

of aluminium alloy EN AW-5754 

(EN AW-AlMg3) made with laser 

beam emitted in pulsed mode of 

rectangular pulse shape; diameter 

of focusing area 0.8 mm, emission 

frequency 8 Hz, pulse energy 

10,5 J, pulse duration 6 ms, 

welding rate 2,6 mm/s [2] 


=3120 W 

penetration depth h=0,2 mm, 

face width s=1,0 mm 

Fig. 10. Geometry of penetration of 

aluminium alloy EN AW-5754 (EN 

AW-AlMg3) made with laser beam 

emitted in pulsed mode of special 

pulse shape; diameter of focusing 

area 0.8 mm, emission frequency 

8 Hz, pulse energy 10.5 J, 

pulse duration 6 ms, 

welding rate 2.6 mm/s [2] 

The basic problem of these types of joints 

in relation to galvanised plates is the area of 

the contact of plates subjected to melting, in 

which the zinc layer undergoes melting followed 

by evaporation. The zinc vapours may become 

confined in the weld, forming numerous 

welding imperfections and deteriorating the 

quality of the joint. 

Fig. 11. Illustration of zinc evaporation zone in process of 

laser welding of galvanised plates placed to form overlap 

joint [7] 



ectangular pulse, P i max 

=1752 W 


=3354 W 

Fig. 12. Geometry of weld in overlap joint of plates of DX-53D steel, 

made with laser beam emitted in pulsed mode of various pulse shape; 

diameter of focus area 0.8 mm, emission frequency 8 Hz, pulse energy 

10.5 J, pulse duration 6 ms, welding rate 2.6 mm/s [2] 


=2628 W 


=5088 W 

Fig. 13. Geometry of weld in overlap joint of plates of DX-53D steel, 

made with laser beam emitted in pulsed mode of various pulse shape; 

diameter of focus area 0.8 mm, emission frequency 8 Hz, pulse energy 

10.5 J, pulse duration 4 ms, welding rate 2.6 mm/s [2] 

ding using a continuous emission laser 

beam. The metal becomes molten 

and crystallised in a cyclical manner 

in accordance with the laser pulse 

emission frequency. The re-melting 

of part of a weld enables the off-take 

of confined zinc vapours. This 

re-melting is also facilitated by the 

appropriate modulation of the course 

of power throughout the duration of 

a pulse (pulse shape). 

Figures 12 and 13 present the socalled 

“through welds” (formed by 

melting through one of the plates being 

joined) in overlap joints made of 

3mm-thick cold-formed galvanised 

low-carbon steel DX-53D (acc. to PN 

-EN 10346:2009). Welds were made 

with a laser beam of a rectangular 

pulse and that of shaped pulses [2]. 

The contact gap between the plates 

being joined was 0.02mm÷0.04mm 

and provided inadequate off-take of 

zinc vapours while welding with a 

rectangular pulse. A favourable effect 

on the process of welding was 

obtained by applying laser beam pulses 

of a falling power curve at the final 

phase of a pulse. 

Summary 

The possibility of shaping the pulse 

of a laser radiation beam emitted 

in pulsed mode (i.e. the possibility of 

shaping changes in power within the 

duration of one pulse) is of significant 

importance particularly in laser 

welding of precision elements as it 

influences the amount of heat supplied 

to the material. A specific laser 

beam shape enables precise supply 



13

of energy in one pulse, particularly through 

defining the value and location of the peak power 

sector of a pulse. The shape of a laser 

beam pulse influences the geometry of a weld 

and the conditions of weld crystallisation. The 

manner of this influence varies depending on 

materials, their chemical composition and 

state of delivery. Changing a pulse shape can 

help limit or eliminate welding imperfections 

characteristic of some metals and their alloys. 

The selection of pulse shape is conditioned by 

the rate of the change of power in time, particularly 

in a pulse section of descending characteristic. 

Pulses of complex characteristic in 

the area of gradual power decrease may prove 

their usability in the welding of numerous materials. 

References 

1. Tzeng Y-F.: Parametric analysis of the 

pulsed Nd:YAG laser seam-welding process. 

Journal of Materials Processing Technology 

102 (2000). 

2. Banasik M., Dworak J., Stano S.: Badania 

procesu spawania laserem impulsowym 

wybranych materiałów konstrukcyjnych /Tests 

of welding selected structural materials 

with pulse laser. Praca badawcza nr /Research 

work no./ Ci-18 (ST-279/10). Instytut Spawalnictwa, 

Gliwice, 2010. 

3. Zhang J., Weckman D.C., Zhou Y.: Effects 

of temporal pulse shaping on cracking 

susceptibility of 6061-T6 aluminium Nd:Yag 

laser welds. Weld.J., 2008, nr 1. 

4. Naeem M. Controlling the Pulse in Laser 

Welding. weldingdesign.com/equipment-automation/news/wdf_11036. 

5. Lienert T.J., Lippold J.C.: Improved 

weldability diagram for pulsed laser welded 

austenitic stainless steels. Science and Technology 

of Welding and Joining, 2003, vol 8, nr 

1. 

6. Laser beam welding: benefits, strategies 

and applications. Weld., J., 2007, nr 5. 

7. Tzeng Y-F.: Pulsed Nd:YAG Laser Seam 

Welding of Zinc-Coated Steel. Weld., J., 1999, 

nr 7. 

8. Tzeng Y-F.: Effects of operating parameters 

on surface quality for the pulsed laser 

welding of zinc-coated steel. Journal of Materials 

Processing Technology 100 (2000). 

9. Bley H., Weyand L., Luft A.: An alternative 

approach for the cost-efficient laser 

welding of zinc-coated sheet metal. Annals of 

the CIRP, 2007,vol., 56, nr 1. 

10. Malek Ghaini F., Hamedi M.J., Torkamany 

M.J., Sabbaghzadeh J.: Weld metal 

microstructural characteristics in pulsed Nd: 

YAG laser welding. Scripta Materialia 56, 

(2007). 



Antoni Sawicki 

Modified Habedank and TWV hybrid models of a variable 

length arc for simulating processes in electrical devices 

Introduction 

The multiplicity, complexity, and problematic 

measurability of the characteristics of 

processes in arc discharges entails the necessity 

of applying various methods of mathematical 

description and quantitative analyses. 

Numerous physical processes including 

electromagnetic, thermal, gasodynamic, and 

acoustic as well as the mechanical processes 

take place in the plasma and electrodes. The 

complexity of such processes results from significant 

nonlinearities of static and dynamic 

characteristics, collectiveness, and interaction 

of plasma components as well as from 

the very short relaxation times of the elementary 

processes. Difficulties in measurability 

are caused by high temperatures, strong heat 

(and light) emission, significant gas flow rates, 

high quantity gradients in state variables, 

very high chemical reaction rates, occasional 

difficulties in accessing sensors (including 

optical ones) to a discharge area because of its 

small size or the fact of being closed. Due to 

this and depending on the needs in designing 

the power-supply and control systems of elecrotechnological 

devices, one adopts various 

simplifying assumptions leading to various 

degrees of approximation of physicochemical 

phenomena using mathematical models. The 

simplest and most commonly applied models 

include those of Cassie-Berger and Mayr-Kulakov. 

However, approximations obtained 

using these models are often considered to be 

very rough in relation to needs connected with 

designing and building various measuring, 

supply, and control systems; this being caused 

by a necessity to apply various electric excitations 

and various conditions of arc burning 

in devices. For this reason, various modifications 

of equations and new mathematical models 

of arcs have been proposed. 

Most of the existing arc models (i.e. also 

those by Cassie-Berger and Mayr-Kulakov) 

take into consideration only one manner of 

heat transfer, either conduction or convection, 

regarding each of them as dominant in 

a variety of technological conditions. The 

Cassie-Berger model provides more satisfactory 

results in cases when strong currents are 

required, whereas the Mayr-Kulakov model is 

preferred when weak currents are preferred. 

Such an approach to modelling is justified by 

an experimentally confirmed assumption, according 

to which there is a boundary between 

a column of thermal plasma and a turbulent 

gas flow around it [1]. 

The extension of the applicability area of 

widely known simplified Cassie-Berger and 

Mayr-Kulakov models required the development 

of several associations. One of them is 

the series connection of two resistances corresponding 

to the nonlinear Cassie-Berger and 

Mayr-Kulakov models suggested by Habedank. 

This combined model, however, lacks 

appropriate physical interpretation of phenomena 

present in the column. A more rational 

solution to the issue of generalisation of description 

of processes taking place in the arc 

Dr hab. inż. Antoni Sawicki, professor at Częstochowa University of Technology – Częstochowa 

University of Technology, Faculty of Electrical Engineering 



15

in a wide range of currents was proposed in 

publication [2], in the form of a parallel connection 

of conductances corresponding to the 

nonlinear Cassie-Berger and Mayr-Kulakov 

models, whose participation is determined by 

appropriate tapering functions of current. 

The basic methods of controlling welding 

and electrothermal (arc and plasma-arc) devices 

include modifications of excitation source 

current as well as modifications of arc (length) 

voltage. Most of the simple and hybrid dynamic 

models applied so far, however, treat 

the arc as an element of the constant length 

of a plasma column. Moreover, there are even 

some cases when taking into consideration the 

modifications of the arc length only in relation 

to a single model (e.g. Cassie-Berger or 

Mayr-Kulakov) does not ensure that the approximation 

of power characteristics within a 

wide range of work current amplitudes can be 

obtained. 

Cassie-Berger and Mayr-Kulakov models 

of arc with constant plasma column 

length 

Dynamic models of an electric arc column 

are created on the basis of the power balance 

equation 

P 

= u 

i = P 

kol kol dys 

+ 

dQ 

dt 

(1) 

where P kol 

– power supplied to the column, 

P dys 

– thermal power dissipated from the column, 

Q –thermal plasma enthalpy, u kol 

, i – 

voltage and current of the arc column. The 

effect of strong nonlinearity of the models 

results from column conductance variability, 

which is a composite function in the form 

of g(t) = F g 

(Q(t)). 

Popular electric arc models by Cassie-Berger 

and Mayr-Kulakov take advantage of two 

different simplifying assumptions [3]: 

• Mayr-Kulakov model: T(t,(x,y,z)) = variab., 

arc power dissipated through conduction 

⎛ QV 

S(i)=const; σ(i)=var; P S (i)=const; g() 

i = K ⋅ 

⎜ 

1 

exp 

⎝ Q 

• Cassie-Berger model: T(t,(x,y,z))= 

const., arc power dissipated through convection, 

Q () i 

S(i)=var; σ(i)=const; P S (i) ~ Q(i) ~ g(i) =var; g() 

i = K 

where T – temperature, K; x,y,z – system coordinates, 

m; S – cross-section area, m 2 , σ- plasma 

conductivity, S/m; P S 

– dissipated power, 

W; Q V 

– plasma enthalpy volumetric density, 

J/m 3 ; Q 0 

– constant reference coefficient, J/m 3 ; 

K 1 

– constant coefficient of approximation 

with exponential function, S/m; K 2 

– approximation 

coefficient, S. As the Mayr-Kulakov 

model makes it possible to obtain the best approximation 

in cases when weak currents are 

required and the Cassie-Berger model in the 

case of strong currents, it is the latter model 

that is of basic importance in simulating electromagnetic 

processes in industrial welding 

and electrothermal devices. Transitory processes 

in the areas of the transition of current through 

zero values are significant for ensuring the 

stability of arc burning and appropriate start 

and stop characteristics. In addition, the processes 

are decisive for the proper operation of 

commutation devices. 

After adopting appropriate simplifying 

assumptions and transformations [3] from formula 

(1), one obtains the already known Cassie-Berger 

models 

- in the conductance form 

1 dg 

g dt 

2 

1 ⎛ u ⎞ 

kol 

= ⎜ −1 

⎟ 

2 

θC 

⎝ U 

C ⎠ 

2 

( σ () i ) 

⋅ 

0 

V 

Q 

0 

⎞ 

⎟ 

⎠ 

(2) 



1 dr 

r dt 

- in the resistance form 

1 ⎛ u 

⎜1 

− 

⎝ U 

2 

= 

kol 

2 

θC 

C 

⎞ 

⎟ 

⎠ 

(3) 

where ϴ C 

– time constant of the model, U C 

– 

model voltage, g = 1/r – conductance and resistance 

of the arc column. 

Similarly, on the basis of the power balance 

equation (1) and after adopting appropriate 

simplifying assumptions and transformations 

[3], one can obtain the Mayr-Kulakov models 

in the conductance form 

1 

g 

dg 

dt 

1 ⎛ u ⎞ 

koli 

= ⎜ −1 

⎟ 

θM 

⎝ PM 

⎠ 

or in the resistance form 

1 

r 

dr 

dt 

1 ⎛ u 

⎜1 

− 

⎝ P 

= 

kol 

θM 

M 

i ⎞ 

⎟ 

⎠ 

(4) 

(5) 

where U stat 

(i) – static voltage-current characteristics, 

G stat 

(i) – static nonlinear conductance, 

R(3) 

stat 

(i) – static nonlinear resistance. 

After substituting (8) and (9) to (6) and (7) 

one obtains a generalised Mayr-Kulakov equation 

in the conductance form 

1 dg 1 ⎡Gstat 

() i ⎤ 

= ⎢ −1 

g dt θ 

⎥ 

(10) 

Ms ⎣ g ⎦ 


1 

r 

(11) 

(4) When conductance does not change in time, 

the static characteristics of the arc in this model 

are as follows: 

U 

(5) 

dr 

dt 

1 ⎡ r 

() ⎥ ⎤ 

= ⎢1 

− 

θ 

Ms ⎣ Rstat 

i ⎦ 

() i 

stat 

= 

P 

i 

M 

(12) 

(1 

( 

where ϴ M 

– time constant of the model, P M 

– 

power of Mayr-Kulakov model. 

The Mayr-Kulakov arc model can be transformed 

into another, general conductance form 

1 

g 

dg 

dt 

() t 

1 ⎡ P 

() ⎥ ⎥ ⎤ 

kol 

= ⎢ −1 

θ Ms ⎢⎣ 

Pdys 

t ⎦ 

or the resistance form 

(6) 

(13) 

Therefore, on the basis of these formulas 

one can write models (6) and (7) in the conductance 

form 

(6) 

1 dg 1 ⎡ i ⎤ 

= ⎢ −1⎥ g dt θ Ms ⎣ g ⋅U 

stat 

() i ⎦ 

1 dr 1 ⎡ P () ⎤ 


= ⎢ − 

kol 

t 

1 ⎥ 

(7) (7) 

r dt θ 

Ms ⎢⎣ 

Pdys 

() t ⎥ ⎦ 

1 dr 1 ⎡ ri 

() 

where ϴ Ms 

– corresponds to relaxation time of 

⎥ ⎤ 

= ⎢1 

− 

(15) 

r dt θ 

Ms ⎣ U 

stat 

i ⎦ 

thermal process, and the supplied electric power 

amounts to 

U stat 

(i) = - U stat 

(-i). 

The application of the appropriate approximation 

of static characteristic U 

2 

i 2 

P 

(8) 

stat 

(i) offers more 

kol 

() t = ukoli 

= = i r 

(8) 

g 

precise determination of arc dynamic characteristics 

if compared with hyperbolic static characteristic, 

pre-set only by one constant Mayr-Ku- 

As the processes of heat dissipation slowly 

respond to external disturbance, one can assume 

that the power of losses is basically deterlakov 

power value. Such an approach extends 

somewhat the range of the model applicability to 

mined by static characteristics [4] i.e. include stronger currents, when a characteristic 

2 

i 2 

P () t U () i i i R () i 

is no longer drooping [5] but becomes flat and, in 

dys 

= 

stat 

⋅ = = 

stat 

() 

(9) 

(9) 

Gstat 

i 

the case of stronger currents, is even rising. 

G 

stat 

() i 

i 

= 

P 

2 

M 

= 

U 

i 

stat 

2 

= 

1 

() i ⋅i 

R () i 

stat 

(14) 

( 



17

Combined models of arc with constant 

column length 

The series connection of the Cassie-Berger 

and Mayr-Kulakov models makes it possible 

to obtain the Habedank model, where substitute 

conductance fulfils the dependence 

(22) 

(23) 

If one now implements the simplified Mayr-Kulakov 

model taking into consideration the 

virtual static characteristics of the arc component 

U Mstat 

(i), instead of (21) one receives 

and after reduction 

1 1 1 

Similarly, instead of (23) the resistance 

= + 

(16) 

(16) 

g g form of the model will be 

M 

g C 

1 

r 

C 

1 

r 

M 

drC 

dt 

dr 

dt 

M 

1 

= 

θ 

C 

⎡ u 

⎢1 

− 

⎢⎣ 

U 

2 

2 

C 

⎛ 

⎜ 

⎝ 

rC 

r 

2 

⎞ 

⎟ 

⎠ 

2 

1 ⎡ u r 

= ⎢ − 

M 

1 

θ ⎣ rP r 

M 

M 

⎤ 

⎥ 

⎥⎦ 

⎤ 

⎥ 

⎦ 

1 

g 

M 

1 

g 

M 

dg 

dt 

M 

dg 

dt 

M 

2 

1 ⎡ u g g ⎤ 

= ⎢ 

−1⎥ θ 

Ms ⎣i 

⋅U 

Mstat 

() i g 

M ⎦ 

1 ⎡ u g ⎤ 

= ⎢ −1⎥ θ ⎣ U () i g ⎦ 

Ms 

Mstat 

M 

(24) 

(25) 

2 

and resistance is 

1 dr ⎡ 

⎤ 

M 

1 u rM 

= ⎢1 

− 

⎥ (26) 

rM 

dt θ 

Ms 

r = r M 

+r C 

(17) 

⎣ r ⋅i 

⋅U 

Mstat 

() i r ⎦ 

As the same current flows through both elements 

and after taking into consideration that 1 dr ⎡ ⎤ 

and after reduction 

M 

1 u r 

= ⎢ − 

M 

1 

⎥ (27) 

g C 

= i / u C 

, g M 

= i / u M 

and g = i / u it can be r 

⎣ () r 

M 

dt θ 

Ms 

U 

Mstat 

i ⎦ 

stated that 

where 

g rC 

uC = u = u 

(18) U Mstat 

(i) (18) = U stat 

(i) - U 0 

sign(i), U C 

= f(U 0 

). 

gC 

r 

The voltage of U 0 

corresponds to ranges of 

and 

strong arc currents. 

g r 

The Habedank model (20)-(23) is sometimes 

used to simulate commutation processes 

M 

uM = u = u 

(19) (19) 

g 

M 

r 

in electric circuits with high voltage electrical 

Then on the basis of (18) and (19), one can 

devices; its expansion being the series connection 

of as many as three models (1 – Cas- 

express the Habedank model in the conductance 

form: 

sie-Berger, 2 – Mayr-Kulakov) [7]. Known as 

2 

⎡ 2 

1 dg 1 ⎛ ⎞ ⎤ 

KEMA, the model was even implemented as a 

C u g 

= ⎢ 

⎜ 

⎟ −1⎥ 

(20) (20) 

2 

gC 

dt θC 

⎣⎢ 

U 

C ⎝ gC 

⎠ ⎥⎦ 

blackbox in simulation programmes [8, 9]. 

In the TWV hybrid arc model [2], the values 

of (21) currents flowing through two parallel 

2 

1 dg 1 ⎡ ⎤ 

M 

u g g 

= ⎢ −1⎥ 

(21) 

g 

M 

dt θ 

M ⎣ PM 

g 

M ⎦ 

nonlinear conductances, corresponding to the 

The resistance form of the formulas is as follows: Mayr-Kulakov and Cassie-Berger models, depend 

on their resultant value and therefore can 

(22) 

be presented as follows: 

2 

⎛ 

2 

⎛ i ⎞ 

⎛ 

() 

(23) 

⎟ ⎞ 

⎜ 

i ⎞ 

i t = u 

⎜ 

⎟ + ⋅ ⋅ 

− 

⎜ − 

⎟ 

kol 

g = ukol 

⋅ gM 

exp − u 1 exp 

2 kol 

gC 

2 

⎝ I0 

⎠ ⎝ ⎝ I0 

⎠⎠ 

(28) 

Hence one receives 

g 

⎛ i − 

2 

⎞ 

⎞⎞ 

() t = g () () ⎜ 

⎜ 

⎟ + ⋅ 

− 

⎜ 

⎟ 

⎟ M 

t ⋅ exp g 

2 C 

t 1 exp 

2 

⎝ I0 

⎠ ⎝ ⎝ I0 

⎠⎠ 

⎛ 

⎛ i − 

2 

(29) 



The conditions of the selection of models are 

as follows: 

- Mayr-Kulakov model 

In practical considerations [2] one usually 

assumes that ϴ (|i|) = const and G min 

= 0. Then, 

formula (32) can be simplified to 

g 

2 

i dg 

1 dg 1 ⎧ u 

⎫ 

koli 

ukoli 

≈ θ (30) (30) = ⎨[ 1− 

ε () i ] + ε () i −1 

2 

⎬ 

P dt 

g dt θ ⎩ gU 

C 

PM 

⎭ 

M 

M 

() t g 

M 

() t = − 

M 

, if i < I 

0 

M 

- Cassie-Berger model 

with the designation 

(34) 

g 

2 

u i dg 

⎛ i 

≈ θ 

2 

(31) () (31) 

U 

C 

dt 

⎟ ⎞ 

ε i = exp 

⎜ − 

(35) 

2 

⎝ I0 

⎠ 

kol C 

C 

() t gC () t = − 

C 

, if i > I0 

In welding [10, 11] and furnace [2] arcs, the 

value of limiting current I0 is approximately 5 

A. In the case of the application of the TWV 

model for the approximation of the characteristics 

of high-pressure arc lamps, the value of 

I0 is almost 10 times lower [12]. 

The hybrid model of the arc column in the 

conductance form is [2] 

g 

kol 

⎡ ⎛ i ⎞⎤ 

u i ⎡ ⎛ i ⎞⎤ 

i dgkol 

⎢1 ⎜ − 

⎢ ⎥ 

I ⎟⎥ 

U ⎜ − 

C ⎣ I ⎟ 

(32) 

2 2 

2 

⎣ ⎝ 0 ⎠⎦ 

⎝ 0 ⎠⎦ 

PM 

dt 

2 

2 2 

() t = 

kol 

G + − exp⎜ 

⎟ + exp⎜ 

⎟ −θ 

( i ) 

min 

(32) 

where G min 

– constant conductance dependent 

on the distance between electrodes, their shape 

and arrangement as well as on the gas and the 

temperature of the environment in currentless 

moments; I 0 

- transition current between the 

Cassie-Berger and Mayr-Kulakov models. In 

a general case, the suppression function ϴ depends 

on current i 

If the current is relatively low, one can assume 

that ϴ≈ϴ 1 

, and when current is high one 

can assume that ϴ≈ϴ 0 

. If ϴ→0, the static characteristic 

results from adopted assumptions 

related to the participation of individual constituent 

models: 

• if │i│ 

and dg/dt = 0, then u = P M 

/i; 

• if │i│ > I 0 

and dg/dt = 0, then u = U C 

sign(i). 

The creation of the resistance form of the 

hybrid model, analogous to the conductance 

TWV, is difficult for computer recording and 

implementation. For this reason, the resistance 

form is not subject to consideration. 

The TWV model is successfully used in simulations 

of stationary processes in welding 

and electrothermal devices as well as in systems 

with discharge light sources [2, 10-12]. 

If here, like previously, one introduces the 

Mayr-Kulakov model, taking into consideration 

the virtual static characteristic of the arc 

component Ustat(iM), instead of (34) one receives 

At time intervals when current |i| values are 

low, the Mayr-Kulakov conductance constituent 

plays an important role and the dependence 

i 

(33) M 

≈i takes place. Thus, one can approximately 

0 

+ θ1 

( −α i ) 

(33) 

write that U stat 

(i M 

) = U stat 

(i) and then 

θ = θ exp 

1 

g 

1 

g 

dg 

dt 

dg 

dt 

1 ⎧ ukoli 

ukoli 

= ⎨[ 1−ε 

() i ] + ε () i 

−1 

2 

θ ⎩ gU 

C 

iM 

⋅U 

stat M 

1 ⎧ ukoli 

ukol 

= ⎨[ 1−ε 

() i ] + ε () i −1 

2 

θ ⎩ gU U () i ⎭ ⎬⎫ 

C 

stat 

( i ) ⎭ ⎬⎫ 

(36) 

(37) 

Representation of the disturbance of 

arc column length with modified Cassie-Berger 

and Mayr-Kulakov 

An increase in the geometric size of the plasma 

arc column is accompanied by an increase 

in energy necessary to generate an additional 



19

volume of plasma. The adopted assumption of 

the axial-cylindrical shape of the column and 

its stretching by length dl corresponds to an 

increase in thermal power 

dQ 

dt 

dQa 

dl dl 

= ql 

(38) (38) 

dl dt dt 

a 

= 

where q l 

– arc energy linear density. Hence 

in simplifying conditions, the thermal power 

necessary to generate the additional volume 

of plasma is approximately proportional to the 

length of the increment rate. The phenomenon 

is accompanied by relaxation times resulting 

from gas thermal inertia and additional cooling 

of the column. Modified equations (2) and (3), 

with a variable value of the Cassie-Berger 

Representation of disturbance of arc 

column length in modified Habedank 

and TWV hybrid models 

The series connection of nonlinear conductances 

(16) corresponding to the Cassie-Berger 

and Mayr-Kulakov models makes it possible 

to obtain the modified Habedank model. 

The conductance form is expressed by the following 

formulas: 

1 

g 

C 

dg 

dt 

C 

⎡ 

⎤ 

⎢ 

2 

2 

1 

⎢ 

u ⎛ g ⎞ 

= − 

⎢ 

⎜ 

⎟ 1 

θ 2 1 ⎛ dl ⎞ 

⎢ 

() + ⎜ ⎟ 

⎝ ⎠ 

⎥ ⎥⎥⎥ C 

gC 

uC 

l pv 

⎣ gC 

⎝ dt ⎠ ⎦ 

1 dg 

M 

i g dl 

(44) 

g dt 

= 1 ⎡ 

⎤ 1 

⎢ 

−1⎥ 

− 

θ ⎛ dl ⎞ 

M 

Ms ⎣ g 

M 

⋅l 

⋅ EMstat 

( i) 

g 

M ⎦ l dt 

voltage, U 

C 

() t = U 

C ⎜l, 

⎟ give the conductance 

⎝ dt ⎠ 

If one takes into consideration the series 

form [13, 14] 

connection of resistances (17), the form of the 

⎛ 

⎞ 

⎜ 

model will be 

2 

1 dg 

= 1 ⎜ ukol 

− 

⎜ 

(39) 

⎛ ⎞ 

1 

() ⎟ ⎟⎟⎟ (39) 

g dt θ 2 1 dl 

⎡ 

⎤ 

C 

⎜ u l + p ⎜ ⎟ 

⎢ 

2 

2 

C 

v 

⎝ g ⎝ dt 

1 drC 

1 

u 

⎠ ⎠ 

⎢ 

⎛ rC 

⎞ 

= 1− 

(45) 

The resistance form is 

() ⎜ ⎟ 

r ⎢ 2 ⎛ dl 

C 

dt θC 

⎞ ⎝ r 

⎢ 

u 

⎠ 

⎥ ⎥⎥⎥ 

C 

l + rC 

⋅ pv 

⎜ ⎟ 

⎣ 

⎝ dt ⎠ ⎦ 

⎛ 

⎞ 

⎜ 

2 

1 dr 1 ⎜ u 

1 dr 

kol 

M 

ir r dl 

= 1− 

(40) 

(46) 

() ⎟ ⎟⎟⎟ (40) 

r dt θ ⎜ 

⎛ dl 

C 2 ⎞ 

r dt 

= 1 ⎡ 

⎤ 

M M 

1 

⎢1 

− 

⎥ + 

θ M 

Ms 

⎜ u l + rp 

⎣ l ⋅ EMstat 

() i r ⎦ l dt 

C 

v⎜ 

⎟ 

⎝ 

⎝ dt ⎠ ⎠ 

where E Mstat 

(i) – virtual characteristic of 

where p v 

(dl/dt) - power necessary to generate electric field intensity. 

additional volume of plasma. 

The hybrid model of the arc column, taking 

Kulakov proposed a modification of model into consideration its length changes, associates, 

by means of an appropriate tapering func- 

(14) taking into consideration the modification 

of the column length. Model I of the order in tion Ɛ(i), models (39) and (41) in the manner 

the conductance form is [15] 

(34). Thus, its form is as follows: 

1 dg 1 ⎡ i ⎤ 1 dl 

⎢ −1⎥ 

− 

g dt 

= θ g l E () i l dt (41) 

Ms ⎣ ⋅ ⋅ 

(41) 

1 dg 

stat ⎦ 

g dt 

= 

⎧ 

⎫ 

where E stat 

(i) – static characteristic of elec- 

⎪ 

2 

1 

⎪ 

⎨[ − ukol 

i 

1 ε () i ] 

+ ε () i 

− ⎬ 

tric field intensity. The resistance form of the θ ⎪ 

⎛ ⎞ ⋅ ⋅ 

() 

( ) 

1 

2 1 dl g l Estat 

iM 

u 

⎪ 

C 

l + pv⎜ 

⎟ 

⎪⎩ 

g ⎝ dt ⎠ 

⎪⎭ 

model is described by the following formula: 

dl 

1 dr 1 ⎡ ir ⎤ 1 dl 

−ε () i 1 

= ⎢1 

− ⎥ + (42) 

(42) 

l dt 

(47) 

r dt θ 

Ms ⎣ l ⋅ Estat 

() i ⎦ l dt 

(43) 



Similarly as previously (37), one can write the 

approximate equation 

⎧ 

1 

⎪ 

⎨ 

θ ⎪ 

⎪⎩ 

[ 1 ε () i ] 

1 dg 

g dt 

= 

⎫ 

2 

u 

⎪ 

kol 

ukol 

− + ε () i −1⎬ 

2 1 ⎛ dl ⎞ l ⋅ Estat 

() 

() i 

u l + p ⎜ ⎟ 

⎪ 

C 

v 

g ⎝ dt ⎠ 

⎪⎭ 

dl 

− ε () i 1 

l dt 

(48) 

For simulations of processes in the circuits 

of electro-technological devices in which the 

electrode travel rate is relatively low (dl/dt≈0), 

formulas for the modified Habedank model are 

reduced to the conductance form 

1 

g 

C 

1 

g 

M 

dg 

dt 

C 

dg 

dt 

M 

2 

⎡ 2 

1 u ⎛ g ⎞ 

() ⎥ ⎥ ⎤ 

= ⎢ 

⎜ 

⎟ −1 

2 

θC 

⎣⎢ 

uC 

l ⎝ gC 

⎠ ⎦ 

= 1 ⎡ i g ⎤ 

⎢ 

− ⎥ 

θ ⎣ ⋅ ⋅ ( ) 

1 

Ms 

g 

M 

l EMstat 

i g 

M ⎦ 

(49) 

(50) 

Similarly, the simplified resistance form of 

this model is as follows: 

1 

r 

C 

1 

r 

M 

drC 

dt 

dr 

dt 

M 

1 

= 

θ 

C 

1 

= 

θ 

⎡ 2 2 

u ⎛ r 

() ⎥ ⎥ ⎤ 

C ⎞ 

⎢1 

− 

2 

⎜ ⎟ 

⎢⎣ 

uC 

l ⎝ r ⎠ ⎦ 

Ms 

⎡ ir 

⎢1 

− 

⎣ l ⋅ E 

M 

Mstat 

r ⎤ 

M 

⎥ 

() i r ⎦ 

(51) 

(52) 

The simplified hybrid model of the arc column 

taking into consideration relatively slow 

changes of the length of the arc, takes the following 

form: 

1 

g 

dg 

dt 

2 

1 ⎧ ukol 

ukol 

= ⎨[ 1−ε 

() i ] + ε () i −1 

2 

θ ⎩ u () l l ⋅ E () i ⎭ ⎬⎫ 

C 

stat 

(53) 

Obtained dependences (43)-(53) are relatively 

simple mathematical models approximating 

very complex physical processes taking 

place in high-pressure electric arcs supplied 

with direct or alternating current and disturbed 

by factors affecting the length of the plasma 

arc column. 

The macro-models of arcs and simulations 

of courses in circuits implemented in the programme 

MATLAB-Simulink can be a subject 

of a separate article. 

Conclusions 

1. The combined Habedank and TWV models 

extend the possibilities of simulating processes 

in electric arcs of electro-technological 

and electrical power engineering devices, yet 

only in cases in which the length of the plasma 

arc column is constant. 

2. The Cassie-Berger model extends the 

possibilities of simulating processes in variable 

length electric arcs of electro-technological 

and electrical power engineering devices, 

but (49) only in case of those with relatively high 

intensity of the plasma arc current. 

3. The Mayr-Kulakov model extends the 

(50) 

possibilities of simulating processes in variable 

length electric arcs of electro-technological 

and electrical power engineering devices, 

yet only in case of those with relatively low 

intensity (51) of the plasma arc current. 

4. The modified Habedank and TWV hybrid 

models extend the possibilities of simulating 

processes in electric arcs of electro-tech- 

(52) 

nological and electrical power engineering 

devices in which the length of the plasma arc 

column is changeable and the range of variability 

of electric current intensity is wide. 

5. The combined series Habedank model 

of the electric 

(53) 

arc, usually preferred in simulating 

processes in high-voltage devices, can 

after the implementation of necessary modification 

take into account the variable length of 

the plasma arc column. 

6. The combined parallel TWV model of 

the electric arc, usually preferred in simulating 

processes in low-voltage devices, can after the 



21

implementation of necessary modification take 

into account the variable length of the plasma 

arc column. 

Research work funded by the Ministry 

of Science and Higher Education from 

science-allocated funds in years 2010-2013 

as research project no. N N511 305038. 

References: 

1. Krouchinin A.M., Sawicki A.: A theory 

of electrical arc heating. The Publishing Office 

of Technical University of Częstochowa, Częstochowa 

2003. 

2. King-Jet Tseng, Yaoming Wang, D. Mahinda 

Vilathgamuwa: An Experimentally Verified 

Hybrid Cassie-Mayr Electric Arc Model 

for Power Electronics Simulations. IEEE 

Transactions on Power Electronics, 1997, vol. 

12, nr 3, s. 429-436. 

3. Ciok Z.: Modele matematyczne łuku łączeniowego. 

Politechnika Warszawska, Warszawa 

1995. 

4. Schőtzau H. J., Kneubühl F. K.: A New 

Approach to High-Power Arc Dynamics. 

ETEP 1994, vol. 4, nr. 2, s. 89-99. 

5. Finkelburg W., Maecker: Elektrische 

Bogen und thermisches Plasma. Handbuch der 

Physik, 1956, Bs. XXII, S. 254-444. 

6. Nitu S., Nitu C., Mihalache C., Anghelita 

P., Pavelescu D.: Comparison between 

model and experiment in studying the electric 

arc. Journal of Optoelectronics and Advanced 

Materials 2008, vol. 10, nr. 5, s. 1192 – 1196. 

7. Koshizuka T., Shinkai T., Udagawa K., 

Kawano H.: Circuit Breaker Model using Serially 

Connected 3 Arc Models for EMTP Simulation. 

International Conference on Power 

Systems Transients (IPST2009) in Kyoto, Japan, 

June 3-6, 2009. 

8. Gustavsson N.: Evaluation and Simulation 

of Black-box Arc Models for High Voltage 

Circuit-breakers. LiTH-ISY-EX-3492-2004, 

Linköping, 19 mars 2004. 

9. Smeets, R.P.P. and Kertész, V.: Evaluation 

of high-voltage circuit-breaker performance 

with a validated arc model. IEE Proc., 

Gener. Transm. Distrib. (2000), 

10. Sawicki A., Świtoń Ł., Sosiński R.: 

Evaluation of usability of Cassie and hybrid 

Cassie-Mayr models to simulate processes in 

AC arc circuits. Przegląd Elektrotechniczny 

2010, nr 1, s. 255-259. 

11. Sawicki A., Świtoń Ł., Sosiński R.: Process 

Simulation in the AC Welding Arc Circuit 

Using a Cassie-Mayr Hybrid Model. Suplement 

to the Welding Journal 2011, March, s. 

41-44. 

12. Sawicki A., Świtoń Ł., Sosiński R.: 

Próba wykorzystania modeli Cassiego i hybrydowego 

Cassiego-Mayra do symulowania 

procesów w obwodach z lampami rtęciowymi. 

Śląskie Wiadomości Elektryczne 2010, nr 1, s. 

4-9. 

13. Berger S.: Mathematical approach to 

model rapidly elongated free-burning arcs in 

air in electric power circuits. ICEC 2006, 6-9 

June 2006, Sendai, Japan, 2006. 

14. Berger, S.: Modell zur Berechnung des 

dynamischen elektrischen Verhaltens rasch 

verlängerter Lichtbögen. Dissertation ETH, 

Zürich 2009. 

15. Математические методы 

исследования динамики и проблемы 

управления низкотемпературной плазмой. 

Низкотемпературная плазма, том 2. Наука, 

Новосибирск 1991. 



Eugeniusz Turyk, Agnieszka Żydzik-Białek, Margrit Bormann, Andrzej Jastrzębiowski, 

Marta Kościelniak, Tadeusz Kuzio, Bogusław Czwórnóg 

Repair welding of elements of the sign ARBEIT MACHT FREI 

of the main gate to the former German Nazi concentration 

and extermination camp Auschwitz I 

Editor’s note 

After the end of the Second World War the sign “ARBEIT MACHT FREI” on the gate 

to the former German Nazi concentration and extermination camp Auschwitz I became one 

of the most important symbols of German Nazi concentration camps, slave labour, inhumane 

conditions and mass genocide — the Holocaust. 

Mieczysław Kościelniak (camp serial number 15261) 

“Work squads marching out to work”, Poland, 1950, from 

the collection of the Auschwitz-Birkenau State Museum 

Fig. 1. Front and back of the sign damaged during the theft. Red colour 

marks spots where the sign was cut or where its elements were torn 

off [1] 

Introduction 

In the former German Nazi concentration 

and extermination camp Auschwitz I in 1940, 

a sign reading “ARBEIT MACHT FREI” 

(work makes one free) was put up over the 

main gate. The sign was made in the shop of 

the camp’s locksmith under the management 

of Jan Liwacz (camp serial number 1010). At 

night, on 17/18 December 2009 the sign was 

stolen from the Auschwitz-Birkenau State 

Museum in Oświęcim. After recovering it, it 

turned out that during the theft the sign (5570 

mm in length and 360 mm in height) sustained 

significant damage – it was cut into three 

parts, bent, the sections of the upper 

and lower pipes (ϕ 33x3 mm [1]) 

were twisted and deformed and one 

of the letters (“I” in the word FREI) 

fell off (Fig. 1). 

After the sign had been recovered, 

its exceptional and symbolic 

significance helped to reach a decision 

on correcting the theft-related 

Mgr Agnieszka Żydzik-Białek, Dipl.-Rest. (FH) Margrit Bormann, mgr Andrzej Jastrzębiowski, 

mgr inż. Marta Kościelniak – the Auschwitz-Birkenau State Museum in Oświęcim, Conservation 

Section; dr hab. inż. Eugeniusz Turyk, mgr inż. Tadeusz Kuzio, dr inż. Bogusław Czwórnóg – 

Instytut Spawalnictwa, Gliwice 



23

deformities, as they considerably distorted 

the primary reception of the sign. Afterwards, 

all the fragments were to be joined to form a 

whole sign again. Straightening and joining 

have an enormous effect on the legibility of 

the primary functions and meaning of the sign; 

therefore, the activities had to be preceded 

by a very thorough investigation. The fundamental 

assumption of the conservation was to 

protect all the components of the sign – pipes, 

letters, welds, and preserve the original paint 

coatings. At first, the conservators thoroughly 

documented the condition of the sign. In doing 

so they used visible light as well as ultraviolet 

and infrared photography. The sign was 

scanned in three dimensions. The tests also 

involved analysis of the chemical composition 

and hardness measurements of the material out 

of which the individual elements of the sign 

were made. Thanks to endoscopy and magnetic 

particle inspection it was possible to identify 

the slightest metal damage, invisible to the 

naked eye. Separate tests were carried out in 

relation to the protective coatings. All of these 

activities allowed the development of a programme 

of conservation [2]. 

According to the assumptions of the conservation 

programme, 

the connections 

of all the 

elements of the 

sign should be 

stable, durable, 

possibly invisible, 

and have no 

detrimental effect 

on the appearance 

of the sign. It 

was decided that 

the method employed 

to join 

Sign 

pipe 


the elements should be the same as that applied 

originally, i.e. welding. Such a method should 

ensure a relatively narrow heat affected zone, 

minimum porosity, and complete penetration 

of the pipe joints (due to changing loads of the 

sign put up on the gate). Other requirements 

included entirely crack-free joints and as little 

difference in the colour of the welds and the parent 

metal of the elements made of carbon steel. 

The Conservation Section of the Auschwitz 

-Birkenau State Museum turned to Instytut 

Spawalnictwa with a request to conduct these 

works aimed at selecting a technology of repair 

welding the sign elements; the technology was 

to meet requirements formulated by the Conservation 

Section. The request also required 

technological supervision over the repair welding 

of the sign elements [5, 6]. The process 

and results of the conservation are presented 

below. 

Parent metal of sign elements 

The upper and lower seamed pipes of the historic 

sign are made of carbon steel having the 

chemical composition as presented in Table 1. 

Carbon steel used in the production of the 

sign pipes is characterised by good metallur- 

Table 1. Results of chemical analysis of pipe material [1] and carbon equivalent 

Contents of chemical elements [%] 

C Si Mn Cr V Ni Cu 

Carbon 

equivalent 

Ce [%] 

upper 0.0585 0.0065 0.3255 0.006 0.002 0.008 0.0228 0.12 

lower 0.0956 0.0065 0.4606 0.006 0.002 0.008 0.0203 0.18 

Lower pipe – Al content: 0.025%; P content: 0.0218%; S content: 0.0468%. 

Upper pipe – Al content: 0.025%; P content: 0.0268%; S content: 0.0661%. 

Carbon equivalent: C Mn Cr + Mo + V Ni + Cu 

= C + + 

+ ,% 

6 5 15 

Table 2. Results of chemical analysis of material of pipes technological welding tests [5] 

Test 

Contents of chemical elements [%] 

pipe C Si Mn Cr Mo V Ni Cu 

Ce [%] 

upper 0.065

gical weldability, confirmed by the chemical 

composition and related carbon equivalent. 

For this reason, welding of the steel does not 

require any special precautions aimed at preventing 

the formation of hardened structure in 

the heat affected zone. 

On the basis of a low silicon content 

(Si

Fig. 3. End of upper part (1GL acc. to 2) after word AR- 

BEIT 

Fig. 7. 120 mm-long crack of lower pipe on section 1DL 

acc. to Fig. 2 

Fig. 4. Broken end of upper pipe (1GP acc. to Fig. 2) before 

word MACHT 

Fig. 8. Ends of upper and lower pipes (2GL and 2DL acc. 

to Fig. 2) after word MACHT. Visible bending of upper 

pipe at angle of approx. 90° 

Fig. 5. Bent end of broken lower pipe (1DL acc. to Fig. 2) 

after word ARBEIT. Visible deformation of letter “T” 

Fig. 9. End of partly cut and broken upper pipe (2GL acc. 

to Fig. 2) after words MACHT 

Fig. 6. End of the lower pipe (1DL acc. to Fig. 2) partially 

cut on along its circumference and then broken 

Fig. 10. End of partly cut and broken upper pipe (2GP acc. 

to Fig. 2) before word FREI 



Damage was also caused to the welded joints 

between the letters and the pipes. During 

the visual inspection it was possible to notice 

cracks – welds partly or fully torn off on their 

whole length. Examples are presented in Figures 

12÷15. 

Fig. 11. Broken and deformed lower pipe at weld joining 

pipe with letter ”I” in word FREI 

Fig. 15. Weld joining the letter ”I” with upper pipe in 

word FREI – letter broken off on the whole length of welded 

joint (part of weld remained on pipe) 

Fig. 12. Torn off welds joining letter ”R” with lower pipe 

in word FREI 

It was also possible to observe cracks (Fig. 

16) and material torn off along the fastening 

on the right side the sign. 

Fig. 13. Crack (partly torn weld) on the length of 15 mm 

in weld on upper left side of letter ”E” in word FREI 

Fig. 14. Weld torn off, located on the upper right side of 

the letter ”E” in word FREI (weld torn of on the length of 

37.5 mm) 



Fig. 16. Cracks in corners of right element fastening sign 

to pole – view from sign side 

In order to eliminate the adverse effect of 

rust and protective varnish covering the sign 

on the quality of the welded joints after straightening, 

prior to welding the zone directly 

adjacent to the area of planned welding underwent 

sand-blast cleaning. After removing 

paint from the existing welds and the adjacent 

area, it was ascertained that some cracks visible 

on the surface of the straightened elements 

were only present in the layer of the paint and 

not in the metal beneath it. The visual inspection 

also revealed the presence of residual 

27

welding slag (i.e. slag formed by molten electrode 

covering) in the welds of the letters “B” 

(from the front side of the sign), “E” (from the 

front side of the sign), “I” (from the front and 

back side of the sign, from the bottom) in the 

word ARBEIT, “M” (from the front side, from 

the bottom of the sign, from the left side) and 

the letter “C” (from the front side, from the 

bottom of the sign), among others. On the basis 

of this inspection it was possible to ascertain 

that the welded joints were welded manually 

with covered electrodes. Removal of the 

paint revealed welding imperfections which 

had been formed during the original welding 

of the historic sign. These faults included a 

burn-through in the upper joint of the letter 

“A” in the word ARBEIT and a gas pore in 

the welded joint of the bottom left base of the 

letter “R” in the same word, from the front 

side of the sign. 

On the basis the visual inspection of the 

sign, after its straightening by the artistic metalwork 

company EDEX-POL in Sułkowice 

and sand-blast cleaning of the zone directly 

adjacent to the area of the planned welding, 

a detailed list of the necessary repair welding 

was prepared. The scope of the work included 

the production of butt joints of the upper and 

lower pipes of the sign, welding the sign-fastening 

elements, as well as welding the fragments 

which had cracked and were torn off 

[6]. 

Tests of historic sign pipe after hot 

straightening 

The damaged fragments of the sign underwent 

cold or hot straightening. According 

to information provided by the Conservation 

Section, in the case of hot straightening the 

elements were first heated up to a temperature 

of 830°C÷1050°C (orange colour of steel incandescence) 

and cooled quickly afterwards. 

Visual inspection did not reveal any cracks 

in the places adjacent to the area which had 

been heated. 

Tests of the microstructure of the historic 

sign pipe were conducted using the damaged 

section of the lower pipe, adjacent to the letter 

“I” (3DP acc. to Fig. 2) in the word FREI. 

The section in question underwent hot straightening 

and next, on the basis of the type 

and size of the damage, was qualified for a 

removal and replacement by a 50 mm-long 

insert. 

Before microstructural analysis the pipe 

material was tested for the contents of carbon, 

sulphur and phosphorus, which amounted to 

0.038%, 0.052% and 0.069% respectively. 

The above results, along with the results cited 

according to the study [1], confirmed that 

the chemical composition of the pipe being 

tested corresponded to low-carbon unalloyed 

structural steel. For this reason, after hot straightening 

followed by cooling in water, the 

material of the pipe should be free from disadvantageous 

hardened structures. In order 

to verify the above statement it was necessary 

to carry out microscopic metallographic 

examination of the pipe material, revealing 

the presence of ferritic structure with numerous 

non-metallic inclusions. The material 

of the pipe after hot straightening and fast 

water cooling did not reveal any hardened 

structures. The hardness of the pipe material 

measured in the metallographic specimen 

was between 119 HV10 and 184 HV10. The 

microscopic examination and hardness measurements 

confirmed that post-straightening 

repair welding did not require any additional 

heat treatment. 



Initial selection of method for welding 

the elements of the sign 

The initial selection of the welding method 

was based on the repair-related requirements 

enumerated above and took into consideration 

the arrangements made with the Conservation 

Section while preparing expertise and connected 

with the necessity to ensure a relatively 

narrow zone of welding-related heat effect on 

the material and paint cover of the pipe and 

a minimum weld reinforcement (aesthetical 

joint appearance). At this stage also the basic 

requirements concerning repair welding were 

specified. 

The initial selection of the repair welding 

method was based on the assessment of pipe joints 

made by means of the following methods: 

oxy-acetylene welding (process 311), manual 

metal arc welding (process 111), semi-automatic 

MAG welding (process 135), TIG welding 

(process 141), plasma arc welding (process 15) 

and laser beam welding (process 52). 

The assessment focused on the girth joints 

of pipes welded at Instytut Spawalnictwa using 

oxyacetylene welding, manual welding with 

covered electrodes, TIG welding and plasma 

arc welding as well as joints welded by outside 

companies (at the request of the Conservation 

Section) with the use of laser beam welding, 

MAG welding with solid wire electrode, TIG 

welding and combined welding i.e. a penetration 

layer and filling layers were made with 

TIG welding whereas the face layer was made 

with a laser beam. After analysis of these 

welding methods it was ascertained that the 

methods useful in the process of making pipe 

joints would be TIG welding, plasma arc welding, 

laser welding with backing, and a combined 

method i.e. penetration by means of TIG 

welding and the face layer using laser beam 

welding. The methods ensured good quality of 

the joints of the sign, including the pipe joints 

with complete penetration, minimum reinforcement 

and a relatively narrow heat affected 

zone. The torn off letters and the cracks in the 

welds joining the letters with the pipe could be 

repaired by means of plasma arc welding and 

TIG welding with a filler material, with fillet 

welds, the same as in the case of the original 

sign. 

Test welding of pipes nos. 1 and 2 supported 

by tests of the quality of welded joints facilitated 

the selection of welding consumables 

ensuring relatively low porosity of welded joints 

made of effervescing steel. Radiographic 

tests revealed the quality level B of girth joints 

made with Castolin Eutectic-manufactured 

rods grade CastoTIG 45255, intended for welding 

of unalloyed steels and ensuring the yield 

point of weld deposit R0.2 > 385 MPa. The 

tensile strength of two test pieces of the joint 

from pipe no. 1 was 411.5 MPa and 382.9 MPa 

with the rupture occurring outside the weld. 

Positive results of radiographic and strength 

tests confirmed the usability of TIG welding, 

plasma arc welding and rods grade CastoTIG 

45255W. 

The tests also confirmed the possibility of 

making irregular decorative spots on the faces 

of welds. The purpose of these spots, made 

with a pulsed laser, was to mask a characteristic 

arrangement of crystallisation isotherms 

(Fig. 17). 

a) b) 

Fig. 17. Joint of pipes (a) and laser-made decorative spots 

on the face of weld (b) 



29

Tests of model joints of partly torn letters 

The welding test also involved carrying 

out model repair welding of letters partly and 

entirely torn off the pipe. At the first stage it 

was necessary to produce T-shaped joints with 

fillet welds, joining the letters made of 4 mm 

-thick steel plate with the pipe (33.9x3.2 

mm). Afterwards, a passage groove in the fillet 

weld was made (to model the crack in the 

lower and upper part of the weld). The cuts 

were welded with a plasma arc. The technological 

conditions of plasma welding were as 

follows: weld groove I, distance 1.0 mm ÷ 1.5 

mm, welding position PA, tungsten electrode 

WTh 20 1.6 mm, plasma gas Ar, shielding 

gas Ar+2%H2, filler material – rod CastoTIG 

45255W 2.0 mm in diameter, welding current 

22 A÷26 A, plasma gas flow rate 0.3 l/min ÷ 

0.4 l/min, shielding gas flow rate 6 l/min. A 

sectional view of a model crack before and 

after welding is presented in Figure 18. 

a) b) 

Fig. 18. Cut in fillet weld, modelling crack along the contact 

line between letter and pipe (a) and macrostructure of 

plasma-welded cut (b) 

The welding tests and examinations demonstrated 

that the cracks in the joints between the 

letters and the pipe could be repaired by means 

of plasma arc welding and TIG welding. The 

application of these methods ensured proper 

fusion and filling of the weld groove formed 

through the crack. 

Technological supervision 

After the Conservation Section of the Museum 

had selected a company to perform repair 

welding i.e. company FormSerwis Sp. z 

o.o. (Ltd.) from Bydgoszcz, Instytut Spawalnictwa 

carried out the following technological 

supervisory works: 

- verification of welding procedure specifications 

developed by the repair welding contractor. 

The technology developed for the 

welding of butt joints assumed that the root 

layer would be TIG welded, whereas the face 

layer would be laser welded. Afterwards, the 

face of the weld would be pulsed laser treated 

to obtain decorative spots, 

- verification of qualification certificates of 

personnel performing the repair welding and 

assessment of test joints produced within 

the procedure of admission of TIG welder 

and laser welding operator to repair welding 

works, 

- pre-welding inspection as to the completeness 

and serviceability of welding equipment. 

- supervision over the production of the joints 

of the sign pipes, 

- post-weld visual inspection of the welded 

joints of the sign. 

Welding station 

The welding station in a room of the 

locksmith’s shop of the Conservation Section 

of the Museum was equipped by company 

FormSerwis Sp. z o.o. with the following welding 

equipment: 

- device Inverter-TIG-Power 1965 DC-HF 

-Puls, manufactured by Italian company CE- 

BORA S.p.A., used for TIG welding, 

- device ALM 200 manufactured by company 

ALPHA LASER, Germany, used for laser 

welding and surfacing by welding with a moving 

head (Fig. 20), provided with a welding 



Fig. 19. Assembly table with fixed sign 

wire feeder. The device is equipped with a 

pulsed laser Nd:YAG (wavelength: 1064 nm, 

average power 200 W, pulse energy 90 J). 

The device is mobile (1400x730x1505 mm, 

weight 345 kg), enabling welding in various 

places, often difficult to access. The movements 

of the arm with a turn-and-tiltable laser 

head are controlled by an operator with a 

joystick. Limitations are similar to 

those experienced while working 

with a TIG welding torch. 

The welding station was also 

equipped with an assembly table 

provided by the Museum Preservation 

Department (Fig. 19). 

The table was used to fix and position 

the sign while welding so 

that a joint to be made was in PA 

position or a position close to PA 

(Fig. 21). 

Summary 

On the basis of the visual inspection of the 

damaged sign from the main gate to the former 

German Nazi concentration and extermination 

camp Auschwitz I, after its straightening and 

sand-blast cleaning, welding tests, examination 

of model joints and technological supervision 

over repair welding, it was possible 

to formulate the following conclusions: 

Fig. 20. Mobile laser welding machine ALM 200 

Fig. 21. ALM 200 laser welding of sign fixed on assembly 

table 



31

1. Repair welding included the 

production of butt joints of the upper 

and lower pipes of the sign, welding 

of the sign-fixing elements as well as 

welding of cracks and torn elements 

according to a detailed list prepared 

on the basis of the visual inspection 

of the sign, following its straightening 

and sand-blast cleaning [6]. 

2. Repair welding was carried 

out by company FormSerwis Sp. 

z o.o., following the requirements 

specified by the Conservation Section of the 

Auschwitz-Birkenau State Museum [1, 2] and 

Instytut Spawalnictwa. 

3. Visual inspection of the repair welded 

joints of the historic sign did not reveal any 

surface welding imperfections and thus confirmed 

the fulfilment of the acceptance criteria. 

During the repair welding the sign did not suffer 

from any deformities which would require 

straightening. The quality of the welded joints 

of the sign met the requirements of the Conservation 

Section of the Auschwitz-Birkenau 

State Museum as to the shape, dimensions and 

surface appearance. 

The conservation, straightening and integration 

of the damaged sign were financed 

by the Auschwitz-Birkenau State Museum in 

Oświęcim. All the work conducted by Instytut 

Spawalnictwa related to material testing, 

technology applied for welding of the sign 

elements, determination of the scope of repair 

welding works after straightening of the sign, 

and technological supervision over the welding 

of the sign [5, 6] were free of charge (as 

was provided in the contract concluded with 

the Museum). 

Prior to its exposition at a new main exhibition 

of the Museum, the re-integrated sign 

(Fig. 22) was subjected to further conservation. 

Fig. 22. Sign after welding, removed from assembly table 

References 

1. Sign ARBEIT MACHT FREI from the 

main gate to the camp AUSCHWITZ I. No. 

A-43”. Opracowanie Sekcji Konserwatorskiej 

Państwowego Muzeum Auschwitz-Birkenau 

w Oświęcimiu, 2010 r. 

2. Żydzik-Białek A., Jastrzębiowski A.: 

Program prac konserwatorskich. Napis AR- 

BEIT MACHT FREI z bramy głównej byłego 

obozu AUSCHWITZ I. Nr inw. A-43. Sekcja 

Konserwatorska Państwowego Muzeum Auschwitz-Birkenau. 

2010 r. 

3. Photographic documentation of the current 

state of the object. Conservation Section 

of the Auschwitz-Birkenau State Museum, 

Oświęcim, 2011 r. 

4. „Mapowanie spawów obrazujące ich 

stan zachowania”. Sekcja Konserwatorska 

Państwowego Muzeum Auschwitz-Birkenau, 

Oświęcim, 2011 r. 

5. „Wykonanie badań dotyczących wyboru 

technologii spawania elementów napisu AR- 

BEIT MACHT FREI z bramy głównej byłego 

obozu Auschwitz I”. Orzeczenie nr ZT/294/10, 

Instytut Spawalnictwa, Gliwice, 2011 r. 

6. „Nadzór technologiczny przy spawaniu 

naprawczym elementów napisu ARBEIT 

MACHT FREI z bramy głównej byłego obozu 

Auschwitz I”. Orzeczenie nr ZT/289/11, Instytut 

Spawalnictwa, Gliwice, 2011 r. 



Agnieszka Kiszka, Tomasz Pfeifer 

Variable polarity MAG welding of thin protective-coated 

steel plates 

Introduction 

Recent development in the field of modern 

structural materials and welding technologies 

has been dictated by the needs of the automotive 

industry. In spite of numerous attempts 

aimed at the implementation of such materials 

as magnesium and aluminium alloys, plastics, 

or composites, steels still dominate in the 

production of cars due to lower costs, better 

operating properties, and ease of joining. Automotive 

industry manufactures continually 

seek solutions which would allow them to obtain 

high-quality welds of thin steel plates provided 

or not provided with protective coatings. 

A technology currently applied in joining of 

3mm-thick steel plates, based on MAG welding, 

is unable to satisfy all quality-related 

requirements. Particularly problematic is the 

supply of excessive heat to the joint, resulting 

in deformations and spatters. Spatters significantly 

reduce the aesthetics of joints and are 

difficult to remove. 

Implementation of modern MAG welding 

technologies in the automotive industry 

has been possible thanks to newly developed 

solutions of advanced welding control systems. 

The new, so-called, low-energy methods 

such as CTM or ColdArc, are indented to meet 

requirements specified by car manufacturers. 

The application of low-energy welding methods 

decreases the amount of deformations 

of welded elements, reduces the number of 

spatters, and as a result significantly improves 

the appearance of joints. The most recent solution 

in relation to innovative MAG welding 

methods consists in the application of variable 

polarity pulsed current (Fig. 1). 

The study presents the analysis of technological 

conditions of the welding of protectivecoated 

structural materials. The welding methods 

tested in the research were those of AC 

Pulse, developed by a Japanese company OTC 

Daihen and the Cold Process, applied using 

Cloos-manufactured equipment. The results 

presented in the study were obtained at Instytut 

Spawalnictwa while conducting research 

work [1]. 

Fig.1 Course of current in various methods of welding 

with consumable electrode 

Mgr inż. Agnieszka Kiszka, dr inż. Tomasz Pfeifer – Instytut Spawalnictwa, Zakład Technologii 

Spawalniczych (Department of Welding Technologies) 



33

Course of tests and obtained results 

The technological tests of welding with 

variable polarity pulsed current were conducted 

on a mechanised station provided with a 

welding tractor equipped with holder-fixing 

fixtures, a guide bar, and an element for setting 

and fixing the position of elements to be 

welded. Technological tests involved the use 

of an OTC Daihen-manufactured device DW 

300 and a Cloos-made welding power source 

Qineo Champ 450 as well as an electrode wire 

PN-EN ISO 14341-A-G3Si1 of 1.0-mm and 

1.2-mm diameter [2]. The shielding gas used 

for welding with the DW 300 was a mix containing 

82 % Ar and 18 % CO2 (PN-EN ISO 

14175-M21-ArC-18). In turn, the shielding 

gas used for welding with the Qineo Champ 

Fig. 2. Course of changes in current and voltage during surfacing of zinc-coated 

plate using DW 300. Neutral setting of EN ratio 


plate using DW 300. Minimum EN ratio 

450 was a mix composed of 92% Ar and 8% 

CO2 (PN-EN ISO 14175-M20-ArC-8) as it 

was for this gas that a specified synergic line 

was developed and used in research-related tests. 

The application of another shielding gas 

would have impeded a welding process [3]. A 

gas flow rate applied in the tests was constant 

and amounted to 12l/min. Steels used in the 

tests were HX 420 LAD Z 100 MBO, HX 260 

LAD Z140 MBO, DX53D ZF 100 RBO, HC- 

T600X ZF100 RBO, H380 LAD Z140 MBO, 

DX56D ZF100 RBO [4, 5]. 

Recording of course of current and 

voltage in time 

The first stage of tests consisted in recording 

the courses of current intensity and arc voltage 

in a function of time. A 

system for monitoring the 

welding process electric parameters 

was developed at 

Instytut Spawalnictwa [6]. 

During recording, several 

padding welds were built up 

in 3mm-thick sheets. Courses 

were recorded for constant 

settings of technological 

parameters. The only 

parameter altered during 

recording was the percentage 

EN ratio (Electrode Negative 

ratio) in the course of 

welding current. The aforesaid 

parameter is a non-dimensional 

value and can be 

set within a range from -30 

to +30 (DW 300) and from – 

50 to + 50 (Qineo Champ). 

Courses for extreme settings 

of EN ratio are presented 

in Figures 2-7. 




plate using DW 300. Maximum EN ratio 

Fig. 5. Course of changes in current and voltage in function of time, recorded 

during surfacing of zinc-coated plate using Qineo Champ 450. Neutral setting of 

EN ratio 


during surfacing of zinc-coated plate using Qineo Champ 450. Maximum EN 

ratio 

Results obtained through the recording of 

electrical parameters during surfacing confirmed 

that current intensity and arc voltage indeed 

alter their polarity. A time-related course 

of welding current revealed 

two components of the EN 

ratio i.e. basic current and 

pulse current. Basic current 

maintains an arc during the 

change of voltage polarity; 

a negative pulse controls a 

drop of liquid filler metal. 

Reference publications indicate 

that this process takes 

place only for ratio values 

exceeding 30%; otherwise, 

the change of polarity may 

destabilise an arc [7]. As 

the EN ratio setting is nondimensional 

in the case of 

both devices, it is not possible 

to directly determine 

the percentage of EN ratio 

in the course of welding current 

intensity and arc voltage 

(works on this topic are 

underway). During the test 

it was possible to observe 

that there was no EN (electrode 

negative) for a setting 

ensuring the minimum EN 

ratio for the Qineo Champ 

device (Fig. 7). In the above 

case, the course of current is 

characteristic of a classical 

pulsed arc welding. 

During the recording of 

parameters it was possible 

to observe that a change of 

EN ratio significantly affects 

the course of a welding 

process and the appearance of padding welds. 

For this reason, the next stage involved technological 

tests of welding and surfacing with 

various settings of the parameter (i.e. course 



35


during surfacing of zinc-coated plate using Qineo Champ 450. Minimum EN 

ratio 

of current) in order to determine its impact 

on the shape of weld/padding welds and the 

aesthetics of a welded joint. 

Impact of various settings of EN ratio 

on the course of welding process 

In order to determine the impact of EN ratio 

on the quality and geometry of a joint as well 

as on the depth 

of penetration, it 

was necessary to 

build up a number 

of padding welds 

at various settings 

of the parameter 

and with constant 

values of other 

technological parameters 

(filler 

wire feeding rate 

and welding rate). 

Padding welds 

were built up on 

3mm-thick plates 

of steel HX420 

LAD Z 100 MBO. 

Table 1 presents 

examples of the 

macrostructure of padding 

welds produced with various 

settings of EN ratio. 

Technological and macroscopic 

metallographic 

tests revealed that EN ratio 

affects the geometry 

and aesthetics of padding 

welds. The maximum EN 

ratio resulted in the smallest 

penetration depth, whereas 

the minimum EN ratio led 

to the greatest depth of penetration. 

The obtained padding welds were 

characterised by good quality and appearance. 

The surfacing process was stable and produced 

very few spatters, resulting in a smooth 

and uniform face of padding welds. Sectional 

views of padding welds did not reveal any welding 

imperfections. Only when settings were 

Table 1.Macrostructures of padding welds built up on 3mm-thick plates of steel HX420 LAD 

Z 100 MBO at various settings of EN ratio 

Macrostructure 

EN ratio 

AC Pule 

Cold Process 

Neutral 

setting 

of EN ratio 

Maximum EN 

ratio 

Minimum 

EN ratio 

Note: Adler etchant 



extreme, the process was less stable, repeatability 

was lower, and spatters became bigger, 

which significantly deteriorated the aesthetics. 

Another purpose of the research was to 

investigate the impact of EN ratio on the course 

of a welding process as well as on the quality 

and aesthetics of welded joints. The plates 

used for the tests were 1.5 mm thick, made 

of steel grade DX 53 D ZF 100 RBO and provided 

with a zinc-iron protective coating. The 

tests involved the production of overlap joints 

for various parameter settings and in constant 

welding conditions (filler wire feeding rate 

and welding rate). During the process, assessment 

was connected with the process stability. 

After the completion of the process, each 

joint underwent a visual inspection. The criterion 

used in the evaluation of the selection 

of parameters and welding conditions was the 

quality level B according to standard PN-EN 

ISO 5817 [8]. Another process-related criterion 

was the smallest possible damage to the 

zinc-iron layer. A visual inspection of joints 

produced at various settings of EN ratio revealed 

that practically in the whole range of 

EN ratio settings (except for extreme ones) it 

is possible to obtain joints 

of a very good quality. The 

smaller the EN ratio in the 

course the greater the damage 

to a zinc-iron layer 

near a weld. A decrease in 

EN ratio resulted in an increase 

in heat supplied to 

the material being welded 

which was manifested by 

an increased width of the 

joint overheating-affected 

area, greater deformations, 

and local burn-throughs of 

elements being joined. 



Technological tests of welding of various 

steels with protective coatings 

The next stage involved technological tests 

related to the welding of various joints (butt, 

T-shaped and overlap joints) made of plates of 

various thicknesses. Tests revealed that MAG 

welding with variable polarity current makes 

it possible to obtain butt, T-shaped, and overlap 

joints characterised by very good quality. 

Apart from technological parameters, the basic 

variable affecting the possibility of joining 

elements and the course of a welding process 

is the EN ratio. Welding of thin elements is 

most advantageous if accompanied by a high 

EN ratio as it translates to small deformations 

and minimum damage to the zinc-iron layer. In 

turn, T-shaped and butt joints of greater thicknesses 

should be welded with a lower EN ratio 

as the process of welding is more “energetic” 

(i.e. heat input is higher). According to the test 

results, the appropriate selection of technological 

parameters makes it possible to produce 

overlap and butt joints of plates having as little 

as 0.75 mm and 0.8 mm thicknesses. Figures 

8-10 present selected joints and their macrostructure. 

Fig. 8 General view and macrostructure of overlap joint of 0.75mm-thick steel 

DX56D ZF100 RBO; etchant: Adler, magnification x8 

37

Fig. 9. Main view and macrostructure of butt joint with square preparation, made of 0.8mm 

-thick steel DC04+ZE 25/25 AO, test piece no. 24 from Table 9. A - view from face of weld, 

B- view from root of weld; etchant: Adler, magnification x8.5 

Fig. 10. Main view and macrostructure of butt joint with square preparation, made of 

3.0mm-thick steel HX 420 LAD Z 100 MBO, test piece no. 10.1 from Table 9. A - view 

from face of weld, B- view from root of weld; etchant: Adler, magnification x5.5 

A considerable advantage of MAG welding 

with variable polarity current is the possibility 

of producing inaccurately matched joints, even 

with a gap of 2 mm. Such a possibility is of particular 

importance in the automotive industry, 

where one often faces the necessity of welding 

such joints. The above mismatching is a frequent 

cause of such welding imperfections as burn-through 

or inadequate joint penetration. Elements 

having such imperfections are forwarded 

to corrective welding which increases the cost 

of production and the number of unacceptable 

products resulting in deteriorating production 

statistics. For this reason, technological 

tests included the welding of inaccurately 

matched overlap joints, butt joints with square 

preparation, and T-shaped joints. Overlap joints 

were made of 

1.2mm-thick steel 

HCT 600X ZF 100 

RBO, butt joints 

with square preparation 

were made 

of 3.0mm-thick 

steel HX 420 

LAD Z100 MBO, 

and T-shaped joints 

were made of 

2.0mm-thick steel 

H380 LAD Z140 

MBO. All the joints 

were made with 

0.5mm and 1.0mm 

gaps. Figures 11- 

13 present selected 

macroscopic photographs 

of inaccurately 

matched 

joints. 

Tests revealed 

that MAG welding with variable polarity current 

can be used for welding of inaccurately 

matched butt, T-shaped and overlap joints. 

Good quality, aesthetics, and an effective bridging 

effect were obtained for all kinds of coatings. 

Properly selected welding conditions 

can minimise or even entirely eliminate spatters. 

Fig. 11. Macrostructure of overlap joint of 1.2mm-thick 

steel HCT600X ZF 100 RBO; joint welded with 1.0 mm 

gap; etchant: Adler, magnification x4 

Fig. 12. Macrostructure of butt joint with square preparation, 

made of 3.0mm-thick steel HX 420 LAD Z100 

MBO; joint welded with 1.0 mm gap; etchant: Adler, magnification 

x3 



Fig. 13. Macrostructure of T-shaped joint, made of 2.0mm 

-thick steel H389 LAD Z140; joint welded with 0.5 mm 

gap; etchant: Adler, magnification x5 

Summary 

Conducted technological tests of the welding 

of thin plates made of unalloyed and low-alloy 

steels of increased strength and protected with 

various zinc-based coatings revealed that the 

application of variable polarity current makes 

it possible to build up joints characterised by 

good quality and aesthetics. A process of welding 

with variable polarity current is less stable 

than traditional MAG welding and emits specific 

sounds, yet joints welded in such a process 

are characterised by good quality and tend to 

be free from spatters. 

The basic process variables having the greatest 

impact on the course of the process as well 

as on the weldability, quality, and aesthetics of 

joints are the technological parameters (filler 

wire feeding rate, welding rate, torch inclination 

angle and arc length) and EN ratio in the 

course of welding current. A change of EN ratio 

significantly affects arc voltage and the amount 

of heat supplied to a joint. Research results revealed 

that the best results are achieved with 

neutral settings of the parameter. An increase 

in EN ratio reduces the penetration depth 

and bridging ability of an arc. If one needs to 

weld thin plates and avoid, as much as possible, 

damage to the zinc coating, a higher EN 

ratio should be applied in the course of current. 

The application of high EN ratio in the course 

of current also makes it possible to weld inaccurately 

matched joints. A decreased EN ratio 

increases heat input of the process and reduces 

the depth of penetration. T-shaped joints and 

thicker elements require a higher EN ratio in 

the course of current. The most convenient solution 

consists in applying a neutral EN ratio, 

as such an approach enables obtaining good 

quality welds and sufficient penetration depth. 

References 

1. Matusiak J., Pfeifer T., Wyciślik J., Kiszka 

A.: Analiza wpływu warunków technologicznych 

innowacyjnych technik spajania 

różnych materiałów konstrukcyjnych z nowoczesnymi 

powłokami ochronnymi na stan środowiska 

pracy. Praca badawcza Instytutu Spawalnictwa 

nr Ma-34, Gliwice 2011 r. 

2. PN-EN ISO 14341:2011 „Materiały dodatkowe 

do spawania. Druty elektrodowe i stopiwo 

do spawania łukowego elektrodą metalową 

w osłonie gazu stali niestopowych 

i drobnoziarnistych. Klasyfikacja” 

3. PN-EN ISO 14175:2009 „Materiały dodatkowe 

do spawania. Gazy i mieszaniny gazów 

do spawania i procesów pokrewnych” 

4. PN-EN 10346:2011 „Wyroby płaskie 

stalowe powlekane ogniowo w sposób ciągły. 

Warunki techniczne dostawy” 

5. PN-EN 10152:2011 „Wyroby płaskie 

stalowe walcowane na zimno ocynkowane 

elektrolitycznie do obróbki plastycznej na 

zimno. Warunki techniczne dostawy” 

6. Szubert L., Skoczewski P, Welcel M.: 

System rejestracji parametrów elektrycznych 

procesu spawania dla wielu stanowisk produkcyjnych. 

Praca badawcza Instytutu Spawalnictwa 

nr Fc-89, Gliwice 2010 r. 

7. Jaskólski K.: Robotyzacja OTC z wykorzystaniem 

niskoenergetycznych metod spawania. 

Materiały firmy SAP, 2010 

8. PN-EN ISO 5817:2009 „Spawanie. Złącza 

spawane ze stali, niklu, tytanu i ich stopów 

(z wyjątkiem spawanych wiązką). Poziomy 

jakości według niezgodności spawalniczych” 



39

Marek St. Węglowski 

Testing electromagnetic radiation of welding arc 

in TIG method from welding process monitoring point of view 

Introduction 

The observation of a welding arc and analysis 

of results can be used in assessment of 

welding process stability and correctness. Information 

related to a welding arc can be obtained 

by registering and analysing a sound 

emitted by an arc or by analysing a course of 

momentary values of electric quantities characterising 

an arc (intensity of arc welding current 

and arc voltage) [1]. Commonly applied 

methods of monitoring welding processes 

through a welding arc (the so-called “through 

the arc sensing) [2] are based primarily on measurements 

and registration of welding current 

intensity and welding arc voltage. The aforesaid 

methods also involve the registration of a 

shielding gas flow rate, welding rate and filler 

metal feeding rate. Monitoring is carried out 

by means of specialist recording equipment 

or universal measurement cards [1, 3]. Measurements 

of welding current intensity and 

welding arc voltage are used in assessing of 

welding process stability, particularly, if one 

applies advanced signal analysis [4]. 

A new approach to assess the stability of 

welding processes and the quality of welded 

joints is the analysis of welding arc radiation. 

The method was first used in the control of 

a welding arc length in the MAG method in 

1966 [5] and was further developed in works 

[6, 7]. The issues related to radiation emitted 

by an electric arc are also investigated at Polish 

research centres. The result of this investigation 

is, among others, monographs [8-10]. 

The aforementioned publications, however, 

are not directly related to issues of monitoring 

arc welding processes. 

New monitoring methods require the application 

of advanced measuring equipment, 

which, in most cases, must be adapted for welding-related 

measurement needs. 

Welding arc radiation 

The sources of radiation in an electric arc 

are, among others, arc column, near-electrode 

areas, liquid metal transported by an arc and 

a heated terminal of an electrode wire. A range 

of lengths of emitted light waves and their 

spectral composition depends on welding 

parameters, arc burning atmosphere, types of 

base and filler metals and a number of other 

parameters [11]. Figure 1 presents an image of 

a 2 mm-long welding arc in the TIG method 

at a welding current of 100 A. Figure 2 presents 

an image of a welding arc depending on 

current intensity and arc length. It can be observed 

that, in case of a constant arc length, an 

increase in welding current intensity results in 

a more stable and more symmetric welding arc 

of the TIG method. 

Fig. 1. Shape of welding arc in TIG method, welding current 

intensity I=100A, welding arc length L=2 mm 

Dr inż. Marek St. Węglowski – Instytut Spawalnictwa, Testing of Materials Weldability and Welded 

Constructions Department 



L=1 mm, I=25 A L=1 mm, I=50 A L=1 mm, I=75 A 

L=1 mm, I=100 A 


L=2 mm, I=100 A 


L=3 mm, I=100 A 


L=4 mm, I=100 A 


L=5 mm, I=100 A 

Fig. 2. Image of welding arc in TIG method for arc length in range from 1 to 5-mm and current intensity 

from 25 to 100 A; shielding gas: argon 

Energy emitted in an arc column is mainly 

scattered by conduction and convection. 

Emission of electromagnetic radiation constitutes 

10÷15% of energy supplied to an arc 

[11]. Heat radiation, the source of which is a 

body emitting high temperature, is characterised 

by a continuous radiation spectrum. The 

source of a continuous spectrum in the area 

of a welding arc is mainly a liquid weld pool 

[12]. The characteristic radiation of atoms and 

ions in an arc is discrete. This type of radiation 

is analysed in reference publications as plasma 

radiation. 

Plasma of a temperature contained in a range 

between several eV and a few dozen keV 

(in energy scale 1 eV = 11600 K) emits infrared 

radiation, visible radiation, ultraviolet 

radiation and X-ray radiation, which, due to 

the mechanism of emission can be divided into 

three basic types [14]: 



41

1. linear radiation emitted during the transition 

of atoms or ions from one discrete energy level 

to another (transition between bound states); 

2. recombination radiation accompanying a 

capture of a free electron by one of the discrete 

atom or ion levels (transition between a free 

state and bound states); 

3. radiation of free electron retardation in an 

ion field (transitions between free states). 

The total radiation of welding arc plasma is 

the sum of the continuous radiation and linear 

radiation of spectral lines [10, 15]. This sum 

can be written as [15]: 

λ 

= ε 

λ, c λ, 

L 

+ ∑ε 

ε 

(1) 

where: ε λ,c 

- intensity of continuous spectrum 

radiation, ε λ,L 

- intensity of spectral line; the 

summation on the right side of the equation is 

carried out including all lines lying in a given 

area. 

For optically thin plasma, the intensity of 

continuous spectrum radiation can be written 

in the following form [15] : 

⎛ ⎛ hc ⎞⎞ 

ε 

λ, 

c = kλ, 

c 

( T ) ⋅ Bλ 

( T ) ⋅ ⎜1 

− exp⎜ − ⎟⎟ 

⎝ ⎝ λ kT ⎠ ⎠ (2) 

where: B λ 

(T) is the Planck function for a black 

body, and k λ,c 

(T) is a total absorption coefficient, 

T – arc temperature [K], h - the Planck 

constant (6.6262×10 -34 [Js]), c - speed of light 

in vacuum (2.9979×10 8 [ms -1 ]), λ - wavelength 

[nm], k - the Boltzmann constant 1.38×10 -23 

[JK -1 ]. 

The formula for continuous radiation intensity 

applies irrespective of whether plasma is 

in a state of thermal equilibrium or not. 

The intensity of a spectral line ε λ,L 

is expressed 

by the following formula [15] : 

3 

hcgq 

AqpN 

eN 

i ⎛ h ⎞ ⎛ Ei, 

q 

− ∆Ei 

⎞ 

ε λ , L 

= 

⎜ ⎟ ⋅ exp⎜ 

⎟ ⋅ P qp 

( λ) 

8πλUi 

( T ) ⎝ 2πmkT 

⎠ ⎝ kT ⎠ 

(3) 


where: g q 

– statistical weight factor of the upper 

level; A qp 

– transition probability; E i,q 

– 

upper level ionisation energy; ∆E i 

– ionisation 

potential reduction; P qp 

– line profile, N e 

- density 

of electrons, N i 

- density of ions, U i 

- statistical 

weight factor of ion, m - particle mass. 

The spectral distribution and intensity of 

thermal radiation depend on the temperature 

of a radiating body. Black bodies of a temperature 

of up to 500 K emit mainly infrared radiation 

of wavelength of > 2 μm. Bodies of a temperature 

exceeding 1000 K emit, in addition to 

long-wave infrared radiation, also near infrared 

radiation in the wavelength range of 0.78 

μm ÷1.4 μm and very little, below 1%, visible 

radiation. Bodies of a temperature exceeding 

3000 K emit, in addition to infrared radiation 

and visible radiation, also some (0.1%) long 

-wave ultraviolet radiation. Only bodies of a 

temperature exceeding 4000 K emit ultraviolet 

radiation shorter than 315 nm [11]. 

Welding arc radiation intensity is the highest 

in the wavelength range between 200 nm 

and 1300 nm [16]. The fraction of infrared, visible 

and ultraviolet radiation in the spectrum 

of welding arc radiation depends on a welding 

technology and, in each technology, on welding 

parameters [11, 16]. 

The greatest intensity of visible radiation 

among arc welding processes can be observed 

in MIG/MAG, MMA, TIG and plasma welding. 

It was ascertained that the intensity of 

ultraviolet radiation increases with a square of 

welding current intensity and that visible radiation 

intensity does not rise so intensively 

[11, 16]. 

The intensity of ultraviolet and visible radiation 

emitted during metal arc welding and 

welding with cored electrodes (MIG/MAG 

methods or self-shielded arc welding) in the 

presence of welding fumes is lower than in the 


case of TIG welding (for similar welding current 

intensity). In the same welding conditions 

the intensity of infrared radiation does not 

change significantly. During submerged arc 

welding visible radiation and ultraviolet radiation 

is absorbed by a flux layer [11]. 

The characteristic radiation of ions and 

atoms in an arc is discrete; argon, iron, oxygen 

and nitrogen atoms and ions being the main 

source of radiation. The radiation intensity 

of other elements is significantly lower. The 

wavelength range of visible radiation contains 

mainly spectra of iron, oxygen, nitrogen and, 

only partially, argon (whose ionisation potential 

is significantly higher) [17]. The latter 

also means that the emission of light by argon 

atoms and ions occurs at higher arc temperatures 

than temperatures obtained during welding 

in e.g. Ar+CO 2 

mixes. 

Examinations of a discrete spectrum provide 

information about a temperature emitting 

particle radiation; this being due to the fact 

that the excitation of a particle requires a supply 

of specific energy, a measure of which can 

be temperature. The source of this type of radiation 

in a welding arc is mainly arc column 

plasma as well as metal transported by an arc, 

slag and the surface of elements being welded 

[18]. The energy of areas in the vicinity of the 

anode and cathode of a welding arc is used 

mainly for heating and melting of an electrode 

and base metal. It is known that the potential 

and kinetic energy of electrons is transformed 

into thermal energy on the surface of an anode 

and causes its intensive heating [17]. 

The radiation of a welding arc is a complex 

phenomenon depending on many welding parameters. 

In order to be able to apply the radiation 

of an arc in the accurate and reliable 

monitoring of a welding process, one should 

create a model binding the intensity of welding 

arc visible radiation with welding parameters 

[19]. 

A welding arc can be treated as a point source 

of radiation. Such an approach, however, 

appears inadequate in many applications. It 

seems more proper to treat an arc as a cylindrical 

source of radiation (Fig. 3) as such a model 

better reproduces the actual shape of a welding 

arc and facilitates accurate examination of arc 

radiation. For this reason, the aforesaid model 

will be discussed in more 

detail. A cylindrical model 

can also be simplified 

and a welding arc can be 

presented as a hemisphere. 

Such an approach is 

used in designing of systems 

for monitoring of 

automated welding processes, 

based on visual 

systems [20, 21]. 

A welding arc column 

Fig. 3. Model of 

welding arc 

in TIG method [6] 

is composed of three types 

of particles: electrons, 

ions and neutral atoms. It 

is assumed that an arc column is in a state of 

local thermodynamic equilibrium, at which 

electron collisions play an important role in 

excitation and ionisation. 

Equation 2 illustrates the emission of welding 

arc radiation of a continuous spectrum. 

After taking into consideration the dependence 

between a wavelength and frequency 

c/λ=ν and the Planck function for a black 

body, the Rayleigh-Jeans law is satisfied when 

hν/kT

ture of electrons [K]. The fit of equation 2 with 

equation 4 is better than 5% for λ L 

T>4.3 cmK, 

where λ L 

is a wavelength expressed in cm. The 

right side of equation 4 amounts to 1 (approximately) 

for infrared and visible radiation. In 

addition, under atmospheric pressure and in a 

normal range of welding current, the temperature 

of an electron is close to the temperature of 

an arc. Taking into consideration the foregoing 

and omitting differences of temperature one can 

write as follows: 

2v 

k () v 

2 

ε v = ′ kT 

c 

2 

(5) 

where: T is the temperature of an arc [K]. 

In order to simplify the discussion, the gradient 

of temperature changes along the arc axis 

has been passed over. By combining the emissivity 

factors for various arc areas, the energy radiated 

from the whole arc can be expressed as: 

B iv 

= ʃʃʃ ε v 

dv (6) 

After calculating emissivity factors in the 

whole welding arc and assuming that electric 

conductivity and voltage gradient are constant 

as well as after taking into consideration the impact 

of the visible radiation of a liquid metal 

pool one can write as follows: 

B 

1 

⎛ 

1 ⎞ 

− ⎟ + 

2 ⎠ 

γ G2 

2 

= G LI 

I 

iv 

⎜ G I + 

⎝ 

e 

3 

G 

4 

(7) 

where: 

γ, G i 

– constants, L – arc length, I – current 

intensity. 

Equation 7 provides the image of a relation 

between the visible radiation of a welding arc 

and welding parameters, including the relation 

between current intensity and arc length. The 

authors of model [6] indicate that the equation 

is satisfied for a welding arc when current intensity 

is up to 150 A. In case of higher intensity, 

the density of current is not constant in the 

whole volume of a welding arc. 

Investigation of welding arc radiation 

The research conducted so far has been 

mainly focused on the examination of arc luminance 

[22], the impact of arc radiation on 

the welder’s health [23], health-protecting 

systems and the development of systems for 

tracking the axis of a joint (welding torch position) 

[2]. The analysis of a visible radiation 

spectrum emitted by a welding arc is used to 

test the distribution of temperature in an arc 

[25], calculate the average temperature of a 

welding arc [26], determine the amount of hydrogen 

in a gas shield [27] and determine the 

temperature of a liquid metal pool [28]. The 

analysis of a welding arc radiation spectrum 

is helpful in the development of a technique 

of photographing a welding arc [29]. Spectroscopic 

methods are a useful tool for investigating 

spins of a shielding gas after leaving 

the gas nozzle in TIG and MIG/MAG methods 

[30], a relation between the spectral distribution 

of an arc and the type of a material being 

welded [31] and the distribution of electron 

density [32]. 

The investigation of welding arc visible radiation 

in MIG/MAG methods was also used 

in the monitoring of a manner in which a metal 

is transferred in an arc [33, 34]. Methods utilising 

electric signals (measurements of welding 

arc voltage and welding current intensity) 

are effective only for observing a short-cut arc 

welding process and with a coarse drop metal 

transfer in an arc. When metal is spray-transferred, 

the signal/noise ratio is too low and, in 

such a situation, greater accuracy is obtained 

by measuring the intensity of welding arc visible 

radiation [33, 34]. The method based on 

the measurement of welding arc radiation is 

also used in tracing the length of an arc in TIG 

[35, 36] and MIG/MAG [34] methods. 



Other, equally important research is focused 

on plasma. Methods applied in the plasma-related 

investigation are those of emission spectroscopy 

and laser radiation scattering (laser 

spectroscopy). The aforesaid methods make it 

possible to calculate such plasma parameters 

as the temperature and concentration of atoms 

(ions, electrons) [37]. 

Emission spectroscopy is a passive method, 

in which electromagnetic radiation originating 

from plasma (one or many spectral lines) is 

registered and analysed. The main advantage 

of this method is the simplicity of carrying out 

measurements. The method requires an optical 

focusing system, monochromator or spectrometer 

and detector (e.g. a photomultiplier or 

CCD matrix). The major disadvantage is the 

fact that radiation being registered is total radiation 

emitted from plasma. In order to obtain 

measurement data from one specific measurement 

point it is necessary carry out the Abel 

transformation [38]. Another disadvantage is 

the necessity to assume that plasma is in a state 

of local thermodynamic equilibrium and is 

optically thin. 

Laser spectroscopy is a more universal method, 

yet it requires the source of laser radiation 

and a detection system. The method of laser 

spectroscopy enables the determination of 

plasma parameters in a given point. In some 

cases, laser spectroscopy makes it possible to 

calculate plasma parameters without assuming 

that plasma is in thermodynamic equilibrium. 

The technique utilises the Rayleigh scattering, 

Tomson scattering, laser-induced fluorescence 

and diphoton laser-induced fluorescence [37]. 

Plasma radiation registered in measurements 

perpendicularly to the discharge axis is a sum of 

contributions from various layers (Fig. 4). The 

so-called Abel transform [37, 38] makes it possible 

to determine ε(x) on the basis of known I(x). 

Fig. 4. Sectional view of plasma column, discharge axis is 

perpendicular to paper sheet plane: A- radial distribution 

of emission factor, B – side view of intensity distribution. 

I(x) – distribution of radiation intensity in plane perpendicular 

to direction, in which plasma is observed, x – distance 

from direction of plasma observation [38] 

When plasma is characterised by cylindrical 

symmetry in the sectional view under observation 

and the phenomenon of self-absorption is 

not present, the distribution of radiation intensity 

in the plane perpendicular to the direction 

of plasma observation is expressed by the following 

formula [38]: 

r0 

ε 

( ) 

() r ⋅ r 

I x = 2⋅ 

∫ dr 

2 2 

x r − x 

(8) 

where: ε(r) – intensity of radiation emitted 

by plasma on the unit of thickness of a layer 

distant from the discharge axis by r, x – distance 

from the direction of plasma observation 

(Fig. 4), 2r 0 

– diameter of an area where plasma 

is present. 

The so-far research into welding arc plasma 

aimed, among others, at the creation of 

a mathematical-physical model of an arc [39, 

40] which could be useful in designing new 

welding devices [41]. Also important, from 

the practical point of view, is research aiming 

to determine the impact of electrical parame- 



45

ters of an arc on its properties [42] as well as 

the changes of the chemical composition of a 

shielding gas [43] and a magnetic field on the 

arc blow [44]. Fundamentally important, however, 

is the possibility of calculating the thermal 

efficiency of an arc [45]. Many conducted 

experiments aimed to calculate the distribution 

of arc temperature [46], the speed of electrons 

and ions in an arc, electronic work function 

[47] and the state of thermodynamic equilibrium 

[48]. Modern welding methods such as 

A-TIG welding encouraged the authors [49] 

to test the impact of additional elements and 

compounds intentionally supplied to the area 

of a welding arc on its properties. 

On the basis of the analysis of reference 

publications concerning welding arc research 

one can draw a conclusion that considerable 

attention is given to the phenomenon of welding 

arc radiation and the impact of arc burning 

stability on emitted radiation, yet there 

are no implementations of results obtained in 

related research. 

An important issue of arc-related research 

is the determination of the impact of individual 

factors on the width of spectral peaks. A 

typical shape of a spectral peak is presented in 

Figure 5 along with characteristic quantities: 

x c 

– wavelength of central line, FWHM (Full 

Width at Half Maximum) – width of spectral 

line, I max 

– maximum value of radiation 

intensity for a given spectral 

line. The natural length of a 

spectral line [28, 50] is the result 

of the finite lifetime of energy levels. 

The width is the greater, the 

shorter the lifetime of an energy 

level is. The profile of an emission 

line, resulting from natural 

extension, is the Lorentz distribution. 


Another important factor is the Doppler 

extension of spectral lines, connected with 

the motion of radiation-emitting particles. If 

an emitter has a speed component of a direction 

compatible with the direction of observation, 

a relative change of wavelength related 

to a change of frequency is produced by the 

Doppler effect. In case of thermal movements, 

when the distribution of speed of emitting particles 

is the Maxwell distribution, the profile 

of an emitted spectral line is the Gaussian profile 

[8]. 

Another type of extension which can be encountered 

while analysing spectral lines is the 

pressure extension of spectral lines. This type 

of spectral line extension is the result of collisions 

of emitter particles with other particles. 

They can limit the lifetime of excited atomic 

levels and thus cause the extension of a line 

profile, in this case – the Lorentz profile. As a 

rule, one differentiates three types of pressure 

extension i.e. the resonant, van der Waals and 

Stark extension [8]. 

The arrangement of measurement system 

components is a factor causing additional 

extension of a spectral line. In this case, the 

equipment profile is Gaussian. Theoretically, 

the equipment function of a spectrometer should 

be linearly dependent on the wavelength. 

In fact, the equipment profile is the combina- 

Fig. 5. Typical shape of spectral line [51] 


tion of a function connected with the matrix 

of a detector and functions related to optical 

elements of a spectrometer system [8]. Factors 

causing the extension of spectral lines can be 

divided into those producing 

the Lorentz and 

Gaussian shapes of line 

profiles. Their impact on 

the value of extension varies 

and may depend on 

conditions present in plasma. 

A spectral line resultant 

profile is a function 

being the combination of 

the Lorentz and Gaussian 

[50] functions called the 

Voigt profile [8, 52]. 

It should be noted that a photoelectric detector 

is reached both by useful signals and 

background radiation. As a result, at the CCD 

detector output there are useful signals accompanied 

by noise originating from the background. 

In order to eliminate the impact of background 

radiation, one should deduct it while 

analysing the distribution of welding arc radiation 

intensity. 

Due to the resolution of converters one should 

take into consideration the fact that registered 

files are a “cluster” of several spectral 

lines of a given element (Fig. 6) or even of a 

few elements of various levels of ionisation. 

Therefore, the matching of a shape function 

matters only for the determination of the gravity 

centre for such a group of files. The first 

element of a system for monitoring welding 

processes is the development of a method for 

identification and measurement of quantities 

characterising registered spectral peaks such 

as the peak width, the location of maximum 

and amplitude. The investigation into which 

function better describes the profile of a peak 

(“cluster” of spectral lines) seems to be decisive 

for the detection of welding process disturbance. 

Peak profiles can be the Gaussian, 

Lorentz and Voigt functions (Fig. 6). 

Fig. 6. Exemplary peak matched with Gaussian, Lorentz 

and Voigt functions, I=200 A, L=3 mm, 100 % Ar with 

marked selected spectral lines 

The matching with functions is usually 

carried out using the least squares method 

(e.g. the Levenberg-Marquardt algorithm). 

One can also adapt specialist software for 

this activity. On the basis of matched parameters 

of a function one can calculate the location 

of the spectral line maximum (x c 

) and 

the width of a spectral line (FWHM). During 

the development of experimental data, one 

should also take into account the so-called 

additive constant y 00 

, the presence of which 

results from additional signals registered by 

measuring equipment. 

Next, on the basis of equation (7) one can 

determine the dependence binding the intensity 

of welding arc radiation (energy radiated 

for a given spectral line x c 

) B iv 

, arc length 

and welding current intensity. Using a computer 

programme, one can use collected data 

to calculate the coefficients G i 

and γ. 



47

Values of parameters characterising a welding 

process can be determined by minimising 

the sum of squares 

2 1 

~ 

2 

χ = ∑∑ [ Bkl 

( I 

k 

, Ll 

, λ) − Bkl 

( I 

k 

, Ll 

, λ, 

{ gi} 

)] 

2 

l k ( ∆Bkl 

) 

(9) 

where: I k 

- welding current intensity; L l 

- welding 

arc length; B kl 

(I k 

, L l 

, λ) - intensity of light 

of wavelength λ registered during welding 

with current of intensity Ik, when welding arc 

length amounted to L l 

; ΔB kl 

- uncertainty of 

determined light intensity B kl 

(I k 

, L l 

, λ); B͠ (I , kl k 

L l 

, λ, {g i 

}) - theoretical 

intensity of light of 

wavelength λ, expressed 

by formula (7), 

registered during welding 

with current of 

intensity I k 

, when welding 

arc length amounted 

to L l 

; {g i 

}={G 1 

, 

γ, G 2 

, G 3 

, G 4 

} - set of 

parameter values present 

in formula (7). 

The uncertainty of the determination of i-th 

parameter gi ϵ {gi}={G 1 

, γ, G 2 

, G 3 

, G 4 

} is determined 

by means of a method described in 

publication [53]: 

ε 

χ 

2 

−1 

i 

= hii 

mp 

− m 

(10) 

where: h ii 

-1 

- component ii of the inverse Hessian 

matrix; χ 2 - sum of squares of deviations 

of theoretical values from experimentally obtained 

results; m p 

- number of experimentally 

obtained results; m - number of parameters determined 

through matching. The components 

of the Hessian matrix are defined by formula 

[53]: 

h 

ij 

2 

∂ χ 

= 

∂g 

∂g 

⎡ 

⎢B 

⎢⎣ 

Own research 

The research-related tests were carried out 

on a station for mechanised TIG welding. A 

measurement system applied in the tests (Fig. 

7) enabled measurements of welding current 

intensity, welding arc voltage, filler metal feeding 

rate and welding arc radiation intensity. 

The intensity of welding current was measured 

with a current probe LEM PR1001 based 

on the Hall effect. The voltage of a welding 

arc was measured with a voltage transducer 

LEM LV 25-P . A filler metal feeding rate was 

Fig. 7. Layout of measurement system for monitoring of welding process 

measured with a rotary measuring impulse 

transmitter. The transmitter was connected 

directly to a system of filler metal feeding rollers. 

The spectral distribution of a welding arc 

was recorded with a spectrophotometric card 

PC 2000 ISA-A Ocean Optics, provided with 

a Sony-made CCD detector type ILX511. The 

card made it possible to examine the spectrum 

of welding arc electromagnetic radiation in a 

range from 200 nm to 1100 nm. A measurement 

time of 3 ms enabled on-line registration 

of spectral distribution. A measurement 

range used in the tests was between 350 nm 

and 850 nm. 

{ g } ∂B 

( I , L , λ, 

g ) ∂B 

( I , L , ,{ g }) 

⎤ 

( I , L , λ, 

) { } 

2 2 

1 

∂ Bkl, 

teor k l i kl, 

teor k l i kl, 

teor k l 

= −2∑∑ 

kl 

( Ik 

, Ll 

, λ) 

− 

λ 

2 

i j l k ( ∆B 

) 

∂gi 

∂g 

j 

∂gi 

∂g 

kl 

j 

i 

⎥ 

⎥⎦ 

(11) 



The intensity of arc radiation was also registered 

with a photodiode of a spectral range 

from 400 nm to 1100 nm. The measurement 

system applied in the registration (Fig. 7) contained 

also an amplifying system, interference 

filter, focusing system and an optical fibre. 

Electric signals corresponding to the intensity 

of arc visible radiation and signals from a 

welding circuit were registered by a recording 

device utilising a measurement card NI DAQ 

6036E in a computer. Next, signals recorded 

by the device underwent an analysis. 

The testing station was also provided with 

a slide for moving a test plate and a cylindrical 

copper element cooled with water. A TIG 

welding torch was fitted to 

a system of slides enabling 

the adjustment of its position 

in both vertical and 

horizontal planes. Such a 

solution enabled precise 

setting of a distance between 

the welding torch 

and the surface of material 

(arc length). During tests 

the table with the test plate 

was moved, whilst the 

welding torch remained 

immovable. A DC welding 

device consisted of a 

universal welding source 

KEMPPI Pro 5000 with an attachment TIG Pro 

400 or ESAB-manufactured device AristoTig, 

ESAB-manufactured cooler COOL 10 and a 

Binzel-made welding torch AUT WIG 400W. 

The tests also involved the use of LabView-based 

software for controlling the operation of a 

measurement card NI DAQ 6036E as well as 

Ocean Optics-developed software OII Base 32 

for controlling the operation of a spectrophotometer. 

The measuring station made it possible 

to test the impact of parameters and disturbance 

of TIG welding with filler metal feeding 

on the spectral distribution and the intensity of 

welding arc radiation. 

The tests carried out within this part of research 

made it possible to determine the impact 

of welding current intensity and welding 

arc length on the intensity of welding arc radiation. 

The tests included the measurement 

of radiation intensity at a welding current of 

between 40 A÷200 A and an arc length of 1, 

2 and 3 mm as well as at a welding current of 

between 30 A÷300 A and an arc length of between 

2 mm and 5 mm (Fig. 8). The tests were 

carried out for arc burning on a copper plate 

cooled with water. 

Fig. 8. Impact of change of welding current intensity in TIG method on intensity 

of welding arc visible radiation, at constant length of welding arc, for wavelength 

of 698 nm; shielding gas: argon 

In order to determine the impact of welding 

parameters on the intensity of welding 

arc radiation, it was necessary to separate four 

exemplary spectral peaks (494.93, 606.31, 

698.23 and 75285 nm) from registered spectral 

distributions. Figure 9 presents the impact 

of welding current intensity (at a constant welding 

arc length in TIG method) on the radiation 

intensity of selected spectral peaks. The 

analysis of registered signals revealed that a 

change of welding current intensity strongly 



49

affects a change of welding arc 

radiation intensity for a given 

wavelength. The aforesaid changes 

are more noticeable when a 

wavelength value increases. The 

foregoing is particularly visible 

if one compares the intensity 

of welding arc radiation for a 

peak of 494 nm and for a peak of 

752 nm (Fig. 9). 

The coefficients G i 

(Tables 1 

and 2) were calculated in equation 

(7) on the basis of collected measurement 

data i.e. arc length, arc 

radiation intensity and welding 

current intensity. While calculating 

constants, the following two 

cases were taken into account: 

• theoretical model acc. to Zhang 

[6]; in this model, the coefficient 

γ=2, in such case one can write 

that: 

B 

1 

⎛ 

⎝ 

1 ⎞ 

− ⎟ + 

2 ⎠ 

2 G2 

2 

= G LI ⎜ I 

iv 

G I + 

e 

3 

G 

(12) 

• generalised model - coefficient 

γ is a parameter depending on 

measurement data. 

Calculations were carried out 

with the use of equation (9) and 

taking into account two cases: 

• ΔB kl 

- uncertainty of determined 

visible radiation intensity is 

constant for all data and is not taken 

into account in calculations; 

in the case under discussion, worse 

matching will be for lower values, 

• ΔB kl 

- uncertainty of determined 

visible radiation intensity is 

not constant for all data and is taken 

into account in calculations. 

4 

Fig. 9. Impact of change of welding current intensity in TIG method on 

intensity of welding arc visible radiation, at constant length of welding 

arc, for selected wavelengths; shielding gas: argon 

Table 1. Calculated coefficients G i 

for theoretical and generalised models 

for welding arc length of between 2 mm and 5 mm, ΔB kl 

is constant 

Theoretical Generalised 

No. Coefficient 

model model 

1 G1 3.8(2)×10 -5 1.11(1)×10 -3 

2 G2 56(3) 9(2) 

3 G3 -4.4(1)×10 -5 -3.98(12)×10 -5 

4 G4 1(57)×10 -3 -1.8(6)×10 -1 

5 γ 2 1.455(4) 

6 

χ 2 sum of least squares 

of deviations 

7.33 3.6 

7 

correlation coefficient 

R 2 

0.98 0.99 

Table 2. Calculated coefficients G i 

for theoretical and generalised models 

for welding arc length of between 2 mm and 5 mm, ΔB kl 

is taken into account 

No. Coefficient 

Theoretical model 

model 

Generalised 

1 G1 4.6(2)×10 -5 1.7(1)×10 -3 

2 G2 34(2) 2(65)×10 -2 

3 G3 -4.06(10)×10 -5 -35.1(6)×10 -6 

4 G4 -1.09(16)×10 -1 -11.4(9)×10 -2 

5 γ 2 1.364(2) 

6 

χ 2 sum of least squares 

of deviations 

5.75 1.07 

7 

correlation coefficient 

R 2 

0.99 0.99 



On the basis of calculations (Tables 1 and 2) 

indicating that the sum of the least squares of 

deviations is the lowest for the generalised model 

and with taking into account the weight ΔB kl 

, 

equation (7) takes the final form as follows: 

0,02 

⎛ 1 ⎞ 

0,0017LI 

1,364 

I 

2 

Biv = 

⎜ 

e − ⎟ − 0,000035I − 0,114 

⎜ 2 ⎟ 

⎝ ⎠ 

(8.4.1.2) 

The equation is satisfied when a wavelength 

amounts to 698 nm and a welding arc length is 

contained in a range 2 mm÷5 mm. A graphic illustration 

of the theoretical [6] and generalised 

models is presented in Figures 10 and 11. The 

tests were carried out for arc burning on a copper 

plate cooled with water. 

Fig. 10. Dependence of welding arc radiation intensity in TIG method on 

welding current intensity, for wavelength of 698 nm and arc length of 2 mm 

Fig. 11. Dependence of welding arc radiation intensity in TIG method on arc length 

L and welding current intensity, for wavelength of 698 nm and arc length of 2÷5 mm 

Summary 

The study presents the results of tests of welding 

arc radiation in TIG method. On the basis of 

the tests it was possible to come to the following 

conclusions: 

• in case of a constant welding arc length, an 

increase in welding current intensity leads to an 

increase in arc visible radiation intensity, 

• in TIG method an increase in an arc length 

causes an increase in welding arc visible radiation 

intensity, 

• determination of parameter values (G 1 

, G 2 

, 

G 3 

, G 4 

and γ) in the generalised semi-empirical 

model enabled better matching of a welding 

arc model for a 2÷5-mm range of welding 

arc lengths . 

On the basis of the test results 

it is possible to state that welding 

arc radiation is a source of rich information 

about a welding process 

course and makes a valuable tool 

in the monitoring of a TIG welding 

process. The tests indicate the 

possibility of using technologically 

advanced spectrophotometers in the 

monitoring of welding processes. If 

applied in combination with optical 

fibre lines, the spectrometers could 

enable the real-time control of arc-based 

welding processes (TIG, 

MIG/MAG, PAW) as well as, due 

to the presence of a plasma cloud 

during welding with a laser beam, 

also the monitoring of the latter 

process. It should be noted that a 

spectrophotometric card enables 

the monitoring of intensity changes 

of many spectral peaks at the same 

time and thus makes it possible to 

obtain more information about an 

object being tested. 



51

Acknowledgements 

The research was partly funded by the Ministry 

of Science and Higher Education within 

research project no. 3 T10C 021 28, realised in 

2005-2007 and within the statutory activity of 

Instytut Spawalnictwa. Some research-related 

tests were carried out in 2007-2008 within the 

confines of Junior Fullbright Gran programme 

at University of Kentucky College of Engineering 

Center for Manufacturing Welding Research 

and Developed Laboratory. The author 

wishes to thank Professor Marian Nowak and 

Mirosława Kępińska Ph. D. for their expertise 

and assistance as well as to YuMing Zhang 

Ph.D, the Head of Welding Research and Developed 

Laboratory, for the possibility of carrying 

out research-related tests. 

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Marek St. Węglowski Ph.D. Eng – Instytut 

Spawalnictwa, Testing of Materials Weldability 

and Welded Constructions Department 



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