Last changes date: October 27, 2003


      At the present time welding as a high performance method of obtaining of metal joining is one of main manufacturing processes in the different industries. To the boundary the XX and XXI centuries the welding production has been formed into the major technological area of engineering and number of branches of industry, closely bound with another technological processes and representing the complexes of high technologies requiring the usage of complicate equipment, adaptive control systems and robots, application of advanced resources of computer technology. Among major number of modern manufacturing processes of materials processing the welding has introduced the most important, revoluting changes in producing of constructions for different applications. More than 50 % of the bulk national product of industrially developed countries forms with the help of welding and related technologies; up to 2/3 global consumptions of a rolled steel goes on production of welded assemblies and constructions2.

The welding is a strategic branch, as largely depends on a state of welding technologies a scientific-technical, economical and technological potentials of any country. It is possible to illustrate it, in particularly, following the known fact: at implantation in an industry of refined steels purified by methods of electroslag refining and having an electroslag under of contents impurities, the arisen problems of metal penetration with the welding arc have reduced in a stopping of defence plants producing the missiles [1].

The welding manufacturing processes will widely be utillized at manufacture of important constructions working in diversified and complicated conditions. The welding processes has been passing the continuous adapting to orbital space conditions3, are widely applied in aviation4. In connection with intensive by mastering of oil(petroleum) deposits of a continental shelf the sizes of application of a underwater welding grow at a building the gas-oil-pipelines and marine oil platforms [2]. Usage guesses composite metal constructions in modern shipbuilding, construction of buildings considerable size of welding operations, application of composite equipment and unique technology. Broad application discover welding high concentrated heat sources: the laser welding of steels and aluminium alloys intensively has been used in motor industry, where an electric resistance welding until recently was applied mainly [3].

At the present stage the major condition of further perfecting and intensification of welding production is not only further development of fundamental theory of welding with usage of advanced achievements in different areas of fundamental and applied sciences, but also creation of high performance methods both resources of simulation and modelling of welding processes, their control and optimal handle in real time. It is especially important in modern conditions, when the science has gained a new system quality, extends on such level of integration, at which scientific researches generating new technologies, appear in a strong dependence from a state of major number of scientific directions, among which there can be enough far on subject. The blanks on main directions of scientific search can plot serious damage to priority technologies, reducing their technological metrics and productivity in manufacturing [4,5].

In conditions of a globalization of world economy and commercial productions the integration of welding technologies with modern high technologies on the basis of application of computers converts a product engineering for joining of materials by welding in the high technology complexes meeting the most strict requirements of modern computer-controlled production, European and World norms of quality, off-the-shelf standards on released production. Thus the accelerated transmission of the off-the-shelf technologies to production is possible only at cooperative scientific researches joining together efforts of different companies, universities, professional societies5.

Volume of the technological information on welding on numerous sites Internet continuously grows; the major sizes of the professional information for the welders are disposed on compact disks CD-ROM, having a considerable informational capacity [6,7].

All is wider in modern welding production, to a science and engineering the modern Internets - technologies will be utillized: corporate development of the composite projects at dispersion of the performers in different corporations, organizations and countries, shared use of research and development and industrial databases, fissile publication of papers in Web-magazines [8 — 10]. It allows to expand and to speed up exchange of the technological information on actual problems of welding production, science and engineering.

At the present stage there is "embedding" of mathematical modelling in frame of an information society: the methods and resources of mathematical modelling become an intellectual core of information technologies and all process of society informatization6. Therefore major attention is now given to application of modern methods of mathematical modelling and information technologies. The Paton Welding Institute (Kiev, Ukraine) has conducted a number of seminars on application of mathematical methods in welding7,8,9,10; to problems of application of computer technologies and the mathematical modelling are dedicated a number of other seminars and subject proceedings11,12 etc.

The British Institute of Welding13 regularly holds the conferences under a common subject title «Computer Technology in Welding»14 (Chairman — prof. Bill Lucas), which transactionses are issued by the separate receiving tanks. Technical University of Graz (Austria) once per 2 years organizes scientific seminars «Numerical Analysis of Weldability » (Chairman — prof. Cerjak H.15), on which the advanced achievements are considered in the field of mathematical modelling of welding processes.

The American Welding Society also regularly will carry out(spend) similar conferences and publishes their transactionses. In Russia at the Tula State University the conferences «Computer technologies in joining of materials» (Chairman — prof. Sudnik V.A.).

The Japan Welding Society had conducted in 1996 an International Workshop on the subject of «A role of a welding science and technologies in 21 century»16. In a number of countries the scientific researches on mathematical modelling of processes will actively be carried out at welding [11,12].

In scientific and applications of welding processes the mathematical methods of simulation of fundamental appearances having a place at derivation of a welded joint are actively applied [13-20 etc.]; the computer technology will widely be utillized, the potent supercomputers are applied to composite models of a welding bath [21].

The modern methods of mathematical modelling have turned to potent tools of research and knowledge of processes happening in complicate welding technological systems. The computer simulation of the process of welding and derivation of a welded joint is referred to a priority direction in development of concrete welding technologies [22].

However is far from being for all important technological schemes of different processes of welding the effective formalised descriptions of their main peculiarities are obtained. It especially concerns to most composite variants of welding technologies, such as multipass arc welding of metal of major width, welding of not rotary junctions of tubes, welding

In different space positions. The task becomes complicated by an extremely major diversity of weld materials, types of welds and joints, ways of welding, technological schemes within the framework of each way, broad bands of variation of main and auxiliary parameters of the mode of welding.

The difficulties of solution of many problems, simulation and optimising of welding processes are linked with high-level interdisciplinarity of the tasks for welding production, science and engineering. In a modern science there is a number of scientific directions having interdisciplinary character: except for information theory and cybernetics a synergetics as a science about processes of self-organizing in composite nonequilibrium and unstable systems17,18 here enters also.

The high level interdisciplinarity of problems of welding causes the appearance of padding barriers between separate technological directions and creates serious difficulties at development of many sections of the theory of welding processes. The creator of cybernetics Norbert Wiener19 spoke that «...the important researches are delayed that in one area the outcomes already for a long time becoming classical in adjacent areas are not known».

As it is scored in [23], in many areas of a science and engineering the application of advanced methods of mathematical modelling and modern information technologies restrains not so much by shortage of facilities and resources of computer technology, but mainly by absence of informative mathematical models. Nevertheless, to the present time the considerable experience is accumulated in the field of developing of mathematical models of the welding processes permitting not only to receive the formalised description of their main peculiarities, but also effectively to control them, to optimise conditions of the processes of derivation from a welded joint, to prevent appearance of intolerable defects. Some outcomes obtained by resources of mathematical modelling, have allowed to obtain the engineering solutions at a level of the inventions or know-how, protected by appropriate patent documents. 

At the same time considerable proportion of the important technological information is scattered on a great many of periodic and proceeding issuings published by the different writers on miscellaneous languages. There are few publications dedicated methodology, philosophy and efficiency of mathematical modeling of physical processes at welding; in particularly, in works of Conn W.M. [24], Engelsht V.S.[25], Lancaster J.F. [26], Sudnik V.A. [27], Kompan Y.J.[28], Radaj D. [29], and also in publications20-24 the common and special problems of mathematical modelling of welding processes are considered.

Therefore present monograph is an attempt of systematization of gained experience with the purpose of definition of the main approaches to build-up of effective mathematical models, principles of their practical implementation on the basis of usage of advanced software and off-the-shelf resources of computer technology. As modern information technologies of steel the essential and important part of production of welded assemblies, in operation considers a set of problems of mathematical modelling of welding processes on the basis of computer technologies.

 Despite of an exceptional variety and complexity of used mathematical models development of mathematical modelling of welding processes as the separate technological direction is subject to particular peculiarities, characteristic for any branch of a science, though has a number of particular features. Therefore one of overall objectives of the given operation consists of detection of these peculiarities and direction finding of further development of methods and resources of simulation for their most effective operational use by optimization of implementation  conditions for manufacturing processes of fusion welding.


Structure of the monograph and principle of presentation of a material. A major diversity of used methods and resources of mathematical modelling of welding processes, and also the major sizes of the publications on these problems predetermine importance of a sequence of presentation of outcomes of numerous operations in this area.

The volume of experimental researches of welding processes and creation of new weld procedures always was anticipated with basic researches in this area25, therefore in the present operation the considerable attention is given to outcomes of experiments for such technological schemes of welding, on which the mathematical models while miss or are advanced unsufficiently.

In the chapter 1 the important role of information technologies in the modern computer-controlled production of welded assemblies is exhibited. The application of these technologies is founded on broad usage of different mathematical models, the features of build-up and principles of which application essentially depend on the solved practical tasks.

The chapter 2 is dedicated to examination of information flows the technological publications as on a problem «Weld formation at fusion welding», and on common problems of welding production, science and engineering. The description of the database under the publications dedicated problems of mathematical modelling of a broad circle of processes happening at derivation of a weld is reduced. On the basis of application of the Bradford law the analysis of streams frame for the technological information concerning is fulfilled to problems of optimization of welding processes and their mathematical modelling. The enumeration of the most informative periodic and prolonging issuings is defined.

In the chapter 3 the philosophy and features of mathematical modelling of processes of arc welding surveyed. The classification of models, and also factors, included in them is given. The numerous examples of build-up of mathematical models of a different type and their practical implementation for solution of problems of formalising of the description of welding processes and optimization of a weld procedure are reduced.

The chapter 4 is dedicated to surface and interphase interactions, as to the important sort of appearances happening in a welding pool and at electrode metal transfer. The considerable attention is given to manifestation in welding processes of Marangoni effect, causing the thermal capillary flows of molten metal and much influential in a number of cases on weld formation and penetration of welded metal. Some types of instabilities of boundary surfaces which are capable to influence on origin of defects of creation of a weld are circumscribed.

In the chapters 5... 9 the number important for practice of the technological schemes and mathematical models circumscribing feature of creation of a seam surveyed at usage of these schemes. The system of capillary-hydrostatic mathematical models permitting on the basis of the uniform theoretical approach variation-energy method, consisting in usage, and solution of the main equation of the theory of capillary attraction is circumscribed, to reveal the major factors defining the form of a weld and influential in origin of defects.

The main features of application of the given approach explicitly are illustrated on an example of creation of a butt weld in a flat position (chapter 5). The effect of welding position is surveyed on such important technological schemes as welding in an overhead position, and also execution of horizontal welds on an inclined and vertical planes (chapter 6).

The considerable attention is given to formation the most frequently of fillets, meeting in welded assemblies, and also execution flute welds superimposed.

In a zone of transition between a weld material and parent metal for lowering stress concentration both rise fatigue and dynamic strength of welded joints and constructions (chapter 7). Fillet and flute welds have a number of common features: close connection with strength properties of welded joints, similarity of conditions of creation, usage of the similar designed equations. Therefore they are considered in one chapter from uniform positions of structurally - technological optimization.

In the chapter 8 the technological scheme of weld formation surveyed important for practical applications at welding of thin metal with through foundering on weight. The factors rendering most strong effect on the form of a seam and a condition of his(its) steady creation are defined.

The chapters 9 and 10 are dedicated to mathematical modeling and optimization most difficult for practical implementation of the technological schemes — to arc welding of not rotary junctions of tubes (chapter 9) and multipass welding of thick metal with bunching of cable conductors of ridges (chapter 10).

In all technological schemes surveyed in the given monography, the emphasis is made in-signalling of mathematical models with technological features of weld formation in different conditions. In this connection the outcomes of many experimental researches pertinent to cases in point are reduced especially when the appropriate mathematical models while are advanced unsufficiently.

In the chapter 11 the main peculiarities of metal penetration are circumscribed at arc welding and the possible(probable) approaches to build-up of mathematical models of this process are exhibited.

Taking into account major importance of such factor, as power effect of an arc on welded metal, in the chapter 12 is given retrospective review of outcomes of researches, bound as with experimental methods of learning of this appearance, and with methods of its mathematical modeling.

In the chapter 13 the problems of derivation of such defects of form of a seam, as undercuts, gas and slag inclusions, nonuniformity of appearance, unmeltings in one-pass and multipass welds are surveyed.

The chapter 14 is dedicated to electrode metal transfer and methods of its mathematical modeling, control and optimization. The main approaches to build-up of mathematical models of this process, detection of the major factors influential in its weep here are exhibited.



1. Savitsky M.M. Weld procedures of high-resistance steels in a rocket manufacturing // Automatic Welding (Kiev). — 1999. — No.8. — P.30 — 36 (in Russian).

2. Habrekke T., Armstrong M., Berge J.O. Deep water pipeline welding and repairs using modern computer technology to create a diverless future for statoil // Proc. 7th Int. Conf. «Computer Technology in Welding» [July 8—11, 1997, San Francisco, CA]. (NIST Spec. Publ. 1997. 923). — 1997. — P.31 — 41.

3. Riches S.T. Laser welding in automobile manufacture // Weld. and Metal Fabric. — 1993. — Vol.61, No.3. — P.79 — 83.

4. Kara-Murza S.G. Problems of intensification of a science: the technology of scientific researches. — Moscow: Science Publishing, 1989. — 248 p. (in Russian)

5. Moscovchenko A.D. A problem for integration of fundamental and technological knowledges. — of Tomsk: TGU Publishing, 1999. — 172 p. (in Russian)

6. Fröling H. De theorie van het TIG-lassen op CD-ROM // Lastechniek. — 2000, 66. — No.7 — 8. — S.6 — 9.

7. Kölsch S. Interaktives Nachschlagewerk für Wissen in der Schweßtechnik // Praktiker. — 2000. — Bd.52, H.8. — S.306 — 307.

8. White W. Welded connections on the Internet // Weld. J. — 1997, Vol.76. — No.5. — Ð.55 — 59.

9. Taraborkin L.A., Makoveckaya O.K., Bernadsky V.N. Introduction in Internet for the experts in the field of welding // Automatic Welding (Kiev). — 1998. — No.4. — C.16 — 24. (in Russian)

10. Kharitonov V.V., Colomein V.A., Bogatov A.A. Development of a knowledge base on production of tubes on the basis of Internets-technologies // Metallurgy and derivation. Proc. 1st Int, Conf. [Ekaterinburg, 7 —9 June, 2000]. — Ekaterinburg, 2000. — P.110 — 111. (in Russian)

11. Yurioka N., Koseki T. Modelling activities in Japan // Mathematical Modelling of Weld Phenomena 3. Eds. H.Cerjak, H.K.D.H.Bhadeishia. — London: TWI, 1996?. — P.489 — 530.

12. Zhang C. Development of numerical analysis on welding in China // Mathematical Modelling of Weld Phenomena 3. Eds. H.Cerjak, H.K.D.H. Bhadeisha. — London: TWI, 1996. — P.531 — 542.

13. Paton B.E. Welding and mathematics // Automatic Welding (Kiev). — 1966. — No.7. — C.1 — 2. (in Russian)

14. Neumann A. Mathematik in der Schweißtechnik // Schweisstechnik (DDR). — 1979. — Bd.29, H.10. — S.453 — 455.

15. Masubuchi K. Applications of numerical analysis in welding // Welding in the World. — 1979, Vol.17. — No.11 — 12. — P.268 — 295.

16. Modeling of fundamental phenomena in welds / T.Zacharia, J.M.Vitek, J.A.Goldak et al // Modelling and Simulation in Materials Science and Engineering. — 1995, Vol.3. — No.2. — P.265 — 288.

17. Zacharia T., Chen Y. Modelling of fundamental phenomena in gas tungsten arc welds // Int. J. of Materials and Product Technology. — 1998, Vol.13. — No.1 — 2. — P.77 — 88.

18. Jönsson P.G., Szekely J., Choo R.T.C. et al Mathematical models of transport phenomena associated with arc-welding processes: a survey // Model. and Simul. in Mater. Sci. and Eng. — 1994. — No.2. — Ð.995 — 1016.

19. Kou S. Transport phenomena in materials processing. — New York; Chichester: John Wiley and Sons, 1996. — 669 ð.

20. DebRoy T., David S.A. Physical processes in fusion welding // Reviews of Modern Physics. — 1995, Vol.67. — No.1. — P.85 — 112.

21. Simunovic S., Zacharia T. Supercomputing applications in welding simulations // Trends in Welding Research: Proc. of 4th Int. Conf., [5 — 8 June, 1995, Gatlinburg, Tennessee]. — 1995. — P.19 — 24.

22. Bernadsky V.N. Japan defines the priorities in the field of welding upon XXI century  // Automatic Welding (Kiev). — 2002. — No.3. — P.46 — 49. (in Russian)

23. Popov J.P., Samarsky A.A. Computational experiment // Computers, models, computational experiment. Introduction to computer science from positions of mathematical modeling. — Moscow: Science Publishing, 1988. — P.16 — 78. (in Russian)

24. Conn W.M. Die technische Physik der Lichtbogen-schweissung einschliefilich der Schweißmittel. — Berlin: Springer, 1959. — 386 s.

25. Mathematical modelling of an electric arc / V.S.Engelsht, D.S.Asanov, V.C.Gurovich et al. — Frunze: Ilim Publishing, 1983. — 363 p. (in Russian)

26. Lancaster J.F. The physics of welding. — Oxford: Pergamon Press, 1983. — 296 ð.

27. Sudnik V.A., Erofeev V.A. Calculations of welding processes on a computer. - Tula: TulPI Publishing, 1986. - 100 p. (in Russian)

28. Kompan Y.J., Shzerbinin E.V. Electroslag welding and melting with controlled MHD-processes. — Moscow: Machinebuilding Publishing, 1989. — 272 p. (in Russian)

29. Radaj D. Schweißprozeßsimalation: Grundlagen und Anwendungen. — Düsseldorf: Verl. für Schweißen und Verwandte Verfahren, DVS-Verl., 1999. — 193 s.


Page references

1 Paton B.E. Science. Engineering. Progress. — Moscow: Science Publishing, 1987. — 414 p. (in Russian)

2 Paton B.E. Problems of welding on a boundary of centuries // Automatic Welding (Kiev). — 1999. — No.1. — P.4—14. (in Russian)

3 Paton B.E. Welding in space and in a world ocean — the technological problems of XXI century

// Automatic Welding (Kiev). — 1997. — No.10. — P.3—8. (in Russian)

4 Shtrikman M.M.  A state and tendencies of development of welding technologies in aircraft manufacturing // Welding Production (Moscow) — 2000. — No.8. — P.23 — 30. (in Russian)

5 Eagar T.W. Technology transfer and cooperative research in Japan // Weld. J. — 1989, Vol.68. — No.1. — P.39 — 43.

6 Samarsky A.A. and Michailov A.P. Mathematical modeling. Ideas. Methods. Examples. — Moscow: Science—Physical-Mathematical Literature Publishing, 1997. — 320 p. (in Russian)

7 Mathematical methods in research of processes of a special electrometallurgy / Ed. Paton B.E. —  Kiev: Naukova dumka Publishing, 1976. — 196 p. (in Russian)

8 Mathematical methods in welding // Materials of IV of summer school of CEH Countries-Members. — Kiev: Naukova dumka Publishing, 1981. — 292 p. (in Russian)

9 Mathematical methods in welding // Proc. of the Paton Welding Institute. — Kiev: PWI Publishing, 1986. — 176 p. (in Russian)

10 Applications of mathematical methods in welding // Proc. of the Paton Welding Institute. — Kiev: PWI Publishing, 1988. — 166 p.

11 Mathematical modeling of metallurgical and welding processes / Ed. Gorinin I.V. — Moscow: Metallurgy Publishing, 1983. — 129 p. (in Russian)

12 Applications of mathematical methods and computer in welding / Eds. K.M.Gatovsky, V.A.Karkhin, L.A.Copelman. — Leningrad: LDNTP Publishing, 1987. — 114 p. (in Russian)

13 TWI, The Welding Institute (Abington, Great Britain).

14 Street J. Computer technology in welding — the first international conference // Metal Constr. — 1987, Vol.19. — No.2. — P.81 — 83.

15 Mathematical Modelling of Weld Phenomena / Eds. H.Cerjak, H.K.D.H.Bhadeshia, K.Easterling. — London: Institute of Materials. — Vol.1,2,3,4,5,6. — 1993... 2001.

16 Proc. of 6th International Symposium "The Role of Welding Science and Technology in the 21st Century" [Nagoya, Japan, 19 — 21 November, 1996]. Ed. Matsunawa A.

17 Hagen H. Synergetics. Instability hierarchies of self-organizing systems and devices. —  Berlin, Springer Verlag, 1983.

18 Pigogine I. and Stengers I. Order out of Chaos: Man's new dialogue with nature. — Bantam: New York. — 1984.

19 Wiener N. Cybernetics : Control and communication in the animal and the machine. — 2nd. Ed //

Cambridge, Mass.: The MIT Press, 1961. — 212 p.

20 Pohodnya I.K., Demchenko V.F. , Demchenko L.I. Mathematical modeling of gases behaviour  in the welds. — Kiev: Naukova dumka Publishing, 1979. — 56 p. (in Russian)

21 Gladkov E.A., Chernishov G.G. Mathematical models at research, calculation and designing of welding processes. — Moscow: MGTU Publishing, 1989. — 109 p. (in Russian)

22 Buchmayr B. Computer in der Werkstoff- und Schweißtechnik // Anwendung von mathematischen Modellen. — Düsseldorf: DVS Verlag, 1991. — 444 p.

23 Mathematical modeling of welding processes // V.V.Bashenko, B.V.Fedotov, N.A.Sosnin etc. — Leningrad: LPI Publishing, 1991. — 70 p. (in Russian)

24 Grong G. Metallurgical modelling of welding. — 2nd Edition. Ed. H.K.D.H. Bhadeisha. — London: Institute of Materials, 1997. — 608 p.

25 Eagar T.W. Welding and joining: moving from art to science // Weld. J. — 1995, Vol.74. — No.6. — P.49 — 55.