**Last
changes date: October 27, 2003**

**INTRODUCTION**

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 constructions^{2}.

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
conditions^{3}, are widely applied in aviation^{4}. 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 societies^{5}.

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 informatization^{6}. 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 welding^{7,8,9,10};
to problems of application of computer technologies and the mathematical
modelling are dedicated a number of other seminars and subject proceedings^{11,12
etc}.

The
British Institute of Welding^{13} 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 systems^{17,18}
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 Wiener^{19} 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 publications^{20-24} 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 area^{25},
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.

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