CONTENT

 VOLUME FIRST

Mathematical modelling and information technologies, model of a weld pool
 and weld formation
INTRODUCTION 9
Chapter 1 MATHEMATICAL MODELING and COMPUTER TECHNOLOGIES in  WELDING PRODUCTION, SCIENCE and ENGINEERING 
1.1. Modern information technologies — major component in an advanced industry 20
1.2 The mathematical models of welding processes and its application 30
1.2.1. The models for a mathematical support of CAD 32
1.2.2. The mathematical models for the expert systems 37
1.2.3. Models for the software of welding robots and robotic setups 42
1.2.4. Mathematical models in control systems of arc welding processes 49
1.2.5. A role of mathematical models in the automized systems of scientific researches  68
Chapter 2 ANALYSIS of INFORMATION STREAMS for TECHNOLOGICAL 
PROBLEM  «WELD FORMATION DURING ARC WELDING» 		72
2.1. Main features and methods of investigation of information streams in scientific and technical literature on welding 73
2.2. The database for the publications in a scientific and technical area «Weld formation during arc welding» 81
2.3. Definition of an information core for the journals on welding 93
Chapter 3 THE PHILOSOPHY and FEATURES of MATHEMATICAL MODELING the ARC WELDING PROCESSES 102
3.1. The system analysis — the main methodology of mathematical modelling the welding processes 102
3.2. The mathematical (computing) experiment 107
3.3. The characteristics and classification of the factors included in the mathematical models of objects and processes 118
3.4. Classification of the mathematical models of welding processes 128
3.4.1.  Main types of models used for mathematical modelling of welding processes 131
3.4.2. The regression mathematical models of welding processes and features of 
their usage		 138
3.4.2. The neuronet mathematical models and their application for simulation of welding
processes		 153
3.5. Main types of theoretical mathematical models of weld pool (weld formation) for 
fusion welding		 163
3.5.1.  Capillary-hydrostatic models and their usage for modeling of a weld shape 169
3.5.2. Volumetric thermal capillary-hydrostatic models (VTCHM) and their application 
for simulation of weld formation		 184
3.5.3. Thermal magnetohydrodynamic models  (TMHDM) and their usage for modelling  
of weld pool		 198
3.5.4. Mathematical models for oscillations of molten metal in a weld pool 205
3.5.5. Main features of models TMHDM and its application for simulation of a weld pool 211
3.6. Adequacy of the mathematical models 222
3.7. Optimization of technological processes of welding by means of application the 
mathematical models		 225
3.7.1. Optimizations with the regression models and multifactor experiment design 231
3.7.2. Optimization by a design of experiments on the Taguchi method 232
3.7.3. The specialized problems of optimising 237
3.7.4. Peculiarities of optimization the technological processes of welding 239
3.7.5. The sinergetic approach to simulation of welding processes 244
Chapter 4 SURFACE TENSION PHENOMENA and ITS ROLE and SIGNIFICANCE for THE WELDING PROCESSES 252
4.1. EFFECT of SURFACE TENSION FORCES on WELD FORMATION DURING
ARC WELDING		 259
4.2. EFFECT of SURFACE TENSION PHENOMENA on WELDED METAL
PENETRATION		 263
4.3. THE THEORY of CAPILLARITY, CAPILLAR EFFECTS and SURFACE TENSION PROPERTIES of LIQUID METALS in the TECHNOLOGICAL PROCESSES 278
4.3.1. Fundamentals of the capillarity theory  278
4.3.2. Main mathematical models of the capillarity theory  291
4.3.2.1. The mathematical model of a sessile drop 292
4.3.2.2. The mathematical model of a pendant drop 302
4.4. THE VARIATION METHODS and THEIR USAGE for PROBLEM SOLVING in THE THEORY of capillarity
4.4.1. Advantages and features of the variation methods application 304
4.4.2. Application of variation methods for definition the equilibrium shape of capillary liquids surfaces 307
4.5. SURFACE (INTERPHASE) TENSION and CAPILLARY CONSTANT VALUE of LIQUID METALS in WELDING SYSTEMS 311
4.6. THE STATIC and DYNAMIC CAPILLARY EFFECTS 316
4.6.1. Static capillary effects 316
4.6.2. Static capillary effects 318
4.7. CAPILLARY-HYDRODYNAMIC INSTABILITIES of  LIQUID BOUNDARY 
SURFACES		 332
4.7.1. Rayleigh-Taylor INSTABILITY 334
4.7.2. Kelvin-Helmholtz INSTABILITY 340
4.7.3. Richtmyer-Meshkov INSTABILITY 344
4.8. MARANGONI EFFECT and the MATHEMATICAL MODELS of THERMAL CAPILLARY FLOWS in THE TECHNOLOGICAL WELDING and RELATED PROCESSES 348
4.8.1. Mathematical models of a Marangoni convection for simple regions  348
4.8.2. Mathematical models of a Marangoni convection for regions with complex forms 
with interphase boundaries moving		 359
Chapter 5 MATHEMATICAL MODELLING of WELD FORMATION in a FLAT POSITION 374
5.1. General formulations of the task, main allowances and simplifications 376
5.1.1. Design of a conceptual model for a weld pool on the analysis of acting forces basis 378
5.1.2. Physical and mathematical models of a weld pool crystallization zone  382
5.1.3. Derivations of an equilibrium equation for an  interphase surfaces of a crystallization zone of  welding pools by a variation-energy method 386
5.1.4. Features of processes of wetting and spreading of molten metal at arc welding 393
5.2. A mathematical model of WELD REINFORCEMENT FORMATION (BEAD-ON-PLATE) DURING welding or surfacing In A FLAT POSITION 403
5.2.1. Formulations of the boundary task 403
5.2.2. Integration of the differential equilibrium equation for a surface of weld pool tail zone 407
5.3. LinkS of physical and geometrical parameters of mathematical models with technological parameters of WELDING CONDITIONS 419
5.3.1. Technological methods of control of weld metal deposits and weld width and methods them calculation on parameters of welding conditions 419
5.3.2. Application of a mathematical model for different types of welds 435
Chapter 6 EFFECT of WELDING POSITIONS on WELD FORMATION 438
6.1. Mathematical modelling and WELD FORMATION optimiSing for weld reinforcement in a ceiling position 440
6.1.1. Technological features of application for arc welding in a ceiling position 440
6.1.2. Physical and mathematical models of the welding process in ceiling position 445
6.1.3. Definition of stability range for ceiling weld formation 453
6.1.4. Experimental check of mathematical model for a ceiling weld formation 462
6.2. Mathematical modelling and optimization for weld formation during arc welding in DIFFERENT positions 467
6.2.1. Technological features of weld formation during arc welding in different positions 467
6.2.2. Features of simulation of creation of a seam at welding in different positions 468
6.3. Mathematical modelling of horizontal welds formation on a inclined plane 473
6.4. A mathematical model of horizontal welds formation on a vertical plane 487
6.4.1. Technological features of welding execution on a vertical plane 487
6.4.2. Mathematical models of horizontal weld formation on a vertical plane 492
6.4.3. Experimental checking of mathematical models 496
ENCLOSURES 508
REFERENCES for VOLUME 1 521
  VOLUME SECOND

Mathematical modeling and optimization of different types welds formation
Chapter 
7		 MATHEMATICAL MODELING and STRUCTURAL- TECHNOLOGICAL OPTIMIZATION of  FILLET and GALTEL WELDS FORMATION 8
7.1. THE FEATURES of APPLICATION of FILLET WELDS in WELDED STRUCTURES 8
7.1.1. Varieties and configurations of fillet welds 9
7.1.2. Principal dimensions of fillet welds and their choice 18
7.1.3. Effect of geometrical parameters of welded joints with fillet welds on their strength 28
7.1.4. Optimization of geometry of fillet welds by a criterion of decrease of stress concentration factor in welded joints 36
7.1.5. Mathematical modelling and optimization of fillet welds formation during welding by a way «in a corner» 51
7.1.6. Technological methods of control for the fillet welds shape  67
7.2. MATHEMATICAL MODELLING and OPTIMIZATION of  FLUTE WELDS FORMATION 75
7.2.1. Effect of geometrical parameters of welded joints on their strength characteristics 75
7.2.2. The purposes and features of application the flute welds for rise of serviceability welded joints and structures 80
7.2.3. The technological features of flute welds execution 83
7.2.4. A mathematical model of flute welds formation for optimization their geometrical parameters 97
7.2.5. Optimization of flute welds formation by a criterion of the stress concentration factor lowering 103
Chapter 
8		 MATHEMATICAL MODELLING and OPTIMIZATION of WELD FORMATION DURING ARC WELDING of a THIN METAL WITH BURNING THROUGH and ROOT WELDS WITH FREE FORMATION 109
8.1. PROBLEMS of OPTIMIZATION for THIN METAL WELDING PROCEDURES 109
8.1.1. The technological features of through welds execution 116
8.1.2. The technological features of root welds execution 125
8.2. MATHEMATICAL MODELS of THROUGH WELDS AND ROOT ONES WITH FREE FORMATION 139
8.2.1. The mathematical models on the basis of pressure balance 142
8.2.2. Two-dimensional capillary-hydrostatic models of through welds formation 147
8.2.3. The mathematical models on the basis of concentrated forces balance 153
8.3. TWO-DIMENSIONAL CAPILLARY-HYDROSTATIC MODEL of  THROUGH WELD FORMATION 157
8.3.1. Optimization of weld formation during welding with burning through on sizes of backing weld 168
8.3.2. Application of the mathematical model for the analysis of weld formation during arc welding of filamentary composite materials 172
8.3.3. Usage of volumetric thermal capillar-hydrostatic models of weld pools 177
8.4. TECHNOLOGICAL WAYS of IMPROVEMENT for WELD FORMATION DURING ARC WELDING WITH BURNING THROUGH  179
8.5. STABILITY of a WELD POOL SURFACES AT WELDING WITH BURNING  THROUGH and FREE FORMATION 204
Chapter 
9		 OPTIMIZATION of WELD FORMATION for a BUTT WELD DURING ARC ORBITAL WELDING of TUBES 210
9.1. TECHNOLOGICAL FEATURES of ORBITAL WELDING of TUBES 214
9.1.1. Mathematical models of weld formation during arc orbital welding 236
9.1.2. An analytical solution of the volumetric task for definition of the surface form a fluid phase at fusion welding in arbitrary position 250
9.2. TECHNOLOGICAL METHODS of OPTIMIZATION of WELD FORMATION DURING ARC WELDING of TUBES 262
Chapter 
10		 MATHEMATICAL MODELLING and OPTIMIZATION of WELD FORMATION DURING MULTIPASS ARC WELDING of a THICK METAL 273
10.1. MAIN TECHNOLOGICAL FEATURES and PROBLEMS of MULTIPASS WELDING of a THICK METAL 274
10.1.1. Process control of automatic multipass arc welding 285
10.1.2. Choice of welding conditions and optimization the process of multipass arc welding of a thick metal 295
10.2. MATHEMATICAL MODELS of METAL LAYER FORMATION DURING ARC SURFACING 306
10.2.1. The empirical and regression mathematical models for optimization of layer formation at arc surfacing 308
10.2.2. An analytical mathematical model of layer metal formation 310
10.3. MATHEMATICAL MODELLING and OPTIMIZATION of WELD FORMATION for NARROW GAP WELDING 320
10.3.1. Basic versions of the technology of multipass narrow gap welding 320
10.3.2. Features of weld formation during narrow gap welding 333
10.3.3. Mathematical modelling and optimization of weld formation narrow gap welds 337
10.3.4. Mathematical model of the process of weld formation on scheme «one bead in a layer» 339
10.3.5. Experimental researches of weld formation during narrow gap welding 358
10.3.6. A mathematical model of the process of bead formation in narrow gap welding under the technological schemes  «Two beads in a layer » and «Three beads in a layer» 362
Chapter 11 MAIN PECULIARITIES and MATHEMATICAL MODELLING of  METAL PENETRATION at ARC WELDING 370
11.1. Main features of welded metal penetration during arc welding 371
11.1.1. Effect of welding parameters and conditions on metal penetration 372
11.1.2. Dependence of metal penetration with geometrical parameters of edges preparation 389
11.1.3. Effect of chemical composition of welded metal, welding materials (fluxes, shielding gases and their mixtures) on metal penetration at welding 400
11.2. WAYS of CONTROL for the FORM and SIZES of a PENETRATION ZONE at ARC WELDING 408
11.2.1. Using the activating fluxes 408
11.2.2. Using of gas mixtures with activating additions 427
11.2.3. The analysis of reasons of rise of penetration depth with activating welding materials usage 430
11.2.4. Technological ways of rise penetrated ability of welding arc and control of the penetration form at arc welding 433
11.3. THE METHODS of SIMULATION and CALCULATION of the PENETRATION FORM and SIZES AT ARC WELDING 447
11.3.1. Empirical models of metal penetration 448
11.3.2. Empirical computational methods of parameters of penetration zone on the welding conditions 453
11.3.3. Models of metal penetration on the basis of the theory of a thermal conduction in solids 457
11.3.4. Mathematical models of weld pool crater surface 465
11.3.4.1. Models of derivation of crater form on the basis of acting forces balance and pressures 466
11.3.4.2. Models of derivation of crater form on the basis of solution of a differential equilibrium equation surface of a welding pool (capillary-hydrostatic models) 468
11.4. CONCEPTUAL, PHYSICAL and MATHEMATICAL MODELS of CRATER PART of WELD POOL 480
11.4.1. A mathematical model crater zone of weld pool   483
11.4.1.1. An equilibrium equation of crater surface 483
11.4.1.2. Solution of a differential equilibrium equation for crater surface of  weld pool 489
11.4.2. A numerical solution of a nonlinear differential equilibrium equation for a crater surface  493
11.4.3. Effect of filler material and edge preparation on the form and sizes of a crater of  weld pool (complex mathematical model of weld pool) 504
11.5. AN EXPERIMENTAL RESEARCH of EFFECT of WELDING PARAMETERS of the FORM and SIZES of CRATER and THICKNESS of a LIQUID INTERLAYER UNDER THE ARC 512
11.5.1. Present methods of experimental definition of depth and form of a weld pool crater 512
11.5.2. An experimental research of effect of parameters of the mode of welding on depth of a crater and width liquid interlayer under the arc 521
ENCLOSURES 533
REFERENCES for VOLUME 2 547
VOLUME THIRD

Arc pressure, the defects of the welds, electrode metal transfer
Chapter 12 FORCE ACTION of an ELECTRIC ARC ON WELDED METAL 7
12.1. The mechanism of arc presuure on welded metal origin 8
12.2. Methods of experimental definition for the arc pressure characteristics 13
12.1.1. Application of a weight method for measurement of arc pressure integral force of 17
12.1.2. Effect type of an arc and main welding conditions on integral force of arc pressure 54
12.1.3. Application of a manometric method for measurement of arc pressure distribution 67
12.1.4. Effect of external magnetic fields on arc pressure distribution 106
12.1.5. The characteristics of pressure for electric arcs used in special electrometallurgy 13
12.2. Methods of arc pressure characteristics calculations for welding arc on the basis of its mathematical models 116
12.3. Calculation of integral values of volumetric electrodynamic forces in a welded workpiece 132
Chapter 13 DEFECTS of WELDS and MODELS of THEIR ORIGIN 145
13.1. Undercuts of welds and character of their origin 149
13.1.1. Definition of undercuts as defects of weld formation and their classification 152
13.1.2. Effect of undercuts on strength of welded joints and constructions 154
13.2. Main technological factors influential in origin of undercuts 156
13.3. Present models of undercuts origin in the welds 171
13.3.1. Models of undercuts origin during arc welding 172
13.4. The analysis of reasons of undercuts appearance 201
13.5. The technological methods of undercuts preventing in the welds 205
13.6. Unmeltings, reasons of their appearance and methods of preventing 222
13.7. Gas and slag inclusiongs in the welds 226
13.7.1. Technological features and forms of appearance of gas concavities in welds 227
13.7.2. Models and mechanisms of gas concavities origin in welds 232
13.7.3. Methods of identification and elimination of gas concavities in welds at welding in shielding gases 242
13.8. Origin of slag concavities at a submerged-arc welding 247
13.8.1. Effect of technology factors on derivation of slag concavities and inclusions in the welds 248
13.8.2. Models of derivation of slag concavities 251
13.8.3. Ways of slag concavities preventing in the welds 257
13.9. Nonuniformity of weld formation, reasons of appearance and methods of elimination 258
13.9.1. Nonuniformity of edge weld formation at welding of thin metal 265
13.9.2. Models of edge weld formation during welding thin metal 265
13.9.2. Models of edge weld formation edge at welding thin metal 270
13.9.3. Optimization of parameters for edge welded joints and welding conditions 275
Chapter 14 ELECTRODE METAL TRANSFER in ARC WELDING: MAIN FEATURES, the MATHEMATICAL MODELS and CONTROL METHODS   279
14.1. ROLE and SIGNIFICANCE of METAL TRANSFER TYPES for ARC WELDING PROCESSES  279
14.2. CLASSIFICATION of METAL TRANSFER TYPES 284
14.3. DROP TRANSFER of ELECTRODE METAL and EFFECT of WELDING PARAMETERS upon the TYPES of METAL TRANSFER 289
14.3.1. Stream metal transfer and its features  297
14.3.1.1. Effect of the different factors on the critical current of transition to stream transfer  298
14.3.1.2. Calculating of the critical current  306
14.3.2. Peculiarities of drop transfer during of consumable electrode welding 307
14.3.3. Features of metal transfer during pulse-arc welding  315
14.3.4. Effect of external magnetic fields upon the metal transfer and spatter at arc welding  318
14.4. SPATTER and LOSSES of ELECTRODE METAL and FACTORS INFLUENTIAL on it  326
14.5. MATHEMATICAL MODELING of the DROP METAL TRANSFER  337
14.5.1. Static Force Balance Method (SFBM) 339
14.5.1.1. Forces acting on a drop of electrode metal  339
14.5.2. Method of surface pressures balance on a drop  355
14.5.3. Models of Pinch Instability Theory (PIT) 371
14.5.4. Variational-energetical methods of drop shape modeling 379
14.5.5. Thermal hydrodynamic models of drop growth on the edge of an electrode 384
14.6. MATHEMATICAL MODELS of METAL TRANSFER with SYSTEMATIC SHORT-CIRCUITS of an ARC GAP  392
14.6.1. Technological features of welding with the short-circuits of an arc gap  394
14.6.2. Model of  surface tensional forces acting during drop bridge break-up 399
14.7. METHODS of SPATTER LOWERING and METAL TRANSFER CONTROL  418
ADDENDUM 430
REFERENCES 434

This monograph is written in Russian language 

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