After introducing the concepts of welding thermal processes and weld pool behaviors, this book addresses essential advances in welding analysis and processes with an emphasis on the latest modeling and simulation methods. It covers techniques and formulas for assessing welding thermal processes, finite difference and finite analysis methods for calculating thermal conduction, numerical simulation of weld pool behaviors in metal-inert-gas/metal-active-gas arc welding, It also covers keyhole and weld pool dynamics in plasma arc welding, and vision-based sensing of weld pool shape and geometry, and provides case studies of fluid flow and heat transfer in tungsten-inert-gas arc welding.
Chapter I Introduction
1.1 The characteristics of welding thermal processes
1.2 Weld pool geometry and behaviors
1.3 The evolution and status quo of analytical method of welding thermal processes
1.4 Numerical analysis of welding thermal conduction
1.5 Numerical analysis of fluid flow and heat transfer in TIG weld pools
1.6 Numerical analysis of fluid flow and heat transfer in MIG/MAG weld pools
1.7 Numerical analysis of welding thermal processes in PAW
1.8 Numerical analysis of dynamic process of metal transfer in GMA W
1.8.1 Static force balance theory and non-equilibrium pinch effect theory
1.8.2 Principle of minimum energy theory
1.8.3 Fluid dynamics theory
1.8.4 "Mass-spring" model
1.9 Numerical analysis of weld pool behaviors in laser welding
Chapter 2 Models for welding heat sources
2.1 Welding thermal efficiency and melting efficiency
2.1.1 Method based on analysis of arc physics
2.1.2 Method based on combining calculation with measurement
2.1.3 Method based on thermometer
2.1.4 Determining the value of 77 through combining theoretical models with temperature measurement
2.2 The deposition modes of welding heat source
2.3 The centralized mode of heat source
2.4 Plane distribution mode of heat source
2.4.1 Gaussian distribution mode of heat source
2.4.2 Double-ellipsis distribution mode of heat source
2.5 Volumetric distribution mode of heat source
2.5.1 Semi-ellipsoid distribution mode of heat source
2.5.2 Double-ellipsoid distribution mode of heat source
2.5.30ther modes of volumetric heat sources
Chapter 3 Analytical method of welding thermal processes
3.1 Mathematical description of thermal conduction
3.2 Thermal conduction in infinite body
3.2.1 Thermal process under instantaneous action of centralized heat source
3.2.2 Cumulative principle
3.3 Rosenthal-Rykalin formulas-analytical method in calculating arc welding thermal processes
3.3.1 Calculating modes of heating metals by arcs
3.3.2 Taking arcs as instantaneous centralized heat source
3.3.3 Taking arcs as traveling centralized heat source with constant power
3.3.4 Quasi -steady state of thermal processes
3.3.5 Effects of body dimensions on thermal processes
3.3.6 Formulas for predicting temperature fields with fast-moving high-power heat sources
3.4 Dimensionless version of Rosenthal-Rykalin formulas
3.4.1 Case for thick plates
3.4.2 Case for thin sheets
3.5 Limitations of Rosenthal-Rykalin formulas
3.6 Modification of Rosenthal-Rykalin formulas
Chapter 4 Finite difference method of welding thermal conduction
4.1 Derivative of function in uniform grids
4.1.1 Direct method
4.1.2 Taylor series method
4.2 Derivatives of function in non-uniform grids
4.2.1 Direct method
4.2.2 Taylor series method
4.3 Finite difference equations for steady-state thermal conduction
4.3.1 Substituting method for partial differential equations
4.3.2 Energy balance method
4.4 Finite difference equations for transient-state thermal conduction
4.4.1 Explicit difference equations
4.4.2 Implicit difference equations
4.4.2 Crank-Nicolson difference equations
4.4.2 Weighted difference equations
4.5 Workpieces with boundary, interface and combined heat transfer conditions and those with non-uniform physical properties
4.5.1 Nodes at boundary
4.5.2 Boundary conditions of heat loss (steady-state)
4.5.3 Boundary conditions of heat loss (transient-state)
4.5.3 Interface
4.5.4 Non-uniform physical properties
4.6 Precision, stability and convergence of solutions for difference equations of thermal conduction
4.6.1 Error analysis
4.6.2 Stability
4.6.3 Precision
4.7 Difference equations under non-rectangular coordinate system
4.8 Computer algorithm offrnite difference equations
4.8.1 Simple iteration
4.8.2 Gauss-Seidel iteration
4.8.3 Ultra-relaxation iteration
4.9 Examples of calculating transient temperature fields in welding
4.9.1 Transient welding thermal conduction model
4.9.2 Varying non-uniform grids
4.9.3 Discretization of governing equations
4.9.4 Calculation results
Chapter 5 Finite element analysis of welding thermal conduction
5.1 Variational problem of thermal conduction in welding
5.2 Mesh generation and discretization of temperature field
5.3 Selection of interpolation functions of temperature
5.4E1ement analysis
5.4.1 Variational calculation for boundary elements
5.4.2 Variational calculation for inner elements
5.5 Total synthesis
5.6 Solution of temperature values at nodes
5.7 Three-dimensional finite element analysis
5.7.1 Variational problem of three-dimensional thermal conduction
5.7.2 Eight-node hexahedron isoparametric element
5.8 FEA example of MIG welding temperature field
5.8.1 Weld reinforcement
5.8.2 Mesh generation and heat source treatment
5.8.3 Prediction results
Chapter 6 Numerical analysis of fluid flow and heat transfer in transient TIG weld pools
6.1 Mathematical description of welding pool behaviors
6.1.1 Governing equations under rectangular coordinate system
6.1.2 Free surface deformation of weld pool
6.1.3 Governing equations under non-orthogonal coordinate system
6.1.4 Boundary and initial conditions
6.2 Solution method of numerical simulation
6.2.1 Algorithm
6.2.2 Derivation of discrete equations
6.2.3 Discretization of boundary conditions
6.3 Calculating process and program development
6.3.1 Main program
6.3.2 Subprogram of weld pool surface defonnation
6.3.3 Calculation of fluid flow and temperature fields
6.4 Workpiece material, dimension and physical properties used in calculation
6.5 Transient development of weld pool shape and fluid flow field
6.6 Transient evolution of weld pool surface deformation
6.7 Dynamic evolution of weld pool shape and fluid flow field after arc extinguishment
6.8 Experimental verification
6.8.1 Comparison of predicted front pool surface with experimental measurement
6.8.2 Comparison of predicted back pool surface with experimental measurement
6.9 Dynamic response of TIG weld pool to step change of welding process parameters
6.9.1 Adjustment of calculation programs
6.9.2 Dynamic response of weld pool to step change of welding current
6.9.3 Dynamic response of weld pool to step change of welding speed
6.9.4 Test validation
Chapter 7 Analysis of dynamic process of metal transfer GMAW
7.1 Model of metal transfer in GMAW
7.1.1 Governing equations
7.1.2 Tracking free surface-VOF method
7.1.3 Analysis of forces acting on droplets
7.1.4 Boundary and initial conditions
7.2 Algorithm and program design
7.3 Results of numerical analysis
7.3.1 Dynamic variation of droplet shape
7.3.2 Velocity field in droplet
7.3.3 Shape variation of remained droplet and detached droplet
7.3.4 Effect of welding current on transferring droplet size
7.4 Dynamic model of metal transfer based on " mass-spnring" theory
7.4.1 Development of mathematical model
7.4.2 Description of action forces
7.4.3 Processing of key technical problems
7.4.4 Analysis method and selection of materials physical properties
7.4.5 Droplet oscillation and detachment under different levels of welding current
7.4.6 Analysis of dynamic droplet transfer
7.4.7 Prediction of droplet size
7.4.8 Comparison of predicted and measured results
Chapter 8 Numerical simulation of weld pool behaviors in MIG/MAG welding
8.1 Development of weld pool model in MIG/MAG welding
8.1.1 Governing equations of MIG/MAG weld pool behaviors under rectangular coordinate system
8.1.2 Pool surface configuration and reinforcement of MIGIMAG welding
8.1.3 Governing equations under non-orthogonal coordinate system
8.1.4 Boundary conditions
8.1.5 Discretization of governing equations
8.2 Current density distribution at the deformed weld pool surface in MIG/MAG welding
8.3 Calculation of body force and arc pressure
8.3.1 Body force in weld pool
8.3.2 Arc pressure distribution at the deformed weld pool surface
8.4 Arc heat flux distribution at the deformed weld pool surface
8.5 Droplet heat content distribution inside MIG/MAG weld pool
8.5.1 Momentum and thermal energy analysis in metal transfer
8.5.2 Distribution volume of droplet heat content inside MIGIMAG weld pool
8.5.3 Calculation results of droplet heat content inside weld pool
8.6 Numerical analysis results of MIG/MAG weld pool behaviors
8.6.1 Program design and selection of parameters used in calculation
8.6.2 Effect of welding process parameters on weld pool surface deformation
8.6.3 Effect of welding process parameters on arc current density
8.6.4 Calculation results of welding temperature field
8.6.5 Calculation results of fluid flow field in weld pool
8.7 Experimental verification
8.7.1 Test method and materials
8.7.2 Verification of predicted weld dimensions
8.7.3 Verification of temperature distribution on weldments
Chapter 9 Weld pool and keyhole shape and behaviors plasma arc welding
9.1 Numerical analysis of quasi-steady state temperature field in keyhole plasma arc welding
9.1.1 Model of volumetric heat source in PAW
9.1.2 Heat source mode of quasi-steady state in keyhole PAW
9.1.3 Mesh generation
9.1.4 Finite element analysis results
9.2 Numerical analysis of transient development of temperature field in keyhole PAW
9.2.1 Heat source mode of transient keyhole PAW
9.2.2 FEA results of transient temperature field in keyhole PAW
9.3 Numerical simulation of double-sided PAW + TIG arc welding
9.3.1 Formulation
9.3.2 Results
9.4 Description of keyhole shape
9.4.1 Symmetric keyhole shape
9.4.2 Arbitrary keyhole shape
9.4.3 Calculation of weld pool shape and temperature field
Chapter 10 Vision-based sensing of weld pool geometry
10.1 Vision sensing system of weld pool geometry in TIG welding
10.1.1 Experimental system structure
10.1.2 Calibration of weld pool images
10.1.3 Analysis of characteristics of weld pool images
10.1.4 Image processing
10.1.5 Deftnition of front side weld pool geometry
10.2 Measuremental results of weld pool geometry in TIG welding thin plates of mild steel
10.2.1 Measurements of weld pool geometry with variation of welding current
10.2.2 Measurements of weld pool geometry with variation of welding speed
10.3 Measuremental results of weld pool geometry in TIG welding thin plates of stainless steel
10.4 Experimental system based on LaserStrobe vision technique
10.5 LaserStrobe vision sensing results of GMAW weld pool
10.5.1 Measurements of weld pool images in CO2 shielded arc welding
1O.5.2Measurements of MAG weld pool images
Chapter 11 Numerical analysis of physical transport mechanisms in welding arcs
11.1 Mathematical model of TIG welding arcs
11.1.1 Governing equations
11.1.2 Boundary conditions
11.1.3 Heat transferred into anode
11.1.4 Calculation results
11.2 Numerical analysis model of anode boundary layer in arcs
11.2.1 Micro-scale analysis of anode boundary layer in arcs
11.2.2 Governing equations
11.2.3 Boundary conditions
11.2.4 Solution method
11.3Main prediction results of anode boundary
Biography
Dr. Chuan Song Wu is a Professor of the Institute for Materials Joining at Shandong University in China. He has performed research at the University of Wisconsin-Milwaukee in USA (Visiting Scholar, 1986-1987), Technical University of Berlin in Germany (Humboldt Scholar, 1993-1995, 2004), Osaka University in Japan (Guest Professor, 1995-1996), and University of Hannover in Germany (Visiting Professor, 1999,2002). Since 2002, he visited University of Kentucky in USA five times for conducting joint research. He is member of the Editorial Boards of Transactions of the China Welding Institution, Welding and Joining, Electric Welding Machine, China Welding Industry and Frontiers of Materials Science in China. His current research deals with modeling, sensing and control of welding processes. He has authored and coauthored more than 137 peer-reviewed journal papers, two books and three book chapters. Dr. Wu is a member of the standing council of Chinese Welding Society, the chairman of Computer-Aided Welding Commission of Chinese Welding Society, and a member of the American Welding Society. Because of his outstanding achievements in welding science and technology, he was recognized as a Humboldt Scholar in Germany, and has collected a number of honors from the Chinese Government.
