Research at Welding Equipment and Engineering Department
Speaker: Andrey Batranin, PhD. Student
Tomsk Polytechnic University
Non-destructive Testing Institute
http://svarka.tpu.ru
Speaker: Andrey Batranin email: [email protected]
Contents
• Modeling of Processing
• Our Methods to Solve the Problems
• Mathematical Definition of the Problems
• Applications of the Methods
• Conclusions
Modeling of Processing
Speaker: Andrey Batranin email: [email protected]
We focus on modeling of different kinds of processing:
• Welding• Cutting• Surface treatment• Hardening• Dynamic (shock) fracture
Speaker: Andrey Batranin email: [email protected]
Our Methods to Solve the Problems
Primarily we use Finite Difference Method.
Sometimes we use Variation-Difference Method and
Smoothed Particle Hydrodynamics (SPH) Method
Also we use state equations for complex materialssuch as mixtures and alloys.
Speaker: Andrey Batranin email: [email protected]
Mathematical Definition of the Problem
С(Т) – heat capacity;(Т) – density; Т – temperature;(Т) – heat conductivity;Q(x,y,z,t) – heat power in a point.
)1(),,,()()()()( tzyxQTgradTdivt
TТTC
To solve problems of welding we use
Spatial Non-linear Dynamic Heat Transfer Equation
Speaker: Andrey Batranin email: [email protected]
Mathematical Definition of the Problem
Initial and Boundary Conditions
Initial condition:
0)0,,,(
)2(),,()0,,,(
ТzyxT
zyxfzyxT
Common boundary condition:
Melting and crystallization by Stephan’s equation
)3(0
Тn
T
)4(_
1
k
kk
k
kkkk n
T
n
TVL
Speaker: Andrey Batranin email: [email protected]
Surface heat sources
I – current, A;
U – voltage, V;
k – heat energy concentration coefficient, 1/m2;
r – distance between a point and the center of a heat spot, m.
TIG-welding )5( exp 2kr
kIUQуд
(6) exp2
02
0
r
rk
r
kIEQуд
Electron beam treatment
Е – accelerating voltage, V;
k – beam concentration coefficient, 1/m2
r0 – beam acting radius, m.
Mathematical Definition of the Problem
Speaker: Andrey Batranin email: [email protected]
Thermophysical properties of materials
considerably depend on temperature.
Mathematical Definition of the Problem
We use the Conservation Laws of Mass, Energy and Linear Momentum in partial differential equations.
Additionally are used state equations for wide range of temperature and component concentration.
Thus the models takes into account the following items:
• Non-linearity of physical properties (thermal dependences)• Spatial geometry of a piece (3D form)• Inhomogeneity: porosity, inclusions• Phase transformations: melting, crystallization, etc.• Complexity of heating: moving sources, preheating, etc.
Speaker: Andrey Batranin email: [email protected]
Mathematical Definition of the Problem
Applications: software
The “Model” Program
Speaker: Andrey Batranin email: [email protected]
Problems were solved:
• Oxygen cutting• TIG-welding• Impulse TIG-welding
The “Meza-cutting” Program
Speaker: Andrey Batranin email: [email protected]
Applications: software
Problems were solved:
• Oxygen cutting• Electron beam treatment
of titanium alloys
Applications: software
Computing of stress and deformed states in welds
Speaker: Andrey Batranin email: [email protected]
Problem was solved:
• Thermal-deformative process during and after welding in a weld joint
t = 0.1 sec t = 0.2 sec
Applications: software
Speaker: Andrey Batranin email: [email protected]
Problem was solved:
• Plastic deformation in HAZ after welding
Computing of stress and deformed states in welds
The “Virtual Workspace” Program (MATLAB)
Speaker: Andrey Batranin email: [email protected]
Applications: software
Trying to use:
• A modern software• HPC possibilities • Collaboration
Applications: developments
Speaker: Andrey Batranin email: [email protected]
Furthermore the following researches are carrying out at our department:
• Stress computation of gradient materials• Composition optimizing of coats• Impulse control of arc welding• Resistance welding of thin-walled pieces
Conclusions
We model different technological processes:
• To determine behaviour of materials during and after a process
• To choose the optimal treatment among possible ones
• To obtain a material or surface or joint with properties we need
• To create a base for automation of processing
Speaker: Andrey Batranin email: [email protected]
Thank you!
http://svarka.tpu.ru