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Research at Welding Equipment
and Engineering Department
Speaker: Andrey Batranin, PhD. Student
Tomsk Polytechnic University
Non-destructive Testing Institute
http://svarka.tpu.ru
Contents
• Modeling of Processing
• Our Methods to Solve the Problems
• Mathematical Definition of the Problems
• Applications of the Methods
• Conclusions
Speaker: Andrey Batranin
email: [email protected]
Modeling of Processing
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 materials
such as mixtures and alloys.
Speaker: Andrey Batranin
email: [email protected]
Mathematical Definition of the Problem
To solve problems of welding we use
Spatial Non-linear Dynamic Heat Transfer Equation
T
C (T )  (Т )
 div (T )  grad (T ) Q( x, y, z, t ) (1)
t
С(Т) – heat capacity;
(Т) – density;
Т – temperature;
(Т) – heat conductivity;
Q(x,y,z,t) – heat power in a point.
Speaker: Andrey Batranin
email: [email protected]
Mathematical Definition of the Problem
Initial and Boundary Conditions
T ( x, y, z,0)  f ( x, y, z ) (2)
Initial condition:
T ( x, y, z,0)  Т 0
Common boundary condition:
T
 
   Т    0 (3)
n
Melting and crystallization by Stephan’s equation
Lk  Vk  k 1 
Speaker: Andrey Batranin
Tk
nk
 k 
_
Tk
( 4)
nk 
email: [email protected]
Mathematical Definition of the Problem
Surface heat sources
TIG-welding
Qуд 
IUk



exp  kr 2 (5)
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.
Electron beam treatment
2




IE k
r
Qуд 
exp   k    (6)
2
  r0  
r0


Е – accelerating voltage, V;
k – beam concentration coefficient, 1/m2
r0 – beam acting radius, m.
Speaker: Andrey Batranin
email: [email protected]
Mathematical Definition of the Problem
Thermophysical properties of materials
considerably depend on temperature.
Speaker: Andrey Batranin
email: [email protected]
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]
Applications: software
The “Model” Program
Problems were solved:
• Oxygen cutting
• TIG-welding
• Impulse TIG-welding
Speaker: Andrey Batranin
email: [email protected]
Applications: software
The “Meza” Program
Speaker: Andrey Batranin
email: [email protected]
Applications: software
The “Meza-cutting” Program
Problems were solved:
• Oxygen cutting
• Electron beam treatment
of titanium alloys
Speaker: Andrey Batranin
email: [email protected]
Applications: software
Computing of stress and deformed states in welds
Problem was solved:
• Thermal-deformative
process during and
after welding in a weld
joint
t = 0.1 sec
Speaker: Andrey Batranin
t = 0.2 sec
email: [email protected]
Applications: software
Computing of stress and deformed states in welds
Problem was solved:
• Plastic deformation in
HAZ after welding
Speaker: Andrey Batranin
email: [email protected]
Applications: software
The “Virtual Workspace” Program (MATLAB)
Trying to use:
• A modern software
• HPC possibilities
• Collaboration
Speaker: Andrey Batranin
email: [email protected]
Applications: developments
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
Speaker: Andrey Batranin
email: [email protected]
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