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Mathematical Modelling of Weld Phenomena 9, 2010-10-29
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Simulation-based optimization for the boundary of the melting pool in
MIG welding process
Pham, X.-T.
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Simulation-based optimization for
p
the boundary of the melting pool in
MIG welding process
X-T. Pham
Aluminium Technology Centre National Research Council Canada
tan.pham@cnrc-nrc.gc.ca
Abstract
In this paper, the bead on plate MIG welding of the aluminum alloy 6061 is studied. The objective is to
predict the boundary of the melting pool through the temperatures measured at several points on the
welded part by thermocouples. The boundary of the melting pool is represented by a parametric curve
whose parameters will be determined by an optimization loop coupled with heat simulations using the finite
element software Sysweld. Both B-spline and Bezier curves with different configurations of thermocouple
l
i
d
d
h
i i i
f h
bl
Th L
b
M
d
i i
i
h d i
locations are used to study the sensitivity of the problem. The Levenberg-Marquardt optimization method is
mainly used in this study as well as the genetic algorithm and gradient free optimization methods.
The heat transfer in the welded part is governed by the following equation:
Heat analysis
Simulation-based optimization algorithm
p g y g q
where T is the tempeperature, t the time, ρ the density, c the specific heat, Q the volume heat source and k the thermal conductivity coefficient. The boudary conditions are as follows:
( ) T c Q k T t
ρ
∂ = + ∇ ∇ ∂ . r i) Presribled temperature: T=TTon ΓTii) Heat flux: q = qn on ΓQ
iii) Convection q = h*(T-T∞) on ΓH
Parametric curve for the boundary
The boundary of the melting pool in the cross-section is represented by a parametric curve such as the Bezier one where the temperature is appro imatel set to the
3 3 2 2 3
0 1 2 3
( )t = −(1 t) +3 (1t −t) +3 (1t −t) +t
b b b b b
Cubic Bezier curve:
Levenberg-Marquardt method
approximately set to the melting temperature of the aluminium
g
q
Numerical results
Melting pool shape optimization using the cubic Bezier curve
Iteration 1 Iteration 2 Iteration 3 Iteration 4 Iteration 5 Iteration 5: Temperature curves
1. The above defined procedure for the simulation-based shape optimization coupled with Sysweld works very well.
Conclusions and discussions
p p p p y y
2. This in-house Levenberg-Marquardt code developed in the object-oriented language C++ is robust for the least square nonlinear problem.
3. The gradients are calculated by the finite difference. Results show that the choice of the incremental value for gradient calculation is sensitive to the convergence.
4. Sysmesh, GMSH and Hypermesh were used as meshing tools in this study. Both Sysmesh and GMSH are very good for parametric meshing. 5. B-Spline curve is more sensitive than Bezier curve for the convergence.
6. Gradient free optimization method (Matlab Condor) and Genetic Algorithm (Matlab) also gave good results. The numbers of function evaluations in this in-house Levenberg-Marquardt code and in the Matlab Condor method are in the same order. In the Genetic Algorithm, the required number of function evaluations is around 50 times larger.
7. The Levenberg-Marquardt method is more sensitive to the initial values than the Genetic Algorithm. A combination of the Genetic Algorithm and the gradient-based method would be a good idea when it is difficult to select the initial values.
8. The thermocouple locations have an important role for the convergence to the solution. It was observed that the solution is not unique for some configurations of p p g q g thermocouple locations.
9. More experimental works will be done to validate this numerical approach. Previous experimental works showed that the thermal contact between thermocouples and the sample is very important. It becomes more difficult when putting thermocouples in a hole.
