Estimation of the parameters of a Gaussian heat source by the Levenberg–Marquardt method: Application to the electron beam welding

2007 ◽  
Vol 46 (2) ◽  
pp. 128-138 ◽  
Author(s):  
S. Rouquette ◽  
J. Guo ◽  
P. Le Masson
Keyword(s):  
Electron Beam ◽  
Heat Source ◽  
Electron Beam Welding ◽  
Marquardt Method ◽  
Levenberg Marquardt

Influence of Forming Residual Stresses on the Welding Distortions of Two Thick Plates

2009 ◽  
Vol 83-86 ◽  
pp. 125-132 ◽  
Author(s):  
Sebastien Gallée ◽  
Antoine Martin ◽  
Vincent Robin ◽  
Daniel Nelias
Keyword(s):  
Numerical Simulation ◽  
Electron Beam ◽  
Heat Source ◽  
Residual Stresses ◽  
Electron Beam Welding ◽  
Initial Conditions ◽  
Rolling Process ◽  
Vacuum Vessel ◽  
Thick Plates ◽  
Simulation Results

The manufacturing of the ITER (International Thermonuclear Experimental Reactor) vacuum vessel involves the welding of thick deformed plates. The aim of this study is to investigate the influence of forming residual stresses on the welding distortions of two thick plates. The plates are deformed using a three point rolling process. A first numerical simulation is performed to investigate the residual stresses induced by this process. The forming residual stresses are taken into account as initial conditions to perform the electron beam welding simulation of a deformed plate. This simulation first requires calibrating the heat source. Two welding simulations are then performed: the first one with residual stresses and the second one without. The comparison of the simulation results points out a low effect of the residual stresses on the electron beam welding distortions. As a result, in the next electron beam welding simulations of the vacuum vessel, no forming residual stresses will be taken into account.

Numerical modelling of heat source during electron beam welding

Vacuum ◽  
2020 ◽  
Vol 171 ◽  
pp. 108991 ◽  
Author(s):  
Peter Petrov ◽  
Manahil Tongov
Keyword(s):  
Electron Beam ◽  
Numerical Modelling ◽  
Heat Source ◽  
Electron Beam Welding

Modeling of the Temperature Field during Electron Beam Welding of Aluminum Alloy by a Pre-Defined Keyhole

2007 ◽  
Vol 353-358 ◽  
pp. 2011-2014
Author(s):  
Yan Hong Tian ◽  
Chun Qing Wang ◽  
Dan Yang Zhu
Keyword(s):  
Temperature Field ◽  
Electron Beam ◽  
Heat Source ◽  
Electron Beam Welding ◽  
Three Dimensional ◽  
Source Model ◽  
Transient Temperature ◽  
Al Alloy ◽  
Welding Pool ◽  
Welding Line

The transient temperature field of Al alloy during electron beam welding (EBW) process was simulated using a three-dimensional finite element method. Different from the most previous models which were based on the assumption that the welding pool was solid and neglected the existence of keyhole by meshing the solid as a whole, a dynamic three-dimensional keyhole was applied in this model. The profile of the keyhole was ellipse and its size was determined before simulation based on the results of experiments. Following the heat source, the pre-defined keyhole moved along the welding line. A three-dimensional complex heat source model, including a modified Gaussian distribution source and a uniform source, was used in this study. The result shows that the shape of the keyhole had a direct effect on the temperature distribution and contribution to the special shape of the welding pool in EBW.

Modelling of Heat Source Dynamics in Electron Beam Welding

2016 ◽  
Vol 1 (1) ◽  
pp. 22-27
Author(s):  
Suresh Akella ◽  
◽  
Harinadh Vemanaboina ◽  
Ramesh Kumar Buddu ◽  
◽  
...  
Keyword(s):  
Electron Beam ◽  
Heat Source ◽  
Electron Beam Welding

Levenberg–Marquardt method for ill-posed inverse problems with possibly non-smooth forward mappings between Banach spaces

2021 ◽  
Author(s):  
Huu Nhu Vu
Keyword(s):  
Inverse Problems ◽  
Heat Source ◽  
Banach Spaces ◽  
Elliptic Boundary ◽  
Uniformly Convex ◽  
Bounded Operators ◽  
Marquardt Method ◽  
Levenberg Marquardt ◽  
Ill Posed ◽  
Forward Mapping

Abstract In this paper, we consider a Levenberg–Marquardt method with general regularization terms that are uniformly convex on bounded sets to solve the ill-posed inverse problems in Banach spaces, where the forward mapping might not Gˆateaux differentiable and the image space is unnecessarily reflexive. The method therefore extends the one proposed by Jin and Yang in (Numer. Math. 133:655–684, 2016) for smooth inverse problem setting with globally uniformly convex regularization terms. We prove a novel convergence analysis of the proposed method under some standing assumptions, in particular, the generalized tangential cone condition and a compactness assumption. All these assumptions are fulfilled when investigating the identification of the heat source for semilinear elliptic boundary-value problems with a Robin boundary condition, a heat source acting on the boundary, and a possibly non-smooth nonlinearity. Therein, the Clarke subdifferential of the non-smooth nonlinearity is employed to construct the family of bounded operators that is a replacement for the nonexisting Gˆateaux derivative of the forward mapping. The efficiency of the proposed method is illustrated with a numerical example.

scholarly journals Research on modeling of heat source for electron beam welding fusion-solidification zone

2013 ◽  
Vol 26 (1) ◽  
pp. 217-223 ◽  
Author(s):  
Yajun Wang ◽  
Pengfei Fu ◽  
Yongjun Guan ◽  
Zhijun Lu ◽  
Yintao Wei
Keyword(s):  
Electron Beam ◽  
Heat Source ◽  
Electron Beam Welding

Heat source model for electron beam welding of nickel-based superalloys

2021 ◽  
Vol 63 (1) ◽  
pp. 17-28
Author(s):  
Torsten Jokisch ◽  
Nikolay Doynov ◽  
Ralf Ossenbrink ◽  
Vesselin Georgiev Michailov
Keyword(s):  
Electron Beam ◽  
Heat Source ◽  
Electron Beam Welding ◽  
Experimental Studies ◽  
Theoretical Models ◽  
Source Model ◽  
Beam Deflection ◽  
Prediction Algorithm ◽  
Model Parameters ◽  
Heat Source Model

Abstract An adapted heat source model is developed for transient thermal numerical analysis of electron beam welded nickel-based alloy with increased susceptibility to hot cracking. The model enables the consideration of heat redistribution due to beam deflection phenomena. The modeling concept is validated by the appropriate theoretical models and in addition, experimental studies especially performed for this purpose. Special attention is given to the calibration of heat source model parameters. The calibration procedure is based on a statistical approach involving a combination of novel analytical solutions and quasi-steady state finite element models. The model parameter field is statistically analyzed, and a prediction algorithm is developed using optimization algorithms from the six sigma theory. The reliability and practicability of the model is demonstrated by validation weldments. The work is dedicated to precisely calculating the temperature field in the high temperature region around the weld pool and thus to provide a more detailed explanation of the formation of hot cracks when welding turbine materials commonly used in industry and aircraft constructions.

Estimation of a heat source by using the measured temperatures and micrographic informations; application to an electron beam welding process

2004 ◽  
Vol 120 ◽  
pp. 279-290
Author(s):  
J. Guo ◽  
P. Le Masson ◽  
E. Artioukhine ◽  
T. Loulou ◽  
P. Rogeon ◽  
...  
Keyword(s):  
Electron Beam ◽  
Heat Source ◽  
Electron Beam Welding ◽  
Solid Phase ◽  
Transfer Problem ◽  
Welding Process ◽  
Iterative Regularization ◽  
Optical Micrograph ◽  
Inverse Heat Transfer ◽  
Inverse Heat Transfer Problem

This paper is concerned with the estimation of a heat source applied in the electron beam welding process by using the micrographic information (hardness, optical micrograph...) and temperature measurements in solid phase. The aim is to identify the energy distribution which is applied in the liquid and vapor zones. This identification is realized at each time in a transversal plan perpendicularly to the welding axis. For this work, the goal is to analyze the feasibility of the estimation. So we don’t use noise with the theoretical measurements. At last, the iterative regularization method will be used for this two-dimensional metallurgical inverse heat transfer problem.

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