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Fast Temperature Field Generation for Welding Simulation and Reduction of Experimental Effort
(2009)

The objective of this paper is to demonstrate a new simulation technique which allows the fast and automatic generation to temperature fields based on a combination of empirical and phenomenological modelling techniques. The automatic calibration of the phenomenological model is performed by a multi-variable global optimisation routine which yields the optimal fit between simulated and experimental weld charcteristics without the need for initial model parameters. For exemplary welding processes it is shown that linear 3D heat conduction models can approximate measured temperature fields with a high accuracy. The modelling approach presented comprises the automatic calibration against multiple experiments which permits simulating the temperature field for unknown process parameters. The validation of this composite simulation model is performed for exemplary welding processes and includes the prediction of the fusion line in the cross section and the corresponding thermal cycles.

The objective of this paper is to demonstrate a new simulation technique which allows fast and automatic generation of temperature fields as input for subsequent thermomechanical welding simulation. The basic idea is to decompose the process model into an empirical part based on neural networks and a phenomenological part that describes the physical phenomena. The strength of this composite modelling approach is the automatic calibration of mathematical models against experimental data without the need for manual interference by an experienced user. As an example for typical applications in laser beam and GMA-laser hybrid welding, it is shown that even 3D heat conduction models of a low complexity can approximate measured temperature fields with a sufficient accuracy. In general, any derivation of model fitting parameters from the real process adds uncertainties to the simulation independent of the complexity of the underlying phenomenological model. The modelling technique presented hybridises empirical and phenomenological models. It reduces the model uncertainties by exploiting additional information which keeps normally hidden in the data measured when the model calibration is performed against few experimental data sets. In contrast, here the optimal model parameter set corresponding to a given process parameter is computed by means of an empirical submodel based on relatively large set of experimental data. The approach allows making a contribution to an efficient compensation of modelling inaccuracies and lack of knowledge about thermophysical material properties or boundary conditions. Two illustrating examples are provided.

Fast temperature field generation for welding simulation and reduction of experimental effort
(2009)

The quality of welding processes is governed by the occurring induced distortions yielding an
increase in production costs due to necessary reworking. Especially for more complex specimens
it is difficult to evaluate the optimal configuration of welding sequences in order to
minimise the distortion. Even experienced welding operators can solve this task only by trial
and error which is time and cost consuming.
In modern engineering the application of welding simulation is already known to be able to
analyse the heat effects of welding virtually. However, the welding process is governed by
complex physical interactions. Thus, recent weld thermal models are based on many simplifications.
The state of the art is to apply numerical methods in order to solve the transient heat
conduction equation. Therefore, it is not possible to use the real process parameters as input
for the mathematical model. The model parameters which allow calculating a temperature
field that is in best agreement with the experiments cannot be defined directly but inversely by
multiple simulations runs. In case of numerical simulation software based on finite discretisation
schemes this approach is very time consuming and requires expert users. The weld
thermal model contains an initial weakness which has to be adapted by finding an optimal set
of model parameters. This process of calibration is often done against few experiments. The
range of model validity is limited. An extension can be obtained by performing a calibration
against multiple experiments.
The focus of the paper is to show a combined modelling technique which provides an efficient
solution of the inverse heat conduction problem mentioned above. On the one hand the inverse
problem is solved by application of fast weld thermal models which are closed form
solutions of the heat conduction equation. In addition, a global optimisation algorithm allows
an automated calibration of the weld thermal model. This technique is able to provide a temperature
field automatically that fits the experimental one with high accuracy within minutes
on ordinary office computers. This fast paradigm permits confirming the application of welding
simulation in an industrial environment as automotive industry.
On the other hand, the initial model weakness is compensated by calibrating the model
against multiple experiments. The unknown relationship between model and process parameters
is approximated by a neural network. The validity of the model is increased successively
and enables to decrease experimental effort. For a test case it is shown, that this approach
yields accurate temperature fields within very short amount of time for unknown process parameters
as input data to the model contributing to the requirement to construct a substitute
system of the real welding process.

The paper presents bounded volume heat sources and the corresponding functional-analytical expressions for the temperature field. The power density distributions considered here are normal, exponential and parabolic. The sources model real heat sources like the welding arc, laser beam, electron beam, etc., the convection in the weld pool as well as the latent heat due to fusion and solidification. The parameters of the heat source models are unknown a priori and have to be evaluated by solving an inverse heat conduction problem. The functional-analytical technique for calculating 3D temperature fields in butt welding is developed. The proposed technique makes it possible to reduce considerably the total time for data input and solution. It is demonstrated with an example of laser beam welding of steel plates.

This paper presents volume heat sources and the corresponding functional analytical Solutions for the transient temperature field. The considered energy distributions are normal, exponential and parabolic. The method follows the common approach in Computational Welding Mechanics (CWM) to account for the physics of the welding process and the resulting temperature field by phenomenological models for heat conduction. Therefore, the used heat source models are apparent heat sources that incorporate the real heat input as well as the fluid flow in the weld pool and the latent heat connected with phase transformations. The heat source models provide welding characteristics like thermal cycle and Fusion line in the cross section within short computational time. Consequently, inverse techniques on basis of optimisation algorithms enable the adaptation of the models to the experimental data efficiently. Furthermore, the direct evaluation of the energy distribution for the experimental fusion line in the cross section is demonstrated which enhances the numerical optimisation by reducing the number of unknown model Parameters and providing a reasonable initial guess within the model parameter space. The proposed temperature field models are validated with real laser beam welding experiments.

The present thesis provides a contribution to the solution of the inverse heat conduction problem in welding simulation. The solution strategy is governed by the need that the phenomenological simulation model utilised for the direct solution has to provide calculation results within short computational time. This is a fundamental criterion in order to apply optimisation algorithms for the detection of optimal model parameter sets. The direct simulation model focuses on the application of functional-analytical methods for solving the corresponding partial differential equation of heat conduction. In particular, volume heat sources with a bounding of the domain of action are applied. Besides the known normal and exponential distribution, the models are extended by the introduction of parabolically distributed heat sources. Furthermore, the movement on finite specimens under consideration of curved trajectories has been introduced and solved analytically. The calibration of heat source models against experimental reference data involves the simultaneous adaptation of model parameters. Here, the global parameter space is searched in a randomised manner. However, an optimisation pre-processing is needed to get information about the sensitivity of the weld characteristics like weld pool dimension or objective function due to a change of the model parameters. Because of their low computational cost functional-analytical models are well suited to allow extensive sensitivity studies which is demonstrated in this thesis. For real welding experiments the applicability of the simulation framework to reconstruct the temperature field is shown. In addition, computational experiments are performed that allow to evaluate which experimental reference data is needed to represent the temperature field uniquely. Moreover, the influence of the reference data like fusion line in the cross section or temperature measurements are examined concerning the response behaviour of the objective function and the uniqueness of the optimisation problem. The efficient solution of the inverse problem requires two aspects, namely fast solutions of the direct problem but also a reasonable number of degrees of freedom of the optimization problem. Hence, a method was developed that allows the direct derivation of the energy distribution by means of the fusion line in the cross section, which allows reducing the dimension of the optimisation problem significantly. All conclusions regarding the sensitivity studies and optimisation behaviour are also valid for numerical models for which reason the investigations can be treated as generic.