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Despite the advances in hardware and software techniques, standard numerical methods fail in providing real-time simulations, especially for complex processes such as additive manufacturing applications. A real-time simulation enables process control through the combination of process monitoring and automated feedback, which increases the flexibility and quality of a process. Typically, before producing a whole additive manufacturing structure, a simplified experiment in the form of a beadon-plate experiment is performed to get a first insight into the process and to set parameters suitably. In this work, a reduced order model for the transient thermal problem of the bead-on-plate weld simulation is developed, allowing an efficient model calibration and control of the process. The proposed approach applies the proper generalized decomposition (PGD) method, a popular model order reduction technique, to decrease the computational effort of each model evaluation required multiple times in parameter estimation, control, and optimization. The welding torch is modeled by a moving heat source, which leads to difficulties separating space and time, a key ingredient in PGD simulations. A novel approach for separating space and time is applied and extended to 3D problems allowing the derivation of an efficient separated representation of the temperature.
The results are verified against a standard finite element model showing excellent agreement. The reduced order model is also leveraged in a Bayesian model parameter estimation setup, speeding up calibrations and ultimately leading to an optimized real-time simulation approach for welding experiment using synthetic as well as real measurement data.
PGD model with domain mapping of Bead-on-Plate weld simulation for wire arc additive manufacturing
(2022)
Numerical simulations are essential in predicting the behavior of systems in many engineering fields and industrial sectors. The development of accurate virtual representations of actual physical products or processes allows huge savings in cost and resources. In fact, digital twins would allow reducing the number of real, physical prototypes, tests, and experiments, thus also increasing the sustainability of the production processes and products’ lifetime. Standard numerical methods fail in providing real time simulations, especially for complex processes such as additive manufacturing applications.
This work aims to build up a reduced order model for efficient wire arc additive manufacturing simulations by using the proper generalized decomposition (PGD) [1,2] method. Model order reduction is a popular concept to decrease the computational effort, where each evaluation of the reduced forward model is faster than evaluations using classical methods, even for complex models. The simulation of a moving heat source leads to a hardly separable parametric problem, which is solved by a new mapping approach [3]. Using this procedure, it is possible to create a simple separated representation of the forward model.
In this contribution, a PGD model is derived for the first part of wire arc additive manufacturing: bead-on-plate weld. An excellent agreement with a standard finite element method is shown. The reduced model is further used in a model calibration set up, speeding up calibrations and ultimately leading to an optimized real-time simulation.