The Application of an Inverse Methodology to Predict Nonlinear Thermal Properties in Laser Beam Welding

Abstract

Modern engineering applications use processes that submit materials to high-temperature gradients. However, the traditional experimentation methods applied to determine thermal properties often do not provide reliable data when working temperatures are up to extreme conditions. Hence, the present work demonstrates the use of an inverse heat conduction problem methodology for estimating the thermal properties of a laser beam welding (LBW) process. The applied technique is the quadrilateral optimization method (QOM), which consists of a multivariable estimation approach developed to calculate the function’s parameters. Additionally, the future time regularization scheme was implemented in the objective function to regularize the results. The applied numerical process solved the energy equation using the finite volume method implemented in an in-house CUDA-C language code. The software is a multi-thread application run in a graphics processing unit for enhanced computational time efficiency. A validation study compared the estimated results with LBW simulated data. The QOM estimates the parameters of a function representing the range of thermal conductivity values. The proposed method is expected to lower experimental costs for obtaining thermal properties at high temperatures by eliminating the need for sophisticated technical equipment and skilled labor required by traditional direct measurements.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors would like to thank the Brazilian sponsors CAPES (process number 88887.512576/2020-00), CNPq, and PETROBRAS for their invaluable financial support.

Notes on contributors

Ernandes José Gonçalves do Nascimento

Ernandes José Gonçalves do Nascimento is a Ph.D. candidate at the Aeronautics Institute of Technology (ITA) and a member of the Applied Thermal Engineering Laboratory (LETA) in Brazil. He received his bachelor’s degree in Mechanical Engineering from the Federal University of Itajubá in 2016. His undergraduate formation includes an international student exchange program at Florida State University. He developed his Senior Design Project in an autonomous aerial vehicle and worked as a research and development intern. He obtained his master’s degree in Aeronautical and Mechanical Engineering at ITA in 2020.

Elisan dos Santos Magalhães

Elisan dos Santos Magalhães is an Assistant Professor and Head of the Energy Department at the Aeronautics Institute of Technology (ITA) in Brazil. He received his bachelors, masters, and doctoral degrees in Mechanical Engineering from the Federal University of Itajubá in Brazil. He is one of the founders of the Applied Thermal Engineering Laboratory (LETA) in ITA. He has 18 published papers in high-impact journals and 25 refereed National/International conference papers in research involving heat transfer, inverse problems, welding, and thermal modeling of machinery processes. He currently advises five Ph.D. students and six master’s students.

Arthur Mendonça de Azevedo

Arthur Mendonça de Azevedo is a Ph.D. candidate at the Aeronautics Institute of Technology (ITA) in Brazil. He received his bachelor’s in Naval Sciences from the Brazilian Navy’s Naval School in 2013 and his degree in Mechanical-Aeronautical Engineering from ITA in 2021. He also received a master’s degree in Aeronautical and Mechanical Engineering from ITA in 2022. He is a member of ITA's Applied Thermal Engineering Laboratory (LETA). In addition, he has experience in mechanical engineering, with an emphasis on heat transfer applied through numerical methods for thermal analysis of welding processes and parallel programming in CUDA-C language.

Luiz Eduardo dos Santos Paes

Luiz Eduardo dos Santos Paes is an Assistant Professor at the Federal University of Uberlândia (UFU) and a member of the LAPROSOLDA welding research group. He received his mechanical engineering degree from the Federal University of Itajubá (UNIFEI-2014). He had a complementary Materials/Solid Mechanics formation at Florida State University in 2013, where he developed his Senior Design Project with the Air Force Research Laboratory (AFRL) partnership. He obtained his master’s degree in mechanical engineering from the Federal University of Santa Catarina (UFSC-2016) in arc welding and metallurgy. He received his Ph.D. from UFSC (2019) in laser welding and additive manufacturing.