An optimal control problem for single-spot pulsed laser welding

We consider an optimal control problem for a single-spot pulsed laser welding problem. The distribution of thermal energy is described by a quasilinear heat equation. Our emphasis is on materials which tend to suffer from hot cracking when welded, such as aluminum alloys. A simple precursor for the...

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Bibliographic Details
Published inJournal of mathematics in industry Vol. 13; no. 1; pp. 4 - 18
Main Authors Herzog, Roland, Strelnikov, Dmytro
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2023
Springer Nature B.V
SpringerOpen
Subjects
Alloys
Aluminum alloys
Aluminum base alloys
Applications of Mathematics
Boundary value problems
Energy distribution
Heat
Hot cracks
Laser beam welding
Lasers
Math. Appl. in Environmental Science
Mathematical and Computational Biology
Mathematical and Computational Engineering
Mathematical Methods in Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Optimal control
Phase transition
Phase transitions
Pulsed laser welding
Pulsed lasers
Quasilinear heat equation
Solidification
Solidification velocity
Solids
Thermal energy
Thermodynamics
Upper bounds
Pulsed laser welding
Solidification velocity
49K20
Quasilinear heat equation
Optimal control
35K59
49M05
Phase transition
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Summary:We consider an optimal control problem for a single-spot pulsed laser welding problem. The distribution of thermal energy is described by a quasilinear heat equation. Our emphasis is on materials which tend to suffer from hot cracking when welded, such as aluminum alloys. A simple precursor for the occurrence of hot cracks is the velocity of the solidification front. We therefore formulate an optimal control problem whose objective contains a term which penalizes excessive solidification velocities. The control function to be optimized is the laser power over time, subject to pointwise lower and upper bounds. We describe the finite element discretization of the problem and a projected gradient scheme for its solution. Numerical experiments for material data representing the EN AW 6082-T6 aluminum alloy exhibit interesting laser pulse patterns which perform significantly better than standard ramp-down patterns.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:2190-5983
2190-5983
DOI:10.1186/s13362-023-00132-7