An Optimal Control Problem for Single-Spot Pulsed Laser Welding

TL;DR

This paper formulates an optimal control problem for pulsed laser welding of aluminum alloys, aiming to minimize hot cracking risk by controlling laser power, and demonstrates improved pulse patterns through numerical experiments.

Contribution

It introduces a novel optimal control framework for laser welding that incorporates solidification velocity penalties to reduce hot cracking.

Findings

Optimized laser pulse patterns outperform standard ramp-down patterns.

Finite element discretization and projected gradient methods effectively solve the control problem.

Numerical results show significant improvements in welding quality for aluminum alloys.

Abstract

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, such as aluminum alloys. A simple indicator 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.