Calibration of bending and membrane strains for iterative laser forming of non-developable surfaces

Laser forming of non-developable surfaces requires an accurate model of both the bending and membrane strains generated. Finite element process simulations typically require detailed material characterisation, take significant computation time [1], are sensitive to process variation and initial conditions, and cannot guarantee to generate an arbitrary complex shape in a single process step [2]. An iterative approach to laser forming can increase the accuracy of the final shape generated without the need for extreme levels of accuracy in material characterisation and process modelling, by using closed loop control of shape generation. The accuracy requirements for the model describing strain generation are reduced, but rapid calculation is required between each iteration to implement closed loop control in real time. We report a simplified process model that has been developed to meet the needs of iterative forming. This model identifies the key laser forming parameters, showing their influence on line bending and shrinkage, and describes the effects of beam profile. To verify the model, the bending and shortening mechanisms were calibrated by generation of developable and nondevelopable surfaces in mild steel. We also report a new algorithm for iterative forming of developable surfaces, based on a fixed scan lattice. We present the results obtained implementing this algorithm using the calibration results.