MATHEMATICAL MODELLING OF LASER ASSISTED DEEP DRAWING

Schuöcker, D.

Vienna University of Technology, Austria

Although laser manufacuing with material rernoval as cutfing and vAth material addition as welding or rapid prototyping has reachod a high degree of industrial maturity, processes vAth a constant mass and volume as forming techniques did not find a broad application up to now with the exception of laser bending. Since in this case the laser is the only source of energy, only small bending angles can be achieved in a single step and therefore the latter process is rather suited for calibration processes than for workpiece shaping. Much stronger deformations could be obtained, if the Laser is not used as the sole source of energy but rather for a selective weakening of the workpiece selectively in those regions, where strong deformations take place, that are achieved conventionafly by mechanical forces.
A first application of the latter idea is deep drawing where Laser beams could be used to weaken the matenal near the drawing edge, where the material is bent and moves then in vertical direction. Thus a beneficial reduction of the drawing force is obtained, also allowing processing of materials, that are difficult to draw due to their low ductility.
Experiments have shown, that a reduction of the drawing force up to 25% can easily be achieved. Nevertheless, mathematical modeling of the process is necessary to predict the upper limit for the reduction of drawing forces. Therefore a mathematical analysis of Laser assisted deep drawing has been carried out recently and is presented in the actual paper.
The solution of the heat conduction equation including heat flowing into the tools along with a calculation of the stress distribution in the workpiece together with Tresca's flow condition, where the influence of elevated temperature and cold strengthening on the yield strength is considered, yields the forming forces at the drawing edge. Additional consideration of frictional forces and the necessary bending moment results in the mathematical description of the drawing force dependent on the mechanical properties of the workpiece, the dimensions of the latter as well as the laser power and the geometry of beam coupling to the workpiece.
A numerical evaluation ofthe latter theory in the case of steel X5 CrNI 18 9 with typical workpiece dimensions (undeformed workpiece diameter 200 mm, finished part 100) and a thickness of 2 mm, shows that a drawing force reduction of 50% can be obtained with beam powers available nowadays. Laser assisted deep drawing seems thus to be an attractive new application of high power lasers.

Keywords: Laser materials processing, deep drawing