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