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Identification of dimension in phase space for cutting

: Schulz, W.; Eppelt, U.; Heesen, H.; Kostrykin, V.; Michel, J.; Niessen, M.

Poprawe, R. ; Wissenschaftliche Gesellschaft Lasertechnik -WLT-:
Lasers in Manufacturing 2003 : Proceedings of the Second International WLT-Conference on Lasers in Manufacturing 2003
München: AT-Verlag, 2003
ISBN: 3-00-011673-7
International Conference on Lasers in Manufacturing <2, 2003, München>
Fraunhofer ILT ()
cutting; modelling; simulation

Laser cutting is an established separation process. Reliable machining at high productivity and quality as well as simplified machine operation are the actual goals in industries. This work describes the advances in fundamental physical modelling of time dependent processes involved in piercing, trepanning and contour cutting. The effects of short laser pulses (>ns) onto the motion of the melting front and the melt flow are discussed. The generic laser beam processes like cutting, welding and drilling are Free Boundary Problems for the motion of two phase boundaries. In the long-time limit of such dissipative dynamical systems a reduction of the dimension in phase space occurs. The degrees of freedom are identified by methods of singular perturbation theory. In particular, the appearance of boundary layer character in heat diffusion and melt flow is discussed. The type and the appropriate number of the degrees of freedom are investigated. Integral and spectral methods are used to derive the equations of motion for the different finite dimensional approximations. Integral methods lead to approximate dynamical systems describing the long-time limit. Spectral methods are used to identify the onset of deviations on short temporal and spatial scales. The long-time limit of the dynamical system is shown to give a very good approximation of the exact solution even for moderate situations. The temporal and spatial scales on which deviations occur are determined to be relevant for example in piercing and trepanning.