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Non-linear dynamic modelling of the abrasive waterjet process


Klocke, F. ; Aachener Demonstrationslabor für Integrierte Produktionstechnik -ADITEC-; Fraunhofer-Institut für Produktionstechnologie -IPT-, Aachen; TH Aachen -RWTH-, Laboratorium für Werkzeugmaschinen und Betriebslehre -WZL-:
Investigation of Nonlinear Dynamic Effects in Production Systems
Aachen, 1999
International Symposium Investigation of Nonlinear Dynamic Effects in Production Systems <2, 1999, Aachen>
Fraunhofer IPA ()
Dynamischer Prozeß; Modellierung; Wasserstrahlschneiden; Wasserstrahltechnik

Abrasive waterjet machining is a very flexible and advanced technique for cutting and shaping all sorts of materials ranging from plastics to steel or ceramics. It utilizes the eroding effect of abrasive particles which are accelerated up to Mach 3 within the waterjet. Although cutting speeds are much higher than with conventional techniques, there are limitations due to a hitherto unexplained spatio-temporal instability in the propagating cutting front.
We give an introduction into the basics of waterjet cutting technique and their applications, describe previous approaches to the instability problem, and present nonlinear dynamics based ideas for the solution of the problem. These are on one hand nonlinear, data driven approaches resulting in empirical models. On the other hand we present microscopic model considerations. In a first approximation the latter describe the front dynamics by a nonlinear partial differential equation of Hamilton-Jacobi type. The relevant solutions are ge neralized for viscosity solutions, which typically develop shocks in finite time. We investigate the dynamics of these shock structures by considering the evolution of associated Lagrangian manifolds in phase space. Especially, implications of symplectic phase space structures for the front dynamics are investigated.