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Non-Linear Dynamics in Modeling of Cutting Edge Geometry

: Ditzinger, T.; Friedrich, R.; Henning, A.; Radons, G.

Hashish, M. ; Water Jet Technology Association:
10th American Waterjet Conference 1999. Proceedings. Vol.1
St. Louis, MO, USA, 1999
ISBN: 1-880342-11-1
American Waterjet Conference <10, 1999, Houston/Tex.>
Fraunhofer IPA ()
cutting tool; Wasserstrahlschneiden

Abrasive waterjet cutting has already been established in many fields of industrial production. Yet limited cutting performance and cutting edge quality hinder a wider distribution of abrasive cutting systems. As a major limiting factor process immament step propagation in the cutting front and thus striation formation can be spotted. In this work we present new nonlinear approaches to the instability problem. In the simplest approximation the front dynamic is described by a first order nonlinear partial differential equation (PDE) of Hamilton-Jacobi type. The relevant solutions typically develop shock structures within finite time. These are understood by considering the evolution of associated Langrangian manifolds in phase space. On this level only the time-averaged behavior of the cutting front but no instability is found. The inclusion of higher order derivatives in the PDE, however, can explain the observed ripple formation. This is shown by numerical simulations of the resulting PDE, which is related to the Kuramoto-Sivashinsky equation known from other erosion phenomena. Our simulations are compared with edge cutting experiments where multiple reflections of the waterjet are avoided. These approaches provide a better understanding of the involved processes, which ultimately should result in a reduction of striations and a better cutting performance.