The linear inverse problem in energy beam processing with an application to abrasive waterjet machining

The linear inverse problem for energy beam processing, in which a desired etched profile is known and a trajectory of the beam that will create it must be found, is studied in this paper. As an example, abrasive waterjet machining (AWJM) is considered here supported by extensive experimental investigations. The behaviour of this process can be described using a linear model when the angle between the jet and the surface is approximately constant during the process, as occurs for shallow etched profiles. The inverse problem is usually solved by simply controlling dwell time in proportion to the required depth of milling, without considering whether the target surface can actually be etched. To address this, a Fourier analysis Is used to show that high frequency components in the target surface cannot be etched due to the geometry of the jet and the dynamics of the machine. In this paper, this frequency domain analysis is used to improve the choice of the target profile in such a way that it can be etched. The dynamics of the machine also have a large influence on the actual movement of the jet. It is very difficult to describe this effect because the controller of the machine is usually unknown. A simple approximation is used for the choice of the slope of a step profile. The tracking error between the desired trajectory and the real one is reduced and the etched profile is improved. Several experimental tests are presented to show the usefulness of this approach. Finally, the limitations of the linear model are studied

On impinging near-field granular jets

In this work a multibody collision model, amenable to large-scale computation, is developed to simulate a jet of near-field grains impinging on a surface. This model is developed by computing momentum exchange for grain–grain and grain–surface interactions. The grain–grain interactions consist of collisions as well as near-field interactions. The analysis of these flows is separated into three components: (1) volume averaged quantities; (2) average surface tractions; and (3) average outflow conditions. For the surface stress calculations, parametric studies are performed on the properties of the surface and the grains through their coefficients of restitution, the strength of the near-field interactions, and the angle of attack of the jet. For the outflow calculations the flux of momentum through the simulation space is performed for varying near-field forces between the grains and varying degrees of surface roughness