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

Axinte, D.; Bilbao Guillerna, A.; Billingham, J.

Authors

DRAGOS AXINTE dragos.axinte@nottingham.ac.uk
Professor of Manufacturing Engineering

A. Bilbao Guillerna

JOHN BILLINGHAM john.billingham@nottingham.ac.uk
Professor of Theoretical Mechanics



Abstract

© 2015 The Authors. Published by Elsevier Ltd. 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.

Journal Article Type Article
Publication Date 2015-12
Journal International Journal of Machine Tools and Manufacture
Electronic ISSN 0890-6955
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 99
Pages 34-42
APA6 Citation Axinte, D., Bilbao Guillerna, A., & Billingham, J. (2015). The linear inverse problem in energy beam processing with an application to abrasive waterjet machining. International Journal of Machine Tools and Manufacture, 99, 34-42. https://doi.org/10.1016/j.ijmachtools.2015.09.006
DOI https://doi.org/10.1016/j.ijmachtools.2015.09.006
Keywords Inverse problem, Controlled depth etching, Energy beam,
Abrasive waterjet machining
Publisher URL http://www.sciencedirect.com/science/article/pii/S0890695515300705
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0
Additional Information This article is maintained by: Elsevier; Article Title: The linear inverse problem in energy beam processing with an application to abrasive waterjet machining; Journal Title: International Journal of Machine Tools and Manufacture; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.ijmachtools.2015.09.006; Content Type: article; Copyright: Copyright © 2015 The Authors. Published by Elsevier Ltd.

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by-nc-nd/4.0





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