Title: Mathematical methods for optimising high precision cutting operations

Authors: Christina Brandt; Peter Maaß; Iwona Piotrowska-Kurczewski; Stefan Schiffler; Oltmann Riemer; Ekkard Brinksmeier

Addresses: Centre for Industrial Mathematics, University of Bremen, Bibliothekstraße 1, D-28334 Bremen, Germany. ' Centre for Industrial Mathematics, University of Bremen, Bibliothekstraße 1, D-28334 Bremen, Germany. ' Centre for Industrial Mathematics, University of Bremen, Bibliothekstraße 1, D-28334 Bremen, Germany. ' Centre for Industrial Mathematics, University of Bremen, Bibliothekstraße 1, D-28334 Bremen, Germany. ' Laboratory for Precision Machining (LFM), Badgasteiner Straße 2, D-28359 Bremen, Germany. ' Laboratory for Precision Machining (LFM), Badgasteiner Straße 2, D-28359 Bremen, Germany

Abstract: The endeavour for establishing high precision cutting processes with nm-precision requires advancements in terms of manufacturing machinery, material selection and optimising the cutting process itself. This paper presents a mathematically founded approach for determining optimised process parameters using regularisation methods for inverse problems. The optimisation is based on an idealised simulation which relates process parameters like depth of cut and feed velocity to the resulting tool path incorporating elastic deformations. The optimised parameters are then obtained by inverting the simulation model, i.e., a prescribed tool path is given and a suitable control, which yields an approximation within the desired range of precision, is computed. In order to incorporate processing limitations a sparsity technique is included. The approach is successfully tested for two different applications, the design of optimal process parameters and the sparse correction of predefined parameters. The simulation results highlight the potential improvements obtained by this approach.

Keywords: inverse problems; microcutting processes; modelling; parameter identification; micromachining; high precision cutting; nanomanufacturing; nanotechnology; depth of cut; feed speed; elastic deformation; simulation; modelling.

DOI: 10.1504/IJNM.2012.048580

International Journal of Nanomanufacturing, 2012 Vol.8 No.4, pp.306 - 325

Received: 16 Jul 2011
Accepted: 09 Dec 2011
Published online: 21 Aug 2014 *

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