Research Repository

See what's under the surface


On modelling of laser assisted machining: forward and inverse problems for heat placement control (2018)
Journal Article
Shang, Z., Liao, Z., Sarasua, J. A., Billingham, J., & Axinte, D. (2019). On modelling of laser assisted machining: forward and inverse problems for heat placement control. International Journal of Machine Tools and Manufacture, 138, 36-50. doi:10.1016/j.ijmachtools.2018.12.001

Laser assisted machining (LAM) is one of the most efficient ways to improve the machinability of difficult-to-cut materials (e.g. Nickel-based superalloys). In the conventional LAM process, the laser beam is focused ahead of the cutting area at a fix... Read More

A dam-break driven by a moving source: a simple model for a powder snow avalanche A dam-break driven by a moving source: a simple model for a powder snow avalanche (2018)
Journal Article
Billingham, J. A dam-break driven by a moving source: a simple model for a powder snow avalanche A dam-break driven by a moving source: a simple model for a powder snow avalanche. Manuscript submitted for publication

We study the two-dimensional, irrotational flow of an inviscid, incompressible fluid injected from a line source moving at constant speed along a horizontal boundary, into a second, immiscible, inviscid fluid of lower density. A semi-infinite, horizo... Read More

Thick drops climbing uphill on an oscillating substrate (2018)
Journal Article
Bradshaw, J., & Billingham, J. (2018). Thick drops climbing uphill on an oscillating substrate. Journal of Fluid Mechanics, 840, doi:10.1017/jfm.2018.71. ISSN 0022-1120

Experiments have shown that a liquid droplet on an inclined plane can be made to move uphill by suffciently strong, vertical oscillations (Brunet, Eggers, and Deegan, Phys. Rev. Lett. 99, 2007). In this paper, we study a two dimensional, inviscid, ir... Read More

New models for energy beam machining enable accurate generation of freeforms (2017)
Journal Article
Axinte, D. A., Billingham, J., & Guillerna, A. B. (in press). New models for energy beam machining enable accurate generation of freeforms. Science Advances, 3(9), doi:10.1126/sciadv.1701201. ISSN 2375-2548

We demonstrate that, despite differences in their nature, many energy beam controlled-depth machining processes (e.g. waterjet, pulsed laser, focused ion beam) can be modelled using the same mathematical framework – a partial differential evolution e... Read More

Waterjet and laser etching: the nonlinear inverse problem (2017)
Journal Article
Bilbao Guillerna, A., Axinte, D. A., Billingham, J., & Cadot, G. (2017). Waterjet and laser etching: the nonlinear inverse problem. Royal Society Open Science, 4(161031), doi:10.1098/rsos.161031. ISSN 2054-5703

In waterjet and laser milling, material is removed from a solid surface in a succession of layers to create a new shape, in a depth-controlled manner. The inverse problem consists of defining the control parameters, in particular, the two-dimensional... Read More

Continuous trench, pulsed laser ablation for micro-machining applications (2016)
Journal Article
Cadot, G., Axinte, D. A., & Billingham, J. (2016). Continuous trench, pulsed laser ablation for micro-machining applications. International Journal of Machine Tools and Manufacture, 107, doi:10.1016/j.ijmachtools.2016.04.011. ISSN 0890-6955

The generation of controlled 3D micro-features by pulsed laser ablation in various materials requires an understanding of the material's temporal and energetic response to the laser beam. The key enabler of pulsed laser ablation for micro-machining i... Read More

A spectral boundary integral method for inviscid water waves in a finite domain (2016)
Journal Article
Im, J., & Billingham, J. (2016). A spectral boundary integral method for inviscid water waves in a finite domain. International Journal for Numerical Methods in Fluids, doi:10.1002/fld.4225. ISSN 0271-2091

In this paper, we show how the spectral formulation of Baker, Meiron and Orszag can be used to solve for waves on water of infinite depth confined between two flat, vertical walls, and also how it can be modified to take into account water of finite... Read More

Stochastic simplified modelling of abrasive waterjet footprints (2016)
Journal Article
Torrubia, P. L., Billingham, J., & Axinte, D. A. (2016). Stochastic simplified modelling of abrasive waterjet footprints. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472(2186), doi:10.1098/rspa.2015.0836. ISSN 1364-5021

Abrasive micro-waterjet processing is a non-conventional machining method that can be used to manufacture complex shapes in difficult-to-cut materials. Predicting the effect of the jet on the surface for a given set of machi... Read More

The linear inverse problem in energy beam processing with an application to abrasive waterjet machining (2015)
Journal Article
Guillerna, A. B., Axinte, D. A., & Billingham, J. (in press). The linear inverse problem in energy beam processing with an application to abrasive waterjet machining. International Journal of Machine Tools and Manufacture, 99, doi:10.1016/j.ijmachtools.2015.09.006. ISSN 0890-6955

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 considere... Read More

Flows of granular material in two-dimensional channels (2015)
Journal Article
Bain, O., Billingham, J., Houston, P., & Lowndes, I. (2015). Flows of granular material in two-dimensional channels. Journal of Engineering Mathematics, doi:10.1007/s10665-015-9810-1. ISSN 0022-0833

Secondary cone-type crushing machines are an important part of the aggregate production process. These devices process roughly crushed material into aggregate of greater consistency and homogeneity. We apply a continuum model for granular materials (... Read More