Stochastic simplified modelling of abrasive waterjet footprints

P. Lozano Torrubia, J. Billingham, D. A. Axinte

Research output: Journal PublicationArticlepeer-review

14 Citations (Scopus)


Abrasive micro-waterjet processing is a nonconventional 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 machine parameters is a key element of controlling the process. However, the noise of the process is significant, making it difficult to design reliable jet-path strategies that produce good quality parts via controlled-depth milling. The process is highly unstable and has a strong random component that can affect the quality of the workpiece, especially in the case of controlled-depth milling. This study describes a method to predict the variability of the jet footprint for different jet feed speeds. A stochastic partial differential equation is used to describe the etched surface as the jet is moved over it, assuming that the erosion process can be divided into two main components: a deterministic part that corresponds to the average erosion of the jet and a stochastic part that accounts for the noise generated at different stages of the process. The model predicts the variability of the trench profiles to within less than 8%. These advances could enable abrasive micro-waterjet technology to be a suitable technology for controlled-depth milling.

Original languageEnglish
Article number20150836
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2186
Publication statusPublished - 1 Feb 2016
Externally publishedYes


  • Mathematical modelling
  • Mechanical engineering

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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