Inverse problem in energy beam controlled-depth machining

Techniques such as abrasive water jet machining (AWJ), pulsed laser ablation (PLA) and ion beam machining (IBM) are all methods of energy beam processing, by which energy is transferred to a surface and material is removed; this group of technologies can be employed to generate freeforms surfaces by controlled-depth machining. Although the way in which the energy is transferred in each of these methods is very different (AWJ: a high speed mixture of air, grit and water mechanically erodes the surface; PLA: laser pulses vaporize the surface; IBM: high speed charged particles erode the surface), they can be dealt under a unified mathematical framework whereby the rate of erosion of the surface is described by a partial differential equation. This equation relates the footprint of an energy beam (its instantaneous rate of removal, which may be a function of the geometry of the eroding surface, its distance from the source of the beam as well as position within the beam and beam orientation) to the evolution of the surface.

The Investigators in this proposal have had significant success in using this mathematical framework to determine the final, machined surface for a given beam footprint and dynamic beam path; this is the forward problem. However, the problem that is of industrial interest is the inverse problem; given a required final surface, how should the beam be moved in order to accurately machine it? Currently, in both academic research and industry, this problem is solved by trial and error (craftmanship).

The aim of this project is to develop methods for solving the inverse problem algorithmically, so that end users of this group of technologies (i.e. energy beam controlled-depth machining) can input their required surface into a software package and automatically generate a beam path. We will do this by tackling a series of increasingly realistic mathematical problems which can be related to real energy beam processes, backed up by an experimental programme against which our models can be verified.

The main impact groups are:
- Manufacturers of energy beam (EB) machining systems.
- End-users of energy beam controlled-depth machining methods, i.e. customers of EB machining systems.
- Developers of specialist software for dwell-time machining/processing methods.
The project will seek to achieve impact by demonstrating the generation of freeforms by solving the inverse problem in EB controlled-depth machining for: (i) partner companies in the project; (ii) the wider industrial community.

The project will demonstrate at the end of the 3rd year the inverse problem solver on three different EB machining systems (AWJ, PLM, IBM) to generate primitive 3D surfaces and freeforms at accuracies and processing times that could not be (economically or technologically) achieved with the current systems; we will provide a clear technology implementation route for the inverse problem solver on groups of EB machining systems while estimating the economic indicators in relation to the advantages of using the developed technology. The partner companies will run annual internal workshops (attended by the University project leads as required) to ensure that the project results are communicated within their organisations. To achieve wider impact, the project will disseminate results not only at academic conferences but also at industry-based events. A database of potential technology users will be assembled by the Research Fellow; these companies will be invited to attend a series of one-day workshops hosted at Nottingham, where the project will seek not only to present the advances, but to explore subsequent collaboration and application via sand-pit type sessions. Following project-end, the University and collaborators will set up a Project Exploitation Committee, with representation from all parties that wish to be involved. The remit of this committee will be to consider avenues of exploitation; the committee will run for at least three years beyond project-end.

Alongside the EB system builders, there is a very wide network of end-users employing EB machining and the impact of our project will be two-fold: i) they will be able to generate complex geometry parts made of advanced (difficult-to-cut) materials for high value-added industries at higher accuracies and lower costs/processing times; ii) develop new products, not feasible with the current technologies due to their inability to create freeforms at acceptable geometrical and form tolerances.

Although the project aims to solve the inverse problem for EB machining, which the industrial partners consider a strategic need for the development of the technology, we foresee that the impact will be far beyond this remit; any dwell-time (e.g. electro-discharge/chemical - EDM/ECM, ultrasonic) machining can be treated similarly. Moreover, our work can be the base for development of similar software for discrete event time-dependent processes such as laser added material deposition.

EB machining is regarded as an enabling manufacturing route for high-end miniature/micro products with high societal impact, such as medical, defence, telecom, aerospace industries.
Thus, our project will have a wide societal impact by improving quality of life through:
- Healthcare improvements produced by sensors and devices for implantation into the human body.
- Better environmental monitoring through development of miniature (e.g. non fouling) sensors.
- Enabling more-affordable MEMS to be manufactured with EB technology

We will disseminate our results through:
- Organisation of industry-targetted workshops (also to be used for technology transfer and training).
- Publication in journals and professional magazines, and at conferences.
- A website that will contain information on the project (e.g. aims/ objectives, advantages of EB controlled-depth machining), videos of EB paths to generate freeform surfaces and programmes of the organised events.