# Inverse problem in energy beam controlled-depth machining

Lead Research Organisation:
University of Nottingham

Department Name: Faculty of Engineering

### Abstract

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 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.

### Planned Impact

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.

- 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.

### Publications

Axinte D
(2019)

*Time-dependent manufacturing processes lead to a new class of inverse problems.*in Proceedings of the National Academy of Sciences of the United States of America
Axinte D
(2017)

*New models for energy beam machining enable accurate generation of free forms*in Science Advances
Bilbao Guillerna A
(2015)

*The linear inverse problem in energy beam processing with an application to abrasive waterjet machining*in International Journal of Machine Tools and Manufacture
Bilbao-Guillerna A
(2017)

*Waterjet and laser etching: the nonlinear inverse problem.*in Royal Society open science
Bilbao-Guillerna A
(2018)

*Novel approach based on continuous trench modelling to predict focused ion beam prepared freeform surfaces*in Journal of Materials Processing Technology
D. Axinte
(2019)

*Time-dependent manufacturing processes lead to a new class of inverse problems*in The Proceedings of National Academcy of Science of AmericaDescription | the same as in the previous submission, i.e. 2020 |

Exploitation Route | the same as in the previous submission, i.e. 2020 |

Sectors | Aerospace, Defence and Marine,Manufacturing, including Industrial Biotechology |

Description | The project has been very successful considering the following aspects: - Publications: 5 journal papers (all Q1) of which 2 papers in the top 1% journals (Science Advances IF >12; PNSA IF>9) - Further research funding: Clean Sky 2 (STIMULANT) project obtained as coordinator (>800k Euro); 2 CASE Awards PhD with Rolls-Royce plc; 1 BBSRC (BB/T012226/1) project as Co-I (allocated funding £90k); 1 China scholarship PhD visiting student for 1 year (2018-2019). - Dissemination: 3 invited talks to top conferences (e.g. CIRP sponsored events) - Software development: 1 software that is used for machining freeform surfaces for industrial customers (via service rendered) - Industry collaborations: Rolls-Royce Plc; Waterjet AG (Switzerland); Synova (Switzerland); GKN Sweden (Sweden) - Academic collaborations: EMPA (Switzerland); Fraunhofer Institute for Integrated Systems and Device Technology (Germany); McGill University (Canada) - New project application: SMART Eureka (THERMACH) - passed the 1 stage and it is under evaluation (2nd stage) |

First Year Of Impact | 2019 |

Sector | Aerospace, Defence and Marine,Manufacturing, including Industrial Biotechology |

Impact Types | Societal,Economic |

Description | Clean Sky 2. Horizon 2020 |

Amount | € 760,000 (EUR) |

Funding ID | - |

Organisation | European Union |

Sector | Public |

Country | European Union (EU) |

Start | 10/2017 |

End | 09/2020 |

Description | Different strategies for path selection in the inverse problem |

Amount | £0 (GBP) |

Organisation | London Mathematical Society |

Sector | Academic/University |

Country | United Kingdom |

Start |

Description | PhD studentship: Waterjet Controlled-Depth (Milling) Machining of Aerospace Materials with Stratified Structures |

Amount | £60,000 (GBP) |

Organisation | Rolls Royce Group Plc |

Sector | Private |

Country | United Kingdom |

Start |

Title | Matlab Programs |

Description | The algorithm used for the solution of the inverse problem has been implement using Matlab. The sotware contains the necessary information, so the scripts can be used by other reserachers of the group. |

Type Of Material | Computer model/algorithm |

Provided To Others? | No |

Impact | The developed programs can be used for other researchers in the group to solve the inverse problem and generated features for their own projects. All the information of the experimental tests has been saved as well. |

Description | Modelling of the inverse problem in fluid jet machining |

Organisation | OpTek Systems |

Country | United States |

Sector | Private |

PI Contribution | - Define the possible methods to address inverse problem in energy beam machining - Define the parameters that can be used to implement the strategies for the inverse problem in energy beam machining |

Collaborator Contribution | Describe the machines/systems (fluid jet, laser, ion beam) on which the inverse problem needs to be implemented |

Impact | As the collaboration/project has just started the outputs/outcomes are on progress |

Start Year | 2014 |

Description | Modelling of the inverse problem in fluid jet machining |

Organisation | Oxford Instruments Plasma Technology |

Country | United Kingdom |

Sector | Private |

PI Contribution | - Define the possible methods to address inverse problem in energy beam machining - Define the parameters that can be used to implement the strategies for the inverse problem in energy beam machining |

Collaborator Contribution | Describe the machines/systems (fluid jet, laser, ion beam) on which the inverse problem needs to be implemented |

Impact | As the collaboration/project has just started the outputs/outcomes are on progress |

Start Year | 2014 |

Description | Modelling of the inverse problem in fluid jet machining |

Organisation | Zeeko Ltd |

Country | United Kingdom |

Sector | Private |

PI Contribution | - Define the possible methods to address inverse problem in energy beam machining - Define the parameters that can be used to implement the strategies for the inverse problem in energy beam machining |

Collaborator Contribution | Describe the machines/systems (fluid jet, laser, ion beam) on which the inverse problem needs to be implemented |

Impact | As the collaboration/project has just started the outputs/outcomes are on progress |

Start Year | 2014 |

Title | EBsim |

Description | EBsim is a software that has been developed by our reserach group. It calculates the machined features under abrasive waterjet ablation and pulsed laser ablation based on the models developed in the STEEP euopean project. The solution of the inverse problem for both systems has been implmented in the software. |

Type Of Technology | Software |

Year Produced | 2017 |

Impact | This new option allows the user to obtain the optimum tarjectory of the beam leading to the desired target surface. The software generates the necessary files with the g-codes to be used in both machines. |

Description | CIRP sponsored DET 2016 conference, Nanjing, China: An integrative approach in modelling and simulation of energy beam machining to generate freeform surfaces |

Form Of Engagement Activity | A talk or presentation |

Part Of Official Scheme? | No |

Geographic Reach | International |

Primary Audience | Study participants or study members |

Results and Impact | The CIRP sponsored DET 2016 conference focuses on the employment of modern Information and Communication Technologies (ICT) for the modelling, The talk was about the modelling of energy beam processes in order to generate freeform surfaces. The first step of the process consists of the development of a good model of the process. Then the solution of the inverse problem obtained in this project is used to produce the freeform features. |

Year(s) Of Engagement Activity | 2014,2016 |

Description | Engagement with the Marie Curie Initial Training Network - STEEP - A Synergetic Training network on Energy Beam Processing: from modelling to industrial applications |

Form Of Engagement Activity | A talk or presentation |

Part Of Official Scheme? | No |

Geographic Reach | International |

Primary Audience | Participants in your research and patient groups |

Results and Impact | The STEEP project deals with the direct problem in energy beam machining. The EPSRC project deals with inverse problem. Hence, there is a great deal of idea sharing since the inverse problem cannot the solved unless the direct problem is known - Acceleration of understanding of the problems to be solved in the inverse problem in energy beam machining by the Research Fellow - Liaise with manufacturers of equipment for energy beam machining - Liaise with industry that uses energy beam machining for part manufacture |

Year(s) Of Engagement Activity | 2014 |

Description | Presentation at the CIRP General Assembly - Birmingham, 18-24 August 2019 |

Form Of Engagement Activity | A talk or presentation |

Part Of Official Scheme? | No |

Geographic Reach | International |

Primary Audience | Professional Practitioners |

Results and Impact | Title of the presentation: New models for time-dependent processes enable accurate generation of freeforms. The presentation was made to make both academics and industry specialists aware about the achievements of the project in terms of the applicability of the models for various time-dependent processes. A short demonstration has been done on the capability of the the developed software that we developed in the project. This presentation triggered interest to the topic by potential end-users. |

Year(s) Of Engagement Activity | 2019 |

URL | http://www.confercare.manchester.ac.uk/events/cirp2019/ |