# 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.

### Organisations

- University of Nottingham, United Kingdom (Lead Research Organisation)
- OpTek Systems, United Kingdom (Collaboration, Project Partner)
- Zeeko Ltd, United Kingdom (Collaboration, Project Partner)
- Oxford Instruments Plasma Tech nology (Collaboration)
- Oxford Instruments plc, United Kingdom (Project Partner)

### 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 proposed technique can be used to generate freeform 3D features using the three energy beam processes described in the project. There are many optimization methods that could be used to achieve a similar solution. However, the large computational time is a problem in most optimization problems and the algorithm developed in this project has been found to achieve a good solution faster than most of them. Moreover, we have fully control of the movement of the beam/Jet. This can be done because we managed to compensate the dynamics of the machine. This means that the feed speed of the beam can be contolled at each moment and complex movements (non-straight lines) can be performed. That was one of the main limitation in previous studies. This leads to better results and the possibility of etching any kind of 3D freeform surface. For example, a 3d surface can be generated from any 2d picture. We managed to etch the shape of the logo of the university or 1 penny coin on graphite using Pulsed Laser Ablation. The size of the etched surfaces is relatively small compared to the size of the beam. The area of smallest one using Laser Ablation is around 0.5-1 mm^2. The developed solution has also been applied for the generation of freeform features using focused on silicon under focused ion beam. The area of the etched surfaces are around 10-20 mum^2. The average tracking errors of the machined features are between 2-10%. |

Exploitation Route | The optimization technique for the inverse problem will be included in a computer program that simulates the behaviour of any energy beam process. The program is being developed in the research group by other researches. There are also industrial problems that require the removal of a concrete amount of material or a particular shape. For example, the removal of the coating of a blade in a motor. The main problem in these cases consists of finding the correct parameters to be used to achieve the desired removal of material at each position. This problem can be solved by using our findings. |

Sectors | Manufacturing, including Industrial Biotechology |

Description | During the last year the developed soution of the inverse problem has been implemented to Focused ion beam (FIB) as well. This is the last year of the project and the inverse problem has been succesfully solved for the energy beam systems (Abrasive Waterjet Machining, Pulsed Laser Ablation and Focused Ion beam). Single trneches and Freeform surfaces can been etched using the optimization technique and the results have been found to improve the previous ones in this area. We managed to have control of the movement of the beam and perform non-straight passes with the beam. Moreover, the feed speed of the beam can be controlled during the whole process. Good experimental results have been obtained. Now the research group is developing a software to simulate the behavior of energy beam processes. The inverse problem optimization technique will be included in this software. This means that the user of this software could define any particular shape and then the program will be able to calculate a solution to the inverse problem. Finally a CNC file will be generated to be loaded in the machine with the movement of the beam. A paper is under review now with the results for Abrasive Waterjet Machining and Pulsed Laser Ablation. Another paper is under preparation with the results for Focused Ion Beam. The research for FIB has been done collaborating with the Fraunhofer Institute for Integrated Systems and Device Technology in Germany. |

Sector | Manufacturing, including Industrial Biotechology |

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 |

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 |