Dr Ed Brambley, UKRI Fellowship
Applied Mathematical Modelling of Industrial Metal Formings
Metal forming is the shaping of metal. Examples from manufacturing include rolling metal to create thin sheets and stamping flat sheets of metal to form car body panels.
There is a current industrial need for smarter metal forming in order to create new products, reduce scrap, compensate for more variable materials (e.g. recycled metals), reduce costs, and reduce energy usage.
State of the Art
In the 21st century, one might expect real-time computer control of metal forming processes, which would monitor the metal workpiece during the forming process and adapt the process to correct any problems and consistently obtain the desired end result.
However, the computer controller needs a theoretical model to predict what would happen if it were to make a change. This would help determine the right changes to make. Yet such theoretical models are not currently available. Computer simulations (using finite elements, for example) are much too slow for use in real-time.
Currently, computer finite element simulations are used during process development or to diagnose problems, and then to use simple controllers (such as PID controllers) to blindly follow the pre-prescribed forming procedure.
Clearly, new modelling techniques could be expected to give a substantial improvement.
There is a need for smarter metal forming to create new products, and reduce scrap, costs and energy use. Pictured: Coils of rolled magnesium sheets and magnesium ingots.
How would you teach a robot to do this?
Mathematical modelling in continuum solid mechanics and plasticity
The ambitious aim of Dr Ed Brambley's Fellowship is to investigate techniques for mathematical modelling in continuum solid mechanics and plasticity, the outcome of which could be used to provide predictive theoretical models for industrial metal forming.
Unlike existing computer simulations (such as finite elements) which work in all situations but which are slow, the aim here is to take advantage of properties of particular metal forming processes (such as symmetry, or small parameters such as thin sheets and small deformations), and create bespoke simplified models for each of these processes.
Both Sufficiently Fast and Sufficiently Accurate
By accounting for these properties in a rigorous way, and using best practice mathematical techniques (such as asymptotics and stability theory), quick-to-compute models with a guaranteeable accuracy could be produced. Such models would be eminently suitable for use in online control of the metal forming process. The research aims to work out how to do this in specific detail, and to produce a number of industrially relevant examples.
There are a number of related areas which will not be directly worked on during the project, but which will help inform and guide the research. These include research into atomic scale modelling of metals and alloys, and research into the correctness of the governing equations of plastic continuum mechanics (a branch of pure mathematical analysis).
Dr Brambley and his team will take the governing equations that are accepted and used in finite element computations of industrial metal forming, and rather than solve them on a computer, will investigate the theoretical development of modelling techniques and simplified models based on these equations.
It is hoped the results of this project will be a number of techniques for creating bespoke mathematical models of particular metal forming processes, together with a few such models specific to a particular metal forming process of industrial relevance. These few models will be validated against either numerical results or practical experiments. The project will also result in a skilled team of researchers and a validated body of new applied mathematical knowledge, giving industry the confidence to partner with the University of Warwick and invest in subsequent projects applying this knowledge in industrial practice.