This fellowship will create a academic team to lead a new research theme dedicated to manufacturing the future. It focuses research on geometrical product specification and verification (GPS) systems to control geometrical variability in manufactured products that facilitate emerging industrial requirements in 21st century. For example, geometrical products used in: next generation freeform optics, interfaces in fluid-dynamics (energy-efficient jet engines, aircraft fuselages and wings), long life human-joint implants, microelectronics and MEMS/NEMS devices in nanotechnology applications. The UK frontier industry is seeking next generation of products having much higher functional capabilities with much lower manufacturing costs. This is driving manufactured products to have more integrated properties but more complex geometries. Without the tools to specify, optimise and verify the allowable geometrical variability, the ability to manufacture complex geometries is not possible.
This Fellowship is to explore the mathematical fundaments for the decomposition of geometry (i.e. size, shape and texture) and create ground-breaking technology to control geometrical variability in manufactured products. The novel approach is to link fundamental geometrical mathematics direct to key component's design, manufacturing and verification from different industrial sectors (i.e. aerospace, optics, healthcare and catapult centre). In this case, the different types of geometrical decompositions (at the ultimate causation level via information content) to specified geometrical surface requirements (spectrum, morphological and segmentation decompositions). This fellowship attempts to establish this emerging new theme that has never happened before, that requires sophisticated industrial manufacturing skills with in depth fundamental academic knowledge.
In practice no surface is manufactured perfectly: there is always some variability in the surface. Tolerance zones only control the size of this variability and not its shape. The approach proposed for the Fellowship is to break up (decompose) the surface variability, for each of the symmetry classes, to enable the shape to be controlled. The challenge is to produce a complete range of geometrical decompositions (together with the associated theory and practical algorithms) that will solve the mathematical grand challenge. For example contact (mechanical, electrical, thermal, etc.) requires the surface envelope to be decomposed. Other functions require decomposition into surface features ('hills and dales') at different scales. This system aims to provide the necessary mathematical foundations for a toolbox of techniques to characterise geometric variability: going far beyond simple tolerance zones as currently defined in national and international standards.
The eight letters of support from different sectors: Rolls-Royce, NPL (Engineering Measurement), NPL (Mathematics and Modeling), Taylor Hobson, British Standards Institute, Catapult - Advanced Manufacturing Research Centre, UCL (Institute of Orthopaedics and Musculoskeletal Science: Royal National Orthopaedic Hospital), Prifysgol Glyndwr (OPTIC) all highlight that there is an urgent need for the proposed technology from a point of view of wide UK industry.