Modelling Contact and Tribology Two questions we are hoping Abaqus and iSight will help us to solve: 1. To what extent does a small error in surface profile lead to increased stress concentration in a component? 2. Can the surface geometry at the region of edge of bedding be optimised to minimise edge-effect high stresses? The answer to both of these questions is that despite a great deal of effort by both Robert Jones and Marian Mielke, this is still very much an open question. The figures to the right, show a schematic of two types of contact, and give an indication of the contact pres- sure which would result from that contact. The ques- tion arises, is there a “perfect” surface geometry that would combine the pressure distribution of characteris- tics and yield an approximately constant contact pres- sure over the complete contact region? To answer that question, the following optimisation scheme was defined (see the figures below). The grey contacting block from the first figure was modified to have rounded corners, where the precise surface pro- file is defined by a spline through a set of points. The location of the individual points is then the subject for an optimisation study using iSight, with the objective function to minimise the peak pressure. Unfortunately the problem is a little more tricky to solve in a consistent way. Although the problem is simply posed, formulating a robust Abaqus model, that has a good mesh for contact analysis, and which remains a good mesh despite significant random reshaping of the corner region has not been so straight forward. The figures to the left show a geometry partitioning scheme, which includes a number of “fixed” points, and two “free” points. The free points have a rea- sonable domain of freedom, while the mesh topology remains robust. The two figures below show FEA results for pressure: the bottom edge indicates the contact pressure. The left hand figure shows the starting design, with the profile “optimised” by eye, and the right hand figure shows the result of optimisation using iSight (Down Hill Simplex method). Note that the pressure reduction was in part achieved by moving the edge of bedding. The optimum profile therefore depends on the applied contact force. The allowable posi- tions of the movable points were heavily constrained in order to preserve consistent meshing. Improved mesh control meth- ods would be needed to drive to a even more optimal design. Tribology in the manufacture of high precision optics The Glyndwr OpTIC team has successfully developed a process chain for the manufacture of 1.4 m, off-axis aspheric, hexagonal mirror segments, as prototypes for the forthcoming 39 m European Extremely Large Telescope (E-ELT). While this process chain achieves the surface quality standard re- quired, the process is slow and has the potential for significant optimisation. Uniquely, this process starts with hexagonal (rather than circular) parts, which are pre-ground aspheric on the Cranfield “BoX” CNC grinding machine. Three such segments have been bonnet-polished to the ESO specification on the 1.6m Zeeko machine at OpTIC. Surface- smoothing using hard tooling was deployed to achieve the challenging mid spatial frequency specification, that is, to control surface ripple amplitude. It has been found that the most significant limiting factor on hard tooling is the aspheric mis-fit between tool and the asphere of the optical surface, which can introduce new mid spatial frequency artefacts. Between each polishing iteration, the surface profile is measured to high precision: the metrology system used is the only metrolo- gy system certified by the European Southern Observa- tory as compliant with requirements of the E-ELT proto- type segment speci- fication. The Abaqus and iSight modelling and optimisation work undertaken to understand the influence of surface profile and surface error on con- tact pressure distribution will inform this work. In- creased local- ised contact pressure under the polishing head is thought to increase the material removal rate, but predictive control of the amount of material removed is es- sential to reduce the number of iterations required to reach the prescribed specification. Initial inves- tigation reveals that the elastic compliance of the material of the head makes very little difference to the contact pressure distribution, but its adaptive formability could be critical. The role of the polishing slurry as a hydrodynamic lubricant will also be investigated. In order to speed-up the overall process-chain, there is also a compelling case for interposing an additional smoothing process between CNC grinding and CNC polishing, to improve the input quality to the Zeeko machine, particularly in terms of mid spatial content that is slow to remove in polishing. In this case, tool mis-fit is again the limiting factor, but is ameliorated by the larger sizes of abrasives that may be used, as these can help to 'fill the gaps' created by the mis-fit. Therefore, characterising and understanding the geometry of the mis-fit, and the contact dynamics, is fundamen- tal to optimising process parameters. [email protected] Mini Biography: Alison McMillan studied Maths and Physics BSc at University College London and Mechanical Engineering MSc at Cranfield. Her PhD from Staffordshire University involved computa- tional modelling of vibration and impact of laminates. Following a series of post-doctoral positions at the University of Oxford and Keele University she moved into industry, working almost 15 years at Rolls-Royce plc in Derby, on the interface between new product introduction and capability acquisi- tion. Between 2007-2011 she held a Royal Society Industry Fellowship, based part-time at the University of Bristol. Alison left Rolls-Royce plc in October 2011, and is currently Professor in Aerospace Technology at Glyndwr University. Contact mechanics and precision components Contact mechanics is an important consideration in many engineering component applications; from blade roots, to bearings, and gear teeth and splines. Fretting fatigue at the sites of edge of bedding indicate that the design of the contacting surface, and control of that surface quality, is critical to performance. Invitation to collaborate Please contact me if you are interested in any of the aspects presented here. Alison McMillan¹, David Walker², Paul Rees³, Marian Mielke⁴ and Robert Jones⁵ 1 Professor in Aerospace Technology, Glyndwr University 2 Professor of Optics, Glyndwr University; Professorial Research Associate, University College London 3 Professor of Metrology, Glyndwr University 4 Final Year student, Engineering Programme, Glyndwr University 5 Recent MSc graduate, Engineering Programme, Glyndwr University We acknowledge the support of: National Facility for Ultra Precision Surfaces, OpTIC, STFC, EPSRC, Innovate UK, and the Welsh Government.