Modelling Contact and Tribology

Two questions we are hoping Abaqus and iSight will helpus to solve:1. To what extent does a small error in surface profile lead to increased stressconcentration in a component?2. Can the surface geometry at the region of edge of bedding be optimised tominimise edge-effect high stresses?The answer to both of these questions is that despite agreat deal of effort by both Robert Jones and MarianMielke, this is still very much an open question.The figures to the right, show a schematic of two typesof 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 thatwould 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 optimisationscheme was defined (see the figures below). The greycontacting block from the first figure was modified tohave rounded corners, where the precise surface pro-file is defined by a spline through a set of points. Thelocation of the individual points is then the subject foran optimisation study using iSight, with the objectivefunction to minimise the peak pressure.Unfortunately the problem is a little more tricky to solve in a consistent way. Although theproblem is simply posed, formulating a robust Abaqus model, that has a good mesh for contactanalysis, and which remains a good mesh despite significant random reshaping of the corner

region has not been so straightforward. The figures to the leftshow a geometry partitioningscheme, which includes a numberof “fixed” points, and two “free”points. The free points have a rea-sonable domain of freedom, whilethe mesh topology remains robust.

The two figures below show FEA results for pressure: the bottom edge indicates the contactpressure. 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 Simplexmethod). 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 movablepoints were heavilyconstrained in orderto preserve consistentmeshing. Improvedmesh control meth-ods would be neededto drive to a evenmore optimal design.

Tribology in the manufacture of high precision opticsThe Glyndwr OpTIC team has successfully developed a process chain for themanufacture of 1.4 m, off-axis aspheric, hexagonal mirror segments, asprototypes 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-groundaspheric on the Cranfield “BoX” CNC grinding machine. Three such segments have beenbonnet-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 factoron hard tooling is the aspheric mis-fit between tool andthe asphere of the optical surface, which can introducenew mid spatial frequency artefacts.Between each polishing iteration, the surface profile ismeasured to high precision: the metrology system usedis the only metrolo-gy system certifiedby the EuropeanSouthern Observa-tory as compliantwith requirementsof the E-ELT proto-type segment speci-fication.The Abaqus and

iSight modelling and optimisation work undertaken tounderstand the influence of surface profile and surface

error on con-tact pressuredistributionwill informthis work. In-creased local-ised contactpressure under the polishing head is thought toincrease the material removal rate, but predictivecontrol of the amount of material removed is es-sential to reduce the number of iterations requiredto reach the prescribed specification. Initial inves-

tigation reveals that the elastic compliance of the material of the head makes very littledifference 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 CNCgrinding and CNC polishing, to improve the inputquality to the Zeeko machine, particularly in termsof mid spatial content that is slow to remove inpolishing. In this case, tool mis-fit is again thelimiting factor, but is ameliorated by the larger sizesof abrasives that may be used, as these can help to'fill the gaps' created by the mis-fit. Therefore,characterising and understanding the geometry ofthe mis-fit, and the contact dynamics, is fundamen-tal to optimising process parameters.

a.mcmillan@glyndwr.ac.ukMini Biography: Alison McMillan studied Maths and Physics BSc at University College London andMechanical 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 atthe University of Oxford and Keele University she moved into industry, working almost 15 years atRolls-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 theUniversity of Bristol. Alison left Rolls-Royce plc in October 2011, and is currently Professor inAerospace Technology at Glyndwr University.

Contact mechanics and precision componentsContact 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 edgeof 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 Jones⁵1 Professor in Aerospace Technology, Glyndwr University2 Professor of Optics, Glyndwr University; Professorial Research Associate, University College London3 Professor of Metrology, Glyndwr University4 Final Year student, Engineering Programme, Glyndwr University5 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.