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    Towards the analytic characterization of micro and nano surface features using the Biharmonic equation

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    Publication date
    2011
    Author
    Gonzalez Castro, Gabriela
    Spares, Robert
    Ugail, Hassan
    Whiteside, Benjamin R.
    Sweeney, John
    Keyword
    Surface profiling
    Biharmonic equation
    Micromoulding
    Rights
    (c) 2011 Elsevier Inc. Reproduced in accordance with the publisher's self-archiving policy.
    Peer-Reviewed
    yes
    
    Metadata
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    Abstract
    The prevalence of micromoulded components has steadily increased over recent years. The production of such components is extremely sensitive to a number of variables that may potentially lead to significant changes in the surface geometry, often regarded as a crucial determinant of the product¿s functionality and quality. So far, traditional large-scale quality assessment techniques have been used in micromoulding. However, these techniques are not entirely suitable for small scales . Techniques such as Atomic Force Mi- croscopy (AFM) or White Light Interferometry (WLI) have been used for obtaining full three-dimensional profiles of micromoulded components, pro- ducing large data sets that are very difficult to manage. This work presents a method of characterizing surface features of micro and nano scale based on the use of the Biharmonic equation as means of describing surface profiles whilst guaranteeing tangential (C1) continuity. Thus, the problem of rep- resenting surface features of micromoulded components from massive point clouds is transformed into a boundary-value problem, reducing the amount of data required to describe any given surface feature.The boundary conditions needed for finding a particular solution to the Biharmonic equation are extracted from the data set and the coefficients associated with a suitable analytic solution are used to describe key design parameters or geometric properties of a surface feature. Moreover, the expressions found for describ- ing key design parameters in terms of the analytic solution to the Biharmonic equation may lead to a more suitable quality assessment technique for mi- cromoulding than the criteria currently used. In summary this technique provides a means for compressing point clouds representing surface features whilst providing an analytic description of such features. The work is applicable to many other instances where surface topography is in need of efficient representation.
    URI
    http://hdl.handle.net/10454/4979
    Version
    Accepted Manuscript
    Citation
    Gonzalez Castro G., Spares R., Ugail H., Whiteside B.R. and Sweeney J. (2011). Towards the analytic characterization of micro and nano surface features using the Biharmonic equation. Journal of Applied Mathematical Modelling, in press.
    Link to publisher’s version
    http://dx.doi.org/10.1016/j.apm.2011.07.049
    Type
    Article
    Collections
    Engineering and Informatics Publications

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