Paper Title:
Some Properties of Mathematical Model for Cylindricity Errors
  Abstract

An unconstrained optimization model, applicable to radial deviation measurement, is established for assessing cylindricity errors by the minimum circumscribed cylinder evaluation. The properties of the objective function in the optimization model are thoroughly investigated. On the basis of the modern theory of convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the four-dimensional Euclidean space R4. Therefore, the minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Thus, any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function to get the wanted values of cylindricity errors by the minimum circumscribed cylinder assessment. An example is given to verify the theoretical results presented.

  Info
Periodical
Edited by
Yi-Min Deng, Aibing Yu, Weihua Li and Di Zheng
Pages
1214-1218
DOI
10.4028/www.scientific.net/AMM.37-38.1214
Citation
P. Liu, H. Y. Miao, "Some Properties of Mathematical Model for Cylindricity Errors", Applied Mechanics and Materials, Vols. 37-38, pp. 1214-1218, 2010
Online since
November 2010
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Price
$32.00
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