Mathematical Model for Evaluating Roundness Errors by Maximum Inscribed Circle Method

Abstract:

An unconstrained optimization model is established for assessing roundness errors by the maximum inscribed circle method based on radial deviation measurement. The properties of the objective function in the optimization model are thoroughly researched. On the basis of the modern theory on convex functions, it is strictly proved that the objective function is a continuous and non-differentiable and convex function defined on the two-dimensional Euclidean space. The minimal value of the objective function is unique and any of its minimal point must be its global minimal point. Any existing optimization algorithm, so long as it is convergent, can be used to solve the objective function in order to get the wanted roundness errors by the maximum inscribed circle assessment. One example is given to verify the theoretical results presented.

• Periodical: Advanced Materials Research (Volumes 314-316)
• Pages: 393-396
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.314-316.393
• Online since: August 2011
• Authors: Ping Liu, Hui Yi Miao
• Keywords: Convex Function, Form Error, Maximum Inscribed Circle, Objective Function, Optimization, Roundness

References

[1] Y. J. Fan and Z. X. Zhao: Chinese Journal of Mechanical Engineering, Vol. 30 (1994) No.2, p.19 (In Chinese).

[2] Z. He and J. W. Liang: Chinese Journal of Metrology, Vol. 17 (1996) No.3, p.219 (In Chinese).

[3] U. Roy and X. Zhang: Computer-Aided Design, Vol. 24 (1992) No.3, p.161

[4] S. T. Huang, K. C. Fan and J. H. Wu: Precision Engineering, Vol. 15 (1993) No.3, p.158

[5] P. Liu: Chinese Journal of Scientific Instrument, Vol. 10 (1989) No.4, p.422 (In Chinese).

[6] S. H. Cheraghi, H. S. Lim and S. Motavalli: Precision Engineering, Vol. 18 (1996) No.1, p.30

[7] J. B. Gao, Y. X. Chu and Z. X. Li: Precision Engineering, Vol. 23 (1999) No.2, p.79

[8] J. Huang: Precision Engineering, Vol. 25 (2001) No.7, p.301

[9] L. M. Zhu, H. Ding and Y. L. Xiong: Computer-Aided Design, Vol. 35 (2003) No.5, p.255

[10] P. Liu: Chinese Journal of Metrology, Vol. 24 (2003) No.2, p.85 (In Chinese).

[11] P. Liu and S. Y. Liu: Applied Mechanics and Materials, Vols. 16-19 (2009), p.1164

[12] P. Liu and H. Y. Miao: Applied Mechanics and Materials, Vols. 37-38 (2010), p.1214

[13] M. Avriel: Nonlinear Programming: Analysis and Methods (Dover Publications, Inc., USA 2003).