Mathematical Model for Evaluating Cylindricity Errors by Maximum Inscribed Cylinder

Abstract:

An unconstrained optimization model applicable to radial deviation measurement is established for assessing cylindricity errors by the maximum inscribed cylinder evaluation. The properties of the objective function in the optimization model are thoroughly researched. 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 a subset of the four-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 to get the wanted values of cylindricity errors by the maximum inscribed cylinder assessment. An example is given to verify the theoretical results presented.

• Periodical: Key Engineering Materials (Volumes 474-476)
• Pages: 1418-1422
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.474-476.1418
• Online since: April 2011
• Authors: Ping Liu, Hui Yi Miao
• Keywords: Convex Function, Cylindricity, Form Error, Objective Function, Optimization

References

[1] Y. J. Fan and Z. X. Zhao: Chinese Journal of Mechanical Engineering, Vol. 30 (1994) No. 2, pp.19-24 (In Chinese).

[2] Z. He, J. W. Liang and X. Z. Liu: Journal of Tsinghua University, Vol. 29 (1989) No. 5, pp.54-58 (In Chinese).

[3] Z. He and J. W. Liang: Chinese Journal of Metrology, Vol. 17 (1996) No. 3, pp.219-221 (In Chinese).

[4] U. Roy and X. Zhang: Computer-Aided Design, Vol. 24 (1992) No. 3, pp.161-168.

[5] S. T. Huang, K. C. Fan and J. H. Wu: Precision Engineering, Vol. 15 (1993) No. 3, pp.158-165.

[6] P. Liu: Chinese Journal of Scientific Instrument, Vol. 10 (1989) No. 4, pp.422-428 (In Chinese).

[7] S. H. Cheraghi, H. S. Lim and S. Motavalli: Precision Engineering, Vol. 18 (1996) No. 1, pp.30-37.

[8] J. B. Gao, Y. X. Chu and Z. X. Li: Precision Engineering, Vol. 23 (1999) No. 2, pp.79-93.

[9] J. Huang: Precision Engineering, Vol. 25 (2001) No. 7, pp.301-308.

[10] L. M. Zhu, H. Ding and Y. L. Xiong: Computer-Aided Design, Vol. 35 (2003) No. 5, pp.255-265.

[11] P. Liu: Chinese Journal of Metrology, Vol. 24 (2003) No. 2, pp.85-87 (In Chinese).

[12] P. Liu and S. Y. Liu: Applied Mechanics and Materials, Vols. 16-19 (2009), pp.1164-1168.

[13] P. Liu and H. Y. Miao: Applied Mechanics and Materials, Vols. 37-38 (2010), pp.1214-1218.

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