Skip to main content
Log in

Evaluation of cylindricity using combinatorics

  • Published:
IIE Transactions

Abstract

Several numerical methods have been developed for finding the minimum zone of a cylinder. This paper presents a combinatorial method termed the Minimum Shell for cylindricity evaluation. For a given set of measured data points, the method efficiently searches for the six points that determine the minimum zone of cylindricity. This method is self-contained, without the requirement of mathematical programming software support, and is equal to or superior to other methods of evaluating cylindricity in terms of accuracy, efficiency, and simplicity. Computational results are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Waldele, F., Bittner, B., Busch, K., Drieschner, R. and Elligsen, R. (1993) Metrology standards news. Precision Engineering, 15, 121–123.

    Google Scholar 

  2. Anon (1994) American National Standards Institute: Dimensioning and Tolerancing for Engineering Drawings, ANSI Standard Y14.5M, ASME, New York.

  3. Anon (1994) American National Standards Institute: Mathematical Definition of Dimensioning and Tolerancing Principles, ANSI Standard Y14.5.1M, ASME, New York.

  4. Whitehouse, D.J. (1994) Handbook of Surface Metrology, Institute of Physics Publishing, London.

    Google Scholar 

  5. Anon (1972) American National Standards Institute: Measurement of Out-of-Roundness, ANSI Standard B89.3.1, ASME, New York.

  6. Carr, K. and Ferreira, P. (1995) Verification of form tolerances, part II: cylindricity and straightness of a median line. Precision Engineering, 17, 144–156.

    Google Scholar 

  7. Foster, L.W. (1994) Geometrics III, Addison-Wesley Publishing, New York, NY.

    Google Scholar 

  8. Shunmugam, M.S. (1986) On assessment of geometric errors. International Journal of Production Research, 24, 413–425.

    Google Scholar 

  9. Goto, M. and Iizuka, K. (1997) An analysis of the relation between the minimum zone deviation and the least squares deviation in circularity and cylindricity, in Proceedings of the ICPE-1997, New Delhi, India.

    Google Scholar 

  10. Murthy, T.S.R. (1982) A comparison of di.erent algorithms for cylindricity evaluation. International Journal of Machine Tool Design and Research, 22, 283–292.

    Google Scholar 

  11. Murthy, T.S.R. and Abdin, S.Z. (1980) Minimum zone evaluation of surfaces. International Journal of Machine Tool Design and Research, 20, 123–136.

    Google Scholar 

  12. Nelder, J.A. and Mead, R. (1965) A simplex method for function minimization. Journal of Computers, 7, 308–313.

    Google Scholar 

  13. Tsukada, T. and Kanada, T. (1985) Minimum zone evaluation of cylindricity deviation by some optimization techniques. Bulletin of the Japanese Society of Precision Engineering, 19, 18–23.

    Google Scholar 

  14. Tang, S.Y.(1995) Minimum zone methods for evaluating standard form tolerances in engineering metrology. Masters' thesis, Industrial Engineering Dept., North Carolina State University, Raleigh, NC 27695–7906.

    Google Scholar 

  15. Houle, M. E. and Toussaint, G.T. (1988) Computing the width of a set. IEEE Transactions on Pattern Analysis and Machine Intelligence, 10, 761–765.

    Google Scholar 

  16. Roy, U. and Zhang, X. (1992) Establishment of a pair of concentric circles with the minimum radial separation for assessing roundness error. Computer-Aided Design, 24, 161- 168.

    Google Scholar 

  17. Roy, U. (1993) Computational methodologies for computer aided inspection, in Proceedings of the 2nd Industrial Engineering Research Conference, Los Angeles, CA, pp. 466–470.

  18. Anthony, G.T. et al. (1993) Chebyshev best-fit geometric elements. NPL Report DITC 221/93.

  19. Anthony, G.T., Anthony, H.M. and Kok, J. (1996) Reference software for finding Chebyshev best-fit geometric elements. Precision Engineering, 19, 28–36.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hodgson, T.J., Kay, M.G., Mittal, R.O. et al. Evaluation of cylindricity using combinatorics. IIE Transactions 31, 39–47 (1999). https://doi.org/10.1023/A:1007572617551

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1007572617551

Keywords

Navigation