Skip to main content
SpringerLink
Log in

Measurement and Evaluation of the Ellipsoid Deviation in Cartesian Coordinates

  • Regular Paper
  • Published:
International Journal of Precision Engineering and Manufacturing Aims and scope Submit manuscript

Abstract

Ellipsoid part is now increasingly applied to the product manufacturing, while the high-quality ellipsoid part depends not only on the manufacturing and machining techniques, but also on the adopted measurement and evaluation approaches. Based on the typical quadratic surface, an evaluation method of the least squares ellipsoid deviation is proposed in this paper to quantify the form deviation of measured ellipsoid. The method can overcome the weakness of the low measurement adaptability compared with other evaluation methods. With obtaining the coefficients of surface equation to replace the linear superposing of the coordinates of measured points, the measurement error existing in the coordinates of measured points is homogenized and reduced effectively, which prompts to obtain the accurate measurement result. Finally, the results from experimental verifications show that the proposed method is effective for the measurement and evaluation of the ellipsoid deviation in Cartesian coordinates, and the adaptability is also a significant advantage in the measurement and evaluation of geometry deviation.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data Availability Statement

Dataset 1: The data that support the findings of this study are openly available in the literature [5]. Dataset 2: The data that support the findings of this study are openly available in the literature [13].

References

  1. Shi, Z., Zhang, H., Tang, J., et al. (2014). On the anisotropy of surface measurement. Journal of Mechanical Engineering, 50(18), 1–6.

    Article  Google Scholar 

  2. BS EN ISO 1101. (2013). Geometrical product specifications (GPS). UK: The Standards Policy and Strategy Committee.

  3. ISO 17450-1. (2011). Geometrical product specifications (GPS)-General concepts—Part 1: Model for geometrical specification and verification. Switzerland: International Standardization Organization.

  4. ISO 17450-2. (2012). Geometrical product specifications (GPS)-General concepts—Part 2: Basic tenets, specifications, operators, uncertainties and ambiguities. Switzerland: International Standardization Organization.

  5. Liao, P. (2009). Calculation of elliptic sphere form error based on genetic algorithm. Chinese Journal of Scientific Instrument, 30, 780–785. (in Chinese).

    Google Scholar 

  6. Zhang, L., Zhang, Z., Zhang, Z., et al. (2015). Calcuiation of elliptic sphere profile error using the combination of the DGA and the PSO algorithm. Acta Metrologica Sinica, 36(6), 584–587. (in Chinese).

    MathSciNet  Google Scholar 

  7. Forbes, A. B., Lam, J., & Tomlins, P. (2009). Capturing local and anisotropic behaviour in surface topography. Wear, 266, 527–529.

    Article  Google Scholar 

  8. Liu, F., Xu, G., Liang, L., et al. (2016). Least squares evaluations for form and profile errors of ellipse using coordinate data. Chinese Journal of Mechanical Engineering, 29(5), 1020–1028.

    Article  Google Scholar 

  9. Kanatani, K., & Rangarajan, P. (2011). Hyper least squares fitting of circles and ellipses. Computational Statistics & Data Analysis, 55, 2197–2208.

    Article  MathSciNet  Google Scholar 

  10. Ahn, S. J., Rauh, W., & Warnecke, H. J. (2001). Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola. Pattern Recognition Letters, 34, 2283–2303.

    Article  Google Scholar 

  11. Chaudhuri, D. (2010). A simple least squares method for fitting of ellipses and circles depends on border points of a two-tone image and their 3-D extensions. Pattern Recognition Letters, 31, 818–829.

    Article  Google Scholar 

  12. Lei, X., Gao, Z., Cui, J., et al. (2015). The minimum zone evaluation for elliptical profile error based on the geometry optimal approximation algorithm. Measurement, 75, 284–288.

    Article  Google Scholar 

  13. Tu, X., Lei, X., Wang, S., et al. (2015). The minimum zone method of fitting and error evaluation for ellipsoidal surface located at arbitrary position in space. Machinery Design and Manufacture, 8, 262–266. (in Chinese).

    Google Scholar 

  14. Liu, F., Xu, G., Liu, D., et al. (2017). Sampling strategy and error estimation for evaluation of quadratic form error using cartesian coordinate data. IET Science, Measurement and Technology, 11, 839–846.

    Article  Google Scholar 

  15. ASME Y 14.5 M. (1995). Dimensioning and Tolerancing. New York: The American Society of Manufacturing Engineers.

  16. DD CEN ISO/TS12181-1:2007. (2008). Geometrical product specifications (GPS)—Roundness—Part 1: Vocabulary and parameters of roundness. UK: The Standards Policy and Strategy Committee.

  17. DD CEN ISO/TS12181-2:2007. (2008). Geometrical product specifications (GPS)—Roundness—Part 2: Specification operators. UK: The Standards Policy and Strategy Committee.

  18. Li, X., & Shi, Z. (2010). Evaluation of roundness error from coordinate data using curvature technique. Measurement, 43(2), 164–168.

    Article  MathSciNet  Google Scholar 

  19. Fei, Y. (2010). Error theory and data processing (2nd ed.). Beijing: China Machine Press.

    Google Scholar 

Download references

Acknowledgements

This research is supported by the National Natural Science Foundation of China (Grant 51775423), the National Key Research and Development Program of China (Grant 2018YFB2000202), the China Postdoctoral Science Foundation (Grants 2017M623159 and 2018T111046), the Postdoctoral Science Foundation of Shaanxi Province (Grant 2017BSHEDZZ68), the Fundamental Research Funds for the Xi’an Jiaotong University (Grant XJJ2018047).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Xi’an Jiaotong Uni versity, No. 28, Xianning West Road, Xi’an, 710049, Shaanxi, People’s Republic of China

    Fei Liu, Lin Liang, Guanghua Xu, Chenggang Hou & Dan Liu

  2. State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, 710054, People’s Republic of China

    Guanghua Xu

  3. Key Laboratory of Education Ministry for Modern Design and Rotor-Bearing System, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Lin Liang, Chenggang Hou & Dan Liu

Authors
  1. Fei Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Lin Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guanghua Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chenggang Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Dan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fei Liu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

See Tables 1 and 2.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, F., Liang, L., Xu, G. et al. Measurement and Evaluation of the Ellipsoid Deviation in Cartesian Coordinates. Int. J. Precis. Eng. Manuf. 21, 2077–2088 (2020). https://doi.org/10.1007/s12541-020-00408-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12541-020-00408-7

Keywords

Search

Navigation