Advertisement

A Registration Method for Profile Error Inspection of Complex Surface Under Minimum Zone Criterion

  • Gaoshan TanEmail author
  • Liyan Zhang
  • Shenglan Liu
Regular Paper
  • 13 Downloads

Abstract

Although registration of the measured model and the design model has been widely studied, it remains an open problem in complex surface profile error inspection. False rejection of some qualified parts is prone to occur due to the improper registration between the measured points and the nominal model. To solve this problem, we define a surface profile error metric in terms of a new range norm under minimum zone criterion. An optimal framework based on the range norm is proposed to find the registration pose of the measurement data set, in which the surface profile error is minimized. To deal with the computational intractability, the non-differentiable merit function is uniformly approximated by a smooth aggregation function, which can be effectively solved with the limited-memory Quasi-Newton method. Distinct numerical stability control and the active set selection mechanism are proposed to guarantee the accuracy and efficiency of the method. Experiments on a simulated and a real part are included to verify the superiority of the proposed method.

Keywords

Surfaces inspection Profile error Registration Minimum zone criterion Aggregation function Norm 

Notes

Acknowledgements

This work was supported by Natural Science Foundation of China (Grant No. 51575276).

References

  1. 1.
    ISO 17450-1. (2011). Geometrical Product Specifications (GPS)—General Concepts—Part 1: Model for Geometrical Specification and Verification.Google Scholar
  2. 2.
    Moona, D., Chunga, S., Kwonb, S., Seoc, J., & Shina, J. (2019). Comparison and utilization of point cloud generated from photogrammetry and laser scanning: 3D world model for smart heavy equipment planning. Automation in Construction, 98, 322–331.CrossRefGoogle Scholar
  3. 3.
    Jang, W., Je, C., Seo, Y., & Lee, S. W. (2013). Structured-light stereo: Comparative analysis and integration of structured-light and active stereo for measuring dynamic shape. Optics and Lasers in Engineering, 51, 1255–1264.CrossRefGoogle Scholar
  4. 4.
    Ahmed, M. N., Mohib, A. M. N., & Elmaraghy, H. A. (2010). Tolerance-based localization algorithm: form tolerance verification application. International Journal of Advanced Manufacturing Technology, 47, 581–595.CrossRefGoogle Scholar
  5. 5.
    Besl, P. J., & McKay, N. D. (1999). A method for registration of 3-D shapes. IEEE Transactions on PAMI, 14(2), 239–256.CrossRefGoogle Scholar
  6. 6.
    Peng, W., Ji, W. X., Chen, W. L., & Shao, K. (2018). Rigid surface matching by analysis and correspondences. International Journal of Precision Engineering and Manufacturing, 19(9), 1360–1376.Google Scholar
  7. 7.
    Wen, X. L., Zhao, Y. B., Wang, D. X., Zhu, X. C., & Xue, X. Q. (2013). Accurate evaluation of free-form surface profile error based on Quasi Particle Swarm Optimization algorithm and surface subdivision. Chinese Journal of Mechanical Engineering, 26(2), 406–413.CrossRefGoogle Scholar
  8. 8.
    Tan, G. S., Zhang, L. Y., Liu, S. L., & Zhang, W. Z. (2015). A fast and differentiated localization method for complex surfaces inspection. International Journal of Precision Engineering and Manufacturing, 16(13), 2631–2639.CrossRefGoogle Scholar
  9. 9.
    Byun, S., Jung, K., Im, S., & Chang, M. (2017). Registration of 3D scan data using inage reprojection. International Journal of Precision Engineering and Manufacturing, 18(9), 1221–1229.CrossRefGoogle Scholar
  10. 10.
    International Organization for Standardization, Geneva, Switzerland. (2004). ISO 1101: Geometrical Product Specifications (GPS)—tolerances of form, orientation, location and run out, 2nd edn.Google Scholar
  11. 11.
    International Standard Organization. (2007). ISO/TS 17450-1-2007, Geometrical product specifications (GPS)-General concepts—Part 1: Model for geometrical specification and verification, Switzerland: ISO Copyright Office.Google Scholar
  12. 12.
    ISO 25178-2. (2012). Geometrical product specifications-surface texture: Areal part 2: Definitions and surface texture parameters.Google Scholar
  13. 13.
    Roque, C., Emilio, G., & Rosario, D. (2014). Vectorial method of minimum zone tolerance for flatness, straightness, and their uncertainty estimation. International journal of precision engineering and manufacturing, 15(1), 31–44.CrossRefGoogle Scholar
  14. 14.
    Samuel, G. L., & Shunmugam, M. S. (1999). Evaluation of straightness and flatness error suing computational geometric techniques. Computer Aided Design, 31(13), 829–843.CrossRefzbMATHGoogle Scholar
  15. 15.
    Kim, W. J., Shimizu, Y., Kimura, A., & Gao, W. (2012). Fast evaluation of period deviation and flatness of a linear scale by using a fizeau interferometer. International journal of precision engineering and manufacturing, 13(9), 1517–1524.CrossRefGoogle Scholar
  16. 16.
    Roy, U., & Zhang, X. (1992). Establishment of a pair of concentric circles with the minimum radial separation for assessing roundness error. Computer Aided Design, 24(3), 161–168.CrossRefzbMATHGoogle Scholar
  17. 17.
    Zhang, X. C., Jiang, X., & Scott, P. J. (2011). A reliable method of minimum zone evaluation of cylindricity and conicity from coordinate measurement data. Precision Engineering, 35(3), 484–489.CrossRefGoogle Scholar
  18. 18.
    Kanada, T. (1995). Evaluation of spherical for errors: computation of sphericity by means of minimum zone method and some examination with using simulated data. Precision Engineering, 17(4), 281–289.CrossRefGoogle Scholar
  19. 19.
    Novaski, O., & Barczak, A. L. C. (1997). Utilization of voronoi diagrams for circularity algorithms. Precision Engeering, 20(3), 188–195.CrossRefGoogle Scholar
  20. 20.
    Zhang, X. C., Xu, M., Zhang, H., He, X., & Jiang, X. (2013). Chebyshev fitting of complex surfaces for precision metrology. Measurement, 46, 3720–3724.CrossRefGoogle Scholar
  21. 21.
    Zhang, X. C., Zhang, H., He, X., & Xu, M. (2015). Fast evaluation of minimum zone form errors of freeform NURBS surfaces. Procedia CIRP, 27, 23–28.CrossRefGoogle Scholar
  22. 22.
    Zhang, X., Xiao, H., Zhang, H., He, X., & Xu, M. (2016). Uncertainty estimation in form error evaluation of freeform surfaces for precision engineering. In Proceedings of SPIE (vol. 9903, p. 99031G).Google Scholar
  23. 23.
    Sun, Y. W., Wang, X. M., Guo, D. M., & Liu, J. (2009). Machining localization and quality evaluation of parts with sculptured surfaces using SQP method. The International Journal of Advanced Manufacturing Technology, 42, 1131–1139.CrossRefGoogle Scholar
  24. 24.
    Venkaiah, N., & Shunmugam, M. S. (2007). Evaluation of form data using computational geometric techniques-part II: Cylindricity error. International Journal of Machine Tools and Manufacture, 47(7-8), 1237–1245.CrossRefGoogle Scholar
  25. 25.
    Samuel, G. L., & Shunmugam, M. S. (2000). Evaluation of circularity from coordinate and form data using computational geometric techniques. Precision Engeering, 24(3), 251–263.CrossRefGoogle Scholar
  26. 26.
    Huang, J., & Lehtihet, E. A. (2001). Contribution to the minimax evaluation of circularity error. International Journal of Product Research, 39(16), 3813–3826.CrossRefzbMATHGoogle Scholar
  27. 27.
    Malyscheff, A. M., Trafalis, T. B., & Raman, S. (2002). From support vector machine learning to the determination of the minimum enclosing zone. Computer and Industrial Engineering, 42(1), 59–74.CrossRefGoogle Scholar
  28. 28.
    Timothy, W., Saeid, M., Behrooz, F., & Hossein, C. (2002). A unified approach to form error evaluation. Precision Engineering, 26, 269–278.CrossRefGoogle Scholar
  29. 29.
    Al-Subaihi, I., & Watson, G. A. (2005). Fitting parametric curves and surfaces by l distance regression. BIT Numerical Mathematics, 45(3), 443–461.MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Giovanni, M., & Stefano, P. (2008). Geometric tolerance evaluation: A discussion on minimum zone fitting algorithms. Precision Engineering, 32, 232–237.CrossRefGoogle Scholar
  31. 31.
    Wen, X., & Song, A. (2007). An immune evolutionary algorithm for sphericity error evaluation. International Journal of Machine Tools and Manufacture, 44(10), 1077–1084.CrossRefGoogle Scholar
  32. 32.
    Cui, C., Lia, T., Blunt, A., Jiang, X., Huang, H., Ye, R., & Fan, W. (2013). The assessment of straightness and flatness errors using particle swarm optimization. In 12th CIRP Conference on Computer Aided Tolerancing, Procedia CIRP 10 (pp. 271–275).Google Scholar
  33. 33.
    Chen, Y. F., Zhu, L. Q., Chen, Q. S., & Meng, H. (2010). Evaluation of the profile error of complex surface through particle swarm optimization. In International conference on advanced technology of design and manufacture (pp. 148–152).Google Scholar
  34. 34.
    Zhang, X. C., Jiang, X., & Scott, P. J. (2011). Minimum zone evaluation of the form errors of quadric surfaces. Precision Engineering, 35(23), 383–389.CrossRefGoogle Scholar
  35. 35.
    Zhang, K. (2008). Spatial straightness error evaluation with an ant colony algorithm. In Proceedings of the IEEE international conference on granular computing (GRC08), Piscataway: IEEE Press (pp. 793–796).Google Scholar
  36. 36.
    Liu, J., Wang, G. L., & Pan, X. D. (2011). Minimum-zone form tolerance evaluation for cylindrical surfaces using adaptive ant colony optimization. Journal of Computational Information Systems, 7(12), 4480–4490.Google Scholar
  37. 37.
    Luo, J., Wang, Q., & Fu, L. (2012). Application on modified artificial bee colony algorithm to flatness error evaluation. Optics and Precision Engineering, 20(2), 422–430.CrossRefGoogle Scholar
  38. 38.
    Li, S. X., & Fang, S. C. (1997). On the entropic regularization method for solving min-max problems with applications. Mathematical Methods of Operations Research, 46, 119–130.MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Bottou, L., Frank, E. C., & Nocedal, J. (2018). Optimization Methods for Large-Scale Machine Learning. SIAM Review, 60, 33–40.MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Tan, G. S., Zhang, L. Y., Liu, S. L., & Ye, N. (2014). An Unconstrained Approach to Blank Localization with Allowance Assurance for Machining Complex Parts. International Journal of Advanced Manufacturing Technology, 73, 647–658.CrossRefGoogle Scholar

Copyright information

© Korean Society for Precision Engineering 2019

Authors and Affiliations

  1. 1.Mathematics and Physics Engineering DepartmentAnhui University of TechnologyMaanshanChina
  2. 2.College of Mechanical and Electrical EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina

Personalised recommendations