Skip to main content
SpringerLink
Log in

Weighted Multilateration in Volumetry of CNC Machine Tools

  • Conference paper
  • First Online:
Recent Advances in Soft Computing (MENDEL 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 837))

Included in the following conference series:

Abstract

Our research study describes utilization of a weighted multilateration principle in the multi axis machine error modeling. Multilateration plays on of the most important role in the identification of the exact position of the point in the machine tool work space. Using laser tracer, the measured data were obtained in spherical coordinates. The multilateration attempts to improve data accuracy using only a radial component. Each of measurements has a different quality of the laserTRACER signal. According to this information, three ways of the weight assignment are presented. The weight of each value of the measurement distance was given as a ration of each signal quality to: the best signal quality that was obtained during the measurement; the sum of all signal quality for each position of the measuring device; the norm of vector of total signal quality for each position of the measuring device. All of our results were compared with the data that were obtained by the original software TRAC-CAL.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ramesh, R., Mannan, M.A., Poo, A.N.: Error compensation in machine tools - a review: part I: geometric, cutting-force induced and fixture-dependent errors. Int. J. Mach. Tools Manuf. 40(9), 1235–1256 (2000). https://doi.org/10.1016/S0890-6955(00)00009-2

    Article  Google Scholar 

  2. Hrdina, J., Vašík, P.: Dual numbers approach in multiaxis machines error modeling. J. Appl. Math. 2014, 1–6 (2014). https://doi.org/10.1155/2014/261759

    Article  MathSciNet  Google Scholar 

  3. Hrdina, J., Vašík, P., Matoušek, R.: Special orthogonal matrices over dual numbers and their applications. Mendel J. ser. 2015(6), 121–126 (2015)

    Google Scholar 

  4. Hrdina, J., Vašík, P., Holub, M.: Dual numbers arithmentic in multiaxis machine error modeling. MM Sci. J. 2017(1), 1769–1772 (2017)

    Article  Google Scholar 

  5. Holub, M., Hrdina, J., Vašík, P., Vetíška, J.: Three-axes error modeling based on second order dual numbers. J. Math. Ind. 5(2), 1–11 (2015). https://doi.org/10.1186/s13362-015-0016-y

    Article  MathSciNet  Google Scholar 

  6. Holub, M., Blecha, P., Bradac, F., Kana, R.: Volumetric compensation of three-axis vertical machining centre. MM Sci. J. 1, 677–681 (2015). https://doi.org/10.17973/MMSJ.2015-10-201534

    Article  Google Scholar 

  7. Holub, M., Knobloch, J.: Geometric accuracy of CNC machine tools. In: Proceedings of the 16th International Conference on Mechatronics, Mechatronika 2014, pp. 260–265 (2014). https://doi.org/10.1109/MECHATRONIKA.2014.7018268

  8. Holub, M., Michalíček, M., Vetíška, J., Marek, J.: Prediction of machining accuracy for vertical lathes. In: Proceedings of the 10th International Conference on Mechatronics 2013, Mechatronics 2013: Recent Technological and Scientific Advances, pp. 41–48 (2013). https://doi.org/10.1007/978-3-319-02294-9-6

  9. Mayr, J., Jedrzejewski, J., Uhlmann, E., Donmez, M.A., Knapp, W., Härtig, F., Wendt, K., Moriwaki, T., Shore, P., Schmitt, R., Brecher, Ch., Würz, T., Wegener, K.: Thermal issues in machine tools. CIRP Ann. - Manuf. Technol. 61(2), 771–791 (2012). https://doi.org/10.1016/j.cirp.2012.05.008

    Article  Google Scholar 

  10. Gomez-Acedo, E., Olarra, A., Zubieta, M., Kortaberria, G., Ariznabarreta, E., López de Lacalle, L.N.: Method for measuring thermal distortion in large machine tools by means of laser multilateration. Int. J. Adv. Manuf. Technol. 80(1), 523–534 (2015). https://doi.org/10.1007/s00170-015-7000-y

    Article  Google Scholar 

  11. Teoh, P.L., Shirinzadeh, B., Foong, Ch.W., Alici, G.: The measurement uncertainties in the laser interferometry-based sensing and tracking technique. Measurement 32(2), 135–150 (2002). https://doi.org/10.1016/S0263-2241(02)00006-4

  12. Takatsuji, T., Goto, M., Kirita, A., Kurosawa, T., Tanimura, Y.: The relationship between the measurement error and the arrangement of laser trackers in laser trilateration. Measure. Sci. Technol. 11(5), 477–483 (2000)

    Article  Google Scholar 

  13. Aguado, S., Santolaria, J., Samper, D., Aguilar, J.J.: Study of self-calibration and multilateration in machine tool volumetric verification for laser tracker error reduction. Proc. Inst. Mech. Eng. Part B: J. Eng. Manuf. 228(7), 659–672 (2014). https://doi.org/10.1177/0954405413511074

    Article  Google Scholar 

  14. Navratilova, B., Hrdina, J.: Multilateration in volumetry: case study on demonstrator MCV 754QUICK. Mendel J. Ser. 2016(1), 295–300 (2016)

    Google Scholar 

Download references

Acknowledgement

This work was supported by the project No. FAST/FSI-J-17-4753.

Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering, Institute of Mathematics, Brno University of Technology, Technicka 2896/2, 61669, Brno, Czech Republic

    Barbora Navrátilová

Authors
  1. Barbora Navrátilová
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Barbora Navrátilová .

Editor information

Editors and Affiliations

  1. Department of Applied Computer Science, Institute of Automation and Computer Science, Faculty of Mechanical Engineering, Brno University of Technology, Brno, Czech Republic

    Radek Matoušek

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Navrátilová, B. (2019). Weighted Multilateration in Volumetry of CNC Machine Tools. In: Matoušek, R. (eds) Recent Advances in Soft Computing . MENDEL 2017. Advances in Intelligent Systems and Computing, vol 837. Springer, Cham. https://doi.org/10.1007/978-3-319-97888-8_26

Download citation

Publish with us

Policies and ethics

Search

Navigation