Weighted Multilateration in Volumetry of CNC Machine Tools

  • Barbora NavrátilováEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 837)


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.


Accuracy of measurement Multilateration Weighted multilateration Machine tool LaserTRACER 



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


  1. 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). Scholar
  2. 2.
    Hrdina, J., Vašík, P.: Dual numbers approach in multiaxis machines error modeling. J. Appl. Math. 2014, 1–6 (2014). Scholar
  3. 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. 4.
    Hrdina, J., Vašík, P., Holub, M.: Dual numbers arithmentic in multiaxis machine error modeling. MM Sci. J. 2017(1), 1769–1772 (2017)CrossRefGoogle Scholar
  5. 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). Scholar
  6. 6.
    Holub, M., Blecha, P., Bradac, F., Kana, R.: Volumetric compensation of three-axis vertical machining centre. MM Sci. J. 1, 677–681 (2015). Scholar
  7. 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).
  8. 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).
  9. 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). Scholar
  10. 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). Scholar
  11. 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).
  12. 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)CrossRefGoogle Scholar
  13. 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). Scholar
  14. 14.
    Navratilova, B., Hrdina, J.: Multilateration in volumetry: case study on demonstrator MCV 754QUICK. Mendel J. Ser. 2016(1), 295–300 (2016)Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Mechanical Engineering, Institute of MathematicsBrno University of TechnologyBrnoCzech Republic

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