Method for Compensation of Radius and Shape of Spherical Probe When Measuring Complex Surfaces with CMMs

  • F. V. Grechnikov
  • A. V. Kochetkov
  • O. V. ZakharovEmail author
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


Measurement practice on coordinate measuring machines showed that the real measurement accuracy is usually much higher than indicated in the technical documentation. The overall error in measuring the geometry consists of the errors in determining the point of contact on the surface of the part, compensation for deviations in the location of the base surfaces, and errors in calculating the surface parameters. The error in determining the touch point of the probe and the part is due to the difference in direction between the normals to the nominal and real surfaces. Therefore, the calculation becomes necessary to compensate the radius of the touch probe. A simple compensation method calculates only the normal to the nominal surface of the workpiece. More advanced methods take into account the coordinates of neighboring touch points and calculate equidistant surfaces. The article proposes an iterative method of compensating the radius of the probe by successively refining the coordinates of the point of tangency with respect to the nominal surface. In this method, the angle between the normals to the nominal and real surfaces at each measured point is minimized. Comparison of the results of compensation of the probe radius by the developed method with the standard method confirmed the high efficiency. The article provides an example of calculating the compensation of the probe radius for the turbine blade of the compressor, which showed a decrease in the measurement error by 23–29%. The application of the new method is useful when there is a small number of measured points and their location on the complex uneven surface.


Coordinate measuring machine Complex surface Measurement error Compensation of probe radius Spherical probe 



The study was performed by a grant from the Russian Science Foundation (project № 16-19-10204).


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • F. V. Grechnikov
    • 1
  • A. V. Kochetkov
    • 2
  • O. V. Zakharov
    • 3
    Email author
  1. 1.Samara National Research UniversitySamaraRussia
  2. 2.Perm National Research Polytechnic UniversityPermRussia
  3. 3.Yuri Gagarin State Technical University of SaratovSaratovRussia

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