Volumetric error formulation and mismatch test for five-axis CNC machine compensation using differential kinematics and ephemeral G-code

  • Mehrdad GiviEmail author
  • J. R. R Mayer


Machine tool kinematic errors directly impact on the accuracy of machined parts. A general volumetric error formulation effectively implementing ISO230-1:2012 definition and an off-line compensation scheme are proposed and partly tested to improve part accuracy on a five-axis CNC machine. Using rigid body kinematics and estimated machine error parameters, the machine position commands contained in a standard G-code are used to calculate the tool erroneous location. The Jacobian, expressing the differential joint space to Cartesian space relationship, is also developed and used to calculate minute joint command modifications so that the effect of inter-axis link errors and intra-axis error motions, for example, can be canceled by making small changes directly to the G-code. Finally, a simple case of a machining sequence producing a surface mismatch in the presence of particular machine deviations is used to illustrate the usefulness of the analytical tools presented. A graphical representation of the volumetric errors assists in understanding the impact of each error source for this particular application. The measurement results are compatible with the predicted volumetric error values and show an accuracy improvement of about 90 % after compensation.


Volumetric error Five-axis machine Off-line compensation G-code Mismatch test 


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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Ecole Polytechnique de MontrealMontrealCanada

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