A full-covariance uncertainty assessment in on-machine probing

Abstract Despite the growing use of machine tools for in-process measurement, the uncertainty evaluation of on-machine probing has mostly remained limited to the method specifically developed in ISO 15530-3 for coordinate-measuring machines. These methods reduce the on-machine measurement problem to a single-output system, so that the law of propagation of uncertainty becomes applicable, which excludes any covariance effect between the input quantities. This study proposes a methodology that inclusively estimates the uncertainty associated with any probing within the working space of a five-axis machine tool. Defined by the machine's forward kinematic model, the on-machine measurement function receives the machine geometric errors and the axis positions for a probed point set, and estimates its compensated position in the workpiece frame. The proposed uncertainty estimator assembles the covariance matrices associated with these input quantities and evaluates the measurement uncertainty through an adaptive Monte Carlo method. Unlike the task-specific method given by ISO 15530-3, this scheme eliminates the need for any part's calibrated counterpart and involves the covariance between the input quantities. The experimental verification of the new method includes the on-machine measurement of the length of a gauge block and the diameter and sphericity of a precision sphere through highly diverse axis positions of a five-axis machine tool. Over the 225 possible combinations of 15 point sets (each of size 2) probed on the gauge block, the coverage probability of the expanded uncertainty (for a coverage factor of 2) estimated for the gauge's length is 90%. Then, 10 point sets (each of size 25) collected on the sphere create 10 accumulated pools, and from each, 200 randomly drawn samples estimate the sphere's diameter. The coverage probabilities of the expanded uncertainty estimated for the pools built of up to 7 point sets remain above 94%. These levels of confidence are comparable to the theoretical level (95%).

[1]  Meirbek Mussatayev,et al.  Thermal influences as an uncertainty contributor of the coordinate measuring machine (CMM) , 2020, The International Journal of Advanced Manufacturing Technology.

[2]  G. Totis,et al.  Polynomial Chaos-Kriging approaches for an efficient probabilistic chatter prediction in milling , 2020 .

[3]  M. Burdekin,et al.  In-process dimensional measurement and control of workpiece accuracy , 1997 .

[4]  Unai Mutilba,et al.  Traceability of on-machine tool measurement: Uncertainty budget assessment on shop floor conditions , 2019, Measurement.

[6]  Xiaobing Feng,et al.  Geometric errors identification considering rigid-body motion constraint for rotary axis of multi-axis machine tool using a tracking interferometer , 2020 .

[7]  Shai Arogeti,et al.  Robust time-delayed H∞ synthesis for active control of chatter in internal turning , 2020 .

[8]  Robert Schmitt,et al.  Traceable Measurements on Machine Tools - Thermal Influences on Machine Tool Structure and Measurement Uncertainty☆ , 2015 .

[9]  J. J. Aguilar,et al.  Analysis of the measurement capacity of a machine tool , 2017 .

[10]  J.R.R. Mayer,et al.  Efficient uncertainty estimation of indirectly measured geometric errors of five-axis machine tools via Monte-Carlo validated GUM framework , 2021 .

[11]  Unai Mutilba,et al.  Uncertainty assessment for on-machine tool measurement: An alternative approach to the ISO 15530-3 technical specification , 2019, Precision Engineering.

[12]  Adam Gąska,et al.  Impact of warm-up period on optical coordinate measuring machine measurement accuracy , 2021 .

[13]  Adam Gąska,et al.  Simulation model for uncertainty estimation of measurements performed on five-axis measuring systems , 2019, The International Journal of Advanced Manufacturing Technology.

[14]  Wim Michiels,et al.  Robust stability of milling operations based on pseudospectral approach , 2020, International Journal of Machine Tools and Manufacture.

[15]  Robert Schmitt,et al.  Traceable Measurements using Machine Tools , 2013 .

[16]  J.R.R. Mayer,et al.  Five-axis machine tool calibration by probing a scale enriched reconfigurable uncalibrated master balls artefact , 2012 .

[17]  Kuang-Chao Fan,et al.  A novel modeling of volumetric errors of three-axis machine tools based on Abbe and Bryan principles , 2020 .

[18]  Shreyes N. Melkote,et al.  Statistical calibration and uncertainty quantification of complex machining computer models , 2019, International Journal of Machine Tools and Manufacture.

[19]  Soichi Ibaraki,et al.  A machining test to evaluate thermal influence on the kinematics of a five-axis machine tool , 2021 .

[20]  Christian Brecher,et al.  Thermal issues in machine tools , 2012 .

[21]  Jürgen Czarske,et al.  Measurement uncertainty propagation in spindle error separation techniques - Investigation by means of stochastic spectral method , 2019 .

[22]  Farbod Khameneifar,et al.  Repeatability of on-machine probing by a five-axis machine tool , 2020 .