• Chinese Journal of Lasers
  • Vol. 47, Issue 12, 1204001 (2020)
Chen Hongfang*, Zhang Shuang, Liang Chaowei, Tang Liang, and Shi Zhaoyao
Author Affiliations
  • Beijing Engineering Research Center of Precision Measurement Technology and Instruments, Beijing University of Technology, Beijing 100124, China
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    DOI: 10.3788/CJL202047.1204001 Cite this Article Set citation alerts
    Chen Hongfang, Zhang Shuang, Liang Chaowei, Tang Liang, Shi Zhaoyao. Method for Volume Error Calibration of CMM Based on Inverse-Distance Weighting Algorithm[J]. Chinese Journal of Lasers, 2020, 47(12): 1204001 Copy Citation Text show less
    Schematic of laser tracing multi-station measurement system
    Fig. 1. Schematic of laser tracing multi-station measurement system
    Schematic of smallest hexahedron which contains point J
    Fig. 2. Schematic of smallest hexahedron which contains point J
    Laser tracing multi-station measurement system
    Fig. 3. Laser tracing multi-station measurement system
    Spatial distribution of sampling points (circle is interpolation sample data, and asterisk is accuracy evaluation data)
    Fig. 4. Spatial distribution of sampling points (circle is interpolation sample data, and asterisk is accuracy evaluation data)
    IDW interpolation results. (a) Volume error in x direction; (b) volume error in y direction; (c) volume error in z direction
    Fig. 5. IDW interpolation results. (a) Volume error in x direction; (b) volume error in y direction; (c) volume error in z direction
    Difference between volume error obtained by IDW algorithm and volume error measured by laser tracing multi-station measurement system
    Fig. 6. Difference between volume error obtained by IDW algorithm and volume error measured by laser tracing multi-station measurement system
    Schematic of trilinear interpolation model
    Fig. 7. Schematic of trilinear interpolation model
    Volume error results obtained by trilinear interpolation algorithm. (a) Volume error in x direction; (b) volume error in y direction; (c) volume error in z direction
    Fig. 8. Volume error results obtained by trilinear interpolation algorithm. (a) Volume error in x direction; (b) volume error in y direction; (c) volume error in z direction
    Station No.X /mmY /mmZ /mm
    1-50-70-620
    2520-50-470
    35201300-620
    4-401250-470
    570-70-620
    6-6040-620
    Table 1. Theoretical station coordinates of laser tracer
    Station No.X /mmY /mmZ /mm
    1-50.0000-69.9999-620.0000
    2520.0001-50.0003-470.0001
    3520.00021300.0004-620.0002
    4-39.99981249.9997-470.0000
    570.0002-69.9996-619.9999
    6-60.000140.0000-620.0000
    Table 2. Position coordinates of laser tracer when CMM has errors
    Station No.ΔX /mmΔY /mmΔZ /mm
    1-0.06×10-40.00010.20×10-4
    21.00×10-4-0.0003-0.80×10-4
    32.00×10-40.0004-2.00×10-4
    42.00×10-4-0.00030.30×10-4
    52.00×10-40.00041.00×10-4
    6-0.90×10-4-0.0900×10-40.09×10-4
    Table 3. Calibration errors of station coordinates
    jXj /mmYj /mmZj /mmdj /mm
    1-55.765970.0572-613.4493-212.7153
    2522.1023-51.4716-465.7633-253.9001
    3526.38571310.3801-613.4811-185.4420
    4-41.32141269.6249-465.7788-206.6375
    572.6585-77.6446-613.4448-212.7214
    6-65.641841.8233-613.4556-212.9387
    Table 4. Station coordinates of laser tracer and initial measurement distances
    DirectionIDW algorithmTrilinear interpolationalgorithm
    RMSER2RMSER2
    x0.0002550.9626290.0003070.943569
    y0.0002250.9732570.0002900.961579
    z0.0003450.9847130.0003600.984293
    Table 5. Algorithm accuracy
    Chen Hongfang, Zhang Shuang, Liang Chaowei, Tang Liang, Shi Zhaoyao. Method for Volume Error Calibration of CMM Based on Inverse-Distance Weighting Algorithm[J]. Chinese Journal of Lasers, 2020, 47(12): 1204001
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