Author Affiliations
Beijing Engineering Research Center of Precision Measurement Technology and Instruments, Beijing University of Technology, Beijing 100124, Chinashow less
Fig. 1. Schematic of laser tracing multi-station measurement system
Fig. 2. Schematic of smallest hexahedron which contains point J
Fig. 3. Laser tracing multi-station measurement system
Fig. 4. Spatial distribution of sampling points (circle is interpolation sample data, and asterisk is accuracy evaluation data)
Fig. 5. IDW interpolation results. (a) Volume error in x direction; (b) volume error in y direction; (c) volume error in z direction
Fig. 6. Difference between volume error obtained by IDW algorithm and volume error measured by laser tracing multi-station measurement system
Fig. 7. Schematic of trilinear interpolation model
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 /mm | Y /mm | Z /mm |
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1 | -50 | -70 | -620 | 2 | 520 | -50 | -470 | 3 | 520 | 1300 | -620 | 4 | -40 | 1250 | -470 | 5 | 70 | -70 | -620 | 6 | -60 | 40 | -620 |
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Table 1. Theoretical station coordinates of laser tracer
Station No. | X /mm | Y /mm | Z /mm |
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1 | -50.0000 | -69.9999 | -620.0000 | 2 | 520.0001 | -50.0003 | -470.0001 | 3 | 520.0002 | 1300.0004 | -620.0002 | 4 | -39.9998 | 1249.9997 | -470.0000 | 5 | 70.0002 | -69.9996 | -619.9999 | 6 | -60.0001 | 40.0000 | -620.0000 |
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Table 2. Position coordinates of laser tracer when CMM has errors
Station No. | ΔX /mm | ΔY /mm | ΔZ /mm |
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1 | -0.06×10-4 | 0.0001 | 0.20×10-4 | 2 | 1.00×10-4 | -0.0003 | -0.80×10-4 | 3 | 2.00×10-4 | 0.0004 | -2.00×10-4 | 4 | 2.00×10-4 | -0.0003 | 0.30×10-4 | 5 | 2.00×10-4 | 0.0004 | 1.00×10-4 | 6 | -0.90×10-4 | -0.0900×10-4 | 0.09×10-4 |
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Table 3. Calibration errors of station coordinates
j | Xj /mm | Yj /mm | Zj /mm | dj /mm |
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1 | -55.7659 | 70.0572 | -613.4493 | -212.7153 | 2 | 522.1023 | -51.4716 | -465.7633 | -253.9001 | 3 | 526.3857 | 1310.3801 | -613.4811 | -185.4420 | 4 | -41.3214 | 1269.6249 | -465.7788 | -206.6375 | 5 | 72.6585 | -77.6446 | -613.4448 | -212.7214 | 6 | -65.6418 | 41.8233 | -613.4556 | -212.9387 |
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Table 4. Station coordinates of laser tracer and initial measurement distances
Direction | IDW algorithm | Trilinear interpolationalgorithm |
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RMSE | R2 | RMSE | R2 |
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x | 0.000255 | 0.962629 | 0.000307 | 0.943569 | y | 0.000225 | 0.973257 | 0.000290 | 0.961579 | z | 0.000345 | 0.984713 | 0.000360 | 0.984293 |
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Table 5. Algorithm accuracy