Method for Volume Error Calibration of CMM Based on Inverse-Distance Weighting Algorithm

Chen Hongfang; Zhang Shuang; Liang Chaowei; Tang Liang; Shi Zhaoyao

doi:10.3788/CJL202047.1204001

Chinese Journal of Lasers, Volume. 47, Issue 12, 1204001(2020)

Method for Volume Error Calibration of CMM Based on Inverse-Distance Weighting Algorithm

Chen Hongfang^*, Zhang Shuang, Liang Chaowei, Tang Liang, and Shi Zhaoyao

Beijing Engineering Research Center of Precision Measurement Technology and Instruments, Beijing University of Technology, Beijing 100124, China

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Figures & Tables(13)

Fig. 1. Schematic of laser tracing multi-station measurement system

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Fig. 2. Schematic of smallest hexahedron which contains point J

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Fig. 3. Laser tracing multi-station measurement system

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Fig. 4. Spatial distribution of sampling points (circle is interpolation sample data, and asterisk is accuracy evaluation data)

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Fig. 5. IDW interpolation results. (a) Volume error in x direction; (b) volume error in y direction; (c) volume error in z direction

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Fig. 6. Difference between volume error obtained by IDW algorithm and volume error measured by laser tracing multi-station measurement system

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Fig. 7. Schematic of trilinear interpolation model

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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

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Table 1. Theoretical station coordinates of laser tracer
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Table 1. Theoretical station coordinates of laser tracer
Station No. X /mm Y /mm Z /mm
1 -50 -70 -620
2 520 -50 -470
3 520 1300 -620
4 -40 1250 -470
5 70 -70 -620
6 -60 40 -620

Table 2. Position coordinates of laser tracer when CMM has errors
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Table 2. Position coordinates of laser tracer when CMM has errors
Station No. X /mm Y /mm Z /mm
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

Table 3. Calibration errors of station coordinates

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Table 3. Calibration errors of station coordinates

Station No.	ΔX /mm	ΔY /mm	ΔZ /mm
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

Table 4. Station coordinates of laser tracer and initial measurement distances

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Table 4. Station coordinates of laser tracer and initial measurement distances

j	X_j /mm	Y_j /mm	Z_j /mm	d_j /mm
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

Table 5. Algorithm accuracy
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Table 5. Algorithm accuracy
Direction IDW algorithm Trilinear interpolationalgorithm
RMSE R² RMSE R²
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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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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