Researching | Measurement uncertainty evaluation and analysis for industrial computed tomography based on forest balls

Optics and Precision Engineering, Volume. 31, Issue 11, 1672(2023)

Measurement uncertainty evaluation and analysis for industrial computed tomography based on forest balls

Zenan YANG1,*... Ziying HUANG2, Haiyong ZHA2, Liyuan ZHOU1 and Kuidong HUANG3 |Show fewer author(s)

Author Affiliations

¹Science and Technology on Advanced High Temperature Structural Materials Laboratory， AECC Beijing Institute of Aeronautical Materials， Beijing00095， China

²AECC Sichuan Gas Turbine Research Establishment， Chengdu610500， China

³The Key Laboratory of High Performance Manufacturing for Aero Engine （Northwestern Polytechnical University）， Ministry of Industry and Information Technology， Xi'an710072， China

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References (24)

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Figures & Tables(20)

Fig. 1. Industrial CT imaging and measurement processes

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Fig. 2. Influencing factors of industrial CT size measurement

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Fig. 3. Schematic diagram of spatial distribution of forest balls

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Fig. 4. Projection and slice images of forest balls

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Fig. 5. Error distribution of dimension measurement system

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Fig. 6. Linear distribution of uncertainty in measurement of center distance of ceramic ball

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Fig. 7. Linear distribution of uncertainty in measurement of ceramic ball center distance

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Fig. 8. Linear distribution of uncertainty in measurement of steel ball center distance

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Table 1. Nominal values of forest balls

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Table 1. Nominal values of forest balls

标准器	球直径		球心距
标准器	球号	标称值	球号	标称值	球号	标称值
陶瓷球	2#	4.974 6	（1#，2#）	16.361 7	（1#，6#）	53.651 4
	4#	4.997 6	（1#，4#）	32.049 1	（4#，6#）	59.938 4
	6#	5.000 3	（3#，5#）	39.457 7	（6#，7#）	88.496 7
红宝石球	2#	5.009 8	（1#，2#）	16.856 8	（1#，6#）	53.807 6
	4#	5.028 4	（1#，4#）	32.433 6	（4#，6#）	60.296 7
	6#	5.011 3	（3#，5#）	39.222 2	（6#，7#）	88.806 7
钢球	2#	4.993 6	（1#，2#）	16.394 2	（1#，6#）	52.918 2
	4#	4.997 5	（1#，4#）	32.453 5	（4#，6#）	59.993 1
	6#	5.000 2	（3#，5#）	39.457 7	（6#，7#）	88.570 5

Table 2. Parameters of CT scanning and reconstruction

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Table 2. Parameters of CT scanning and reconstruction

参数	数值
管电压/kV、管电流/mA	120/1.5，180/0.8，280/0.45
焦点尺寸/mm	0.4
放大倍数	1.44
投影幅数	720
探元尺寸/mm	0.2
投影矩阵	1 024×1 024
重建矩阵	1 024×1 024×300
体素尺寸/mm³	0.138 9
重建方法	FDK

Table 3. Value and uncertainty of ball diameter

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Table 3. Value and uncertainty of ball diameter

标准器类型	标称值	测量值1	测量值2	测量值3	$\bar{y}$	u_p
陶瓷球	4.974 6	4.987 5	4.987 0	4.987 2	4.987 2	0.000 3
	4.997 6	4.986 1	4.985 6	4.986 6	4.986 1	0.000 5
	5.000 3	4.991 6	4.990 9	4.992 0	4.991 5	0.000 6
红宝石球	5.009 8	4.995 7	4.994 8	4.995 5	4.995 3	0.000 5
	5.028 4	5.010 4	5.009 6	5.009 7	5.009 9	0.000 4
	5.011 3	5.001 8	5.001 3	5.002 0	5.001 7	0.000 4
钢珠球	4.993 6	5.026 6	5.025 8	5.026 8	5.026 4	0.000 5
	4.997 5	5.031 4	5.030 6	5.030 5	5.030 9	0.000 5
	5.000 2	5.030 8	5.031 0	5.030 7	5.030 8	0.000 2

Table 4. Value and uncertainty of ball center distance

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Table 4. Value and uncertainty of ball center distance

标准器类型	标称值	测量值1	测量值2	测量值3	$\bar{y}$	u_p
陶瓷球	16.361 7	16.352 5	16.352 7	16.352 1	16.352 5	0.000 3
	32.049 1	32.039 6	32.039 5	32.039 7	32.039 6	0.000 1
	38.836 7	38.827 2	38.827 1	38.827 3	38.827 2	0.000 1
红宝石球	53.651 4	53.641 8	53.642 0	53.642 2	53.642 0	0.000 2
	59.938 4	59.928 9	59.929 2	59.929 7	59.929 3	0.000 4
	88.496 7	88.486 9	88.487 4	88.488 6	88.487 6	0.000 9
钢珠球	16.856 8	16.847 2	16.846 0	16.847 2	16.846 8	0.000 7
	32.433 6	32.424 7	32.423 0	32.424 1	32.423 9	0.000 9
	39.222 2	39.212 5	39.212 4	39.212 6	39.212 5	0.000 1

Table 5. Uncertainty introduced by measuring temperature

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Table 5. Uncertainty introduced by measuring temperature

参数	直径
参数	陶瓷球			红宝石球			钢球
u_a	3.0×10^-6/℃			6.65×10^-6/℃			12×10^-6/℃
标称尺寸	4.974 6	4.997 6	5.000 3	5.009 8	5.028 4	5.011 3	4.993 6	4.997 5	5.000 2
u_w	0.000 0	0.000 0	0.000 0	0.000 0	0.000 0	0.000 0	0.000 1	0.000 1	0.000 1
参数	球心距
参数	铝合金（陶瓷球）						铝合金（红宝石球）
u_a	23.21×10^-6/℃						23.21×10^-6/℃
标称尺寸	16.361 7	32.049 1	38.836 7	53.651 4	59.938 4	88.496 7	16.856 8	32.433 6	39.222 2
u_w	0.000 4	0.000 8	0.000 9	0.001 2	0.001 4	0.002 1	0.000 4	0.000 8	0.000 9
参数	球心距
参数	铝合金（红宝石球）			铝合金（钢球）
u_a	23.21×10^-6/℃			23.21×10^-6/℃
标称尺寸	53.807 6	60.296 7	88.806 7	16.394 2	32.453 5	39.457 7	52.918 2	59.993 1	88.570 5
u_w	0.001 2	0.001 4	0.002 1	0.000 4	0.000 8	0.000 9	0.001 3	0.001 4	0.002 1

Table 6. Diameter uncertainty of ceramic ball

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Table 6. Diameter uncertainty of ceramic ball

球号	u_cal	u_p	u_w	u_b	U	$\bar{y}$	校正结果
2#	0.000 5	0.000 3	0.000 0	0.000 0	0.001 2	4.987 2	Y=4.987 2-b±0.001 2
4#	0.000 5	0.000 5	0.000 0	0.000 0	0.001 4	4.986 1	Y=4.986 1-b±0.001 4
6#	0.000 5	0.000 6	0.000 0	0.000 0	0.001 5	4.991 5	Y=4.991 5-b±0.001 5

Table 7. Diameter uncertainty of ruby ball

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Table 7. Diameter uncertainty of ruby ball

球号	u_cal	u_p	u_w	u_b	U	$\bar{y}$	校正结果
2#	0.000 5	0.000 5	0.000 0	0.000 0	0.001 4	4.995 3	Y=4.995 3-b±0.001 4
4#	0.000 5	0.000 4	0.000 0	0.000 0	0.001 3	5.009 9	Y=5.009 9-b±0.001 3
6#	0.000 5	0.000 4	0.000 0	0.000 0	0.001 3	5.001 7	Y=5.001 7-b±0.001 3

Table 8. Diameter uncertainty of steel ball

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Table 8. Diameter uncertainty of steel ball

球号	u_cal	u_p	u_w	u_b	U	$\bar{y}$	校正结果
2#	0.000 5	0.000 5	0.000 1	0.000 1	0.001 5	5.026 4	Y=5.026 4-b±0.001 5
4#	0.000 5	0.000 5	0.000 1	0.000 1	0.001 4	5.030 9	Y=5.030 9-b±0.001 4
6#	0.000 5	0.000 2	0.000 1	0.000 1	0.001 1	5.030 8	Y=5.030 8-b±0.001 1

Table 9. Uncertainty of ball center distance of ceramic ball

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Table 9. Uncertainty of ball center distance of ceramic ball

球号	u_cal	u_p	u_w	u_b	U	$\bar{y}$	校正结果
（1#，2#）	0.000 5	0.000 3	0.000 4	0.000 4	0.001 6	16.352 5	Y=16.352 5-b±0.001 6
（1#，4#）	0.000 5	0.000 1	0.000 8	0.000 8	0.002 5	32.039 6	Y=32.039 6-b±0.002 5
（3#，5#）	0.000 5	0.000 1	0.000 9	0.000 9	0.002 7	38.827 2	Y=38.827 2-b±0.002 7
（1#，6#）	0.000 5	0.000 2	0.001 2	0.001 2	0.003 6	53.642 0	Y=53.642 0-b±0.003 6
（4#，6#）	0.000 5	0.000 4	0.001 4	0.001 4	0.004 2	59.929 3	Y=59.929 3-b±0.004 2
（6#，7#）	0.000 5	0.000 9	0.002 1	0.002 1	0.006 3	88.487 6	Y=88.487 6-b±0.006 3

Table 10. Uncertainty of ball center distance of ruby ball

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Table 10. Uncertainty of ball center distance of ruby ball

球号	u_cal	u_p	u_w	u_b	U	$\bar{y}$	校正结果
（1#，2#）	0.000 5	0.000 7	0.000 4	0.000 4	0.002 1	16.846 8	Y=16.846 8-b±0.002 1
（1#，4#）	0.000 5	0.000 9	0.000 8	0.000 8	0.003 1	32.423 9	Y=32.423 9-b±0.003 1
（3#，5#）	0.000 5	0.000 1	0.000 9	0.000 9	0.002 7	39.212 5	Y=39.212 5-b±0.002 7
（1#，6#）	0.000 5	0.000 6	0.001 2	0.001 2	0.003 7	53.798 2	Y=53.798 2-b±0.003 7
（4#，6#）	0.000 5	0.000 5	0.001 4	0.001 4	0.004 2	60.287 8	Y=60.287 8-b±0.004 2
（6#，7#）	0.000 5	0.000 4	0.002 1	0.002 1	0.006 1	88.797 7	Y=88.797 7-b±0.006 1

Table 11. Uncertainty of ball center distance of steel ball

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Table 11. Uncertainty of ball center distance of steel ball

球号	u_cal	u_p	u_w	u_b	U	$\bar{y}$	校正结果
（1#，2#）	0.000 5	0.006 6	0.000 4	0.000 4	0.013 3	16.384 9	Y=16.384 9-b±0.013 3
（1#，4#）	0.000 5	0.005 9	0.000 8	0.000 8	0.012 1	32.444 3	Y=32.444 3-b±0.012 1
（3#，5#）	0.000 5	0.005 1	0.000 9	0.000 9	0.010 6	39.448 3	Y=39.448 3-b±0.010 6
（1#，6#）	0.000 5	0.005 0	0.001 3	0.001 3	0.010 7	52.908 7	Y=52.908 7-b±0.010 7
（4#，6#）	0.000 5	0.004 6	0.001 4	0.001 4	0.010 1	59.983 9	Y=59.983 9-b±0.010 1
（6#，7#）	0.000 5	0.007 6	0.002 1	0.002 1	0.016 3	88.561 3	Y=88.561 3-b±0.016 3

Table 12. Length measurement calibration results

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Table 12. Length measurement calibration results

球类型	标称值	平均值	示值误差	U （k=2）
陶瓷球	16.361 7	16.352 5	-0.009 2	0.001 6
	32.049 1	32.039 6	-0.009 5	0.002 5
	38.836 7	38.827 2	-0.009 5	0.002 7
	53.651 4	53.642 0	-0.009 4	0.003 6
	59.938 4	59.929 3	-0.009 1	0.004 2
	88.496 7	88.487 6	-0.009 1	0.006 3
红宝石球	16.856 8	16.846 8	-0.010 0	0.002 1
	32.433 6	32.423 9	-0.009 7	0.003 1
	39.222 2	39.212 5	-0.009 7	0.002 7
	53.807 6	53.798 2	-0.009 4	0.003 7
	60.296 7	60.287 8	-0.008 9	0.004 2
	88.806 7	88.797 7	-0.009 0	0.006 1
钢珠球	16.394 2	16.384 9	-0.009 3	0.013 3
	32.453 5	32.444 3	-0.009 2	0.012 1
	39.457 7	39.448 3	-0.009 4	0.010 6
	52.918 2	52.908 7	-0.009 5	0.010 7
	59.993 1	59.983 9	-0.009 2	0.010 1
	88.570 5	88.561 3	-0.009 2	0.016 3

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Zenan YANG, Ziying HUANG, Haiyong ZHA, Liyuan ZHOU, Kuidong HUANG. Measurement uncertainty evaluation and analysis for industrial computed tomography based on forest balls[J]. Optics and Precision Engineering, 2023, 31(11): 1672

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Paper Information

Category: Information Sciences

Received: Nov. 9, 2022

Accepted: --

Published Online: Jul. 4, 2023

The Author Email: YANG Zenan (yanzn719@126.com)

DOI:10.37188/OPE.20233111.1672

Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology