High-Precision Pose Measurement Method for Pipeline Flanges Based on Three-Point Centering

Table 1. Initial values of system parameters for three-point centering model
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Table 1. Initial values of system parameters for three-point centering model
Parameter Value Parameter Value
$a$ /（°） 11.117 $x_{S, b}$ /mm -7.153
$b$ /（°） 70.957 $y_{S, b}$ /mm 51.380
$c$ /（°） -49.119 $x_{S, c}$ /mm -23.982
$x_{S, a}$ /mm 54.292 $y_{S, c}$ /mm -28.000
$y_{S, a}$ /mm -2.505

Table 2. System parameters of three-point centering model
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Table 2. System parameters of three-point centering model
Parameter Value Parameter Value
$a$ /（°） 11.800 $x_{S, b}$ /mm -6.001
$b$ /（°） 67.745 $y_{S, b}$ /mm 51.542
$c$ /（°） -52.157 $x_{S, c}$ /mm -24.158
$x_{S, a}$ /mm 54.094 $y_{S, c}$ /mm -27.411
$y_{S, a}$ /mm -2.652

Table 3. Error of circle center between three-point centering model and instrument measurement

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Table 3. Error of circle center between three-point centering model and instrument measurement

Number	$x_{0}$		$y_{0}$		Center error	Average center error
Number	Fitted value	Measured value	Fitted value	Measured value	Center error	Average center error
1	1.654	1.663	12.166	12.169	0.010	0.018
2	4.793	4.803	8.826	8.858	0.034
3	6.612	6.612	11.523	11.515	0.008
4	11.484	11.470	12.888	12.868	0.024
5	6.432	6.432	8.470	8.486	0.017
6	8.469	8.471	5.397	5.382	0.016
7	11.137	11.121	6.227	6.212	0.022
8	3.690	3.685	6.318	6.327	0.010

Table 4. Center coordinates of infrared light emitting diode in the target coordinate system
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Table 4. Center coordinates of infrared light emitting diode in the target coordinate system
Point x y z
Mark point 58.111 -3.095 32.770
Point 1 43.102 -0.087 32.859
Point 2 32.150 32.847 32.793
Point 3 -2.129 39.919 32.498
Point 4 -25.534 13.438 32.301
Point 5 -14.329 -19.615 32.683
Point 6 20.035 -26.445 32.724

Table 5. Results of repeatability accuracy

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Table 5. Results of repeatability accuracy

Number	Flange center			Flange normal vector			Center error /mm	Angle error /（°）
Number	x /mm	y /mm	z /mm	$x$	$y$	$z$	Center error /mm	Angle error /（°）
Average value	-147.051	-128.173	488.663	-0.500	-0.769	-9.958	0.033	0.051
1	-147.032	-128.142	488.655	-0.499	-0.766	-9.958	0.037	0.017
2	-147.006	-128.192	488.705	-0.516	-0.775	-9.957	0.065	0.098
3	-147.073	-128.157	488.660	-0.491	-0.762	-9.959	0.028	0.067
4	-147.041	-128.181	488.627	-0.491	-0.764	-9.959	0.038	0.055
5	-147.045	-128.161	488.656	-0.498	-0.772	-9.958	0.015	0.019
6	-147.058	-128.182	488.663	-0.505	-0.772	-9.957	0.011	0.034
7	-147.062	-128.185	488.682	-0.505	-0.763	-9.958	0.025	0.044
8	-147.092	-128.187	488.654	-0.492	-0.780	-9.957	0.044	0.075

Table 6. Results of integrated tooling and laser tracker

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Table 6. Results of integrated tooling and laser tracker

Number	Flange center distance /mm			Flange end angle /（°）
Number	Laser tracker	Integrated tooling	Error	Laser tracker	Integrated tooling	Error
1	294.578	294.344	0.234	0.230	0.310	0.070
2	324.667	324.479	0.188	0.574	0.471	0.103
3	322.370	322.128	0.242	4.187	4.107	0.080

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Shirui Liu, Yongjie Ren, Zhiyuan Niu, Jiarui Lin. High-Precision Pose Measurement Method for Pipeline Flanges Based on Three-Point Centering[J]. Laser & Optoelectronics Progress, 2025, 62(6): 0615002

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