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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2020, Vol. 54 Issue (6): 1218-1227    DOI: 10.3785/j.issn.1008-973X.2020.06.020
Mechanical Engineering     
High-precision calibration methods of thickness measurement for insulation coation on curved surface based on eddy current
Zheng-rui TAO1(),Jia-qiang DANG1,Jing-yang XU1,Qing-long AN1,*(),Ming CHEN1,Li WANG2,Fei REN2
1. School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
2. Shanghai Aerospace Equipment Manufacturer Co. Ltd, Shanghai 200245, China
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Abstract  

A certain type of eddy current displacement sensor was taken as an example, and three calibration testing experiments were conducted, in order to increase the accuracy of thickness measurement for insulating coating on curved surface. The 9th-degree polynomial, 7th-order Fourier series, Gaussian multi-peak function, and radial basis function neural network were used for fitting. The squared sum of errors, root mean square, coefficient of determination and single-point operation time were compared and analyzed in terms of measurement accuracy and operation rate, for reference on how to choose the calibration method in different applications. Aiming at the requirements of thickness measurement of polyurethane foam on the outer surface of the fuel tank, chose the method based on radial basis function neural network for verification test. Results show that the measurement error can be controlled between ?0.15 mm to 0.15 mm by optimizing the calibration method.

Key words： eddy current thickness measurement      high-precision calibration      Gaussian multi-peak fitting      radial basis function neural network     
Received: 30 May 2019      Published: 06 July 2020
CLC:  TG 156  
Corresponding Authors: Qing-long AN     E-mail: taozhengrui@sjtu.edu.cn;qlan@sjtu.edu.cn
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Zheng-rui TAO
Jia-qiang DANG
Jing-yang XU
Qing-long AN
Ming CHEN
Li WANG
Fei REN
Cite this article:

Zheng-rui TAO,Jia-qiang DANG,Jing-yang XU,Qing-long AN,Ming CHEN,Li WANG,Fei REN. High-precision calibration methods of thickness measurement for insulation coation on curved surface based on eddy current. Journal of ZheJiang University (Engineering Science), 2020, 54(6): 1218-1227.

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http://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2020.06.020     OR     http://www.zjujournals.com/eng/Y2020/V54/I6/1218


曲面基体绝缘涂镀层涡流测厚高精度标定方法

为了提高金属零件表面绝缘涂镀层厚度测量精度，以某型电涡流位移流传感器为例，开展3种不同曲率的曲面试件标定试验；对比分析9次多项式、7项傅里叶级数、多峰高斯函数和径向基函数神经网络这4种标定方法的误差平方和、均方根、决定系数以及单点运算时间；综合评价4种标定方法在测量精度、计算速率方面的优劣，为涡流位移传感器在不同应用场合的标定方法选择提供参考. 针对燃料贮箱外表面聚氨酯泡沫层厚度测量要求，选用基于径向基函数神经网络的曲面基体涡流测厚法进行验证试验. 结果表明，通过优化标定方法，测量误差可以控制在?0.15~ 0.15 mm.


关键词： 涡流测厚,  高精度标定,  高斯多峰拟合,  径向基函数神经网络 
Fig.1 Structural block diagram of eddy current thickness measurement testing system
技术指标 数值 单位
供电电源 +24 V
灵敏度 0.32 mA/mm
输出 4~20 mA
平板测量误差 ?0.01~ +0.02 mm
输出波纹 ≤20 mV
频响 0~10 kHz
温漂 ≤0.1 %fs/°C
外形尺寸 60×60×120 mm×mm×mm
Tab.1 Technical indicators of eddy current displacement sensor
技术指标 数值 单位 技术指标 数值 单位
X 行程 1 067 mm 最大主轴转速 12 000 r/min
Y 行程 610 mm 主轴功率 18 000 W
Z 行程 610 mm 定位精度 0.01 mm
A 轴 ±110 （°） 重复定位精度 0.000 5 mm
C 轴 ±110 （°） ? ? ?
Tab.2 Performance parameters of machine tool
Fig.2 Measurement system data acquisition module
Fig.3 Site settings of eddy current thickness measurement testing
Fig.4 Radial basis function neural network（RBFNN）structure
神经元 W L 神经元 W L
1 19.26 1 396.53 13 19.96 ?360 615.5
2 16.47 70.69 14 19.55 ?4 928.79
3 13.5 12.6 15 12.58 ?13.82
4 10.98 5.47 16 7.43 2.67
5 19.99 199 409.31 17 4.58 2.00
6 18.82 ?118.45 18 16.28 ?24.85
7 15.00 13.22 19 9.18 2.38
8 8.53 2.27 20 14.23 0.77
9 12.39 20.54 21 19.92 164 938.2
10 17.12 128.32 22 16.97 ?143.89
11 6.12 1.86 23 2.90 ?1.95
12 10.03 3.39 ? ? ?
Tab.3 Parameters of RBFNN
Fig.5 Four calibration curves and data samples for testing part 1
Fig.6 Training process of RBFNN
Fig.7 Trend between current signal and lifting distance
Fig.8 Error distribution within sensor range of four calibration methods
标定方法 SSE / mm2 RMSE / mm R2 Emax / mm
Poly9 0.316 8 0.058 7 0.999 98 0.217 9
Fourier7 0.122 2 0.036 5 0.999 99 0.137 9
Gauss8 0.198 5 0.046 5 0.999 93 0.187 0
RBFNN 0.046 7 0.022 5 0.999 99 0.124 7
Plane 1 289.000 0 3.743 2 0.740 50 8.786 2
Tab.4 Error statistics of calibration methods for part 1
试件 标定方法 SSE /
mm2		 RMSE /
mm 		Emax /
mm 		Δt /
ms
试件2 Poly9 0.307 3 0.057 8 0.216 5 0.12
Fourier7 0.114 5 0.035 3 0.136 5 0.19
Gauss8 0.143 8 0.039 5 0.157 8 1.19
RBPNN 0.040 8 0.021 9 ?0.103 6 3.77
Plane 1 300.000 0 3.759 9 8.816 5 0.17
试件3 Poly9 0.974 8 0.107 7 0.437 2 0.11
Fourier7 0.296 8 0.059 4 ?0.198 3 0.15
Gauss8 0.177 8 0.046 ?0.200 5 1.12
RBFNN 0.033 0 0.018 9 ?0.068 5 6.51
Plane 739.000 0 2.966 8 7.273 9 0.12
Tab.5 Error statistics of five calibration methods on tow different testing parts
Fig.9 Measurement of coating thickness on surface of metal substrate by acupuncture method
Fig.10 Measurement of coating thickness on surface of metal substrate by eddy current method
Fig.11 Coating thickness measurement verification testing results for curved specimen 1
Fig.12 Coating thickness measurement verification testing results for curved specimen 2
Fig.13 Comparison of coating thickness measurement verification testing results for curved specimen 3
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