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1. 大连理工大学 精密与特种加工教育部重点实验室, 大连 116024;
2. 南方科技大学 机械与能源工程系, 深圳 518055;
3. 中国航发西安航空发动机有限公司 技术中心, 西安 710021

Eddy current testing of internal defect in additive/subtractive hybrid manufacturing
WANG Longqun1,2, ZHANG Bi2, PENG Ying3, XIE Guoyin3, BAI Qian1, WANG Yibo1,2
1. Key Laboratory for Precision and Non-traditional Machining Technology of Ministry of Education, Dalian University of Technology, Dalian 116024, China;
2. Department of Mechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen 518055, China;
3. Technology Center, Xi'an Aero Engine Ltd., Aero Engine Corporation of China, Xi'an 710021, China
Abstract: Eddy Current Testing (ECT) technology is suitable for the complex processing environment of Additive/Subtractive Hybrid Manufacturing (ASHM) due to its non-contact, couplant-free and high-sensitive features. An analytical model is established to calculate the internal current distribution of the semi-infinite sample without defects. A titanium alloy sample with internal artificial-defects is fabricated by ASHM and the ECT experiments are conducted on it to study the effect of the excitation frequency and the lift-off distance on the testing depth. Both the theoretical and experimental results show that for a deep internal defect, a lower excitation frequency leads to a larger reactance increment signal and the lift-off distance has little effect on the reactance increment signal. The study concludes that the optimal excitation frequency of ECT is 90 kHz, and the optimal lift-off distance is 0.97 mm. The conclusion provides a theoretical foundation for the integration of ASHM and ECT.
Keywords: eddy current testing    additive/subtractive hybrid manufacturing    internal defect    testing depth    excitation frequency    lift-off distance

1 无缺陷钛合金增材试样内部涡流分布

 图 1 无缺陷半无限大试样解析模型 Fig. 1 Analytical model of semi-infinite sample without defects

 $\nabla \times \mathit{\boldsymbol{H}} = {\mathit{\boldsymbol{J}}_{\rm{s}}} + \mathit{\boldsymbol{J}}$ （1）
 $\nabla \times \mathit{\boldsymbol{E}} = - {\rm{j}}\omega \mathit{\boldsymbol{B}}$ （2）
 $\nabla \cdot \mathit{\boldsymbol{B}} = 0$ （3）
 $\nabla \cdot \mathit{\boldsymbol{D}} = \rho$ （4）

 $\mathit{\boldsymbol{D}} = {\varepsilon _0}\mathit{\boldsymbol{E}}$ （5）
 $\mathit{\boldsymbol{B}} = {\mu _0}\mathit{\boldsymbol{H}}$ （6）
 $\mathit{\boldsymbol{J}} = \sigma \mathit{\boldsymbol{E}}$ （7）

 ${\mathit{\boldsymbol{n}}_{12}} \times \left( {{\mathit{\boldsymbol{H}}_2} - {\mathit{\boldsymbol{H}}_1}} \right) = {\bf{0}}$ （8）
 ${\mathit{\boldsymbol{n}}_{12}} \times \left( {{\mathit{\boldsymbol{E}}_2} - {\mathit{\boldsymbol{E}}_1}} \right) = {\bf{0}}$ （9）
 ${\mathit{\boldsymbol{n}}_{12}} \cdot \left( {{\mathit{\boldsymbol{D}}_2} - {\mathit{\boldsymbol{D}}_1}} \right) = q$ （10）
 ${\mathit{\boldsymbol{n}}_{12}} \cdot \left( {{\mathit{\boldsymbol{B}}_2} - {\mathit{\boldsymbol{B}}_1}} \right) = 0$ （11）

 $\mathit{\boldsymbol{E}} = - \nabla \varphi - {\rm{j}}\omega \mathit{\boldsymbol{A}}$ （12）

 $\begin{array}{*{20}{c}} {\mathit{\boldsymbol{A}}\left( {\rho ,z} \right) = \frac{{\rm{j}}}{{\omega \sigma }}{\mathit{\boldsymbol{J}}_{\rm{s}}}\int_0^\infty {x\left( {x - \sqrt {{\rm{j}}F} } \right)K\left( {{r_1}x,{r_2}x} \right)} \cdot }\\ {\left( {1 - {{\rm{e}}^{ - hx}}} \right){{\rm{e}}^{ - lx + \sqrt {{z^2} + {\rm{j}}F} {z_0}}}{J_1}\left( {{\rho _0}x} \right){\rm{d}}x{\mathit{\boldsymbol{e}}_\theta }} \end{array}$ （13）

 $\mathit{\boldsymbol{J}}\left( {\rho ,z} \right) = - {\rm{j}}\omega \sigma \mathit{\boldsymbol{A}}\left( {\rho ,z} \right)$ （14）

 图 2 激励频率对无缺陷半无限大试样内部涡流分布的影响 Fig. 2 Effect of excitation frequencies on internaleddy current distribution in semi-infinitesample without defects

 图 3 提离量对无缺陷半无限大试样内部涡流分布的影响 Fig. 3 Effect of lift-off distances on internal eddycurrent distribution in semi-infinite samplewithout defects

2 实验验证 2.1 实验设备

 图 4 ECT实验设备 Fig. 4 ECT experimental setup

 参数 内径/mm 外径/mm 高度/mm 圆柱线圈 1.60 2.52 1.10 磁芯 1.52 4.32 外壳 2.80 3.68 3.80
2.2 试样制备及检测

 图 5 人工缺陷试样的制备 Fig. 5 Preparation of artificial-defect sample

 图 6 人工缺陷试样示意图(单位:mm) Fig. 6 Schematic of artificial-defect sample (Unit: mm)
 $d = {d_0}\cos \beta + \left[ {{d_0}\sin \beta + \left( {16 - y} \right)} \right]\tan \beta$ （15）

2.3 实验结果与讨论

 图 7 激励频率对不同深度内部缺陷ECT信号的影响 Fig. 7 Effect of excitation frequencies on ECT signalof internal defects at different depths

 图 8 提离量对不同深度内部缺陷ECT信号的影响 Fig. 8 Effect of lift-off distances on ECT signal ofinternal defects at different depths
3 结论

1) 在钛合金增材试样内部缺陷检测中，不同激励频率条件下，缺陷产生的电抗增量信号强度均随其深度的增加而减小，且高激励频率下电抗增量信号强度的变化量更大，这将使缺陷较深时高频激励的电抗增量信号强度反而小于低频激励的电抗增量信号强度。因此，浅表层缺陷检测应使用高频激励，而深层内部缺陷检测则应在仪器分辨率的基础上适当降低激励频率，增材沉积层厚度的确定需要考虑ECT检测深度及频率。

2) 在钛合金增材试样内部缺陷检测中，当内部缺陷较深时，不同提离量下缺陷产生的电抗增量信号强度相差不大。在本文实验条件下，当提离量从0.57 mm增加到0.97 mm时，直径为0.4 mm的孔型缺陷的有效检测深度仅减小了6.25%。因此在增减材复合制造中可以采用较大的提离量从而减小增材余热对检测探头的损害。

http://dx.doi.org/10.7527/S1000-6893.2019.23170

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#### 文章信息

WANG Longqun, ZHANG Bi, PENG Ying, XIE Guoyin, BAI Qian, WANG Yibo

Eddy current testing of internal defect in additive/subtractive hybrid manufacturing

Acta Aeronautica et Astronautica Sinica, 2020, 41(3): 423170.
http://dx.doi.org/10.7527/S1000-6893.2019.23170