﻿ 减小舰船静电场的隔离电阻估算方法
 舰船科学技术  2018, Vol. 40 Issue (8): 123-127 PDF

Research on evaluation method for the least isolation resistance which decreases the corrosion related static electric field
YU Peng, JIANG Run-xiang, CHENG Jin-fang
Department of Weaponry Engineering, Naval University of Engineering, Wuhan 430033, China
Abstract: Electric isolation measuring is one of the important methods of reducing the ship's corrosion related static electric field. In order to solve the key technical problem of estimating the minimum isolation resistance based on the electric field of target, firstly, the electrochemical corrosion circuit model between dissimilar metal materials of ship hull is established. Secondly, the relationship between electric field and corrosion current at the bottom of dissimilar metal material under the condition of both insulation and un-insulation hull was established based on point charge model, and the mathematical formula between the minimum insulated resistance and corrosion related static electric field has been proposed. Finally, the correctness of the proposed method was tested by BEM software simulated data, the results show that the proposed method can predict the minimum isolation resistance accurately.
Key words: ship     corrosion     static electric field     isolated resistance
0 引　言

1 舰船腐蚀相关静态电场

 图 1 船体—螺旋桨构成的电解偶等效电路图 Fig. 1 Electrolytic pair equivalent circuit of hull and shaft

 $I = \frac{{{\varphi _a} - {\varphi _c}}}{{{R_p} + R + {R_a} + {R_c}}}\text{，}$ (1)
 ${R_a} = \frac{{{\beta _a} + {\rho _a}}}{{{S_a}}}\text{，}$ (2)
 ${R_c} = \frac{{{\beta _c} + {\rho _c}}}{{{S_c}}}\text{。}$ (3)

2 隔离电阻估算方法

2.1 非绝缘船体最小隔离电阻估算方法

 $\begin{split} {R_p} = \frac{1}{{2\pi \sigma {a_a}}} + \frac{1}{{2\pi \sigma {a_c}}} + \frac{1}{{2\pi \sigma l}} \approx \\ \frac{1}{{2\pi \sigma {a_a}}} + \frac{1}{{2\pi \sigma {a_c}}} \text{，} \\ \end{split}$ (4)

 $I \approx \frac{{{\varphi _a} - {\varphi _c}}}{{\frac{{{\beta _a} + {\rho _a}}}{{{S_a}}} + \frac{{{\beta _c} + {\rho _c}}}{{{S_c}}} + \frac{1}{{2\pi \sigma {a_a}}} + \frac{1}{{2\pi \sigma {a_c}}} + R}}\text{。}$ (5)

 ${U_a} \approx \frac{I}{{2\pi \sigma \left( {{a_a} + d} \right)}}\text{，}$ (6)
 ${U_c} \approx \frac{{ - I}}{{2\pi \sigma \left( {{a_c} + d} \right)}}\text{，}$ (7)

 $\left| {{U_a} - {U_c}} \right| \approx \left| {\frac{I}{{2\pi \sigma \left( {{a_a} + d} \right)}} + \frac{I}{{2\pi \sigma \left( {{a_c} + d} \right)}}} \right|\text{，}$ (8)

 $\begin{split} R \geqslant \frac{{\left| {{\varphi _a} - {\varphi _c}} \right|}}{{\Delta {U_{\max }}}}\left[ {\frac{1}{{2\pi \sigma \left( {{a_a} + d} \right)}} + \frac{1}{{2\pi \sigma \left( {{a_c} + d} \right)}}} \right] - \\ \left[ {\frac{{{\beta _a} + {\rho _a}}}{{{S_a}}} + \frac{{{\beta _c} + {\rho _c}}}{{{S_c}}} + \frac{1}{{2\pi \sigma {a_a}}} + \frac{1}{{2\pi \sigma {a_c}}}} \right]\text{。} \\ \end{split}$ (9)
2.2 绝缘船体最小隔离电阻估算方法

 图 2 $n$ 种金属构成的电化学系统的等效电路图 Fig. 2 Equivalent circuit of electrochemical system consisting of n kinds of metal

$n$ 种电极电化学反应时的混合电位值为 $\varphi$ ，由图2可知，第 $i$ 个等效电极的电流强度为

 ${I_i} = \frac{{\varphi - {\varphi _i}}}{{{r_i} + {R_i} + \frac{1}{{2\pi \sigma {a_i}}}}} = \frac{{\varphi - {\varphi _i}}}{{\frac{{{\beta _i} + {\rho _i}}}{{2\pi {a_i}}} + \frac{1}{{2\pi \sigma {a_i}}} + {R_i}}}\text{。}$ (10)

 ${U_i} \approx \frac{{{I_i}}}{{2\pi \sigma \left( {{a_i} + d} \right)}}\text{，}$ (11)

 ${R_i} \geqslant \frac{{\left| {\varphi - {\varphi _i}} \right|}}{{\Delta {U_{\max }}\pi \sigma \left( {{a_i} + d} \right)}} - \left[ {\frac{{{\beta _i} + {\rho _i}}}{{2\pi a_i^2}} + \frac{1}{{2\pi \sigma {a_i}}}} \right]\text{。}$ (12)

 \begin{aligned}\frac{{{\varphi _1} {\!}-{\!} \varphi }}{{{R_{a1}}}} {\!}+{\!} \frac{{{\varphi _2} {\!}-{\!} \varphi }}{{{R_{a2}}}} {\!}+{\!} \cdots {\!}+{\!} \frac{{{\varphi _p} {\!}-{\!} \varphi }}{{{R_{ap}}}} {\!}= \\\frac{{\varphi {\!}-{\!} {\varphi _1}}}{{{R_{c1}}}} {\!}+{\!} \frac{{\varphi {\!}-{\!} {\varphi _2}}}{{{R_{c2}}}} {\!}+{\!} \cdots {\!}+{\!} \frac{{\varphi {\!}-{\!} {\varphi _q}}}{{{R_{cq}}}}\text{，}\end{aligned} (13)

 $\left\{ \begin{gathered} {R_{ai}} = \frac{1}{{2\pi {a_i}\sigma }} + \frac{{{b_{ai}} + {\rho _i}}}{{{S_i}}}\text{，} \\ {R_{cj}} = \frac{1}{{2\pi {a_j}\sigma }} + \frac{{{b_{cj}} + {\rho _j}}}{{{S_j}}}\text{。} \\ \end{gathered} \right.$ (14)

 $\left( {\sum\limits_{i = 1}^p {\frac{1}{{{R_{ai}}}} + \sum\limits_{j = p + 1}^n {\frac{1}{{{R_{ci}}}}} } } \right)\varphi = \sum\limits_{i = 1}^p {\frac{{{\varphi _i}}}{{{R_{ai}}}} + \sum\limits_{j = p + 1}^n {\frac{{{\varphi _j}}}{{{R_{ci}}}}} } \text{。}$ (15)

 ${\varphi _{p + 1}} \leqslant \varphi \leqslant {\varphi _p}\text{，}$ (16)

$\varphi$ 即为电化学系统的混合电位值。若第 $i$ 种金属的电极电位 ${\varphi _i} < \varphi$ ，则该金属为阳极，反之为阴极。

 $\overline {{R_i}} = {R_i} + \frac{1}{{2\pi \sigma {a_i}}} + \frac{{{\beta _i} + {\rho _i}}}{{2\pi a_i^2}}\text{。}$ (17)

 ${\varphi _R} = \frac{{\sum\limits_{i = 1}^n {\frac{{{\varphi _i}}}{{\overline {{R_i}} }}} }}{{\sum\limits_{i = 1}^n {\frac{1}{{\overline {{R_i}} }}} }}\text{，}$ (18)

 ${I_i} = \frac{{\varphi - {\varphi _R}}}{{\overline {{R_i}} }}\text{，}$ (19)

 $\overline {{U_i}} = \frac{{\varphi - {\varphi _R}}}{{\overline {{R_i}} }}\frac{1}{{2\pi \sigma \left( {{a_i} + d} \right)}}\text{，}$ (20)

 ${R_i} \geqslant \frac{{\left| {{\varphi _R} - {\varphi _i}} \right|}}{{\Delta {U_{\max }}\pi \sigma \left( {{a_i} + d} \right)}} - \left[ {\frac{{{\beta _i} + {\rho _i}}}{{2\pi a_i^2}} + \frac{1}{{2\pi \sigma {a_i}}}} \right]\text{。}$ (21)

3 算例

 图 3 材料的极化曲线 Fig. 3 Polarization curve of material

3.1 算例1

 图 4 自然腐蚀时艇体正下方3 m的电位信号 Fig. 4 The potential signal 3 meters below the submarine on the condition of natural corrosion

 图 5 增加隔离电阻时艇体正下方3 m的电位信号 Fig. 5 The potential signal 3 meters below the submarine when the isolation resistance was added
3.2 算例2

 图 6 自然腐蚀时艇体正下方3 m的电位信号 Fig. 6 The potential signal 3 meters below the submarine on the condition of natural corrosion

 图 7 增加隔离电阻时艇体正下方3 m的电位信号 Fig. 7 The potential signal 3 meters below the submarine when the isolation resistance was added
4 结　语

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