1.College of Electrical and Information Engineering, Hunan University, Changsha 410082, China 2.College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China
Fund Project:Project supported by the National Natural Science Foundation of China (Grant No. 51675086) and the China Postdoctoral Science Foundation (Grant No. 2020M672482)
Received Date:16 October 2020
Accepted Date:18 December 2020
Available Online:06 May 2021
Published Online:20 May 2021
Abstract:The cable harness provides a main gateway for electromagnetic interference(EMI) in electromechanical system. The unreasonable electromagnetic compatibility (EMC) design of cable harness will produce EMI to other on-board electronic equipment, bringing great safety risks to the system. Theoretical research and engineering practice indicate that most of the electromechanical systems cannot satisfy EMC standards, which can be attributed to the EMI generated by cables. As for the eletromagnetic(EM) illumination analysis, reliably and efficiently generating a full numerical model of cable harness is becoming more prominent for the EMC designers. Therefore, it is necessary to develop a more effective method to solve the modeling problem of cable harness. In the practical application, the cable harness has the characteristics of spatial layout, and its characteristics such as “large number of core wires”, “arbitrary curvature of space” and “randomness of wiring” bring challenges to the modeling of EM coupling to cable harness. The numerical simulation of the whole cable harness model requires severe conditions for computational resource and even makes the EM coupling analysis impossible. Thus, considering the uncertainty of wire position, this paper proposes a generalized simplified modeling method for the EM coupling effect of uncertainty strapping cable harness. Firstly, the Gaussian distribution and spline interpolation are used to determine the location of the core conductors in the random bundling. Then, the distribution parameters of the cable harness at different positions are established by using the transposition relationship between the subsegments of the wires. Finally, the effectiveness of the proposed method is verified by numerical examples of the arc-shaped and sine-shaped harness. In conclusion, this paper proposes a generalized simplification technique to model the EM illumination on cable harness with uncertainty wiring factors. By grouping the conductors together, the required computation time is markedly reduced and the complexity of modeling the completely cable harness is significantly simplified within a good accuracy. The proposed method provides a way of solving the modeling problem caused by “uncertainty strapping” of the complex wiring harnesses in electromechanical systems. Keywords:cable harness/ electromagnetic coupling/ uncertainty strapping/ generalized simplified modeling method
本文采用电磁仿真软件CST (Cable Studio工作室)对本文方法进行验证, 利用CST全波仿真方法求解计算平面波照射下圆弧不确定捆扎线束等效前后的电磁耦合效应大小. 如图8所示, 在CST中建立21根多导体不确定性捆扎线束模型, 线束中所有导体长度为3/4个半径为R = 825 mm的圆弧; 芯线具有相同的半径$r = 0.2$ mm, 绝缘层厚度为1 mm, 绝缘层介电常数为2.5, 相对磁导率为1.0. 中间一排导线(编号2, 6, 11, 16, 20)距离地面高度60 mm. 参考地面为长4000 mm, 宽4000 mm, 厚2 mm的PEC良导体. 平面波入射方向沿y方向平行于参考地面, 采用线极化方式, 电场方向沿x方向, 幅值为50000 V/m, 干扰源波形为CST默认脉冲激励源. 线束负载阻抗均为50 Ω. 图8中编号为1—21的导线近端端点坐标如表1所列. 图 8 平面波照射下21根圆弧捆扎线束模型示意图 Figure8. Schematic diagram of a 21-conductor circular arc-shaped binding cable harness model illuminated by the plane wave.
导线编号
1
2
3
4
5
6
7
坐标x, y
–8, 4
–8, 0
–8, –4
–4, 8
–4, 4
–4, 0
–4, 4
导线编号
8
9
10
11
12
13
14
坐标x, y
–4, –8
0, 4
0, 4
0, 0
0, –4
0, –8
4, 8
导线编号
15
16
17
18
19
20
21
坐标x, y
4, 4
4, 0
4, –4
4, –8
8, 4
8, 0
8, –4
表1直角坐标系中21-线束模型近端位置(单位: mm) Table1.Coordinates of each conductor near end of the 21-conductor cable harness (unit: mm).
使用高斯分布和样条插值法获取不确定性捆扎线束内21根导线的位置. 首先, 通过线束两端位置确立弧形线束的始端坐标, 确立捆扎线束初始位置处电容矩阵${{C}}\left( z \right)$和电感矩阵${{L}}\left( z \right)$. 然后, 在MATLAB中使用高斯分布函数建立每根导线中心位置的随机坐标. 开始时, 在线长方向上依次将所有导线的N个截面在参考位置处进行填充, 从而建立不确定性捆扎线束模型. 基于简化线束单位长度电感和电容矩阵计算结果, 根据简化线束几何截面参数建立方法可以得到简化导体半径为4 mm, 绝缘层厚度1 mm, 对地高度为60 mm. 根据本文提出的不确定性捆扎线束广义ECBM 方法, 简化线束模型耦合电流值等于其全线束模型内各导线耦合电流之和, 21根不确定性捆扎线束模型等效前后近端和远端负载上耦合电流对比曲线如图9(a)和图9(b)所示. 图 9 圆弧不确定性捆扎线束简化前后负载耦合电流对比 (a)近端; (b)远端 Figure9. Comparison of the load coupling current on the circular arc-shaped binding cable harness: (a) Near end; (b) far end.
不确定性捆扎线束布线路径呈正弦弧形, 如图10所示. 弧形路径满足函数$f(t) \!=\! 500\sin \!\left( {\dfrac{{{\rm{\pi t}}}}{{1000}}} \right)$ mm, 其中t为线束长度方向位置坐标, 取值范围为(0, 2000 mm). 线束内导线参数不变, 中间一排导线(编号2, 6, 11, 16, 20)距离地面高度40 mm. 外部电磁环境为平面波, 幅值和入射方向与图8中保持一致. 图 10 平面波照射下21根正弦弧形不确定性捆扎线束模型 Figure10. Schematic diagram of a 21-conductor sine arc-shaped binding cable harness model illuminated by the plane wave.
根据本文提出的不确定性捆扎线束广义ECBM方法, 21根正弦弧形线束模型简化前后近端和远端负载上耦合电流对比曲线如图11(a)和图11(b)所示. 从仿真结果看, 在0—1 GHz频段内, 不确定性捆扎线束简化模型近端和远端负载耦合电流与其全模型耦合电流符合良好, 再次验证了本文提出的广义ECBM方法的正确性. 图 11 正弦不确定性捆扎线束简化前后负载耦合电流对比 (a)近端; (b)远端 Figure11. Comparison of the load coupling current on the sine arc-shaped binding cable harness: (a) Near end; (b) far end.
24.3.误差分析 -->
4.3.误差分析
本文采用特征选择验证技术(FSV), 对完整模型和简化模型之间的仿真结果进行评价[20,21]. FSV技术根据特定标准显示了两组数据之间相关性. FSV技术评价指标主要包括: 总幅差测度(ADMtot)、总特征差测度(FDMtot)和总全局差测度(GDMtot). 根据ADMtot, FDMtot和GDMtot 大小对数据间符合程度划分等级描述: excellent (0—0.1), very good (0.1—0.2), good (0.2—0.4), fair (0.4—0.8), poor (0.8—1.6)和very poor (> 1.6). 表2列出了图9和图11仿真结果的FSV技术评价结果. 从表2可以看出, 圆弧和正弦捆扎线束等效前后对比结果评价良好, 进一步说明了本文方法的有效性.
线束终端
FSV
ADMtot
FDMtot
GDMtot
圆弧线束
近端
0.265/good
0.181/very good
0.317/good
远端
0.289/good
0.200/very good
0.345/good
正弦线束
近端
0.313/good
0.172/very good
0.376/good
远端
0.290/good
0.157/very good
0.350/good
表2本文方法的FSV评价结果 Table2.The FSV evaluation results of the proposed method.