Computation of Ship’s 3D Magnetostatic Field Utilizing Integral Equation Method of Scalar Magnetic Potential

doi:10.12382/bgxb.2022.0622

Abstract

Abstract:

Mastering the magnetic field distribution of ship is an important prerequisite for implementing the ship magnetic protection technology. Using the integral equation method to calculate the three-dimensional static magnetic field of the ship is one of the effective means.The integral equation method usually establishes the equation sets with the magnetization or magnetic flux density in the discrete elements as quantity to be calculated, and therefore obtains the solution of entire field based on the source region values. To further improve the calculated accuracy of magnetic field, it is necessary to increase the grid density at the cost of a sharp increase in computer memory requirement and computation. An integral equation method with scalar magnetic potential as quantity to be solved is used to address this problem. The ferromagnetic source is divided into tetrahedral elements, the unknown function is expanded in pieces according to the variational principle, and the singular integrals are found based on the relative positions of elements and nodes. The singular integrals are transformed into non-singular integrals by parameter substitution. The spherical analytical model shows that the modeling method using scalar magnetic potential only needs to discretize the source region into coarse grid cells to obtain the high-accuracycalculation results ofmagnetic field. After grids encryption, the scalar modeling method can maintain the computational accuracy, while its memory requirement and CPU execution time are significantly lower than those of vector modeling method. A virtual verification experiment is made for the three-dimensional ship magnetic field. For ferromagnetic objects such as ship hulls that need to be finely divided into elements, the static magnetic field calculated by the integral equation method based on the scalar magnetic potential agrees well with the results calculated by the finite element commercial software, and the integral equation methodis more efficient and save memory compared with the vector modeling method.

Key words: ship’s magnetic field, integral equation method, scalar magnetic potential, tetrahedral element, singular integral

CLC Number:

TM153.1

HE Baowei, ZHOU Guohua, LIU Shengdao, ZONG Jingwen, TANG Liezheng. Computation of Ship’s 3D Magnetostatic Field Utilizing Integral Equation Method of Scalar Magnetic Potential[J]. Acta Armamentarii, 2024, 45(3): 948-956.

Figures/Tables 9

Fig.1 Tetrahedral discrete elements model of ship

Fig.2 Schematic diagram of tetrahedral element

Fig.3 Local coordinate system of triangular surface

Fig.4 Integral area when P is located on the plane of Q

Fig.5 The relationship between the local coordinate system and the global coordinate system

Fig.6 Schematic diagram of iron solid sphere model and measuring points

Fig.7 The relationship between the sphere’s magnetic field calculation result and the number of discrete elements

Table 1 Differences between different methods for calculating ship induced magnetic field

感应磁场分量	标量磁位建模方法			磁感应强度建模方法
感应磁场分量	相对误差/%	计算时间/h	内存消耗/Mb	相对误差/%	计算时间/h	内存消耗/Mb
X_i_x	11.0	0.8	26	20.0	1.6	3533
Z_i_x	8.6	0.8	26	19.4	1.6	3533
X_i_z	4.9	0.9	26	14.2	1.7	3533
Z_i_z	2.7	0.9	26	7.3	1.7	3533

Fig.8 Ship’s induced magnetic fields calculated by different methods

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