{"id":182,"date":"2019-09-03T11:14:26","date_gmt":"2019-09-03T02:14:26","guid":{"rendered":"https:\/\/www.ssil.co.jp\/product\/EMSolution\/en2\/?post_type=case&p=182"},"modified":"2022-09-22T19:28:07","modified_gmt":"2022-09-22T10:28:07","slug":"magnetic_field_strength","status":"publish","type":"case","link":"https:\/\/www.ssil.co.jp\/product\/EMSolution\/en\/case\/magnetic_field_strength\/","title":{"rendered":"Magnetic field strength (H) in magnetic material"},"content":{"rendered":"

Summary<\/h3>\n

Previously, EMSolution had the ability to output the magnetic flux density B (T) and magnetization M (T) as physical quantities in magnetic materials, but not the magnetic field strength H (A\/m). Although it is possible to calculate the magnetic field strength from the relationship between the output magnetic flux density, BH curve, and magnetization, it is not easy to calculate the magnetic field strength H in the case of two-dimensional magnetic anisotropy because two-dimensional interpolation is required. We are pleased to report that it is now possible to output the magnetic field strength in magnetic materials. In addition, the magnetization M can now be output for two-dimensional magnetic anisotropy analysis, whereas previously it could not be output. However, since the magnetic field strength in air and nonmagnetic materials does not have magnetization M and can be easily calculated backward using the magnetic permeability of vacuum, this function is intended for magnetic materials only.<\/p>\n

Explanation<\/h3>\n

The relationship between the magnetic flux density B, the magnetic field strength H, and the magnetization M in a magnetic material is expressed by the following equation.<\/p>\n

$$B = \\mu_0 H + M \u3000\u3000\u3000\u3000\u3000(1)$$<\/p>\n

As an example, let us analyze the coil and magnet of TEAM Workshop Problem 23, which is also used in “Problems in Electromagnetic Force Analysis<\/u>“<\/span><\/a>. This is an analysis of the magnet only, with the coil current set to 0A, and corresponds to Fig. 5 in\u3000“Problems in Electromagnetic Force Analysis<\/u>“<\/span><\/a>.\u00a0We confirm that the magnetic flux density B and the magnetic field strength H are in opposite directions in the magnet. Fig. 1 shows the distribution of magnetization, magnetic flux density, and magnetic field strength. The magnetization of 1.22T is given as an input in the -Z direction, and it can be seen that the magnetic flux density is in the same direction and the magnetic field strength is in the opposite direction.<\/p>\n

\n
\n \"\"<\/a><\/p>\n

(\u2170) \u78c1\u5316M [T]<\/p>\n<\/p><\/div>\n

\n \"\"<\/a><\/p>\n

(\u2171) Magnetic field strength H [A\/m]<\/p>\n<\/p><\/div>\n<\/div>\n

\n
\n \"\"<\/a><\/p>\n

(\u2172) \u00a0Magnetic flux density B [T]<\/p>\n<\/p><\/div>\n

Fig.1\u00a0 Magnet magnetization, magnetic field strength,
and magnetic flux density distribution<\/p>\n<\/div>\n

Next, let us output the magnetic field intensity using the ring model shown in “Analysis using nonlinear two-dimensional anisotropic magnetic properties”<\/span><\/a>.\u00a0The magnetic material is 35G165 with large uniaxial anisotropy, and the easy direction of magnetization is in the x direction (0 degrees) and the hard direction is in the y direction (90 degrees). For reference, we show an analysis in which the BH curve in the easy direction of magnetization (0 degree) is given as isotropic. Also shown is an analysis in which independent characteristics are given in the XYZ directions, with the BH curve in the easy direction of magnetization (0 degrees) in the X direction, the BH curve in the difficult direction (90 degrees) in the Y direction, and the specific magnetic permeability in the Z direction.<\/p>\n

This is a static magnetic field analysis where a current of 48 AT is applied to the coil. In the isotropic case, the magnetic flux density and field strength are in the same direction, but in the XYZ-direction independent and two-dimensional magnetic anisotropy cases, the magnetic flux density and field strength have angular differences, resulting in different magnetic flux density and field strength distributions. In addition, the two-dimensional magnetic anisotropy analysis can now output magnetization, which is shown here for reference. The angular difference between magnetic flux density and magnetic field strength shown in these analyses is due to the magnetic anisotropy of the material, and the magnetic properties are based on the initial magnetization curve, which does not take hysteresis into account. If you are interested in hysteresis-aware analysis, please contact us from “here”<\/span><\/a>.<\/p>\n

\n
\n \"\"<\/a><\/p>\n

(\u2170) Magnetic flux density B [T]<\/p>\n<\/p><\/div>\n

\n \"\"<\/a><\/p>\n

(\u2171) Magnetic field strength H [A\/m]<\/p>\n<\/p><\/div>\n

Fig.2 Magnetic flux density and magnetic field intensity distribution in isotropic magnetic properties<\/p>\n<\/div>\n

\n
\n \"\"<\/a><\/p>\n

(\u2170) Magnetic flux density B [T]<\/p>\n<\/p><\/div>\n

\n \"\"<\/a><\/p>\n

(\u2171) Magnetic field strength H [A\/m]<\/p>\n<\/p><\/div>\n

Fig.3\u00a0Magnetic flux density and magnetic field intensity distribution for independent magnetic properties in XYZ direction<\/p>\n<\/div>\n

\n
\n \"\"<\/a><\/p>\n

(\u2170) Magnetic flux density B [T]<\/p>\n<\/p><\/div>\n

\n \"\"<\/a><\/p>\n

(\u2171) Magnetic field strength H [A\/m]<\/p>\n<\/p><\/div>\n<\/div>\n

\n
\n \"\"<\/a><\/p>\n

(\u2172) \u00a0Magnetization M [T]<\/p>\n<\/p><\/div>\n

Fig.4\u00a0Magnetic flux density and magnetic field strength distribution in two-dimensional magnetic anisotropy<\/p>\n<\/div>\n

Here we have shown that it is possible to output the magnetic field intensity within a magnet or magnetic body. In addition, magnetization output is now also available for two-dimensional magnetic anisotropy analysis. These can be easily output by post-processing, and we hope you will use them.<\/p>\n

<\/p>\n

How to use<\/h3>\n

Magnetic field strength can be output by setting MAGNETIZATION to -1 as described in “Handbook 10. Input\/Output Files”. As mentioned earlier, the magnetic field strength in magnetic materials can be output. As with the magnetization output function, only the element amount (ELEM_OUT=1) can be output.
\nIt is also possible to output as post-processing:
\n  \u30fbPRE_PROCESSIONG=0,
\n  \u30fbMAKING_MATRICES=SOLVING_EQUATION=0,
\n  \u30fbPOST_PROCESSING=1<\/p>\n

* PRE_PROCESSING * MAKE_SYSTEM_MATRICES *<\/span>
\n 1 1<\/span>
\n* SOLVE_EQUATION * POST_PROCESSING *<\/font><\/span>
\n 1 1<\/font><\/span>
\n\u30fb\u30fb\u30fb<\/span>
\n* POST_DATA_FILE * ELEM_OUT *<\/font> NODE_OUT *NUMBER_OUTPUT_MATS * AVERAGE * WIDE * SUF_OPTION *<\/span>
\n 5 1<\/font> 1 0 0 0 0<\/span>
\n* MESH * CURRENT * MAGNETIC * FORCE_J_B* FORCE_NODAL * DISP * ELEM * HEAT * MAGNETIZATION *<\/font><\/span>
\n 1 0 1 0 0 0 0 0 -1<\/font><\/span>\n<\/p>\n

When using two-dimensional magnetic anisotropy, the element coefficient matrix is asymmetric, so please set up an asymmetric solver in MATRIX_ASYMMETRICITY (Handbook Section 3.2.6).<\/p>\n

* TREE_GAUGE * REGULARIZATION * RENUMBERING * SCALING * LINE_SERACH * MATRIX_ASYMMETRICITY *<\/font><\/span>
\n -1 0 0 0 0 1<\/font><\/span>\n<\/p>\n

Download<\/h3>\n

Problem23 model<\/h4>\n