X-MINING Polar anisotropic SmFeN magnets simulation with 20 poles outer circumference [Analysis case: Magnetic field analysis simulation]

• You want to reduce computation time by converting a 3D magnetic field analysis calculation to a 2D one.
• You want to know how the surface flux density of a magnet is affected by a 3D analysis and a 2D analysis.
• You don’t know which is better to using 2D/3D analysis?

This section presents examples of surface magnetic flux density waveforms simulated in 2D and 3D analysis using Wellmax^TM SmFeN magnetic material and the commercial magnetic field analysis software “JMAG” with several different configurations of orientation.

Step 1: Orientation analysis

Several molds with embedded permanent magnets are modeled and the orientation of the Wellmax^TM material during molding is calculated using 2D and 3D analysis in “JMAG”.

Step 2: Surface magnetic flux density analysis

Calculate the waveform of the surface flux density of the magnet with orientations obtained in Step1 using 2D and 3D analysis in “JMAG”.

Model: Magnet to simulate magnetic field analysis

• Shape of the magnet: Φ35×Φ32×L17 (mm)
• Magnetic matrial: Wellmax^TM-S3A12M
• Magnetic poles：20 poles in outer surface
• Anisotropic type：Polar
• Specifications：Surface magnetic flux density≧ 0.25T (Gap=0.02mm from outside magnet surface, Center of magnet height)
• Waveform：Sinusoidal wave
• Accessories：Inner york (magnetic), sleeve (magnetic/ non-magnetic)

Figure １　Shape of magnet

Analytical model

The orientation model was constructed using one or two permanent magnets (orientation magnets) per magnet pole, and the arrangement and angle of the orientation magnets and the materials of the mold components were varied.
Cylindrical coordinates were used in the two-dimensional analysis, and the model was constructed with the center axis of the magnet as the center axis of the cylindrical coordinates.

Figure 2 Example of magnetic circuit design

Table 1 Six patterns of analysis model setup

Result of analysis

The direction and magnitude of the magnetization of Wellmax^TM magnetic material filled in the cavities were calculated using the magnetic field analysis software “JMAG” for each orientation model in two and three dimensions.

Figure 3 Example of vector diagram in cavity

Analytical model

Each case of 2D/3D model, we used magnetic field analysis to simulate the waveform of the surface flux density of each magnet with the orientation obtained in Step 1 for the Wellmax^TM material.

Result of analysis

The peak values of the surface magnetic flux density and odd-order component values of the waveforms of the magnets simulated by magnetic field analysis for each 2D/3D orientation model were compared with the configuration of the orientation model.

Figure 4 Example of vector diagram of magnet analysis results based on each orientation

Figure 5 Surface magnetic flux density waveforms of magnets in six orientation model patterns

Figure 6 FFT analysis results for six orientation model patterns.

Surface magnetic flux density waveforms from 2D and 3D analyses were simulated and compared using Wellmax^TM SmFeN magnetic material and the commercial magnetic field analysis software “JMAG” for several different orientation configurations.

At the same time, we investigated an orientation configuration in which the surface flux density of the magnet is close to a sinusoidal wave.

The 2D analysis resulted in a slightly different waveform shape compared to the 3D analysis, especially in the case of a waveform shape close to a radial orientation, resulting in a concavity in the center of the poles.

In the measurement of the surface magnetic flux density of a single magnet, the effect of differences in permeance is significant.
Especially in the case of radial orientation, the permeance is lower in the center of the poles than in the pole-switched area, and this effect is noticeable in a 2D analysis.
When magnetic material is placed on the opposite side of the magnet, the difference in permeance is smaller and the waveform changes.

In the six orientation configurations examined in this study, the first-order component of the waveform was nearly 90% in patterns 5 and 6, and the third-order and fifth-order components were low, resulting in a waveform close to a sinusoidal waveform.