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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (

NdFeB permanent magnets (PMs) are widely used in high performance electrical machines, but their relatively high conductivity subjects them to eddy current losses that can lead to magnetization loss. The Finite Element (FE) method is generally used to quantify the eddy current loss of PMs, but it remains quite difficult to validate the accuracy of the results with complex devices. In this paper, an experimental test device is used in order to extract the eddy current losses that are then compared with those of a 3D FE model.

Due to their high energy density, rare earth permanent magnets are widely used in electrical machines. However, as these magnets are electrically conductive, high spatial frequencies and temporal harmonics can lead to significant eddy current loss density. In this case, irreversible demagnetization can occur because of the temperature rise [

In this paper, a dedicated test device, to measure the eddy current losses in sintered NdFeB magnets, is built. A 3D FE analysis of the eddy current losses is performed and results are compared with the experiment by a loss balance technique combining experiment and FE results.

The test device used for the measurements of the eddy current loss is presented in

Magnetic circuit: 130 × 140 × 60 mm (LxWxD);

NdFeB magnet: 4 × 30 × 60 mm (LxWxD);

Air gap: 5 mm.

The test device is composed of a magnetic circuit made of high performance electrical steel (FeSi NO 20) of 0.2 mm thickness and an iron loss density of 15 W/kg @ 1T-400 Hz. A sintered NdFeB (NEOFLUX-GSN35), with a remnant flux density of B_{r} = 1.214 T and an identified electrical conductivity of

In practice, the direct measurement of eddy current losses in the permanent magnet cannot be easily achieved. Indeed, the total losses _{t}_{Cu}_{iron}_{PM}_{p}_{p}_{h}_{cl}_{exc}_{h}, α, k_{cl}_{exc}

The validity of the proposed approach is verified by realizing 3D Finite Element (FE) simulations with _{r}_{s}_{s}_{c}

The eddy currents losses _{PM-FE}_{PM}^{2} and 8.764 are used to keep the same parameters as in

In

From measurements on an Epstein frame, the parameters of the iron loss model were identified for different frequencies (5–600 Hz) and different peak values of flux density _{m}

First, the validity of the iron loss model is verified without the permanent magnet for an air-gap of 1mm. The iron losses measured from the total losses minus the copper losses are compared to the calculated ones at 50 Hz and 600 Hz with a symmetric excitation (see

The iron loss model gives good results when the B-H cycles of hysteresis are centered. The introduction of a PM in the system with an air-gap of 1mm induces an offset of the magnetic flux density of 0.96 T. As shown in other works, this offset will greatly increase the quasi-static hysteresis losses _{h}

In order to compensate for this error in the computation of iron losses a polynomial variation of the _{h}_{max}_{h}_{h}_{h}

Once the iron loss model is validated for the experimental device without the magnet, the calculation of eddy currents in the permanent magnet are performed as explained previously.

To ensure the validity of the approach, the measured global magnetic flux density of the PM is first compared with the calculated one. The obtained results for 400 Hz are presented in

Once the copper losses _{Cu}_{iron-FE}_{PM}

These results are satisfactory considering the combination of experimental and modeling errors as well as the modeling hypotheses. This allows then to validate the losses obtained from the numerical model for a further use in a thermal calculation.

In this study an opened-circuit experimental system was fabricated to measure the eddy current losses in a NdFeB sintered magnet. A loss balance technique combining experimental and FE results was proposed in order to quantify eddy currents losses in PMs. The eddy current losses estimated with this method were then compared to those obtained directly by the 3D FEM analysis. The eddy current losses found by the 3D FE method was close to the result obtained by the proposed approach. Considering the hypothesis in the modelling procedure and experimental errors, these results confirm that the eddy current losses in a NdFeB magnet can be calculated in a satisfactory way by a 3D FE analysis.

The authors declare no conflict of interest.

Experimental device.

FE mesh of ¼ of the experimental device.

Iron losses at 400 Hz for (

Calculation and measurement of the iron losses in the experimental device at (

Calculation and measurement of the iron losses in the experimental device with an offset of 0.96 T at (

Evolution of the _{h}

Iron losses with the new _{h}

Magnetic flux density in the magnet for: (

Iron loss parameters.

_{h} |
190 | 251 |

1.841 | 1.623 | |

_{cl}. |
0.013 | 0.016 |

_{exc} |
0 | 1.4E-7 |

Loss separation from the experiment.

f [Hz] | 50 | 200 | 400 | 600 | 50 | 200 | 400 | 600 | 50 | 200 | 400 |

P_{t} [W] |
0.34 | 1.06 | 2.71 | 5.31 | 1.77 | 5.41 | 15.8 | 27.3 | 3.48 | 10.4 | 30.7 |

P_{Cu} [W] |
0.22 | 0.22 | 0.21 | 0.23 | 1.04 | 1.04 | 1.06 | 1.36 | 2.08 | 2.02 | 2.12 |

P_{iron}+P_{PM} [W] |
0.12 | 0.84 | 2.49 | 5.08 | 0.72 | 4.36 | 14.7 | 26.0 | 1.40 | 8.38 | 28.5 |

Eddy current losses in the permanent magnet at 400 Hz.

| ||||||||
---|---|---|---|---|---|---|---|---|

FE calculation | P_{iron-FE} |
[W/kg] | 0.42 | 0.41 | 1.4 | 1.4 | 2.5 | 2.5 |

P_{PM-FE} |
[W/kg] | 22.09 | 22.71 | 146 | 149 | 299 | 304 | |

| ||||||||

Proposed approach | P_{PM} |
[W/kg] | 27.89 | 24.11 | 148 | 128 | 288 | 249 |