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users_manual [2020/10/20 22:08]
stanzurek [A.4 Nonlinear Time Harmonic Formulation] |
users_manual [2021/11/22 21:25] (current)
stanzurek [A.1 Modeling Permanent Magnets] |
| (A.1) $ Hc = \frac{5·10^5· \sqrt{E}}{π} $ | (A.1) $ Hc = \frac{5·10^5· \sqrt{E}}{π} $ |
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| where //E// is the energy product in MGOe and the resulting //Hc// is in units of A/m (e.g. 40 MGOe ≈ 106 A/m). | where //E// is the energy product in MGOe and the resulting //Hc// is in units of A/m (e.g. 40 MGOe ≈ 10<sup>6</sup> A/m). |
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| {{fig_a-3.png}} | {{fig_a-3.png}} |
| Figure A.9: Solved problem. | Figure A.9: Solved problem. |
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| A “nonlinear hysteresis lag” parameter is then applied to the effective BH curve. The lag is assumed to be proportional to the permeability, which gives a hysteresis loss that is always proportional to |B|2. This form was suggested by O’Kelly [22]. It has been suggested that that the Steinmetz equation could be used to specify hysteresis lag, but the Steinmetz equation is badly behaved at low flux levels (i.e. one can’t solve for a hysteresis lag that produces the Steinmetz |B|1.6 form for the loss as B goes to zero.) | A “nonlinear hysteresis lag” parameter is then applied to the effective BH curve. The lag is assumed to be proportional to the permeability, which gives a hysteresis loss that is always proportional to |B|<sup>2</sup>. This form was suggested by O’Kelly [22]. It has been suggested that that the Steinmetz equation could be used to specify hysteresis lag, but the Steinmetz equation is badly behaved at low flux levels (i.e. one can’t solve for a hysteresis lag that produces the Steinmetz |B|<sup>1.6</sup> form for the loss as B goes to zero.) |
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| For nonlinear in-plane laminations, an additional step is taken to obtain an effective BH curve that also includes eddy current effects. At each H level on the user-defined BH curve, a 1D nonlinear time harmonic finite element problem is solved to obtain the total flux that flows in the lamination as a function of the H applied at the edge of the lamination. Then dividing by the lamination thickness and accounting for fill factor, and effective B that takes into account saturation, hysteresis, and eddy currents in the lamination is obtained for each H. | For nonlinear in-plane laminations, an additional step is taken to obtain an effective BH curve that also includes eddy current effects. At each H level on the user-defined BH curve, a 1D nonlinear time harmonic finite element problem is solved to obtain the total flux that flows in the lamination as a function of the H applied at the edge of the lamination. Then dividing by the lamination thickness and accounting for fill factor, and effective B that takes into account saturation, hysteresis, and eddy currents in the lamination is obtained for each H. |
