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by Dr Stan Zurek

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users_manual [2020/10/20 22:06]
stanzurek [A.3.3 Kelvin Transformation] 		users_manual [2021/11/22 21:25] (current)
stanzurek [A.1 Modeling Permanent Magnets]
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 (A.1)  $  Hc = \frac{5·10^5· \sqrt{E}}{π}  $ (A.1)  $  Hc = \frac{5·10^5· \sqrt{E}}{π}  $
  
-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).
  
 {{fig_a-3.png}} {{fig_a-3.png}}
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 ==== A.4 Nonlinear Time Harmonic Formulation ==== ==== A.4 Nonlinear Time Harmonic Formulation ====
  
-Starting with the the 3.3 version of FEMM, the program includes a “nonlinear time harmonic” +Starting with the the 3.3 version of FEMM, the program includes a “nonlinear time harmonic” solver. In general, the notion of a “nonlinear time harmonic” analysis is something of a kludge. To obtain a purely sinusoidal response when a system is driven with a sinusoidal input, the system must, by definition, be linear. The nonlinear time harmonic analysis seeks to include the effects of nonlinearities like saturation and hysteresis on the fundamental of the response, while ignoring higher harmonic content. This is a notion similar to “describing function analysis,” a widely used tool in the analysis of nonlinear control systems. There are several subtly different variations of the formulation that can yield slightly different results, so documentation of what has actually been implement is important to the correct interpretation of the results from this solver. 
-solver. In general, the notion of a “nonlinear time harmonic” analysis is something of a kludge. + 
-To obtain a purely sinusoidal response when a system is driven with a sinusoidal input, the system +An excellent description of this formulation is contained in [21]. FEMM formulates the nonlin-ear time harmonic problem as described in this paper. Similar to Jack and Mecrow, FEMM derives an apparent BH curve by taking H to be the sinusoidally varying quantity. The amplitude of B is obtained by taking the first coefficient in a Fourier series representation of the resulting B. For the purposes of this Fourier series computation, FEMM interpolates linearly between the user-defined points on the BH curve to get a set of points with the same H values as the input set, but with an adjusted B level. The rationale for choosing H to be the sinusoidal quantity (rather than B) is that choosing B to be sinusoidal shrinks the defined BH curve–the B values stay fixed while the H values become smaller. It then becomes hard to define a BH curve that does not get interpolated. In contrast, with H sinusoidal, the B points are typically larger than the DC flux density levels, creating a curve with an expanded range.
-must, by definition, be linear. The nonlinear time harmonic analysis seeks to include the effects +
-of nonlinearities like saturation and hysteresis on the fundamental of the response, while ignoring +
-higher harmonic content. This is a notion similar to “describing function analysis,” a widely used +
-tool in the analysis of nonlinear control systems. There are several subtly different variations of +
-the formulation that can yield slightly different results, so documentation of what has actually been +
-implement is important to the correct interpretation of the results from this solver. +
-An excellent description of this formulation is contained in [21]. FEMMformulates the nonlin-+
  
 {{fig_a-9.png}} {{fig_a-9.png}}
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 Figure A.9: Solved problem. Figure A.9: Solved problem.
  
-ear time harmonic problem as described in this paper. Similar to Jack and Mecrow, FEMM derives +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.)
-an apparent BH curve by taking H to be the sinusoidally varying quantity. The amplitude of B is +
-obtained by taking the first coefficient in a Fourier series representation of the resulting B. For the +
-purposes of this Fourier series computation, FEMM interpolates linearly between the user-defined +
-points on the BH curve to get a set of points with the same H values as the input set, but with +
-an adjusted B level. The rationale for choosing H to be the sinusoidal quantity (rather than B) is +
-that choosing B to be sinusoidal shrinks the defined BH curve–the B values stay fixed while the H +
-values become smaller. It then becomes hard to define a BH curve that does not get interpolated. +
-In contrast, with H sinusoidal, the B points are typically larger than the DC flux density levels, +
-creating a curve with an expanded range. +
- +
-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.)+
  
-For nonlinear in-plane laminations, an additional step is taken to obtain an effective BH curve +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.
-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.+
users_manual.1603224367.txt.gz · Last modified: 2020/10/20 22:06 by stanzurek

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