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Model fidelity & known limitations

The fast layers are deliberately simple. This page is the canonical statement of what they leave out; know it before trusting absolute numbers. Each item is also documented at the relevant docstring.

Topology

Single-gap machine (one rotor disk, one stator disk). Real axial-flux machines are often double-gap (TORUS, YASA, AFIR). A single-sided rotor carries a large unbalanced axial pull; AnnularResult.axial_force_n reports it (≈5–6 kN for the reference motor) and the bearing stack must absorb it. Torque, mass, and inertia for double-gap variants are not modeled.

Magnetics

The 1D load line is an upper bound on the gap field. FEA validation (guide) measured, for the reference motor:

  • under-magnet mean flux density: −11.2% vs the load line,
  • fundamental \(B_1\): −6.8%,

from inter-magnet leakage and circumferential fringing the 1D magnetic circuit cannot see, plus a measured Carter factor \(k_C = 1.44\) for the slotted stator. Both models accept carter_factor= to fold a measured correction back in; the residual fringing bias remains otherwise.

No magnetic saturation: torque is exactly linear in current. The yoke-flux-density constraint (vs the steel's saturation knee) and the current-density limit are the guards; near or beyond them the linear prediction is optimistic.

Fixed winding factor (default 0.933 for the assumed integral-slot 3-phase layout). Changing phase/pole/slot combinations does not update it.

Electrical

The voltage constraint neglects inductive drop (\(I\,X_L\)): it compares \(\sqrt{3}\,(E + I R)\) against \(V_{dc}/\sqrt{2}\). Fine at low electrical frequency; optimistic when \(f_e\) is high and the bus margin is tight (≈100 µH at several kRPM adds tens of volts).

Thermal

Single lumped RC from winding to ambient with a constant thermal resistance: no speed-dependent cooling, no radial or axial temperature distribution. Half of core loss is assigned to the winding node.

Magnet temperature is fixed at ambient + 40 °C, not coupled to the solved winding temperature. Remanence derating uses that assumption everywhere.

Losses omitted

  • AC copper loss (skin and proximity effects), relevant above ~1 kHz electrical frequency.
  • Magnet eddy-current loss.
  • PWM harmonic losses (sinusoidal current assumed).
  • Mechanical loss defaults to zero (bearing/windage coefficients are parameters of AnnularModel), so efficiency is optimistic unless you set them.

Numerical conventions

  • The runout average uses the exact circumferential mean of the load line; because the load line is convex in the gap, mean torque rises slightly with runout; the real penalties are the 1/rev ripple proxy and the axial force modulation. This sign is test-pinned; it is not a bug.
  • The 2D FEA validation linearizes the annulus at the mean radius (one pole pair, periodic), so radial end effects are outside its scope.