Axial Flux Motor Design Tool

The machine has one coreless three-phase wye stator and two PM rotors. This is a reduced analytical sizing model, not a reproduction of the full magnetic equivalent circuit, iron-loss or thermal model in Parviainen's dissertation.

The active annulus is divided into equal radial slices, evaluated at their midpoints, following the quasi-3-D principle described by Parviainen (2005), attached pp. 36–38. The prescribed fundamental field is interpolated linearly between inner and outer radii.

For total poles $P$, overlapping windings use $Q=3P/2$ coils and concentrated type-I windings use $Q=3P/4$, one coil per phase group. Coil width and mean end-turn length follow Kamper et al. (2008), attached pp. 4–6: Eqs. (18)–(19), (24), (26), (30) and (32). The maximum side width can be reduced by the entered geometric width fraction. At each radius, $\theta_j=Pw/(2r_j)$; the overlap factor is $\sin(\theta_j/2)/(\theta_j/2)$. The concentrated factor also includes $\sin[(\theta_m-\theta_j)/2]$. This is an explicitly unskewed radial extension of their finite-width coil model; the concentrated active-side length correction is neglected.

The peak fundamental phase flux linkage is

where $N_s=N_{turn}(Q/3)/a$. Hence $E_{ph}=\omega_e\lambda_{pk}/\sqrt2$ and $T_{em}=3(P/2)\lambda_{pk}I_{rms}/\sqrt2$. The air-gap field is not multiplied by two: it already describes the field crossing the central winding. This sinusoidal power conversion is consistent with the general sizing framework of Huang et al. (1998), attached pp. 1–2. A 120-slice recalculation reports numerical convergence independently of the selected slice count.

Conductor area includes all strands in hand. With identical parallel paths,

Copper temperature correction uses $\alpha_{Cu}=0.0038\ \mathrm{K}^{-1}$ from Parviainen, attached p. 52, Eq. (2.31). Nominal annealed-copper resistivity and density are stated assumptions. The AC multiplier is supplied, not calculated from the skin-depth screening result.

Rotational loss allowances scale as speed (bearing), speed cubed (windage), and speed squared (additional eddy allowance). These are explicit user assumptions, not fitted paper correlations. Shaft power is converted power minus rotational losses, clipped to zero below drag torque. Efficiency divides that available output by converted power plus copper loss; it is defined as zero at zero electrical input. The raw shaft balance is retained for conservation checks.

Voltage uses $V_{ph}=\sqrt{(E_{ph}+IR_{AC})^2+(\omega_eLI)^2}$ with current in phase with the PM EMF, and $V_{LL}=\sqrt3V_{ph}$. The ideal linear SVPWM line-line RMS limit is $V_{dc}/\sqrt2$. Both the selected current and target shaft current are checked.

The optional ideal field is derived here from a one-dimensional linear magnetic circuit: $B_0=B_r(2h_m)/[2h_m+\mu_r(h_w+2g)]$ and $B_1=(4/\pi)B_0\sin(\pi\alpha_p/2)$. It assumes rectangular alternating pole fields and is not a validated substitute for the field solution in either named paper.

• Uniform round bare copper strands; all coils have equal turns and length. Copper resistivity at 20 °C is $1.724\times10^{-8}\ \Omega\,m$ and density is $8960\ \mathrm{kg/m^3}$. Leads, insulation and joints add mass and resistance in a real winding.
• Three balanced wye phases; parallel paths are identical and connected with the correct polarity. The tool sizes two established coil-count families; it does not generate a winding connection diagram.
• Sinusoidal fundamental field and current, aligned for torque production; no reluctance torque, field weakening or armature-reaction correction. Entered field is at operating magnet temperature and includes the effect of both rotor disks.
• Each bare round strand must fit both the axial winding thickness and the coil-side width; the copper-area fill check also applies. These necessary geometric checks do not establish an achievable strand-packing arrangement or insulation clearance.
• Radial active conductors are approximated as straight and unskewed. End-turn formulas are geometric approximations. Copper fill is copper area divided by gross coil-side cross-section.
• Copper temperature, phase inductance, AC resistance factor and rotational losses are supplied design estimates. Default inductance (0.3 mH), bearing loss (8 W) and windage loss (2 W at 300 rpm) are illustrative assumptions, not measurements of the published prototypes.
• With a known field, changing the air gap does not automatically change that field: update its inner and outer values. The gap still enters overlapping end-turn clearance. The ideal field option updates the field from gap and coil thickness.
• No stator iron is present, so stator iron loss is zero. Rotor and winding eddy losses are not guaranteed to be zero; enter an additional allowance and/or an AC multiplier as appropriate. Inverter and supply losses are excluded.
• The ideal field and loss scaling are derived/assumed here; they are not claimed to be Parviainen's complete quasi-3-D model. The static schematic needs no animation.

Use for preliminary comparison of dual-rotor coreless AFPM motors with the two supported balanced winding families. Concentrated windings require pole counts divisible by four; overlapping windings require even pole counts. Parallel circuits must divide the coils per phase. For overlapping windings the inner radius must exceed the total magnet-to-magnet nonmagnetic gap used by the end-turn approximation.

The numerical input ranges are editing limits, not validated operating envelopes. Published machine validation is at 400 mm active diameter, inner/outer ratio 0.7, 24 poles, peak fundamental field 0.527 T, and 120 W copper loss. Prediction versus measurement is 45.49 versus 43.9 N·m for overlap and 44.87 versus 44.6 N·m for concentrated coils. Copper-mass tolerances are wider because simplified end turns omit leads and detailed construction. These are limited validation points, not a universal accuracy specification.

The third reference verifies only the rated shaft requirement in Parviainen Table 3.1 (5 kW, 300 rpm, 159 N·m). The iron-cored dissertation prototype has a different topology; its measured 211 V EMF and efficiency are not claimed as predictions of this calculator. The Kamper checks use torque and copper mass, not the Table VI rated-voltage entries: its voltage labeling is not used to establish independent back-EMF accuracy.

Verify field, end turns and effective resistance for a final design. Low pole counts, severe radial field variation, thick coreless windings, large gaps, skew and unusual magnet shapes can exceed the simplified model. Refine radial slices until the reported integration difference is small; this only checks numerical integration. The ideal one-dimensional field neglects saturation, flux leakage, radial end effects and fringing.

Current sweeps are theoretical at fixed field and temperature; they do not enforce a continuous thermal rating or inverter current rating. Below drag torque, available motoring output and efficiency are zero while the raw power balance is negative. No stall solution, rotor stress, magnet retention, bearing force, thermal equilibrium, demagnetization or fault behavior is calculated.