Estimate gap flux and core density, then check the assumptions and evidence needed for your next design review.
Reviewed 2026-10-25 · Use the calculator
Linear estimate; demagnetization and local saturation are unassessed. Next checks.
Core above assumed 1.40 T screen; nonlinear review needed.
Core screen: above screen (assumed 1.40 T level)
Ag = Am; At = 0.62 Ag; Ay = 0.65 At; fixed μr; μrec = 1.05. Effective series path: 2.30 mm total gap and 8.00 mm total magnet length, with one equivalent tooth. Two equal yoke branches are assumed where a stator return yoke is present. Rotor back-iron is omitted; topology comparisons do not establish an optimum.
The fundamental amplitude assumes a rectangular pole waveform and can exceed its plateau value. Leakage is a heuristic external-reluctance penalty. Read the equations and limitations.
Confirm the flux path before selecting a core. YASA omits the stator yoke; rotor paths remain part of the real machine. Do not transfer the simplified circuit unchanged between architectures. [S1]
Use material data at its stated conditions. A maximum permeability is not the operating permeability, and B at a specified H is not a saturation limit. [S2]
Request comparable loss evidence. Check specimen type, waveform and frequency before comparing ring and electrical-steel measurements. [S3] [S4]
Leave magnet safety open until hot curves and current are known. A geometry proxy alone cannot establish a demagnetization margin. [S5] [S6]
The following equations describe this implementation, not a validated complete-machine solver. Use SI units internally: lengths in m, areas in m², reluctance in A/Wb; displayed MA/Wb is 10⁶ A/Wb. μ0 = 4π × 10⁻⁷ H/m.
Ag = Am = π(Do² − Di²) αp / (8p); At = 0.62 Ag; Ay = 0.65 At
g_eff = kc g; Rg = gΣ/(μ0 Ag); Rt = lt/(μ0 μr At)
ly = π Rmean / p; Ry,eq = ly/(2 μ0 μr Ay), or 0 without a stator return yoke
Ccore = 1 + (Rt + Ry,eq)/Rg; Rm = lmΣ/(μ0 μrec Am)
Fm = Br(T) lmΣ/(μ0 μrec); μrec = 1.05 (assumed)
Br(T) = Br20 [1 + αBr (T − 20)/100]
Bg = Br(T) / [1 + μrec kσ (gΣ/lmΣ) Ccore]
Φp = Bg Ag; Bt = Φp/At; By = Φp/(2 Ay)
Pc_proxy = lmΣ/(gΣ kσ); f_e = p n / 60
Here gΣ and lmΣ are the effective total gap and magnet lengths in the selected approximation. kσ is a heuristic penalty on external reluctance, not an explicit leakage branch. The geometry-only Pc proxy excludes core reluctance and is not the actual magnet B/(μ0|H|) load-line coefficient. Ccore describes linear core reluctance; it is not a nonlinear saturation factor. The source term uses remanence and recoil permeability, not intrinsic coercivity Hcj.
| Quantity | Current assumption | Required engineering evidence |
|---|---|---|
| Tooth / yoke area | At = 0.62 Ag; Ay = 0.65 At | Net CAD areas and local tooth-root geometry |
| Core | One equivalent tooth; constant μr | Actual path lengths, parallel branches and nonlinear B–H data |
| Return yoke | Two equal half-flux branches; Ry,eq is half the single-branch reluctance | Topology-specific return circuit and rotor back-iron |
| Gap field | Uniform radial field; rectangular pole waveform | Radial slices and 3D fringing/leakage analysis |
| Magnet | Am = Ag; constant μrec = 1.05; linear reversible Br(T) | Supplier curves at temperature, current reaction and local field |
The calculator accepts kc as an input; it does not derive it from a slot sketch. Record slot count Qs, slot opening bs(r), tooth profile and minimum operating gap. Compare inner, mean and outer slices, then refine where gradients are large. This is an engineering check recommendation, not a fixed validated number of slices or a predicted gain.
Höganäs lists the following typical portfolio data at 800 MPa compaction and 1 T, 5 × 5 mm cross-section. These measured examples do not calibrate the calculator’s illustrative candidates. [S2]
| Grade | Density (g/cm³) | B at 10,000 A/m (T) | Maximum μr | 400 Hz loss (W/kg) | 1 kHz loss (W/kg) |
|---|---|---|---|---|---|
| Somaloy 700 3P | 7.57 | 1.61 | 850 | 45 | 132 |
| Somaloy 1000 3P | 7.56 | 1.63 | 950 | 46 | 143 |
The supplier warns that ring-component data and sheet test data are not directly comparable. Confirm density, heat treatment and section size, then compare under a common component duty. Electrical steel also needs an orientation and stacking specification; the calculator omits those effects. [S2] [S4]
Request engineering review of your material evidence| Decision item | Known from this page | Unknown / next evidence |
|---|---|---|
| Fundamental frequency | f_e = p n/60 | PWM harmonic amplitudes and local B(t) |
| Material loss | Published specimen values at stated conditions | Actual part loss map, temperature and rotational flux |
| SMC versus steel | Different specimen methods and processing conditions | Matched component tests; no universal crossover is established |
| Efficiency / cooling | Not calculated | Copper, magnet, mechanical and inverter losses; thermal network |
IEC measurement scopes help specify evidence, not predict machine efficiency. Keep the fundamental and carrier excitation separate and ask the laboratory to document the waveform and specimen preparation. [S3] [S4]
| Concept | Gap / magnet count | Stator return yoke | Boundary |
|---|---|---|---|
| YASA / TORUS-NS | 2 / 2 | Omitted | One equivalent through-flux tooth; rotor return paths omitted |
| TORUS-NN | 2 / 2 | Equivalent pair included | Parallel paths are collapsed; needs a topology-specific branch network |
| SSSR | 1 / 1 | Equivalent pair included | One gap face; unbalanced axial attraction is not calculated |
| AFIR | 2 / 1 | Equivalent pair included | Effective surrogate; two stators and actual magnet arrangement need separate modeling |
The original YASA paper supports the absence of its stator yoke. Other path counts above are implementation assumptions; they do not prove torque, mass, efficiency or temperature superiority. [S1]
| Risk | Consequence | Mitigation / alternative |
|---|---|---|
| Mistaking a proxy for safety approval | Demagnetization or an unsuitable core can remain undetected | Request hot curves and peak-current analysis; leave release status open |
| Unmodeled local saturation or leakage | Linear flux estimate can be overstated | Use net CAD sections and nonlinear radial/3D analysis |
| Choosing a material from unmatched loss data | Cooling and efficiency targets may be missed | Compare a common component geometry and waveform; test both candidates |
| Committing tooling before process qualification | Tooling iterations, scrap and sample delays | Request density and dimensional capability evidence; compare a low-volume sample route |
| Symmetry assumed across real tolerances | Rotor contact, bearing load or gap closure | Couple force-displacement and structural checks with thermal growth |
The default N45SH reference uses typical Br20 = 1.35 T and αBr = −0.12%/°C from Arnold’s sheet. Its coefficient note covers 20–150°C; higher calculator temperatures are visibly marked as extrapolation. Other magnet rows are illustrative inputs. None of these choices supplies a temperature-dependent intrinsic knee or a safe operating temperature rating. [S5]
Request the actual grade’s B–H and J–H curves at the hottest local magnet temperature, then evaluate the most adverse opposing current and fault case. Geometry affects an operating slope, but safety requires the full magnetic circuit and local field distribution. [S5] [S6]
These are the same four presets offered in the tool. Values are calculated by this page’s model with the declared assumptions; no prototype tests, torque gains or production outcomes are claimed. Load a preset to inspect every input or export the summary.
| Scenario | Do / Di (mm) | g / lm (mm) | p / rpm | Gap / tooth (T) | Pc proxy | Next action |
|---|---|---|---|---|---|---|
| eVTOL / Aerospace High-Speed YASA | 180 / 112 | 1.0 / 4.0 | 8 / 4500 | 0.902 / 1.454 | 3.11 | Inspect assumptions, obtain actual curves and request engineering review |
| EV Direct-Drive Traction TORUS-NS | 240 / 150 | 1.2 / 5.0 | 10 / 3000 | 0.870 / 1.403 | 3.15 | Inspect assumptions, obtain actual curves and request engineering review |
| Robotic Joint Compact Actuator SSSR | 160 / 105 | 0.8 / 3.5 | 14 / 1200 | 0.963 / 1.553 | 3.55 | Inspect assumptions, obtain actual curves and request engineering review |
| Marine Pod Propulsion AFIR | 350 / 220 | 1.5 / 6.0 | 16 / 1500 | 0.688 / 1.110 | 1.47 | Inspect assumptions, obtain actual curves and request engineering review |
First version 2026-10-25 · Technical review 2026-10-25. The first-version date records creation, not a verified public publication date.
Review policy: AxialFluxCore will recheck the source editions, material conditions and model assumptions within six months of this review, or sooner when a cited datasheet or the model changes. Send corrections through the engineering inquiry form.
Public source scope checked 2026-10-25. Model equations, screening levels and topology surrogates are this page’s declared assumptions; citations do not imply third-party validation of the tool. Public evidence is insufficient to claim universal loss savings, magnet safety thresholds, certification or delivery time.
[S1] · 2007 · IEEE IEMDC · DOI 10.1109/IEMDC.2007.382753
Original YASA topology research. Its prototype-specific results do not establish a universal mass or torque benefit.
[S2] · 2025 · 2273HOG-3 · product portfolio p. 4
Grade/process-specific ring-sample properties. Maximum permeability and induction at a specified field are not a constant permeability or a saturation knee.
[S3] · 2018 · amendment 1 published 2021; public scope checked 2026-10-25
Soft metallic and powder materials, excluding electrical steels and soft ferrites; 20 Hz–100 kHz. This page uses the public scope, not the paid test procedure.
[S4] · 2016 · 2018 corrigendum; public scope checked 2026-10-25
Grain-oriented and non-oriented strip/sheet; Epstein-frame AC measurements at 400 Hz–10 kHz. A test method does not prescribe a material loss coefficient.
[S5] · Revision 210607 (2021-06-07) · checked 2026-10-25
Typical Br and reversible coefficient plus temperature-dependent B–H/J–H curves. Actual properties vary with magnet size and shape; no universal safe Pc is specified here.
[S6] · Undated resource page · accessed 2026-10-25
Explains Pc as an operating slope and the assumptions behind open-circuit approximations. It does not validate this simplified motor model.
It estimates no-load gap flux, equivalent tooth/yoke density, external reluctances, electrical frequency and a geometry-only Pc proxy. It uses constant material permeability and simplified topology counts, so the results support sensitivity analysis rather than design release.
Start with outer/inner diameter, physical gap and magnet thickness. Then open topology, materials and operating inputs. All fields are required; defaults and allowed ranges appear beside each numerical field.
No. This proxy excludes core reluctance, local fields and armature reaction. Hot B–H/J–H curves, peak opposing current and fault conditions are needed to assess irreversible demagnetization; no safety margin is calculated.
For an ideal rectangular pole waveform, the first spatial Fourier amplitude is (4/π) Bg sin(παp/2). That amplitude can exceed the local plateau. Real field shape, slotting and radial variation require field analysis.
Correct the marked field using decimal digits and a dot within its displayed range, or use Reset Defaults. Invalid combinations suppress the result and export. If dimensions are unavailable, send a drawing through the engineering inquiry form.
Use Copy MEC Sizing Summary or View Text Export. If clipboard access fails, a status message appears and the selectable export opens automatically. The summary includes every numerical input and the model limitations.
No. They are illustrative constant-permeability candidates with explicitly assumed screening levels. Obtain the selected supplier grade, density, heat treatment, B–H curve and loss map before applying the estimate to a component.
No. It compares modeled core density with an assumed screening level while keeping permeability constant. Near or above the screen, flux may be overstated; use a nonlinear model with actual B–H data.
No universal crossover frequency is established here. Compare matched flux waveforms, temperature, frequency, component cross-section and manufacturing condition. Ring-sample and Epstein-frame results require careful normalization before a component decision.
No. The electrical fundamental is pole pairs × rpm / 60. PWM carrier harmonics add a different excitation spectrum; this tool calculates neither harmonic losses nor efficiency.
IEC 60404-6 covers AC ring measurements for the soft materials in its scope, excluding electrical steels and soft ferrites. IEC 60404-10 covers electrical steel at 400 Hz–10 kHz. Confirm the applicable edition, specimen geometry and excitation with the test laboratory.
The YASA stator has separate tooth segments without a stator yoke. This model omits stator return-yoke reluctance for YASA and its TORUS-NS through-flux approximation. Rotor return paths still exist and are omitted from this simplified estimate.
No. Their actual branch circuits, rotor back-iron, tooth areas, winding currents and cooling differ. The topology counts are declared approximations; use architecture-specific electromagnetic and thermal models for comparisons.
Slot pitch changes with radius, and the slot opening may change too. A mean-radius correction does not bound local field crowding. Use the actual slot profile and compare radial slices; no universal Carter gradient is assumed.
No. Nominal axial-force balance does not establish stability under runout, thermal growth, disc deflection or bearing compliance. Evaluate force versus displacement and the mechanical tolerance stack.
Attach the exported summary, topology sketch, tooth and yoke CAD, minimum/nominal/maximum gaps, material B–H and loss curves, magnet thermal curves, speed/current duty, cooling and intended sample quantity. Request a review of the missing evidence before tooling release.
Send the exported input summary, topology sketch, tooth/yoke CAD, gap tolerance stack, material curves and current/temperature duty. Identify the missing evidence before choosing a prototype or tooling route.
