CC0 · public domain Free Humanoid Corpus/ AXF-1 · rev A/ design target — not measured data/ quote geometry & process, not performance

AXF-1 — printable axial-flux actuator

A fully-printable joint actuator: yokeless axial-flux PMSM with printed Fe-Si armature poles, Cu-LPBF concentrated coils, bonded-NdFeB Halbach rotors, and an 8:1 printed cycloidal reduction. Every rating below is derived from the sizing physics shown in §REL — a bureau quotes the dimensioned geometry and per-part process; the numbers are design intent to be confirmed by EM sim and coupon test.

Ⅼ axis of rotation 8:1 cycloidal rotor Halbach NdFeB gap 0.6 SMC pole + Cu-LPBF coil rotor Ø110 Ø63.5 Rᵢ/Rₒ=0.577
Fig.1 — axial cross-section (thicknesses exaggerated). Dual bonded-Halbach rotors · single yokeless Fe-Si/Cu stator · two active airgaps · 8:1 printed cycloidal output. Active material is annular; centre is shaft.
Joint torque — continuous
≈ 46 N·m
= T_rotor · 8 · η_gear
Joint torque — peak (short)
≈ 95 N·m
σ_peak ≈ 25 kPa
Motor constant — target
≥ 1.3 N·m/√W
the figure to actually optimize
Motor torque density — floor
≥ 25 N·m/kg pk
≈ 0.55× sintered — accepted
Ledger metric — pass/fail
J/N·m·s
measured across T–ω, replayable
EM

Electromagnetic & geometry

quote these dimensions
ParameterValueBasis / note
TopologyYokeless axial-flux PMSM (YASA-type)Segmented poles, no stator yoke → short 3D flux path. The one geometry where isotropic printed iron beats laminations.
Slot / pole count12s / 14pFractional-slot concentrated winding, kw0.933. Cogging order LCM(12,14)=84 → inherently smooth.
Outer diameter Do110 mmSets the torque via Ro³ (§REL). Scale Do to buy torque back from the bonded-magnet penalty.
Inner / outer ratioRi/Ro = 0.577 → ID ≈ 63.5 mm1/√3 maximizes torque for a given Do — the classic axial-flux optimum.
Axial length (motor)≈ 30 mmPancake. Envelope only; active-material stack is thinner.
Airgap (×2)0.6 mm target · <0.5 mm hardPrint + assembly + thermal-growth + bearing runout limited. Bonded machines are less gap-sensitive than sintered (lower Br, longer magnetic length).
Gap flux Bg,rms (fundamental)≈ 0.40 T (sintered ≈ 0.85 T)The crux number. Follows from bonded Br + Halbach one-sided boost. Confirm by coupon (MEAS-1).
Electric loading Arms30 kA/m contEnabled by Cu-LPBF fill. σ = Bg·A ≈ 12 kPa continuous.
Electrical frequency≈ 350 Hz @ 3000 rpm7 pole-pairs. Drives the core-loss requirement on printed Fe-Si → SMC-class resistivity (MEAS-2).
Reduction8:1 printed cycloidal, η ≥ 0.85Quasi-direct-drive. Backlash + η set control bandwidth (MEAS-5).
MAT

Materials & per-part process

one line = one printed part
PartMaterialProcessKey spec / caveat
Armature poles ×12Fe-6.5%Si / SMCmetal LPBFIsotropic, high resistivity for 350 Hz. Target ≥ 1.5 T at knee. Bound-metal FFF+sinter is the low-cost fallback.
Concentrated coils ×12Cu (≥87% IACS)Cu-LPBF green-λFill ≥ 65% (goal 79%). Turn insulation is NOT printable → conformal dielectric coat (parylene / ceramic e-coat) + hi-pot post-print.
Rotor magnets ×2bonded NdFeB, HalbachFFF / binder-jetNet-shape segmented Halbach, then magnetize in fixture. Br target 0.60–0.65 T. Self-shielding → no back-iron.
Rotor discs ×2PA-CF or AlMJF / FDM / LPBFStructural only. Halbach removes the flux-return duty → thin discs, lower rotor inertia.
Cycloidal set (8:1)PA-CF / PPA-CFMJF / SLSIsotropic powder part; disc + pins + eccentric. η ≥ 0.85, backlash to be characterized.
Bearings / gap control316L flexure or x-rollerLPBF + post-machineSets airgap concentricity — target ≤ 50 µm runout. The airgap is a bearing-precision problem.
Frame / pole carrierPA-CFMJF / FDMHolds the 12-pole ring, both gaps, and stator reaction torque.
↳ consolidationFe-Si + CuCrZrAerosint SPDPoles + coils co-printed in one multi-metal LPBF build — collapses the two hardest parts into a single job. Phase-3 target.
The number to beat is not torque density

A bonded-magnet machine loses on raw torque density. Torque scales linearly with gap flux, and bonded NdFeB delivers roughly half the Bg of sintered — so at equal size and current this motor lands near 0.5–0.6× a sintered QDD (Unitree M8010 ≈ 45 N·m/kg peak). Worse, lower flux means lower Kt, so it draws more current per newton-metre → more copper loss → the efficiency penalty compounds the torque penalty.

The single lever that fights both is copper fill: Cu-LPBF reaches 65–79% vs ~45% for round wire, which lowers phase resistance, raises Km, and reclaims thermal headroom (Additive Drives: 65% fill → +45% output). So the targets that matter here are Km, joint torque after reduction, and joules per N·m·s — plus the things sintered can't buy: full printability and a CC0 prior-art release. Density is the tax you knowingly pay for sovereignty.

MEAS

Measure first — ranked by leverage

coupons before the CAD is frozen
1

Br of the printed + magnetized bonded-NdFeB coupon

Everything scales off this. T ∝ Bg ∝ Br — linear. If Br comes in at 0.50 T instead of 0.65 T, the whole torque envelope drops ~23%. Print a coupon, magnetize, measure on a B-H loop before committing geometry.

2

Core loss of printed Fe-Si / SMC at 200–500 Hz

Sets efficiency, the thermal ceiling, and max usable speed. Printed iron loses more than laminations at frequency — verify the resistivity is high enough that 350 Hz is comfortable, not marginal.

3

Achieved Cu fill · IACS · insulation integrity

Directly sets Km, phase resistance, and thermal margin. Measure the real fill fraction, conductivity vs annealed copper, and hi-pot the coated coil turn-to-turn.

4

Assembled airgap after thermal soak

Magnet CTE + bearing runout + disc deflection under magnetic pull. Confirm the 0.6 mm gap survives a hot rotor and doesn't close to a rub.

5

Cycloidal efficiency & backlash of the printed gearset

Sets joint efficiency and the achievable control bandwidth. η and lost motion in a printed cycloidal are the two numbers that decide whether the joint is stiff enough to walk on.

REL

Governing relations

every rating above traces here
T = (4π/3) · σ · (Ro³ − Ri³)
Dual-airgap axial torque. Plug σ=12 kPa, Ro=55 mm, Ri=31.75 mm → ≈ 6.8 N·m at the rotor (continuous). ×8×0.85 → ≈ 46 N·m joint.
σ = Bg,rms · Arms
Airgap shear stress. The single knob is the product of flux and current loading. Bonded magnets cut Bg; Cu fill raises A.
Ri/Ro = 1/√3 ≈ 0.577
Ratio that maximizes axial-flux torque for a fixed outer diameter.
Km = T / √(Pcu)
Motor constant [N·m/√W] — torque per root-watt of heating, independent of current. The size-and-fill figure of merit; where Cu-LPBF earns its cost.
η = Pmech / (Pmech + Pcu + Pfe + Pmech,loss)
Target ≥ 80% continuous at nominal — lower than sintered because bonded flux forces more current per N·m.
Ledger = Ein / ∫ T·ω dt
Joules of electrical input per newton-metre-second of joint impulse, mapped across the T–ω plane and replayable. The MathGround pass/fail — the number the whole track is accountable to.