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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.