Linear alternator module, 2 in tri-clamp: datasheet, closed and open frame (mass, stiffness, frequency, Bl, R, L, stroke, pressure) and test procedure

sizes

23 in table

Notes

• Built once and moved from engine to engine: the same mover, leaves, magnets and coil every time, so the difference in electricity is the difference in the engines. Its own numbers are below; the numbers marked model are my estimates from the drawings and cited methods, and the tests in the procedure check each of them on the built unit.
• Two versions share the face-A spool, the mover, the leaves, the magnets and the whole stator. Closed: the leaves sit in spool-to-spool joints and face B is closed by the four-port cap, a sealed bounce space you can charge; use it on charged engines, in thermoacoustic loops and rings, and in line with face B on another device. Open frame: the leaves sit on an open frame clamped on the face-A spool, the back of the piston is at the room's pressure; use it on unpressurised desk and demo engines at 1 bar, for quick swaps, and when you want to see and retune the leaves.
• Leaves that fit both: leaf-2in-piston-t0.8 and the soft leaf-2in-piston-t0.5 (Ø64 rim, Ø18 hub). In the closed module, and in any 2 in spool-to-spool joint, the rim goes between two half gaskets (0.45 webs beside a 0.8 leaf, 0.6 beside a 0.5); in the open frame it sits in a Ø64 × 0.8 seat under a clamp ring, on a 0.3 rim shim if it is a 0.5 leaf. Both mounts clamp the rim inside r 23.75, so stiffness and stress are the same.
• Method. Mass from the CAD volumes; leaf stiffness and stress from a 3D Euler-Bernoulli frame model of the spiral arms (rim clamped, hub rigid); bounce spring γ p A²/V (adiabatic); force constant, coil resistance and inductance from the free-piston generator's magnetic-circuit estimate of the same stator and magnets; side pull from the same estimate against the leaves' radial stiffness as a 2 × 2 lateral / tilt stiffness matrix. Linear free-piston dynamics as in Redlich & Berchowitz; Sunpower's convertors (NASA reports) are the reference for clearance-seal pistons on spiral flexures with a moving-magnet alternator.
• Electrical model of the module: an EMF E = Bl·v in series with R = 3.40 Ω and L ≈ 25 mH. A series capacitor C = 1/(ω² L) cancels L at the running frequency (20 Hz 2500 µF, 30 Hz 1111 µF, 40 Hz 625 µF, 50 Hz 400 µF, 60 Hz 278 µF, 80 Hz 156 µF); rated above the voltage across it.
• Example (model): helium 10 bar behind the piston, 35.8 Hz, ±5 mm: EMF 32.4 V peak; into 6.8 Ω with the series capacitor, 34.2 W in the load and 17.1 W in the coil, if the engine supplies that much.
• Measurement procedure (each engine the same way):
• 1. Check the unit alone (once, and after any change). Ohmmeter on the coil leads: R_c. LCR meter at the running frequency: L. Face A up and open, depth gauge on the crown: 9.00 mm below face A when centred. Turn it face A down: the mover sags by m·g/k; pass DC current through the coil until it is back at 9.00: Bl = m·g / I (m the moving mass, g 9.81 m/s²).
• 2. Resonance and damping (motoring test). Closed: face B on its cap, the charge you will test at, face A closed with a plain end cap and gasket. Open frame: face A open to the room (the leaves-only resonance) or on a plain end cap (leaves plus the trapped face-A volume). Drive the coil from an audio amplifier through a 1 Ω sense resistor and sweep the frequency: the current dips at the resonance f₀ (the EMF opposes the drive). Stop the drive and record the coil voltage as it rings down: the decay rate σ (1/s, from successive peaks) gives the open-circuit mechanical damping c_m = 2·m·σ. Repeat with one mass disc fitted: m = m_disc / ((f₀/f₁)² − 1) and k = m (2π f₀)², a check of the published mass and stiffness.
• 3. On the engine. Clamp face A to the engine (Type B gasket and clamp; high-pressure clamp on a charged engine). Closed: face B on its cap at the engine's charge, or face B into the loop. Open frame: nothing to charge; keep fingers and loose wires off the exposed leaves while it runs. Connect a non-inductive load resistor R_L (power rated above the expected output) in series with the capacitor C for the expected frequency. Never run with the coil open: the load is what holds the stroke.
• 4. Read a true-RMS voltmeter across R_L and the frequency f. Load power P = V_rms² / R_L. Current I_rms = V_rms / R_L.
• 5. Stroke check. EMF E_rms = I_rms · |R_c + R_L + j(ωL − 1/(ωC))| (= I_rms (R_c + R_L) with C tuned); amplitude X = √2 · E_rms / (Bl · ω), ω = 2π f. Keep X at or below 6 mm: if it is above, lower R_L (more load, shorter stroke) or reduce the heat.
• 6. Power the engine delivered to the piston: P_engine = P + I_rms² R_c + ½ c_m ω² X² (load, coil, and the unit's own mechanical loss from step 2 at the same charge and frequency). Compare engines at the same X, the same charge and gas, and say which numbers were measured.
• Geometry, closed: a stack of three plain 2 in spools (42 bored, 3 in bored, 25.4) with leaves 1 and 2 clamped in the two inner joints; nothing of it lies beyond face A or face B, so either face clamps on any 2 in ferrule.
• Geometry, open frame: the 42 bored spool, then the open frame on its second ferrule: frame base, leaf 1, a clamp ring on 10 mm posts, the stator sleeve with the stator, a top plate on 5 mm posts, the leaf-2 seat ring, leaf 2 and a clamp ring; 167.7 mm from face A to the top ring. Only face A is a clamp face.

Sizes

Where the files are

Other publishers' files are linked, not hosted. "verify" = check the license at the link before commercial use.

Xem Studio	tools/gen_la_module.py: the module's geometry, masses, bounce volume, natural frequencies and every number on these pages	code	CC BY 4.0
Xem Studio	tools/gen_fpse_gen.py: the free-piston generator whose stator, magnets, leaves and collars this module reuses; its leaf frame model and magnetic-circuit estimate	code	CC BY 4.0
Proc. IMechE Part A	Redlich & Berchowitz (1985), Linear dynamics of free-piston Stirling engines	PDF	journal; method cited verify
NASA (NTRS, public domain)	Wood, Gedeon et al.: Sunpower free-piston convertors on planar spiral flexure bearings (Advanced Stirling Convertor: moving magnet linear alternator, flexure-supported clearance-seal piston)	PDF	US Government work, public domain
NASA (NTRS, public domain)	Geng, Mason, Dyson & Penswick (2008): Sunpower EG-1000, 1.1 kWe, 50 Hz, 3.0 MPa helium, 550 / 50 °C	PDF	US Government work, public domain
K&J Magnetics	Neodymium magnet specifications: N42 Br 1.30–1.32 T, density 7.4–7.5 g/cm³	web	maker page; values are facts verify
IEC	IEC 60028 international standard of resistance (1.7241 × 10⁻⁸ Ω·m at 20 °C, the conductor value used for the coil); IEC 60317 enamelled round winding wire (0.71 mm nominal conductor)	standard	values are facts verify

Xem scan

Not needed Published standard; the sheet is the geometry.

Plain text: sheet.txt · JSON: /api/geometry?object=linear-alternator-module-2in-datasheet

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