Free-piston Stirling core: displacer, power piston, liner, gas spring, stops, clearance-seal and tuning tables — dimension sheet Source: Xem Studio, https://xemstudio.com/objects/free-piston-core/ (CC BY 4.0) Basis: Beta free-piston layout (displacer and power piston in one bore, as Sunpower RE-1000 / NASA convertors): dimensionless rules from the public FPSE literature; parts sized for Ø30 and Ø40 bores to match the flexures, alternator and tube sizes in the library Catalog version: 2026-10-20 Sizes: see table below - No crank: the displacer and power piston are each a mass on a spring (flexure + gas spring) and the engine runs at the resonance f = (1/2π)√(k/m). Thermodynamics sets the phase (displacer leads the piston by ~60–90°) through the displacer's gas spring and rod area, not a linkage. Design order: pick bore D and stroke S (S ≈ 0.3–0.5 D), then piston mass and alternator load, then tune the displacer spring so it leads. - Clearance seals: the piston runs in the bore with no rings; the radial gap must be small enough that leakage over one cycle is a few % of swept volume. Rule of thumb from the literature: radial gap ≈ 10–20 µm for Ø20–40 mm at 50 Hz; a hobby engine at 10–15 Hz tolerates 25–40 µm. That is a lapped fit (piston turned 0.05 under, lapped into a honed liner), not a printed one: the printed piston blanks here are 0.1 mm under for you to finish, or use a glass syringe (10 mL: Ø14.5) or a graphite piston in a glass liner for a zero-effort seal. Displacer gap is generous (0.5–1 mm radial): it is a shuttle, not a seal. - Gas spring: a sealed bounce space behind the piston; stiffness k_gas = γ·p·A² / V (γ 1.4 air, p mean pressure, A piston area, V bounce volume). Ø20 gas piston at 1 bar with 20 cm³ bounce → k ≈ 1.4 × 10⁵ × (3.14e-4)² / 2e-5 ≈ 690 N/m. Smaller volume → stiffer. Centring ports (two 0.5 mm holes the piston uncovers at mid-stroke) keep the mean position from drifting. - Stops: the piston must never hit metal; TPU bumpers at both ends of the stroke, 6 mm tall, stroke limited to 85% of the free travel. Over-stroke is the normal failure when the load drops. - Dimensionless checks: Beale number ≈ 0.015 for a hobby engine (W = Bn · p_mean · V_swept · f; 1 bar, 10 cm³, 15 Hz → ~0.2 W), 0.1+ for pressurised helium machines; West number ~0.25. Dead volume ratio under 1.5; regenerator porosity 0.7; heater and cooler as copper/stainless tube from the library. - LES: the Ø40 core on flexures with the linear alternator is the next test bed after the crank engines; the tri-clamp spools are its pressure vessel. bore_mm stroke_mm displacer_len_mm radial_gap_um_piston radial_gap_mm_displacer gas_spring_bore_mm freq_hz_hobby 30 10–15 75 25–40 (lapped) 0.5 15 10–20 40 12–20 100 25–40 (lapped) 0.5 20 10–20 60 20–30 150 20–30 0.8 30 10–15 Files elsewhere (not hosted by Xem Studio; license as stated by the publisher): - NASA (NTRS, public domain): Free-piston Stirling engine design and analysis (RE-1000 test results) (1984) — PDF — US Government work, public domain — https://ntrs.nasa.gov/search?q=19840017543 - NASA (NTRS, public domain): Dynamics of free-piston Stirling engines (1987) — PDF — US Government work, public domain — https://ntrs.nasa.gov/search?q=19870011457 - Wikipedia: Free-piston engine — web — CC BY-SA 4.0 (text) — https://en.wikipedia.org/wiki/Free-piston_engine - Wikipedia: Beale number — web — CC BY-SA 4.0 (text) — https://en.wikipedia.org/wiki/Beale_number - Ohio University: Stirling cycle machine analysis (Urieli), free online — web — Author's site — https://www.ohio.edu/mechanical/stirling/ - Long Earth Society: Engine builds — web, video — LES site — https://longearthsociety.com/engineering/ Free files (CC BY 4.0, Xem Studio; STEP + STL, 11 parts): https://xemstudio.com/files/hardware/free-piston-core/index.json API: https://xemstudio.com/api/geometry?object=free-piston-core