# Free-piston Stirling core: displacer, power piston, liner, gas spring, stops, clearance-seal and tuning tables

> How do I design a free-piston Stirling engine: displacer, power piston, gas spring and clearance seals?

- Category: Stirling engines › Free-piston
- Kind: Hardware
- 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
- Page: https://xemstudio.com/objects/free-piston-core/ · JSON: https://xemstudio.com/api/geometry?object=free-piston-core · Plain text: https://xemstudio.com/objects/free-piston-core/sheet.txt
- License: dimension sheet CC BY 4.0 (Xem Studio); linked files under their publishers' licenses

## Notes

- 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.

## Sizes

| 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 |

## Where the files are

- NASA (NTRS, public domain): [Free-piston Stirling engine design and analysis (RE-1000 test results) (1984)](https://ntrs.nasa.gov/search?q=19840017543) — PDF — US Government work, public domain
- NASA (NTRS, public domain): [Dynamics of free-piston Stirling engines (1987)](https://ntrs.nasa.gov/search?q=19870011457) — PDF — US Government work, public domain
- Wikipedia: [Free-piston engine](https://en.wikipedia.org/wiki/Free-piston_engine) — web — CC BY-SA 4.0 (text)
- Wikipedia: [Beale number](https://en.wikipedia.org/wiki/Beale_number) — web — CC BY-SA 4.0 (text)
- Ohio University: [Stirling cycle machine analysis (Urieli), free online](https://www.ohio.edu/mechanical/stirling/) — web — Author's site
- Long Earth Society: [Engine builds](https://longearthsociety.com/engineering/) — web, video — LES site

## Free STEP/STL (11 parts, CC BY 4.0, Xem Studio)

Index: https://xemstudio.com/files/hardware/free-piston-core/index.json

- displacer-30x75: [STEP](https://xemstudio.com/files/hardware/free-piston-core/displacer-30x75.step) · [STL](https://xemstudio.com/files/hardware/free-piston-core/displacer-30x75.stl) — displacer Ø29 (0.5 mm radial gap in a Ø30 bore) × 75, hollow 1.2 wall, Ø5 rod boss
- power-piston-30x30: [STEP](https://xemstudio.com/files/hardware/free-piston-core/power-piston-30x30.step) · [STL](https://xemstudio.com/files/hardware/free-piston-core/power-piston-30x30.stl) — power piston Ø29.9 × 30 (clearance-seal blank: lap to fit), Ø5 rod
- cylinder-liner-30x120: [STEP](https://xemstudio.com/files/hardware/free-piston-core/cylinder-liner-30x120.step) · [STL](https://xemstudio.com/files/hardware/free-piston-core/cylinder-liner-30x120.stl) — cylinder liner Ø30 bore × 120, 3 wall (print to check layout; real liner is honed tube or a glass/brass tube from the library)
- gas-spring-piston-15x15: [STEP](https://xemstudio.com/files/hardware/free-piston-core/gas-spring-piston-15x15.step) · [STL](https://xemstudio.com/files/hardware/free-piston-core/gas-spring-piston-15x15.stl) — gas-spring piston Ø14.9 × 15 for a Ø15 bounce-space bore
- stop-bumper-30: [STEP](https://xemstudio.com/files/hardware/free-piston-core/stop-bumper-30.step) · [STL](https://xemstudio.com/files/hardware/free-piston-core/stop-bumper-30.stl) — end-stop bumper for a Ø30 bore (TPU), 6 tall
- displacer-40x100: [STEP](https://xemstudio.com/files/hardware/free-piston-core/displacer-40x100.step) · [STL](https://xemstudio.com/files/hardware/free-piston-core/displacer-40x100.stl) — displacer Ø39 (0.5 mm radial gap in a Ø40 bore) × 100, hollow 1.2 wall, Ø5 rod boss
- power-piston-40x40: [STEP](https://xemstudio.com/files/hardware/free-piston-core/power-piston-40x40.step) · [STL](https://xemstudio.com/files/hardware/free-piston-core/power-piston-40x40.stl) — power piston Ø39.9 × 40 (clearance-seal blank: lap to fit), Ø5 rod
- cylinder-liner-40x160: [STEP](https://xemstudio.com/files/hardware/free-piston-core/cylinder-liner-40x160.step) · [STL](https://xemstudio.com/files/hardware/free-piston-core/cylinder-liner-40x160.stl) — cylinder liner Ø40 bore × 160, 3 wall (print to check layout; real liner is honed tube or a glass/brass tube from the library)
- gas-spring-piston-20x20: [STEP](https://xemstudio.com/files/hardware/free-piston-core/gas-spring-piston-20x20.step) · [STL](https://xemstudio.com/files/hardware/free-piston-core/gas-spring-piston-20x20.stl) — gas-spring piston Ø19.9 × 20 for a Ø20 bounce-space bore
- stop-bumper-40: [STEP](https://xemstudio.com/files/hardware/free-piston-core/stop-bumper-40.step) · [STL](https://xemstudio.com/files/hardware/free-piston-core/stop-bumper-40.stl) — end-stop bumper for a Ø40 bore (TPU), 6 tall
- displacer-rod-5x150-grooved: [STEP](https://xemstudio.com/files/hardware/free-piston-core/displacer-rod-5x150-grooved.step) · [STL](https://xemstudio.com/files/hardware/free-piston-core/displacer-rod-5x150-grooved.stl) — Ø5 × 150 displacer rod with E-clip grooves

## Questions

**What is the piston clearance in a free-piston Stirling engine?**

10–20 µm radial for the real machines at 50+ Hz; 25–40 µm is workable for a slow hobby engine. It is a lapped or honed fit, never a printed one: print the blank, lap it in, or use a glass syringe or graphite-in-glass piston.

**How does a free-piston Stirling engine keep its phase without a crank?**

The displacer is a tuned mass-spring system (flexure + gas spring on its rod) that resonates slightly ahead of the piston; rod area and gas-spring volume set the phase angle, typically 60–90° lead.

**What is the Beale number?**

W = Bn · p_mean · V_swept · f with Bn ≈ 0.015 for a low-temperature hobby engine and ~0.1–0.15 for pressurised, high-ΔT machines. 1 bar, 10 cm³, 15 Hz → about 0.2 W.

**What stops a free-piston engine from over-stroking?**

The load: alternator current is the brake. Plus TPU bumpers at both ends and a stroke limited to 85% of the free travel for when the load drops.

## Fits with

- [Planar spiral flexure bearings (Sunpower / NASA free-piston style): Ø40–120, DXF + STEP](https://xemstudio.com/objects/spiral-flexure-bearings/)
- [Moving-magnet linear alternator kit (free-piston Stirling power take-off)](https://xemstudio.com/objects/linear-alternator-kit/)
- [Regenerator and heat materials: stainless mesh counts, steel wool, scrubbers, mica, fiberglass, ceramic, firebrick](https://xemstudio.com/objects/regenerator-and-heat-materials/)
- [Plastic syringes 1–60 mL as pistons and cylinders](https://xemstudio.com/objects/plastic-syringes/)
- [Borosilicate test tubes, 10×75 to 30×200 mm](https://xemstudio.com/objects/borosilicate-test-tubes/)
- [Tri-clamp spool (two ferrules on a tube), 1.5 and 2 inch](https://xemstudio.com/objects/tri-clamp-spool/)
- [O-rings, common metric sizes (ISO 3601)](https://xemstudio.com/objects/o-rings-metric/)
- [NASA and Sunpower free-piston Stirling references (public domain) and design numbers](https://xemstudio.com/objects/nasa-fpse-references/)