{
 "version": "2026-10-20",
 "license": "Dimension sheets are written by Xem Studio from the cited sources and are free to use (CC BY 4.0, attribute 'Xem Studio'). Linked files belong to their publishers under the license shown; Xem Studio does not host them. 'license_verified: false' means the license shown is from memory or the publisher's page as last read and should be confirmed at the link before commercial use.",
 "slug": "fpse-generator-2in-performance",
 "name": "Free-piston Stirling generator, 2 in tri-clamp: performance, dynamics and losses (air and helium, 1 and 10 bar)",
 "kind": "standard",
 "category": "Stirling engines",
 "group": "Guide",
 "year": null,
 "question": "How much power does a small free-piston Stirling make at 1 bar and pressurised, in air and helium?",
 "tags": [
  "free piston",
  "stirling",
  "generator",
  "analysis",
  "performance",
  "tri-clamp"
 ],
 "aliases": [
  "free piston stirling performance",
  "small fpse power helium",
  "free piston stirling 1 bar"
 ],
 "overall_mm": {
  "length": null,
  "width": null,
  "height": null
 },
 "official_cad": false,
 "xem_status": "not-scanned",
 "les": true,
 "free_files": 0,
 "url": "https://xemstudio.com/objects/fpse-generator-2in-performance/",
 "sheet_txt": "https://xemstudio.com/objects/fpse-generator-2in-performance/sheet.txt",
 "sheet": {
  "basis": "My analysis of the 2 in tri-clamp free-piston generator (tools/gen_fpse_gen.py): Urieli & Berchowitz adiabatic + simple analysis, Redlich & Berchowitz linear dynamics, at the drawn geometry and the computed masses",
  "overall_mm": {
   "length": null,
   "width": null,
   "height": null
  },
  "notes": [
   "Method. Cycle: the Urieli & Berchowitz ideal-adiabatic model with their simple analysis (gas-to-wall temperature drops in the heater and cooler, regenerator enthalpy loss from its NTU, pumping loss from the friction of the slots and screens; screen correlations of Gedeon & Wood). Motion: Redlich & Berchowitz linear dynamics of the piston and displacer (masses, leaf and gas springs, the working-space pressure coefficients taken from small-amplitude adiabatic runs, the bounce space, the flow damping), solved for the frequency, the displacer's amplitude and phase and the start condition. The stroke is set where the net cycle power equals what the alternator absorbs.",
   "Assumptions: inside of the heater wall 800 K, cooler wall 300 K; running clearances 15 µm radial (piston land, rod, stinger gland) and 10 µm (gas-spring piston) for the leakage estimates only; wall conductivity 16 W/m·K for conduction; metal parts 7.9 g/cm³, magnets 7.5 g/cm³ for the masses; flexure modulus 200 GPa.",
   "Design point: helium at 10 bar mean (fill about 9.2 bar at 20 °C, cold), ±5.0 mm piston: 45.1 Hz, displacer ±4.47 mm leading by 68°, pressure swing ±1.60 bar (8.59–11.79 bar).",
   "Power at the design point: PV 70.3 W, pumping loss 11.3 W, seal and gas-spring leakage 3.06 W, net 55.9 W to the alternator; 43.2 W electrical into 11.5 Ω (31.5 V peak, 2.74 A peak), 12.7 W in the coil.",
   "Heat: 123 W through the heater, plus 5.4 W regenerator loss, 4.4 W shuttle conduction (Martini), 47.4 W wall conduction: 180 W into the head, 24.0 % to electricity; 53 W to the cooler. With 30–50 % of a burner's heat reaching the head that is 28–47 g of propane per hour.",
   "Stroke against load (helium 10 bar): ±3.0 mm at 9.2 Ω → 17.3 W; ±4.0 mm at 10.3 Ω → 29.1 W; ±5.0 mm at 11.5 Ω → 43.2 W; ±5.5 mm at 12.1 Ω → 50.9 W. The stroke rises steeply as the load resistance rises: the load is the stroke control.",
   "Start (helium 10 bar, design load connected, from rest): growth rate -0.1 s⁻¹ at 500 K, +3.3 s⁻¹ at 600 K, +5.4 s⁻¹ at 700 K, +6.8 s⁻¹ at 800 K (positive: the oscillation grows by itself). Air at 1 bar: +0.2 s⁻¹.",
   "Without the optional heater and cooler inserts (helium 10 bar, ±5 mm): 6.6 W.",
   "Sensitivity: displacer mass −10 % / +10 %: lead 82° / 54°, 41.4 / 40.7 W: re-tune with the gas-spring column if the built displacer differs.",
   "Vibration: the piston and displacer are not balanced; the vessel feels about 436 N peak at the running frequency. Bolt the stand to a heavy bench or add a tuned absorber.",
   "Vessel: relief 15 bar gauge; hoop stress at relief 23.0 MPa (hot spool), 27.5 MPa (bored spool); end load on each joint 4.0 kN."
  ],
  "table": {
   "columns": [
    "case",
    "f_Hz",
    "Xp_mm",
    "Xd_mm",
    "lead_deg",
    "swing_bar",
    "PV_W",
    "pumping_W",
    "leak_W",
    "net_W",
    "R_L_ohm",
    "EMF_V_pk",
    "P_e_W",
    "Q_in_W",
    "eff_pct"
   ],
   "rows": [
    [
     "helium 10 bar",
     45.1,
     5,
     4.47,
     68,
     1.6,
     70.33,
     11.35,
     3.06,
     55.92,
     11.5,
     40.8,
     43.17,
     180,
     24
    ],
    [
     "air 10 bar",
     42.8,
     5,
     3.45,
     57,
     1.411,
     42.88,
     7.44,
     1.95,
     33.5,
     19,
     38.7,
     28.41,
     132,
     21.4
    ],
    [
     "helium 1 bar",
     20.5,
     5,
     0.43,
     63,
     0.174,
     0.23,
     0.07,
     0.02,
     0.14,
     1213.2,
     18.5,
     0.14,
     48,
     0.3
    ],
    [
     "air 1 bar",
     20,
     5,
     0.34,
     65,
     0.161,
     0.18,
     0.05,
     0.02,
     0.11,
     1436.4,
     18.1,
     0.11,
     48,
     0.2
    ]
   ]
  }
 },
 "sheet_text": "Free-piston Stirling generator, 2 in tri-clamp: performance, dynamics and losses (air and helium, 1 and 10 bar) — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/fpse-generator-2in-performance/  (CC BY 4.0)\nBasis: My analysis of the 2 in tri-clamp free-piston generator (tools/gen_fpse_gen.py): Urieli & Berchowitz adiabatic + simple analysis, Redlich & Berchowitz linear dynamics, at the drawn geometry and the computed masses\nCatalog version: 2026-10-20\n\nSizes: see table below\n- Method. Cycle: the Urieli & Berchowitz ideal-adiabatic model with their simple analysis (gas-to-wall temperature drops in the heater and cooler, regenerator enthalpy loss from its NTU, pumping loss from the friction of the slots and screens; screen correlations of Gedeon & Wood). Motion: Redlich & Berchowitz linear dynamics of the piston and displacer (masses, leaf and gas springs, the working-space pressure coefficients taken from small-amplitude adiabatic runs, the bounce space, the flow damping), solved for the frequency, the displacer's amplitude and phase and the start condition. The stroke is set where the net cycle power equals what the alternator absorbs.\n- Assumptions: inside of the heater wall 800 K, cooler wall 300 K; running clearances 15 µm radial (piston land, rod, stinger gland) and 10 µm (gas-spring piston) for the leakage estimates only; wall conductivity 16 W/m·K for conduction; metal parts 7.9 g/cm³, magnets 7.5 g/cm³ for the masses; flexure modulus 200 GPa.\n- Design point: helium at 10 bar mean (fill about 9.2 bar at 20 °C, cold), ±5.0 mm piston: 45.1 Hz, displacer ±4.47 mm leading by 68°, pressure swing ±1.60 bar (8.59–11.79 bar).\n- Power at the design point: PV 70.3 W, pumping loss 11.3 W, seal and gas-spring leakage 3.06 W, net 55.9 W to the alternator; 43.2 W electrical into 11.5 Ω (31.5 V peak, 2.74 A peak), 12.7 W in the coil.\n- Heat: 123 W through the heater, plus 5.4 W regenerator loss, 4.4 W shuttle conduction (Martini), 47.4 W wall conduction: 180 W into the head, 24.0 % to electricity; 53 W to the cooler. With 30–50 % of a burner's heat reaching the head that is 28–47 g of propane per hour.\n- Stroke against load (helium 10 bar): ±3.0 mm at 9.2 Ω → 17.3 W; ±4.0 mm at 10.3 Ω → 29.1 W; ±5.0 mm at 11.5 Ω → 43.2 W; ±5.5 mm at 12.1 Ω → 50.9 W. The stroke rises steeply as the load resistance rises: the load is the stroke control.\n- Start (helium 10 bar, design load connected, from rest): growth rate -0.1 s⁻¹ at 500 K, +3.3 s⁻¹ at 600 K, +5.4 s⁻¹ at 700 K, +6.8 s⁻¹ at 800 K (positive: the oscillation grows by itself). Air at 1 bar: +0.2 s⁻¹.\n- Without the optional heater and cooler inserts (helium 10 bar, ±5 mm): 6.6 W.\n- Sensitivity: displacer mass −10 % / +10 %: lead 82° / 54°, 41.4 / 40.7 W: re-tune with the gas-spring column if the built displacer differs.\n- Vibration: the piston and displacer are not balanced; the vessel feels about 436 N peak at the running frequency. Bolt the stand to a heavy bench or add a tuned absorber.\n- Vessel: relief 15 bar gauge; hoop stress at relief 23.0 MPa (hot spool), 27.5 MPa (bored spool); end load on each joint 4.0 kN.\n\ncase  f_Hz  Xp_mm  Xd_mm  lead_deg  swing_bar  PV_W  pumping_W  leak_W  net_W  R_L_ohm  EMF_V_pk  P_e_W  Q_in_W  eff_pct\nhelium 10 bar  45.1  5.0  4.47  68.0  1.6  70.33  11.35  3.06  55.92  11.5  40.8  43.17  180.0  24.0\nair 10 bar  42.8  5.0  3.45  57.0  1.411  42.88  7.44  1.95  33.5  19.0  38.7  28.41  132.0  21.4\nhelium 1 bar  20.5  5.0  0.43  63.0  0.174  0.23  0.07  0.02  0.14  1213.2  18.5  0.14  48.0  0.3\nair 1 bar  20.0  5.0  0.34  65.0  0.161  0.18  0.05  0.02  0.11  1436.4  18.1  0.11  48.0  0.2\n\nFiles elsewhere (not hosted by Xem Studio; license as stated by the publisher):\n- Ohio University (Urieli): Stirling cycle machine analysis: ideal adiabatic and simple analysis (after Urieli & Berchowitz, Stirling Cycle Engine Analysis, 1984) — web — author's site — https://www.ohio.edu/mechanical/stirling/\n- Proc. IMechE Part A: Redlich & Berchowitz (1985), Linear dynamics of free-piston Stirling engines — PDF — journal; method cited [verify license at link] — https://journals.sagepub.com/doi/pdf/10.1243/PIME_PROC_1985_199_025_02\n- NASA (NTRS, public domain): Gedeon & Wood (1996), Oscillating-flow regenerator test rig: correlations for screens and felts, NASA CR-198442 (f = 129/Re + 2.91 Re^-0.103; Nu = (1 + 0.99 Pe^0.66) β^1.79) — PDF — US Government work, public domain — https://ntrs.nasa.gov/citations/19960015878\n- NASA (NTRS, public domain): Martini (1983), Stirling Engine Design Manual, NASA CR-168088 (shuttle conduction) — PDF — US Government work, public domain — https://ntrs.nasa.gov/search?q=Stirling%20Engine%20Design%20Manual%20Martini\n- Wikipedia: Hagen–Poiseuille flow between parallel plates (clearance-seal leakage Q = π D δ³ Δp / 12 μ L) — web — CC BY-SA 4.0 (text) — https://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_equation\n- 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 license at link] — https://www.kjmagnetics.com/specs.asp\n- NASA (NTRS, public domain): Wong, Wood & Wilson (2008), Advanced Stirling Convertor (ASC): 88 We, 850 °C hot end, 38 % efficiency, 1.3 kg — PDF — US Government work, public domain — https://ntrs.nasa.gov/api/citations/20080047351/downloads/20080047351.pdf\n- 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 — https://ntrs.nasa.gov/api/citations/20080033114/downloads/20080033114.pdf\n- Engineering ToolBox: Fuels: higher and lower calorific values (propane lower heating value 46.35 MJ/kg) — web — reference values [verify license at link] — https://www.engineeringtoolbox.com/fuels-higher-calorific-values-d_169.html\n\nXem Studio scan: not needed; this is a published standard. The sheet is the geometry.\nAPI: https://xemstudio.com/api/geometry?object=fpse-generator-2in-performance\n",
 "sources": [
  {
   "publisher": "Ohio University (Urieli)",
   "title": "Stirling cycle machine analysis: ideal adiabatic and simple analysis (after Urieli & Berchowitz, Stirling Cycle Engine Analysis, 1984)",
   "url": "https://www.ohio.edu/mechanical/stirling/",
   "formats": [
    "web"
   ],
   "license": "author's site",
   "license_verified": true,
   "hosted": false
  },
  {
   "publisher": "Proc. IMechE Part A",
   "title": "Redlich & Berchowitz (1985), Linear dynamics of free-piston Stirling engines",
   "url": "https://journals.sagepub.com/doi/pdf/10.1243/PIME_PROC_1985_199_025_02",
   "formats": [
    "PDF"
   ],
   "license": "journal; method cited",
   "license_verified": false,
   "hosted": false
  },
  {
   "publisher": "NASA (NTRS, public domain)",
   "title": "Gedeon & Wood (1996), Oscillating-flow regenerator test rig: correlations for screens and felts, NASA CR-198442 (f = 129/Re + 2.91 Re^-0.103; Nu = (1 + 0.99 Pe^0.66) β^1.79)",
   "url": "https://ntrs.nasa.gov/citations/19960015878",
   "formats": [
    "PDF"
   ],
   "license": "US Government work, public domain",
   "license_verified": true,
   "hosted": false
  },
  {
   "publisher": "NASA (NTRS, public domain)",
   "title": "Martini (1983), Stirling Engine Design Manual, NASA CR-168088 (shuttle conduction)",
   "url": "https://ntrs.nasa.gov/search?q=Stirling%20Engine%20Design%20Manual%20Martini",
   "formats": [
    "PDF"
   ],
   "license": "US Government work, public domain",
   "license_verified": true,
   "hosted": false
  },
  {
   "publisher": "Wikipedia",
   "title": "Hagen–Poiseuille flow between parallel plates (clearance-seal leakage Q = π D δ³ Δp / 12 μ L)",
   "url": "https://en.wikipedia.org/wiki/Hagen%E2%80%93Poiseuille_equation",
   "formats": [
    "web"
   ],
   "license": "CC BY-SA 4.0 (text)",
   "license_verified": true,
   "hosted": false
  },
  {
   "publisher": "K&J Magnetics",
   "title": "Neodymium magnet specifications: N42 Br 1.30–1.32 T, density 7.4–7.5 g/cm³",
   "url": "https://www.kjmagnetics.com/specs.asp",
   "formats": [
    "web"
   ],
   "license": "maker page; values are facts",
   "license_verified": false,
   "hosted": false
  },
  {
   "publisher": "NASA (NTRS, public domain)",
   "title": "Wong, Wood & Wilson (2008), Advanced Stirling Convertor (ASC): 88 We, 850 °C hot end, 38 % efficiency, 1.3 kg",
   "url": "https://ntrs.nasa.gov/api/citations/20080047351/downloads/20080047351.pdf",
   "formats": [
    "PDF"
   ],
   "license": "US Government work, public domain",
   "license_verified": true,
   "hosted": false
  },
  {
   "publisher": "NASA (NTRS, public domain)",
   "title": "Geng, Mason, Dyson & Penswick (2008): Sunpower EG-1000, 1.1 kWe, 50 Hz, 3.0 MPa helium, 550 / 50 °C",
   "url": "https://ntrs.nasa.gov/api/citations/20080033114/downloads/20080033114.pdf",
   "formats": [
    "PDF"
   ],
   "license": "US Government work, public domain",
   "license_verified": true,
   "hosted": false
  },
  {
   "publisher": "Engineering ToolBox",
   "title": "Fuels: higher and lower calorific values (propane lower heating value 46.35 MJ/kg)",
   "url": "https://www.engineeringtoolbox.com/fuels-higher-calorific-values-d_169.html",
   "formats": [
    "web"
   ],
   "license": "reference values",
   "license_verified": false,
   "hosted": false
  }
 ],
 "xem": {
  "status": "not-scanned",
  "sheet_free": true,
  "mesh_price_usd": null,
  "step_price_usd": null,
  "tolerance_mm": null
 },
 "related": [
  "list-fpse-generator-2in",
  "nasa-fpse-references",
  "free-piston-displacer",
  "sanitary-high-pressure-clamp"
 ],
 "fits": [],
 "dimensions": "exact (nominal, no printing tolerance)",
 "dimension_rule": "All geometry on Xem Studio is exact (nominal, true size) with no printing tolerance. Where a part meets another part, the object lists its mating features (feature, exact size, what it mates with, fit class: press, slide, run, socket, clamp or designed). Apply your process's allowance to those features only; 'designed' gaps are part of the design and stay as drawn.",
 "mating": [],
 "faq": [
  {
   "q": "Does a free-piston Stirling work at this small size?",
   "a": "Yes, if it is pressurised. Power goes with mean pressure × swept volume × frequency; at 1 bar this 48 mm piston gives 0.1 W in air and 0.1 W in helium at ±5 mm, at 10 bar helium 43 W. NASA's Sunpower ASC is the proof of scale: about 80 W from a 1.3 kg convertor on helium."
  },
  {
   "q": "What charge pressure is needed for useful power?",
   "a": "10 bar helium running (about 9 bar filled cold) gives 43 W at ±5 mm; 1 bar gives a fraction of a watt to a few watts."
  },
  {
   "q": "What must the clamps and gaskets be rated for?",
   "a": "Above the 15 bar gauge relief setting at their temperature. The high-pressure bolted 2 in clamps are published at 1000 psi (69 bar) at 70–75 °F and 800 psi (55 bar) at 250 °F; the gasket's own rating is the other half."
  }
 ],
 "files_license": null,
 "offers": [],
 "markdown": "https://xemstudio.com/objects/fpse-generator-2in-performance/index.md"
}