{
 "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-displacer-gas-spring",
 "name": "Free-piston displacer gas spring: double-acting Ø18 cylinder, gland and piston in a 2 in tri-clamp spool",
 "kind": "hardware",
 "category": "Hardware",
 "group": "Stirling & thermoacoustic",
 "year": null,
 "question": "What sets the displacer's spring in a free-piston Stirling engine?",
 "tags": [
  "gas spring",
  "displacer",
  "free piston",
  "tri-clamp",
  "stirling",
  "long earth society"
 ],
 "aliases": [
  "displacer gas spring stirling",
  "free piston gas spring design",
  "double acting gas spring"
 ],
 "overall_mm": {
  "length": null,
  "width": null,
  "height": null
 },
 "official_cad": false,
 "xem_status": "free-files",
 "les": true,
 "free_files": 3,
 "url": "https://xemstudio.com/objects/fpse-displacer-gas-spring/",
 "sheet_txt": "https://xemstudio.com/objects/fpse-displacer-gas-spring/sheet.txt",
 "sheet": {
  "basis": "Gas-spring stiffness k = γ p (A²/V₁ + (A − a)²/V₂) (two closed columns either side of the piston); tuned with the Redlich & Berchowitz linear dynamics of the generator",
  "overall_mm": {
   "length": null,
   "width": null,
   "height": null
  },
  "notes": [
   "The displacer must resonate a little below the running frequency so that it leads the piston; with 365 g moving that takes about 28 kN/m at 10 bar helium. A flexure that stiff would be overstressed at the displacer's stroke, so the spring is gas: two 30 mm columns of the working charge either side of a Ø18 piston on the end of the stinger (7.63 + 7.42 cm³).",
   "It scales with the charge, as the engine's other gas forces do, so the displacer stays in tune from 1 to 10 bar. Its compression ratio is mild: ±15 % of the column at the design stroke.",
   "Tuning: the column height sets the frequency of the displacer and so its phase lead; my analysis puts 30 mm at about 70° lead. Shorter columns make it stiffer (less lead), longer columns softer. The analysis on the performance page shows the effect of ±10 % displacer mass.",
   "The cylinder is pressed into the top spool with its vent flats letting the bounce gas past to the port cap; the gland closes its bottom with a spigot and three M3 × 16; the stinger runs in the gland's Ø3 bore. Both clearances (piston and stinger) leak only between gas springs at the same mean pressure."
  ],
  "table": {
   "columns": [
    "part",
    "size"
   ],
   "rows": [
    [
     "cylinder",
     "Ø47.5 × 93.0, bore Ø18"
    ],
    [
     "piston",
     "Ø18 × 25"
    ],
    [
     "gland",
     "Ø47.5 × 10 + Ø18 × 3 spigot"
    ],
    [
     "columns",
     "2 × 30 mm"
    ],
    [
     "stiffness at 10 bar He",
     "27.9 kN/m"
    ]
   ]
  }
 },
 "sheet_text": "Free-piston displacer gas spring: double-acting Ø18 cylinder, gland and piston in a 2 in tri-clamp spool — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/fpse-displacer-gas-spring/  (CC BY 4.0)\nBasis: Gas-spring stiffness k = γ p (A²/V₁ + (A − a)²/V₂) (two closed columns either side of the piston); tuned with the Redlich & Berchowitz linear dynamics of the generator\nCatalog version: 2026-10-20\n\nSizes: see table below\n- The displacer must resonate a little below the running frequency so that it leads the piston; with 365 g moving that takes about 28 kN/m at 10 bar helium. A flexure that stiff would be overstressed at the displacer's stroke, so the spring is gas: two 30 mm columns of the working charge either side of a Ø18 piston on the end of the stinger (7.63 + 7.42 cm³).\n- It scales with the charge, as the engine's other gas forces do, so the displacer stays in tune from 1 to 10 bar. Its compression ratio is mild: ±15 % of the column at the design stroke.\n- Tuning: the column height sets the frequency of the displacer and so its phase lead; my analysis puts 30 mm at about 70° lead. Shorter columns make it stiffer (less lead), longer columns softer. The analysis on the performance page shows the effect of ±10 % displacer mass.\n- The cylinder is pressed into the top spool with its vent flats letting the bounce gas past to the port cap; the gland closes its bottom with a spigot and three M3 × 16; the stinger runs in the gland's Ø3 bore. Both clearances (piston and stinger) leak only between gas springs at the same mean pressure.\n\npart  size\ncylinder  Ø47.5 × 93.0, bore Ø18\npiston  Ø18 × 25\ngland  Ø47.5 × 10 + Ø18 × 3 spigot\ncolumns  2 × 30 mm\nstiffness at 10 bar He  27.9 kN/m\n\nFiles elsewhere (not hosted by Xem Studio; license as stated by the publisher):\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- 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- Long Earth Society: Engine builds — web, video — LES site — https://longearthsociety.com/engineering/\n\nFree files (CC BY 4.0, Xem Studio; STEP + STL, 3 parts): https://xemstudio.com/files/hardware/fpse-displacer-gas-spring/index.json\nAPI: https://xemstudio.com/api/geometry?object=fpse-displacer-gas-spring\n",
 "sources": [
  {
   "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": "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": "Long Earth Society",
   "title": "Engine builds",
   "url": "https://longearthsociety.com/engineering/",
   "formats": [
    "web",
    "video"
   ],
   "license": "LES site",
   "license_verified": true,
   "hosted": false
  }
 ],
 "xem": {
  "status": "free-files",
  "sheet_free": true,
  "mesh_price_usd": null,
  "step_price_usd": null,
  "tolerance_mm": null
 },
 "related": [
  "fpse-displacer-rod",
  "fpse-displacer",
  "list-fpse-generator-2in"
 ],
 "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": [
  {
   "feature": "OD",
   "exact": "Ø47.5 (four 0.75 vent flats)",
   "mates": "S6 spool bore",
   "fit": "press",
   "files": "fpse-gas-spring-cylinder"
  },
  {
   "feature": "bore",
   "exact": "Ø18",
   "mates": "gas-spring piston Ø18 × 25 (seal)",
   "fit": "run",
   "files": "fpse-gas-spring-cylinder"
  },
  {
   "feature": "tapped holes",
   "exact": "3 × Ø2.5 × 10 on r 16",
   "mates": "M3 × 16 up through the gland",
   "fit": "designed",
   "files": "fpse-gas-spring-cylinder"
  },
  {
   "feature": "spigot",
   "exact": "Ø18 × 3",
   "mates": "cylinder bore (seal)",
   "fit": "press",
   "files": "fpse-gas-spring-gland"
  },
  {
   "feature": "OD",
   "exact": "Ø47.5",
   "mates": "S6 spool bore",
   "fit": "slide",
   "files": "fpse-gas-spring-gland"
  },
  {
   "feature": "bore",
   "exact": "Ø3 × 13",
   "mates": "stinger (seal)",
   "fit": "run",
   "files": "fpse-gas-spring-gland"
  },
  {
   "feature": "screw holes",
   "exact": "3 × Ø3.4 on r 16",
   "mates": "M3 clearance (ISO 273 medium)",
   "fit": "designed",
   "files": "fpse-gas-spring-gland"
  },
  {
   "feature": "OD",
   "exact": "Ø18 × 25",
   "mates": "cylinder bore (seal)",
   "fit": "run",
   "files": "fpse-gas-spring-piston"
  },
  {
   "feature": "stinger socket",
   "exact": "Ø3 × 10",
   "mates": "stinger, held by an M3 grub",
   "fit": "slide",
   "files": "fpse-gas-spring-piston"
  }
 ],
 "fit_classes": {
  "press": "stays put: pin, tube, bearing or magnet held by interference. Typical FDM: hole +0.0 to +0.1 mm on diameter.",
  "slide": "assembles by hand and is held by a grub, pinch or clamp: shaft in a hub, rod in a socket, spigot in a bore. Typical FDM: +0.2 mm.",
  "run": "turns or slides in use: pin in a link, rod through a guide. Typical FDM: +0.3 mm.",
  "socket": "large sliding fit: syringe barrel, sleeve, bobbin in a bore. Typical FDM: +0.3 mm.",
  "clamp": "split part that closes on the mating part with screws: make it at size.",
  "designed": "a gap that is part of the design (piston fit option, displacer gap, air gap): do not change."
 },
 "faq": [
  {
   "q": "Why double-acting?",
   "a": "With one closed column above and the bounce space below, the bounce pressure (which the piston drives) would push the displacer along with the piston and cancel its drive. Closing both sides makes the spring answer to the displacer alone."
  }
 ],
 "files_license": null,
 "offers": [
  {
   "file": "fpse-gas-spring-cylinder-18",
   "formats": [
    "step",
    "stl"
   ],
   "price_usd": 0,
   "license": "CC BY 4.0 (Xem Studio)",
   "step": "https://xemstudio.com/files/hardware/fpse-displacer-gas-spring/fpse-gas-spring-cylinder-18.step",
   "stl": "https://xemstudio.com/files/hardware/fpse-displacer-gas-spring/fpse-gas-spring-cylinder-18.stl",
   "note": "gas-spring cylinder: Ø47.5 × 93.0 pressed into S6, blind Ø18 bore 88.0 deep, 3 × M3 tapped (Ø2.5 × 10) on r 16 in its bottom, four 0.75 vent flats on the OD"
  },
  {
   "file": "fpse-gas-spring-gland-18",
   "formats": [
    "step",
    "stl"
   ],
   "price_usd": 0,
   "license": "CC BY 4.0 (Xem Studio)",
   "step": "https://xemstudio.com/files/hardware/fpse-displacer-gas-spring/fpse-gas-spring-gland-18.step",
   "stl": "https://xemstudio.com/files/hardware/fpse-displacer-gas-spring/fpse-gas-spring-gland-18.stl",
   "note": "gland plate: Ø47.5 × 10, Ø18 × 3 spigot into the cylinder's bore, Ø3 stinger bore (running fit), 3 × Ø3.4 on r 16"
  },
  {
   "file": "fpse-gas-spring-piston-18",
   "formats": [
    "step",
    "stl"
   ],
   "price_usd": 0,
   "license": "CC BY 4.0 (Xem Studio)",
   "step": "https://xemstudio.com/files/hardware/fpse-displacer-gas-spring/fpse-gas-spring-piston-18.step",
   "stl": "https://xemstudio.com/files/hardware/fpse-displacer-gas-spring/fpse-gas-spring-piston-18.stl",
   "note": "gas-spring piston Ø18 × 25 (running fit in the cylinder), Ø3 × 10 stinger socket from below, M3 tapped radial hole (Ø2.5) at 5"
  }
 ],
 "markdown": "https://xemstudio.com/objects/fpse-displacer-gas-spring/index.md"
}