{
 "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": "tri-clamp-flexure-leaf",
 "name": "Tri-clamp flexure leaf: spiral planar spring clamped in a 2 in joint like a gasket (displacer and piston)",
 "kind": "hardware",
 "category": "Hardware",
 "group": "Stirling & thermoacoustic",
 "year": null,
 "question": "Can a flexure bearing be clamped in a tri-clamp joint?",
 "tags": [
  "flexure",
  "leaf",
  "planar spring",
  "tri-clamp",
  "free piston",
  "stirling",
  "long earth society"
 ],
 "aliases": [
  "flexure in tri clamp joint",
  "spiral flexure gasket",
  "free piston flexure leaf"
 ],
 "overall_mm": {
  "length": null,
  "width": null,
  "height": null
 },
 "official_cad": false,
 "xem_status": "free-files",
 "les": true,
 "free_files": 2,
 "url": "https://xemstudio.com/objects/tri-clamp-flexure-leaf/",
 "sheet_txt": "https://xemstudio.com/objects/tri-clamp-flexure-leaf/sheet.txt",
 "sheet": {
  "basis": "Leaf stiffness and stress from a 3D Euler-Bernoulli frame model of the spiral arms (rim clamped at the bore, hub rigid), modulus 200 GPa assumed",
  "overall_mm": {
   "length": null,
   "width": null,
   "height": null
  },
  "notes": [
   "Each leaf is a flat disc the size of the gasket web (Ø64) with three spiral arms inside the bore. It sits in a tri-clamp joint between two half gaskets whose webs add up, with the leaf, to the Type B gasket's 1.7: the clamp closes on it exactly as on a gasket, and it centres on the Ø64 flange rims.",
   "Displacer leaf (joint B, 0.5 thick, 3 arms × 3 wide, 400°): axial 730 N/m, radial 40 kN/m, bending stress 14.3 MPa per mm of travel (86 MPa at ±6).",
   "Piston leaves (joints C and D, 0.8 thick, 3 × 4 wide, 330°, the second turned over for the opposite hand): axial 3949 N/m each, radial 154 kN/m each, 23.3 MPa per mm (117 MPa at the ±5 design stroke, 140 MPa at ±6).",
   "The two piston leaves hold the piston against the stator's magnetic side pull: about 55 kN/m of negative radial stiffness (estimate) against 308 kN/m from the leaves (5.6 ×).",
   "The leaf must not fatigue at the stress above for 10⁹ cycles and more: the leaf's material and finish are the builder's choice and the builder's check."
  ],
  "table": {
   "columns": [
    "leaf",
    "t_mm",
    "arm_w_mm",
    "sweep_deg",
    "hub_bore_mm",
    "k_axial_N_m",
    "k_radial_kN_m",
    "MPa_per_mm"
   ],
   "rows": [
    [
     "displacer",
     0.5,
     3,
     400,
     12,
     730,
     40,
     14.3
    ],
    [
     "piston",
     0.8,
     4,
     330,
     18,
     3949,
     154.1,
     23.3
    ]
   ]
  }
 },
 "sheet_text": "Tri-clamp flexure leaf: spiral planar spring clamped in a 2 in joint like a gasket (displacer and piston) — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/tri-clamp-flexure-leaf/  (CC BY 4.0)\nBasis: Leaf stiffness and stress from a 3D Euler-Bernoulli frame model of the spiral arms (rim clamped at the bore, hub rigid), modulus 200 GPa assumed\nCatalog version: 2026-10-20\n\nSizes: see table below\n- Each leaf is a flat disc the size of the gasket web (Ø64) with three spiral arms inside the bore. It sits in a tri-clamp joint between two half gaskets whose webs add up, with the leaf, to the Type B gasket's 1.7: the clamp closes on it exactly as on a gasket, and it centres on the Ø64 flange rims.\n- Displacer leaf (joint B, 0.5 thick, 3 arms × 3 wide, 400°): axial 730 N/m, radial 40 kN/m, bending stress 14.3 MPa per mm of travel (86 MPa at ±6).\n- Piston leaves (joints C and D, 0.8 thick, 3 × 4 wide, 330°, the second turned over for the opposite hand): axial 3949 N/m each, radial 154 kN/m each, 23.3 MPa per mm (117 MPa at the ±5 design stroke, 140 MPa at ±6).\n- The two piston leaves hold the piston against the stator's magnetic side pull: about 55 kN/m of negative radial stiffness (estimate) against 308 kN/m from the leaves (5.6 ×).\n- The leaf must not fatigue at the stress above for 10⁹ cycles and more: the leaf's material and finish are the builder's choice and the builder's check.\n\nleaf  t_mm  arm_w_mm  sweep_deg  hub_bore_mm  k_axial_N_m  k_radial_kN_m  MPa_per_mm\ndisplacer  0.5  3.0  400  12.0  730  40.0  14.3\npiston  0.8  4.0  330  18  3949  154.1  23.3\n\nFiles elsewhere (not hosted by Xem Studio; license as stated by the publisher):\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- Long Earth Society: Engine builds — web, video — LES site — https://longearthsociety.com/engineering/\n\nFree files (CC BY 4.0, Xem Studio; STEP + STL, 2 parts): https://xemstudio.com/files/hardware/tri-clamp-flexure-leaf/index.json\nAPI: https://xemstudio.com/api/geometry?object=tri-clamp-flexure-leaf\n",
 "sources": [
  {
   "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": "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": [
  "tri-clamp-leaf-half-gasket",
  "spiral-flexure-bearing",
  "fpse-hub-collars",
  "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": "rim",
   "exact": "Ø64 × 0.5 / 0.8, clamped from Ø47.5 out",
   "mates": "two half gaskets in the joint; centred on the Ø64 flange rims by the clamp",
   "fit": "clamp",
   "files": "all"
  },
  {
   "feature": "hub bore",
   "exact": "Ø12 (displacer) / Ø18 (piston)",
   "mates": "rod / tube rod, hub clamped by collars",
   "fit": "slide",
   "files": "all"
  },
  {
   "feature": "arms",
   "exact": "three spiral arms inside Ø47.5",
   "mates": "free (no contact)",
   "fit": "designed",
   "files": "all"
  }
 ],
 "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 clamp the leaf in the joint?",
   "a": "The joint is already the most accurate datum in the vessel: the clamp centres both flanges and the leaf on the same Ø64, and the gaskets seal over it. No bracket, no screws, no extra seal."
  },
  {
   "q": "Does the leaf add dead volume?",
   "a": "Almost none: it is 0.5 or 0.8 thick and its arms move in the clearance the piston and displacer need anyway."
  }
 ],
 "files_license": null,
 "offers": [
  {
   "file": "leaf-2in-displacer-t0.5",
   "formats": [
    "step",
    "stl"
   ],
   "price_usd": 0,
   "license": "CC BY 4.0 (Xem Studio)",
   "step": "https://xemstudio.com/files/hardware/tri-clamp-flexure-leaf/leaf-2in-displacer-t0.5.step",
   "stl": "https://xemstudio.com/files/hardware/tri-clamp-flexure-leaf/leaf-2in-displacer-t0.5.stl",
   "note": "displacer leaf: Ø64 × 0.5 rim (clamped from Ø47.5 out), hub Ø18 with Ø12 bore, 3 arms 3 wide sweeping 400° from r 9 to r 23.75"
  },
  {
   "file": "leaf-2in-piston-t0.8",
   "formats": [
    "step",
    "stl"
   ],
   "price_usd": 0,
   "license": "CC BY 4.0 (Xem Studio)",
   "step": "https://xemstudio.com/files/hardware/tri-clamp-flexure-leaf/leaf-2in-piston-t0.8.step",
   "stl": "https://xemstudio.com/files/hardware/tri-clamp-flexure-leaf/leaf-2in-piston-t0.8.stl",
   "note": "piston leaf: Ø64 × 0.8 rim (clamped from Ø47.5 out), hub Ø24 with Ø18 bore, 3 arms 4 wide sweeping 330° from r 12 to r 23.75"
  }
 ],
 "markdown": "https://xemstudio.com/objects/tri-clamp-flexure-leaf/index.md"
}