# Planar spiral flexure bearing leaves: Ø40 to Ø120, 3-arm and 2-arm, 0.5 and 2 mm

> What is a spiral flexure bearing and what are its dimensions?

- Category: Stirling engines › Free-piston
- Kind: Hardware
- Basis: Archimedean planar springs as on Sunpower / NASA free-piston Stirling convertors; hub Ø = max(bore + 8, 0.22 OD), rim 0.12 OD, arms sweep 330° (2-arm 350°)
- Page: https://xemstudio.com/objects/spiral-flexure-bearing/ · JSON: https://xemstudio.com/api/geometry?object=spiral-flexure-bearing · Plain text: https://xemstudio.com/objects/spiral-flexure-bearing/sheet.txt
- License: dimension sheet CC BY 4.0 (Xem Studio); linked files under their publishers' licenses

**Exact dimensions.** Every file is drawn at true size with no printing tolerance. The holes and pins that meet another part are listed below under Mating features, with the fit each joint needs; open those by your printer's or process's clearance before making the part.

## Notes

- A flexure bearing leaf: a flat spring with a hub, spiral arms and a rim. Stacked leaves let a piston move axially while holding it on centre, so it runs in a clearance seal with no contact.
- Sizes Ø40, 60, 80, 100, 120. Each has a 3-arm leaf 0.5 mm thick (with a DXF), the same 3-arm leaf 2.0 mm thick, and a 2-arm leaf 0.5 mm thick (with a DXF). 3-arm arms sweep 330°, 2-arm 350°, from the hub to the rim.
- Hub Ø12 / 13.2 / 17.6 / 22 / 26.4 with bore Ø4 / 5 / 5 / 8 / 8; rim width 0.12 × OD; three Ø3.2 rim holes on a circle 0.88 × OD.
- Axial stiffness per leaf scales with E·t³·w / L³ (L = arm length), so the 2.0 mm leaf is 64 times the 0.5 mm leaf in the same material. Natural frequency of the suspended mass: f = (1/2π)√(k/m).
- Three arms give equal radial stiffness in every direction; two-arm leaves are softer axially but let the hub tilt.

## Mating features (exact size; open press / slide / run / socket by your process clearance, leave designed and clamp as drawn)

| feature | exact | mates with | fit | files |
|---|---|---|---|---|
| leaf hub bore | Ø4 / Ø5 / Ø8 | rod, tube or centring bush | slide | flexure-* |
| rim holes | Ø3.2 | M3 screws (clearance) | designed | flexure-* |

## Sizes

| od_mm | hub_mm | rim_mm | arm_w_mm | bore_mm | arm_radial_span_mm | rim_hole_circle_mm |
|---|---|---|---|---|---|---|
| 40 | 12 | 4.8 | 1.6 | 4 | 9.2 | 35.2 |
| 60 | 13.2 | 7.2 | 2.0 | 5 | 16.2 | 52.8 |
| 80 | 17.6 | 9.6 | 2.5 | 5 | 21.6 | 70.4 |
| 100 | 22.0 | 12.0 | 3.0 | 8 | 27.0 | 88.0 |
| 120 | 26.4 | 14.4 | 3.5 | 8 | 32.4 | 105.6 |

## Where the files are

- NASA (NTRS, public domain): [Free-piston Stirling convertor flexure bearing development and life testing (2005)](https://ntrs.nasa.gov/search?q=20050182933) — PDF — US Government work, public domain
- NASA (NTRS, public domain): [Flexure bearing design for free-piston Stirling engines (1986)](https://ntrs.nasa.gov/search?q=19860020334) — PDF — US Government work, public domain
- NASA (NTRS, public domain): [Advanced Stirling Radioisotope Generator (ASRG) engineering unit (2011)](https://ntrs.nasa.gov/search?q=20110016393) — PDF — US Government work, public domain
- Wikipedia: [Flexure bearing](https://en.wikipedia.org/wiki/Flexure_bearing) — web — CC BY-SA 4.0 (text)
- Sunpower (AMETEK): [Free-piston Stirling technology overview](https://sunpowerinc.com/) — web — Sunpower site (verify at link)
- Long Earth Society: [Engine builds](https://longearthsociety.com/engineering/) — web, video — LES site

## Free STEP/STL (15 parts, CC BY 4.0, Xem Studio)

Index: https://xemstudio.com/files/hardware/spiral-flexure-bearing/index.json

- flexure-40-3arm-w1.6-t0.5: [STEP](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-40-3arm-w1.6-t0.5.step) · [STL](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-40-3arm-w1.6-t0.5.stl) · [DXF](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-40-3arm-w1.6-t0.5.dxf) — planar spiral flexure Ø40, 3 arms 1.6 wide, 0.5 thick (DXF outline included), hub Ø12 bore Ø4, 3 × Ø3.2 rim holes on R17.6
- flexure-40-3arm-w1.6-t2: [STEP](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-40-3arm-w1.6-t2.step) · [STL](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-40-3arm-w1.6-t2.stl) — planar spiral flexure Ø40, 3 arms 1.6 wide, 2.0 thick, hub Ø12 bore Ø4, 3 × Ø3.2 rim holes on R17.6
- flexure-40-2arm-w1.6-t0.5: [STEP](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-40-2arm-w1.6-t0.5.step) · [STL](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-40-2arm-w1.6-t0.5.stl) · [DXF](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-40-2arm-w1.6-t0.5.dxf) — 2-arm variant Ø40 (lower axial stiffness, less radial)
- flexure-60-3arm-w2-t0.5: [STEP](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-60-3arm-w2-t0.5.step) · [STL](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-60-3arm-w2-t0.5.stl) · [DXF](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-60-3arm-w2-t0.5.dxf) — planar spiral flexure Ø60, 3 arms 2.0 wide, 0.5 thick (DXF outline included), hub Ø13.2 bore Ø5, 3 × Ø3.2 rim holes on R26.4
- flexure-60-3arm-w2-t2: [STEP](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-60-3arm-w2-t2.step) · [STL](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-60-3arm-w2-t2.stl) — planar spiral flexure Ø60, 3 arms 2.0 wide, 2.0 thick, hub Ø13.2 bore Ø5, 3 × Ø3.2 rim holes on R26.4
- flexure-60-2arm-w2-t0.5: [STEP](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-60-2arm-w2-t0.5.step) · [STL](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-60-2arm-w2-t0.5.stl) · [DXF](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-60-2arm-w2-t0.5.dxf) — 2-arm variant Ø60 (lower axial stiffness, less radial)
- flexure-80-3arm-w2.5-t0.5: [STEP](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-80-3arm-w2.5-t0.5.step) · [STL](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-80-3arm-w2.5-t0.5.stl) · [DXF](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-80-3arm-w2.5-t0.5.dxf) — planar spiral flexure Ø80, 3 arms 2.5 wide, 0.5 thick (DXF outline included), hub Ø17.6 bore Ø5, 3 × Ø3.2 rim holes on R35.2
- flexure-80-3arm-w2.5-t2: [STEP](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-80-3arm-w2.5-t2.step) · [STL](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-80-3arm-w2.5-t2.stl) — planar spiral flexure Ø80, 3 arms 2.5 wide, 2.0 thick, hub Ø17.6 bore Ø5, 3 × Ø3.2 rim holes on R35.2
- flexure-80-2arm-w2.5-t0.5: [STEP](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-80-2arm-w2.5-t0.5.step) · [STL](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-80-2arm-w2.5-t0.5.stl) · [DXF](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-80-2arm-w2.5-t0.5.dxf) — 2-arm variant Ø80 (lower axial stiffness, less radial)
- flexure-100-3arm-w3-t0.5: [STEP](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-100-3arm-w3-t0.5.step) · [STL](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-100-3arm-w3-t0.5.stl) · [DXF](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-100-3arm-w3-t0.5.dxf) — planar spiral flexure Ø100, 3 arms 3.0 wide, 0.5 thick (DXF outline included), hub Ø22 bore Ø8, 3 × Ø3.2 rim holes on R44
- flexure-100-3arm-w3-t2: [STEP](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-100-3arm-w3-t2.step) · [STL](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-100-3arm-w3-t2.stl) — planar spiral flexure Ø100, 3 arms 3.0 wide, 2.0 thick, hub Ø22 bore Ø8, 3 × Ø3.2 rim holes on R44
- flexure-100-2arm-w3-t0.5: [STEP](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-100-2arm-w3-t0.5.step) · [STL](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-100-2arm-w3-t0.5.stl) · [DXF](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-100-2arm-w3-t0.5.dxf) — 2-arm variant Ø100 (lower axial stiffness, less radial)
- flexure-120-3arm-w3.5-t0.5: [STEP](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-120-3arm-w3.5-t0.5.step) · [STL](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-120-3arm-w3.5-t0.5.stl) · [DXF](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-120-3arm-w3.5-t0.5.dxf) — planar spiral flexure Ø120, 3 arms 3.5 wide, 0.5 thick (DXF outline included), hub Ø26.4 bore Ø8, 3 × Ø3.2 rim holes on R52.8
- flexure-120-3arm-w3.5-t2: [STEP](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-120-3arm-w3.5-t2.step) · [STL](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-120-3arm-w3.5-t2.stl) — planar spiral flexure Ø120, 3 arms 3.5 wide, 2.0 thick, hub Ø26.4 bore Ø8, 3 × Ø3.2 rim holes on R52.8
- flexure-120-2arm-w3.5-t0.5: [STEP](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-120-2arm-w3.5-t0.5.step) · [STL](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-120-2arm-w3.5-t0.5.stl) · [DXF](https://xemstudio.com/files/hardware/spiral-flexure-bearings/flexure-120-2arm-w3.5-t0.5.dxf) — 2-arm variant Ø120 (lower axial stiffness, less radial)

## How it fits

### Parts that fit it
- [Flexure hub centring bush: Ø5 and Ø8 OD × Ø3 / Ø5 bore × 6](https://xemstudio.com/objects/flexure-hub-centring-bush/): OD = leaf hub bore

### Goes in or on
- [Tri-clamp flexure head: ISO 2852 cap with Ø60, Ø80 and Ø100 flexure seats](https://xemstudio.com/objects/tri-clamp-flexure-head/): rim in the flexure-OD seat, 3 × M3

### Connects to
- [Flexure stack spacer ring: Ø40 to Ø120 × 2 mm](https://xemstudio.com/objects/flexure-stack-spacer/): spacer between leaf rims
- [Flexure hub washer: Ø12 to Ø26.4 × 2 mm](https://xemstudio.com/objects/flexure-hub-clamp-washer/): washer between leaf hubs

### Alternatives
- [Compression springs, wire Ø0.5–1.6, OD 6–16](https://xemstudio.com/objects/compression-springs/): coil springs

### Also needed
- [Flexure rim clamp plate: Ø40 to Ø120 × 3 mm, 3 × M3](https://xemstudio.com/objects/flexure-rim-clamp-plate/): clamps the stack rims
- [Flexure hub collars: split collars Ø13.2, Ø17.6 and Ø22 for Ø3 rod and Ø5 tube](https://xemstudio.com/objects/flexure-hub-collar/): clamps the hubs to the rod

## Questions

**What is a flexure bearing in a Stirling engine?**

A stack of flat spiral springs that holds the piston on centre while it moves axially, so it runs in a clearance seal with no contact; NASA's free-piston convertors use them.

**How many arms should a spiral flexure have?**

Three for equal radial stiffness; two-arm leaves are softer axially but let the hub tilt. Alternate the spiral hand between leaves to cancel rotation.

**What are the dimensions of the Ø80 flexure?**

Hub Ø17.6, bore Ø5, rim 9.6 wide, three arms 2.5 wide, Ø3.2 rim holes on a Ø70.4 circle; 0.5 or 2.0 mm thick.

## Fits with

- [Flexure stack spacer ring: Ø40 to Ø120 × 2 mm](https://xemstudio.com/objects/flexure-stack-spacer/)
- [Flexure rim clamp plate: Ø40 to Ø120 × 3 mm, 3 × M3](https://xemstudio.com/objects/flexure-rim-clamp-plate/)
- [Flexure hub washer: Ø12 to Ø26.4 × 2 mm](https://xemstudio.com/objects/flexure-hub-clamp-washer/)
- [Tri-clamp flexure head: ISO 2852 cap with Ø60, Ø80 and Ø100 flexure seats](https://xemstudio.com/objects/tri-clamp-flexure-head/)
- [Flexure hub collars: split collars Ø13.2, Ø17.6 and Ø22 for Ø3 rod and Ø5 tube](https://xemstudio.com/objects/flexure-hub-collar/)
- [Free-piston Stirling displacer Ø29 × 75 and Ø39 × 100](https://xemstudio.com/objects/free-piston-displacer/)