Reference math and workflow for sizing circular seals and gaskets from real groove measurements.

Seal Math – Torus & Gasket Sizing

This reference explains how to calculate round (torus) and square/rectangular gasket dimensions from

real, tapered groove measurements. It is intended for 3D‑printed filament cases with tongue‑and‑groove

seals .

Round Gasket (Torus)

What a torus represents

A round gasket is modeled as a torus (donut shape): - The gasket follows a circular centerline path inside

the groove - The gasket has a round cross‑section (cord / O‑ring style)

FreeCAD Torus parameters: - Radius1 (Major Radius) → distance from model center to gasket centerline -

Radius2 (Minor Radius) → radius of the gasket cross‑section

Measure the groove (tapered grooves)

For tapered grooves, measure both top and bottom :

Groove Outer Diameter (OD):

OD_top

OD_bottom

Groove Inner Diameter (ID):

ID_top

ID_bottom

Average the taper (centerline diameters)

Outer diameter at groove center:

OD_c = (OD_top + OD_bottom) / 2

Inner diameter at groove center:

ID_c = (ID_top + ID_bottom) / 2•

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Groove centerline diameter

This is the diameter the gasket naturally wants to sit on.

D_center = (OD_c + ID_c) / 2

Convert to FreeCAD Torus values

Major Radius (Radius1):

R1 = D_center / 2

Minor Radius (Radius2):

R2 = gasket_diameter / 2

Example (real measurements)

Measured: - OD_top = 221 mm - OD_bottom = 219 mm - ID_top = 213 mm - ID_bottom = 215 mm - Desired

round gasket diameter = 2.5 mm

Calculations:

OD_c = (221 + 219) / 2 = 220 mm

ID_c = (213 + 215) / 2 = 214 mm

D_center = (220 + 214) / 2 = 217 mm

R1 = 217 / 2 = 108.5 mm

R2 = 2.5 / 2 = 1.25 mm

Final FreeCAD Torus Settings: - Radius 1 = 108.5 mm - Radius 2 = 1.25 mm

Square / Rectangular Gasket Ring

A rectangular gasket is created by cutting the center out of a cylinder (washer shape). This type of gasket

resists rolling and works well in narrow grooves.

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Use the same groove centerline

R_center = D_center / 2

(From the example above: R_center = 108.5 mm)

Choose gasket width

Choose a gasket slightly narrower than the groove radial width for easy seating.

Let: - W = gasket radial width - w = W / 2

Calculate inner and outer radii

R_out = R_center + w

R_in = R_center − w

Choose gasket height (Z)

Height should be slightly taller than the available cavity so it compresses when the lid closes.

Typical starting value for TPU: - 2.1–2.3 mm

Example (rectangular gasket)

From above: - R_center = 108.5 mm

Choose: - W = 2.7 mm → w = 1.35 mm - Height (Z) = 2.3 mm

Computed radii:

R_out = 108.5 + 1.35 = 109.85 mm

R_in = 108.5 − 1.35 = 107.15 mm

Final Rectangular Gasket Geometry: - Outer radius = 109.85 mm - Inner radius = 107.15 mm - Height (Z) =

2.3 mm

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Build method (FreeCAD)

Create outer cylinder (R = 109.85, H = 2.3)

Create inner cylinder (R = 107.15, H = 2.3)

Boolean Cut (outer − inner)

Key Takeaways

Round gaskets want the groove centerline

Rectangular gaskets are easier to retain in narrow grooves

Always average tapered grooves

Let compression come from geometry , not brute force

This math applies to any circular tongue‑and‑groove enclosure , not just filament cases.1.

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