---
jupyter:
  description: 'A flange gasket as a 2D CAD exercise: a dimensioned drawing to model in planex2d or any CAD system, a
    solution as a fully constrained sketch with a circular pattern, and the area to check a model against.'
---

# Flange gasket

A flange gasket seals the joint between two pipe flanges, with the bolts of the joint through its holes. The holes sit
on a bolt circle, equally spaced, which makes the gasket an exercise in patterns. Model the gasket from the drawing in
planex2d or in any CAD system, then check its area against the value at the end of the page. A solution in planex2d
follows.

![The flange gasket exercise: a dimensioned drawing of a round gasket with a bore and four holes on a bolt circle](../_static/gallery/flange-gasket.png){.result}

```python
import math
import planex as px
```

```python nbsphinx="hidden"
from docs_figures import Row
```

## The circles

The gasket is drawn as four circles around the origin, the outside, the bore, the bolt circle as a construction circle,
and the first hole, placed roughly on the bolt circle to the right. The first three are drawn at the pen, the sketch's
current point, so they share one center, and `auto_constraint` makes them concentric. `CircularPattern` copies the hole
around the origin, 4 in all, and keeps the copies tied to it, 90° apart. The sizes are rough, and the dimensions in the
next section set them (Figure 1).

```python
gasket = px.Sketch(auto_constraint=True)
gasket.Circle(80, id="outside")
gasket.Circle(30, id="bore")
gasket.Circle(60, id="bolt_circle", construction=True)
gasket.Circle(9, center=(60, 0), id="hole")
gasket.CircularPattern(["hole"], "origin", 4, id="holes");
```

```python nbsphinx="hide-input"
Row((gasket, "The circles and the pattern of the hole, the bolt circle dashed", {"fill": False}),
    caption="The circles")
```

## The dimensions

The outside's center is the origin, which the bore and the bolt circle share, and the first hole sits on the bolt circle
and on the horizontal axis. Its copies follow. The four diameters give the sizes (Figure 2):

```python
gasket.Constrain("outside.center", "origin", px.Coincident)
gasket.Constrain("hole.center", "bolt_circle", px.Coincident)  # a point on a circle
gasket.Constrain("hole.center", "H", px.Coincident)
gasket.Constrain("outside", px.Diameter, 165, id="outside_d")
gasket.Constrain("bore", px.Diameter, 61, id="bore_d")
gasket.Constrain("bolt_circle", px.Diameter, 125, id="bolt_circle_d")
gasket.Constrain("hole", px.Diameter, 18, id="hole_d")
print("status", gasket.status, "| degrees of freedom", gasket.dof)
```

```python nbsphinx="hide-input"
Row((gasket, "Every dimension and tie of the sketch", {"constraints": True}), caption="The fully constrained sketch")
```

## The checks

This is the area, to compare with your own model. It is the outside less the bore and the four holes,
$\tfrac{\pi}{4} \cdot (165^2 - 61^2 - 4 \cdot 18^2)$ (Figure 3):

```python
face = gasket.Face()
print("area", round(face.mass, 2), "mm², exact", round(math.pi / 4 * (165**2 - 61**2 - 4 * 18**2), 2))
```

```python nbsphinx="hide-input"
Row((face, "The gasket"), caption="The gasket")
```

The gasket as DXF in millimeters, for a cutting plotter or a laser cutter:

```python
gasket.WriteDXF("flange_gasket.dxf", unit=px.mm, scale=1)  # scale=1: the numbers as they are
```

The gasket as DXF: [flange_gasket.dxf](flange_gasket.dxf)

```python nbsphinx="hidden"
import sys
sys.path.insert(0, "..")
import matplotlib.pyplot as plt
from drawings import SheetFigure, View
from gallery import save_figure

r = gasket.Measure("outside")["radius"]
view = View([(gasket, {"outside_d": 20, "bolt_circle_d": 62, "bore_d": 135, "hole_d": (45, "leader", 4)},
              {"bolt_circle": "pitch"})],
            axes=[((-r - 5, 0), (r + 5, 0), (0, 0)), ((0, -r - 5), (0, r + 5), (0, 0))])
drawing = SheetFigure([view], margin=20, notes=("planex2d.org", "2D exercise 03"))
print("scale 1 :", round(1 / drawing.planex_scale), "| paper", [round(v * 25.4) for v in drawing.get_size_inches()], "mm")
save_figure(drawing, "flange-gasket", dpi=200)
plt.close(drawing)
```