# Axisymmetric

Axisymmetric solves the r-z half-plane of a model that is symmetric about an axis, so a rotationally symmetric part such as a coil or a tubular actuator solves as a 2D problem. You author the full 3D model, and the frame sections it for the 2D solve. See [Frames](<https://docs.femforge.io/user-guide/frames/index.md>) for what a frame decides.

```python
import femforge as ff

config = ff.SimulationConfig(
    frame=ff.Axisymmetric(axis=ff.Axis.Z),
    mesh=ff.MeshConfig(step="models/tubular.step", global_mesh_size=0.5 * ff.U.mm),
    domain=ff.DomainConfig(
        materials=[ff.materials.Air(), ff.materials.N52()],
        tags=[
            ff.EntityTag(
                selector={ff.TagKey.MAGNETIZATION: "N"},
                conditions=[ff.Magnetization(direction=ff.Direction(0, 0, 1))],
            ),
            ff.EntityTag(selector={ff.TagKey.NAME: "mover"}, conditions=[ff.ForceComponent(label="mover")]),
        ],
    ),
)

print(config.frame.label, config.solved_physics())
```

| Property | Value |
| --- | --- |
| `kind` | `"axisymmetric"` |
| Mesh dimension | 2 |
| Solve coordinates | X = radial (\>= 0), Y = along the axis, Z = 0 |
| Elmer coordinate system | `Axi Symmetric`, which integrates per radian |

## Fields

| Field | Default | Meaning |
| --- | --- | --- |
| `axis` | `ff.Axis.Z` | The axis of symmetry, in the authored frame. |
| `radial` | `None` | The direction from the axis toward the half-plane femforge sections. |

femforge stores `radial` as its unit part perpendicular to the axis and rejects a radial parallel to the axis. With `radial=None`, the half-plane faces the world axis least aligned with the symmetry axis, X first: `Axis.Z` maps the authored X to the radial direction, and `Axis.Y` leaves the coordinates as authored. An unset `radial` is left out of the serialized config, so it adds nothing to the run identity.

For an axis that does not pass through the origin, give it an origin:

```python
import femforge as ff

frame = ff.Axisymmetric(
    axis=ff.Axis(origin=ff.Vec3(10, 0, 0), direction=ff.Direction(0, 0, 1)),
    radial=ff.Direction(0, 1, 0),
)

print(frame.label, frame.plane)
```

Axisymmetric.plane is the SolvePlane that rule picks: the authored origin of the section and the authored directions of its +X (radial) and +Y (axis). The section and the workbench's expansion both read it.

## How femforge sections the model

The driver converts the STEP in its first stage, `prepare_geometry`, through Axisymmetric.prepare\_geometry:

1. It builds the parametric geometry when the config has one, else it reads the authored STEP.
2. import\_tagged\_step imports the STEP as tagged parts, one per named solid. Every body needs a `key=value` name, and a STEP that holds only faces is rejected: author the 3D model and let the frame section it.
3. axisymmetric\_cross\_section places the parts in the solve frame through `plane`, then intersects each solid with the X \>= 0 half of the Z = 0 plane. Each face keeps its solid's tags and color.
4. It writes the section to `geometry.step` in the run directory, and the mesher meshes it in 2D.

The section raises when a solid does not reach the half-plane, and when a section reaches X \< 0, which Elmer's axisymmetric solve would reject silently. The mesher names each body's edge on the symmetry axis `<BODY>__AXIS`, and magnetostatics pins the potential to zero there.

cross\_section\_3D is the 3D counterpart for pictures: it cuts away a quarter wedge and keeps the tags.

## Physics

| Selected physics | Solves as |
| --- | --- |
| `MAGNETOSTATICS` | `MAGNETOSTATICS_2D` |
| `THERMAL` | `THERMAL` |
| every other Physics member | raises: solve it with `Solid()` |

The solved stack runs in the `Axi Symmetric` coordinate system. Authored `physics.overrides` must integrate per radian too, so customize the physics after you set the frame.

## Conditions

| Condition | Rule |
| --- | --- |
| CurrentDensity | The axisymmetric coil drive: a signed azimuthal current density over a winding window. |
| Magnetization | The direction must be parallel to the symmetry axis, either sign; it is emitted as its signed axial component. |
| ForceComponent | Torque is rejected: drop `calculate_magnetic_torque`, `torque_origin` and `torque_axis`. |

## Results

Results come back in the solve frame: a vector's Y component is the axial one and its X component the radial one. Elmer integrates per radian in its 2D symmetric coordinate systems, and femforge converts only the typed force and torque fields to full-revolution totals:

| Quantity | Value |
| --- | --- |
| `Result.force`, `Result.torque`, `Result.component_forces`, `Result.component_torques` | Full revolution: the axial component times 2π, the radial component set to zero (its net is zero by symmetry). |
| `Result.raw` | Per radian, exactly as Elmer printed it. |
| magnetic\_field\_energy, eddy\_current\_power, force\_triples and the other readers of `raw` | Per radian. |
| FieldQuery.integrate | The plane-slice integral ∫ value dA. |
| FieldQuery.integrate\_revolved | The full-revolution volume integral ∫ value 2πr dA, with r the cell center's X. |

Result.axial\_force takes an axis in the authored frame:

| `axis` | Returns |
| --- | --- |
| `None` | The force along the symmetry axis. |
| parallel to the symmetry axis | The axial force times the cosine to `axis`. |
| any other | Raises. |

The [workbench](<https://docs.femforge.io/user-guide/workbench/index.md>) field viewer shows the section as solved, mirrors it into the full plane, or revolves it around the axis back into the authored frame.

## Limits

- Only magnetostatics and heat conduction have an axisymmetric form.
- An axisymmetric run computes no torque.
- femforge sections one half-plane and does not check that the model is symmetric.
- Every solid must cross the half-plane; a part off to the side of the section raises.