Additive manufacturing: layers, cusps and break-even
Введено| English | Значение |
|---|---|
| additive manufacturing | Making a part by adding material layer by layer from a digital model, as in 3D printing. |
| staircase effect | The stepped surface left on curved or sloping faces of a part built in layers. |
| cusp height | The height of the small ridge left between neighbouring passes of a tool or layers of a print. |
| anisotropy | Having properties that depend on direction, such as a printed part being weaker between layers. |
| machining | Removing material with a cutting tool to make a part to its final shape and size. |
| overhang | A surface in a printed part that leans too far from vertical to rest on the layer below without support. |
Channels no tool can reach
- A flow straightener with internal channels cannot be machined, but it can be built layer by layer. Additive manufacturing makes such shapes easily, but layers bring their own limits.
- The main families: material extrusion (FDM), powder bed fusion (SLS, metal LPBF), vat photopolymerisation (SLA) and binder jetting. All slice the model into layers of thickness $t$.
The staircase
- A sloped surface becomes a staircase effect, with cusp height $c = t\cos\theta$, where $\theta$ is the angle between the surface normal and the build direction. Flat and vertical faces have no cusp.
- Parts are usually weaker across the layers than along them: anisotropy.
Which lever changes it?
Link each print outcome to the decision that controls it.
Which face of a printed part has no cusp?
Сложность 1/5 · 100 монет + небольшой бонус за первое завершение сегодня
cos of 90 degrees is zero.
A printed part is equally strong in every direction.
Сложность 1/5 · 100 монет + небольшой бонус за первое завершение сегодня
It is usually weaker across the layers.
Choosing a layer
- The straightener is 60 mm tall. At 0.2 mm: $\mathbf{300}$ layers, and a 45° wall has $c = \mathbf{0.141}$ mm.
- At 0.1 mm: 600 layers and $c = 0.071$ mm, which is twice the time for half the roughness.
- Turning the wall vertical removes the cusp entirely: orientation is the first lever.
Layers in a 60 mm part at 0.2 mm?
Сложность 2/5 · 140 монет + небольшой бонус за первое завершение сегодня
60 over 0.2.
Cusp height on a 45 degree wall at 0.2 mm layers (three decimals, mm)?
Сложность 2/5 · 140 монет + небольшой бонус за первое завершение сегодня
t cos 45.
Cusp at 0.1 mm layers on the same wall (three decimals, mm)?
Сложность 2/5 · 140 монет + небольшой бонус за первое завершение сегодня
Half of 0.141.
Print or machine?
- Printing costs about €40 per part with no set-up. Machining a simpler two-part version costs €400 of set-up plus €12 per part.
- Break-even: $400/(40 - 12) = \mathbf{14.3}$, so printing wins up to 14 parts and machining from 15.
Break-even quantity: 400 euro set-up, 12 euro machined, 40 euro printed (one decimal)?
Сложность 2/5 · 140 монет + небольшой бонус за первое завершение сегодня
Set-up over the difference in unit cost.
A wall leaning 60° from vertical prints cleanly without supports.
Сложность 1/5 · 100 монет + небольшой бонус за первое завершение сегодня
Beyond about 45° from vertical each layer overhangs the last too far and sags; it needs supports or a redesign.
Overhangs and supports
- Each layer must sit on the one below. A wall leaning more than about 45° from vertical is an overhang 悬垂 that sags unless supports are printed under it, and the supports must later be removed.
- The straightener's internal channels are the hard case: supports inside cannot be reached. Teardrop or diamond channel sections keep every surface within 45° and print without them.
Strength 30 MPa across the layers, design stress 30 MPa: safety factor (two decimals)?
Сложность 2/5 · 140 монет + небольшой бонус за первое завершение сегодня
$30/30 = 1.00$: no margin.
Same part with the load along the layers, strength 50 MPa (two decimals)?
Сложность 2/5 · 140 монет + небольшой бонус за первое завершение сегодня
$50/30 = 1.67$.
Worked example: load along the layers
- A printed bracket reaches 50 MPa along its layers but only 30 MPa across them. The design stress is 30 MPa.
- Built so the load runs across the layers, the safety factor is $30/30 = \mathbf{1.00}$: no margin. Rotated so it runs along them, $50/30 = \mathbf{1.67}$. Orientation is chosen for strength as well as for finish.
Three printing slips
- Orientation chosen last. Choose it first.
- Leaving out supports and post-machining. They belong in the cost.
- Bulk properties in every direction. Printed parts are weaker across layers.
Recap
- $c = t\cos\theta$: 0.141 mm at 0.2 mm layers on a 45° wall.
- Build time scales with $H/t$: 300 layers against 600.
- Break-even $N = \text{set-up}/(\text{AM cost} - \text{unit cost}) = 14.3$.