Jimmy Etienne, et al.
Since we don't do a lot of digital fab...
Additive
Subtractive
Computer Numerically Controlled = CNC
Generally a simple concept, FDM deposits material via CNC machineary
Anatomy
Hotend
Slicing
Addresses a weakness of FDM printers
High level approach
Tetrahedralize
Optimization
Toolpath Generation
Post Processing
Tetrahedralization
Provides a means of representing M\mathcal{M}M
Ω\OmegaΩ - Mesh
Γ\GammaΓ - Tetrahedral mesh (ΓI\Gamma_IΓI inside ΓO\Gamma_OΓO and out)
F\mathcal{F}F - Faces on mesh
∀p∈V,M(p)=h\forall p \in V, \mathcal{M}(p) = h∀p∈V,M(p)=h (height)
Layer thickness
Minimum and maximum layer thicknesses
τmin=0.1d\tau_{min} = 0.1dτmin=0.1d, τmax=0.75d\tau_{max} =0.75dτmax=0.75d
For 0.4mm nozzle, this gives [0.04mm, 0.3mm], depending on calibration
Slope
Slice at τmax\tau_{max}τmax in M(Ω)\mathcal{M}(\Omega)M(Ω), optimize M\mathcal{M}M to flatten as many faces as possible
Flatten which faces?
F‾\overline{\mathcal{F}}F - other faces
F‾\underline{\mathcal{F}}F - faces to be flattened
Define an energy function to minimize
λ\lambdaλs are user-chosen trade-off parameters
h0=zh^0=zh0=z
Attempts to pull vertices of a triangle to the same height
C(F‾)\mathcal{C}(\underline{\mathcal{F}})C(F) is the set of connected components of the set to flatten
Constraints on optimization
Thickness constraint
∀t∈ΓI\forall t\in \Gamma_I∀t∈ΓI
Slope constraint
What if flattened surfaces aren't flat?
Extrusion rate must be modified in T\mathcal{T}T, but is available from the gradient of M\mathcal{M}M
Error Comparison
By Joshua Horacsek
