Defining constraints and success metrics for prototype 1

[wgbowley]

1. Define application specific constraints
2. Define technical constraints
3. Define metrics for measuring success of prototype 1
4. Conclude with most important constraints and metrics

[wgbowley]

$$ \text{Volumetric Flow} = \text{layer height} \times \text{extrusion width} \times \text{print speed} $$

• Layer Height: $Q \propto h$
• Extrusion Width: $Q \propto w$
• Print Speed: $Q \propto v$

Given a constant volumetric flow determined by the hot end, linear motors can achieve thinner layer heights or extension width due to potential higher accelerations than standard motion systems (However this is still to be determined)

[wgbowley]

** means that print speed does increase like expected nothing crazy:

$$v = \frac{Q}{h \times w}$$

Fouier number of the material changes the volumetric heat flow. So the system improvements also changes based on the selected filament to measure each improvements against:

$$Fo = \frac{\alpha \cdot t_{cool} \cdot v \cdot w \cdot h}{Q \cdot L^2}$$

Symbol	Definition	Unit
$E_v$	Volumetric Energy Density	$\text{J/mm}^3$
$Fo$	Fourier Number (Dimensionless)	-
$P$	Thermal Power Input	$\text{W}$
$v$	Print Speed	$\text{mm/s}$
$w$	Extrusion Width	$\text{mm}$
$h$	Layer Height	$\text{mm}$
$\alpha$	Thermal Diffusivity	$\text{mm}^2/\text{s}$
$t_{cool}$	Dwell/Cooling Time	$\text{s}$
$L$	Characteristic Length	$\text{mm}$