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3D Printing Cheat Sheet

Calculators

Table of contents

Perimeters Width

In Slic3r and PrusaSlicer, the perimeters are overlapping each others while being printed (two perimeters of 0.45mm extrusion width will be 0.86mm and not 0.90mm). More information here: Slic3r Flow Math and PrusaSlicer Layers and Perimeters.

\textit{extrusion spacing}=w-h(1-\frac{\pi}{4})
\textit{perimeters width}=w+\textit{extrusion spacing} \cdot (N-1)

Where:

variable description unit
w extrusion width (eg. 0.45mm) mm
h layer height (eg. 0.20mm) mm
N number of perimeters
extrusion spacing spacing between extrusions with overlapping mm
perimeters width width of perimeters as printed in Slic3r or PrusaSlicer mm

Extrusion Multiplier

\textit{extrusion multiplier}=\frac{\textit{original extrusion multiplier} \cdot \textit{extrusion width}}{\textit{perimeter thickness}}

Where:

variable description unit
extrusion multiplier extrusion multiplier adjusted
original extrusion multiplier original extrusion multiplier set in your slicer
extrusion width extrusion width set in your slice (0.45mm if you are using a 0.4mm nozzle and PrusaSlicer) mm
perimeter thickness measured perimeter thickness (average of measured perimeters thickness if you measure more than one) mm

More information here: Extrusion multiplier calibration guide

Extruder steps/mm

\textit{steps per mm}=\frac{\textit{motor steps} \cdot \mathit{\mu step} \cdot \textit{gear ratio}}{\textit{hobb dia} \cdot \pi}

Where:

variable description unit
steps per mm number of extruder steps for one full rotation
motor steps number of step for one full rotation of the motor. In general, 200 for 1.8° motor and 400 for 0.9° motor
μstep micro stepping configured in the 3D printer firmware (eg. 16, 32, 64...)
gear ratio gear ratio (eg. 3:1)
hobb dia effective hobb gear diameter mm

Example:

For an 1.8° stepper, 16 micro-stepping configuration, a gear ratio of 50:17 and Bondtech 1.75/5.0 drive gears:
\textit{steps per mm}=\frac{200 \cdot 16 \cdot ^{50}/_{17}}{7.22 \cdot \pi}=414.94 \Rightarrow 415

Part Scaling

As the printed parts are printed warm and then cooldown to room temperature they will shrink in size. The shrinkage depends on the thermal expansion coefficient of the filament material used. Note that filament additives can change the thermal expansion factor of your material.

Slicer scaling factor

To calculate the scale percentage to use in your slicer to account for shrinkage.

s=100(1+ \alpha \cdot \Delta_t)

Where:

variable description unit
s percentage to scale your print part in your slicer %
α filament material thermal expansion coefficient (see table bellow) m/mK
Δt difference between the bed temperature and the room temperature

Example:

For a PETG part with a bed at 85°C and room temperature at 25°C:
\textit{scale factor}=100(1+60 \cdot 10^{-6} \cdot (85-25))=100.36%
This means if you print a part who is 50mm long (in CAD) and want to have it at 50mm in reality, then you have to scale your part by 100.36%.

Slicer scaling factor from one material to another

To calculate the scale percentage to use in your slicer if a printed part has been design specifically for a material and will need to be printed in another material. For example, a precise mechanical part designed for PETG that you want to print in ABS.

s_p=100 \cdot \frac{(1+ \alpha_p \cdot \Delta_{tp})}{(1+ \alpha_o \cdot \Delta_{to})}

Where:

variable description unit
sp percentage to scale your print part in your slicer for a different material than used by the designer %
αo thermal expansion coefficient of the original filament material used by the designer (see table bellow) m/mK
αp thermal expansion coefficient of the filament material used to print your part (see table bellow) m/mK
Δto difference between the bed temperature and the room temperature of the original filament material used by the designer
Δtp difference between the bed temperature and the room temperature of the filament material used to print your part

Example:

For a printed part designed to be printed for PETG that you will print in ABS:
PETG values: αo=60 · 10-6 m/mK, bed temperature=85°C, room temperature=25°C
ABS values: αo=90 · 10-6 m/mK, bed temperature=110°C, room temperature=25°C
s_p=100 \cdot \frac{(1+90 \cdot 10^{-6} \cdot (110-25))}{(1+60 \cdot 10^{-6} \cdot (85-25))}=100.40%
This means that the original part designed for PETG needs to be scaled by 100.40% to be printed with ABS.

Printed part size

To calculate a dimension after printing and cooldown.

L_2=\frac{L_1}{1+ \alpha \cdot \Delta_t}

Where:

variable description unit
L1 length in CAD or slicer (before printing) mm
L2 length after printing and cooldown mm
α filament material thermal expansion coefficient (see table bellow) m/mK
Δt difference between the bed temperature and the room temperature

Example:

For a PETG part with a width of 50mm, bed at 85°C and room temperature at 25°C:
L_2=\frac{50}{1+60\cdot10^{-6} \cdot (85-25)}=49.82mm

Common coefficients of linear thermal expansion

material α source
ABS 72 to 110 · 10-6 m/mK 1, 2, 3
ASA 60 to 110 · 10-6 m/mK 1
PC 65 to 70 · 10-6 m/mK 1, 2
PETG 51 to 68 · 10-6 m/mK 1, 2, 3
PLA (4043D) 41 to 68 · 10-6 m/mK 1, 2, 3

Pulley Diameters

Calculations for Gates 2GT and GT3 pulleys. More details here: Timing Belt and Pulley

Belt and Pulley Glossary

pd = \frac{P \cdot N}{\pi}
od = pd - 2 \cdot U

Where:

variable description unit
pd pitch diameter mm
P belt pitch mm
N number of pulley teeth
od pulley outside diameter mm
U Distance from pitch line to belt tooth bottom.
- U = 0.254mm for 2GT and GT2/3 2mm pitch belts
- U = 0.381mm for 3GT and GT2/3 3mm pitch belts		 mm

Example:

For a GT3 2mm pitch belt and 20T pulley:
pd = \frac{2 \cdot 20}{\pi} = 12.732mm
od = 12.732 - 2 \cdot 0.254 = 12.224mm

Resources

Resources used for those calculations: