Heated Bed Theory
Release status: experimental
| Description | theory on heated beds
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From time to time there's a lot of talking about an optimal heated bed. So far, a few solutions surfaced, from using industry parts to high-tech carbon fibre products. This page tries to enlighten a few of the attempts with theoretical background in the hope we get something open source and replicatable some day.
Contents
Heating with an industry application
Here we have an existing solution already, the Heated WolfBed.
Warping
So far, there is no real countermeasure against warping, other than to apply this to a fairly thick sheet of aluminium, which is expected to warm up evenly, and thus to prevent warp. This is said to work reasonably, but to result in a rarther heavy bed, which in turn limits movement speeds.
Etched or Isolation Milled Copper Clad
With this approach, copper clad in manufactured in a way resulting in one (or few) tracks over the whole surface. As a voltage is applied and the resistance of the long copper track is not neglibile, the copper gets heated.
Calculation of the track length
First of all, we have to find out how much resistance we need. Heated beds are typically driven by a 12 V power supply and a current of 10 A appears to be sufficient, so we need:
- <math>R = \frac {U} {I} = \frac {12\,V} {10\,A} = 1.2\, \Omega</math>
If you fill a board with parallel tracks, connected zig-zag at the ends, the length of the entire track is approximately
- <math>l_{tr} = l_b \cdot n_{tr}</math>
where
- <math>\begin{align}
l_b & = \mbox {the length of the board} \\ n_{tr} & = \mbox {the number of parallel tracks} \end{align}</math>
<math>n_{tr}</math> can be calculated as well:
- <math>n_{tr} = \frac {w_b} {w_{tr}+w_i}</math>
where
- <math>\begin{align}
w_b & = \mbox {the width of the board} \\ w_{tr} & = \mbox {the width of one track part} \\ w_i & = \mbox {the isolation width between two track parts} \\ \end{align}</math>
With some back and forth you get this formula
- <math>w_{tr} = \frac {-w_i + \sqrt {w_i^2 + 4 \cdot \frac {R_{s,cu} \cdot l_b \cdot w_b} {R \cdot t{cu}}}} {2}</math>
where
- <math>\begin{align}
R_{s,cu} & = \mbox {specific resistance of copper} \\ t_{cu} & = \mbox {thickness of the copper} \end{align}</math>
Let's insert a typical application with:
- <math>\begin{align}
R & = 1.2\, \Omega \\ R_{s,cu} & = 1.68 \cdot 10^{-2}\,\Omega \cdot mm^2 / m = 1.68 \cdot 10^{-5}\,\Omega \cdot mm \\ t_{cu} & = 35\,\mu m = 0.035\,mm \\ l_b & = 130\,mm \\ w_b & = 100\,mm \\ w_i & = 0.5\,mm \end{align}</math>
So we get:
- <math>\begin{align}
w_{tr} & = \frac {-0.5\,mm + \sqrt {0.5^2\,mm^2 + 4 \cdot \frac {1.68 \cdot 10^{-5}\,\Omega \cdot mm \cdot 130\,mm \cdot 100\,mm} {1.2\, \Omega \cdot 0.035\,mm}}} {2} \\ & = 2.044\,mm \end{align}</math>
The number of tracks is
- <math>n = \frac {100} {2.044 + 0.5} = 39.3</math>
which needs to be rounded down to 39 for obvious technical reasons. Inserting that into a formula found elsewhere in this wiki, we get a specific resistance of 0.2348 Ω/m, or a total resistance of 39 * 0.13 m * 0.2348 Ω/m = 1.19 Ω
Warping
The idea is to manufacture two such clads with tracks and to glue them together on their backs. This way both sides are heated evenly and no warp should occur.
Experimental Results
TBD
References
Embedded Carbon Fibres
Carbon fibres have two properties which make them look pretty ideal:
- Carbon fibres can conduct elictricity. So, no copper or other conductor needs to be applied.
- Carbon fibres have a very small and even slightly negative temperature coefficient. Unlike most materials, carbon fibres get shorter when heated up. In combination with other materials, like glass fibres, you can achieve a zero shrink material.
The later of the two obviously requires a careful design. Throwing a bunch of fibres into a bag and filling up with resin won't suffice :-)
Warping
As there is no shrink or grow when raising temperature, there is no warp. This has been proven in many applications.
References
R&G Wiki about heatable molds and a thesis founding that.
