The Wanhao printer bed is made of Aluminium, below this is a flexible heating element.
It’s been widely reported that the D9 doesn’t level very easilly, Here’s why people are having issues….
Aluminium expands when heated!
If you’re having ‘levelling issues’ ensure to do the electronic bed levelling whilst the bed is hot! – (pre-heat to typical printing temperature first)
Anyways, some math.
Two things I note here –
|Thermal Expansion||24 x10^-6 /K|
Density – Steel (which the carriage is made of) is generally around the 7 – 8 g/cm³ – or Three times that of Aluminium! – win there, I can use a sheet of aluminium Three times thicker than the steel on the carriage and have the same weight (in theory)
Thermal Expansion – Translated this means that Aluminium expands by 24 micrometers per millikelvin. Also known as 0.000024 meters per degree
How does this affect the D9 Printbed?
When heated, the 325 x 325 x 2mm thick aluminium bed becomes a bit larger
Here follows some very rough calcuations……..
has a good explaination……
Lets assume Room temperature is 20 degrees Celsius
lets heat the bed up to Standard PLA temperature – 60 Degrees Celsius, that’s 40 Degrees additional temperature
Our Bed is 0.325m on a side (325mm x 325mm x 2mm high)
temperature change multiplied by the thermal coefficient of expansion, multiplied by length of thing
40 Degrees x 24 x10^-6 = 0.0000024 x 40 = 0.000096
0.325m x 0.000096 = 312 x 10^-6 meters, or about 0.3mm
For ABS- a 60 degrees increase in temperature, gives us
0.468mm expansion! (HALF A MILLIMETER!)
If a bed is constrained – locked in place or heated unevenly, the plate will expand in different ways at different places……This 0.3mm expansion for PLA – or a typical layer height will push on the supports and assuming all is even, each will need to move by 0.15mm or something will break
Finally, Uwards expansion – consider that the bed is restrained in the X and Y directions…by the 4 levelling screws – the only way for the bed to expand would be ‘upwards’
This upwards expansion would cause a ‘hump’ in the bed
Using these websites to calculate the stress / force caused by heating…….
- 0.325 – Length of Restricted object
- 0.00065 – Area of restricted object (325mm by 2mm height of bed)
- 40 – Temperature difference (PLA)
- 71 – Youngs modulus (from the datasheet)
- 24 – expansion coefficient (from the datasheet)
- 0.334 – Poisson’s Ratio for Aluminium (from Google)
- Stress – PSI – 68160000
- Force – 44304 Newtons – or roughly 4,500 Kilograms!!, 4.5 metric tons!
and from there, i’ve no idea how to calculate the upwards deflection!
When heated by 40 degrees, the bed expands by 0.3mm with 4.5 tons (metric) of force!
Either way we can see that the changes in length involved are around the range of typical layer heights / widths and nozzle diameters so there’s much further investigation to do.