Aluminium beds – some thoughts on levelling

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.

Here’s a datasheet for the Aluminium I purchased for my carriage upgrade

Two things I note here –

Physical Property Value
Density 2.71 g/cm³
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

………How large?

 

Here follows some very rough calcuations……..

https://www.amesweb.info/StructuralAnalysisBeams/Linear-Thermal-Expansion.aspx

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)

To calculate

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…….

Ames Web

Engineering Toolbox 

  • 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)

We get

  • 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!

Any takers?

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.

Author: Bleugh

Early Fourties, Wife, two kids in primary school. Both of us work full time...5 years now we’ve been Back in Blighty after a decade away...It's a new country for everyone! Still finding time to tinker!

5 thoughts on “Aluminium beds – some thoughts on levelling”

  1. It’s been over a year since this post but I recently got a MP ‘D9’ second hand and have been killing myself trying to get it level. I am really embarrassed I didn’t realize this problem with aluminum before, specially since the person who owned it before me printed almost exclusively in ABS.

    Did you ever end up replacing the lower bed?

    Turns out (and mine seems to be evidence of) it will actually sag almost 3mm with an ABS load of 60C. https://imgur.com/a/5KEkgPn

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    1. I haven’t replaced the bed yet!, too many other projects juggling and I purchased an Ender 3 Pro to be a day-day workhorse whilst this is stripped down. There’s the M420 S1 command thing to remember the bed mesh – ensure to level whilst the bed is hot at 60 degrees, that will help a fair amount with the ‘levelling’ …..

      G28 X0 Y0 ;move X/Y to min endstops
      G28 Z0 ;move Z to min endstops
      M420 S1 ;enable ABL mesh data
      G29 ;perform new ABL (yes it’s redundant, but it doesn’t hurt)

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    2. Just looked at that image! – love the idea behind it, could never figure out if there were any easy-ish math behind the expansion of metals. I don’t think the actual deformation is as bad as 3mm – it’s a lot less on my 300…due to the support of the glass bed above the aluminium and the sandwich structure of the overall bed providing some stiffness…I really need to buy an indicator dial like they use in machine shops but even a 1mm deflection is 5 layers at 0.2mm…Can you use your software to determine a better material for the bed? – or is there a better structure that can be cut from the aluminium?

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      1. I’m really new to Solidworks simulations so I’ll have to play around with it a bit more to figure out what else it can tell me but I agree it does seem exaggerated, and this is just a representation of max deformation, although there are points at the screw holes where the stress passes the yield strength and would cause permanent changes. (Quick glance at A36 Steel, it has ~40% lower thermal expansion and much higher yield strength)

        I’ve added the M420 S1 but also recently flashed the Waggster firmware which I believe should solve that issue anyway since it is an updated version of Marlin. I do have a piece of glass that I have been trying to use too but I have a feeling that there are small undulations or a ‘wave’ that the mesh isn’t fully accounting for.

        I hesitate to ask since I would perhaps rather live in ignorance but, how are you liking the Ender?

        Thank you for all the information you’ve put out on here, it’s been a big help in getting this thing (and my own knowledge) up and running!

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      2. Good to hear you’ve found the waggster firmware, the DGUS display in the D9 was preventing fully mainstream Marlin use….till the CR20s Pro came along :-p

        You can up the number of mesh points the D9 does when you level…though going above about 125 or so seemed to cause some issues with Marlin last time I looked.
        That may help with the waves.

        I’m loving the ender 3 so far..it seems to ‘just work’
        It definitely has lots of minor issues with upgrades needed, but the issues are different to the D9
        Mainly ringing / under shoots / overshoots

        But I have done zero calibration / setup / upgrades , out of the box the prints were better than the D9 and it just goes every time.

        With a new build surface and better extruder along with some serious PID control on the bed, I’ve no doubt the D9 can beat the ender…

        But I’m time poor right now so it’s a slow-Burn project whilst my ender churns out trinkets 🙂

        The plan was to use the ender to print the parts to repair / upgrade the D9!

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