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Wood Proto
We decided to build a wood proto before building the final design.
Basically, to try to save money. There are a lot of details in the design that will benefit from having a real working printer. Things like the exact location and mounting of tool holders, filament reels, and enclosures. Getting ALL the holes and features we will eventually want cut into the aluminum top and bottom plate fully understood before we start cutting aluminum can save us a lot of hassles later, and may save us the cost of remaking a whole piece.
The wood proto has top and bottom plates made from MDF. We used the CNC machine in the wood studio to cut out the same design as is planned in aluminum. The aluminum design is planning to use 3/8" cast aluminum plate. For the wood proto, we selected 1/2" MDF. We picked 1/2" because it was more readily available (at Home Depot, ins 2' x 4' sheets) than 3/8" and will be stiffer than 3/8".
MDF is not as strong as aluminum - DUH! But how will the MDF compare to the aluminum plate? Specifically, will we be able to predict how "bendy" our aluminum plate will be by looking at the bendiness of the MDF? Yes! Without going into all the details of the equations for deflection under load, we can use two facts about the equations to help us.
Moment of Inertia (I) is a measure of the strength of a beams cross sectional shape, and the relative deflection of two beams is proportional to their relative I values. Lots of fun and Calculus (also fun) can be used to calculate the Moment of Inertia of various shapes. But luckily for us there are equations for simple shapes. Our top-plate looks a lot like a rectangular beam, and the equation for I of a rectangular bean is
I = (b h^3 ) / 12, where
b = width of the beam
h= height of the beam
Our MDF is the same width as the final aluminum plate, but it is thicker. This means is has more "shape strength" that the .5" aluminum top plate will have. Specifically, the increase in strength is
0.5 ^3 / 0.375 ^3 = .125 / .0527 = 2.37
A materials Modulus of Elasticity is a measure of it's stiffness. If two shapes are identical and have an identical load applied to them, but are made from different materials, the one with the higher Modulus will deflect less.
Thanks to the data sheets for our target aluminum material, we know that the Modulus of Elasticity is 70GPa. And from online sources we can find that the Modulus of Elasticity on MDF is 3.59Gpa.
This means that MDF will bend 70/3.59 = 19.5 times as much as MDF under the same load.
A .5" plate is 2.37 times stronger than a .5" plate, but the aluminum is 19.5 Times stronger than the MDF. The net is that our final aluminum top plate will be
19.5 / 2.37 = 8.23
times stiffer than the MDF.
So, we can apply a load (like the tension of the belts) to the MDF top plate and measure the deflection, then divide by 8.23 to find the deflection of the aluminum.