### Parametric Cantilever Spring Test Sample

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Published on February 20, 2012

#### Description

It is somtimes useful to include cantilever springs in a plastic mecanism. But, because of the many variables involved in printed plastic parts, there is very little information on the properties of the material. Thus experimenting with many different desings become a solution that consume a lot of time and resources.
This device is intended to measure the elasticity constant (Young's modulus), the yield strength (the force required to deform the part) and the ultimate strength (the force required to break the part)

#### Instructions

1- In openScad, enter the size of the desired beam. Or one can use the .stl file included where the beam is l=80 mm, w=10 mm and h=3 mm.

2-Convert the part to Gcode using your favorite software. Note that, the object infill, number of shells and other option will have an effect on the results. For the best results, since the biggest force will be in the length of the beam, it is desirable to also get most filaments printed followind the length. To do that, one can raise the number of shells. As long as one leave enough space to get an infill to join the two sides of the beam together.

3-Print the part using your favorite printer.

4-Test the part.
4.1 - Tools required:
-Clamp to hold the base of the beam.
-Ruler or other mesurement device
-Force sensor (Any kind of scale, force meter ...) I used this one : dealextreme.com/p/1-9-lcd-electronic-hook-scale-with-time-temperature-tape-calculator-50kg-max-20g-resolution-20313

4.2 - To measure the Young's modulus, one as to measure the force required to deflect the tip of the beam for a small distance (Too much can cause warping or break the part... let's keep it for later.)

Using the following equation, derived from cantilever beam equations, one can calculate the elastic modulus (e):
e = (4 * f * l^3 ) / (x * w * h^3 )
Where: f is the force applied at the tip,
l is the length of the beam from the clamp to the point where the load is applied,
x is the deflexion of the tip from the unloaded state,
w is the width of the beam,
h is the thickness of the beam

4.3 - To measure the yield strength (Sy), one as to measure the force required to permanantly deform the beam. Press on the beam using a certain force, release the beam and check if the tip comes back to its initial position. Repeat until the force is enough to cause a permanent deformation. Note the force used.

In the case of a cantilever beam, the maximum force will be at the base of the clamp where strain is higher.
The following equation allows to calculate the base strength (s) according to the load.
S = (6 * f *l) /(w* h^2)

4.4 - Now the fun part (WEAR SAFETY GLASSES!!!) To measure the ultimate strength (Su), one as to measure the force required to break the beam. Press on the beam until it breaks. Note the force used. Raising the force slowly allow the read the result just before it breaks. Note one can use the last equation to get an idea of the ultimate strength. But this equation is base on a small deflection hypothesis, wich normally doesn't hold under the deflexion usually needed to break the beam. So the results have to be taken as a large guideline.

5 - Repeat steps 1 to 5 with other desings to maxise you results until satisfaction.

6 - Desing a real part.

7 - Recycle the plastic from the broken parts (if using abs: thingiverse.com/thing:14490) Very useful to improve parts adherance to the build surface!

For the .STL beam included, printed on TOM HBP with MK7 using:
1.75mm White ABS from 3dprinterstuff.com (it is somewhat more flexible)
layer heigth: 0.3
number of shell: 1
Infill: 100%
feedrate: 30

I got the following results:
e = 1.1 MPa (Newton/meter²) ±10%
Sy = 1.9 MPa ±15%
Su = 4.7 MPa ±20%

Happy experimentation!
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