Our next goal, after choosing the appropriate tubes and doing the first design iteration, is to validate the chosen solution. This is the time when we go to a more elaborate analysis methods, like Finite Element Method, or FEM.

We will do this in two phases, first will look at the tubes alone and next look at the full frame and obtain the stress levels at the end units. Let’s first see the material properties of the frame:

Material properties for the analysis

Right from the start you can see the challenge – PLA is waaay softer and weaker than our tubes! Around 30 times softer and weaker… This is certainly a challenge, and an interesting one. Just one note to start, the table above is provided with three types of units, personally I work with metric units, but whatever you feel comfortable with is perfectly fine. And another note, I’m aware that carbon fiber material cannot be described fully with the values in the table, it is sufficient for now. I’m trying to make the picture as clear as possible at this point, if there ever be a need for this, I will sure to add the additional required information.

First, we will validate the closed form calculations that were performed here and here. At this point we are talking about the 16mm OD and 12mm ID carbon tubes, maximum length of 860 mm and a single central load of 120 kg divided between three tubes.

Boundary conditions and loads

The following pictures show the result. The maximum deflection is in the middle and it’s not surprisingly around 26 mm, just see the previous post.

Deflection of the tubes (scaled up for clarity) 860 mm frame
Side view, scaled up deflection

The deflection shown in the pictures is of course exaggerated (for visualization reasons), but the numbers are the true outcome. What we did here is validation of the calculation methods against closed form solutions, this is always important and it’s kind of sanity check.

Now, we will go to the actual frame that will be made first, which is the 690 mm length. Intuitively the deflection will be smaller, and it is:

Deflection results for 690 mm frame (scaled up)

Next, we will see the “all up” frame with the end unit loaded. I used a slightly different software here, but the essence is the same. Note that we get slightly lower deflection (~10 mm) due to slightly updated boundary conditions, not a big deal once we aware of this.

Frame under load

In the above analysis I used only half a model with symmetric boundary conditions, a common “trick” that is used to reduce the size of the problem. Now, let’s see the stresses:

Stresses in PLA [MPa]
The maximum stress in the PLA unit is ~7 MPa, this gives us a nice factor of safety of ~5, which we can live happily with. Note the lower stresses around the tubes, this can give us a buffer in case the glue won’t hold perfectly. For the tubes there is no surprise, the stresses are really low compared to what the material can take. Not surprisingly the maximum stresses occur at the bottom of the frame where the maximum stretching happens.

The upper surface is in compression, stresses in [MPa]
Maximum stresses in the carbon tubes [MPa], at the bottom of the “belly”
This is it for now. This important step validated and increased the confidence in the preliminary design. Now I’m waiting for the tubes to arrive, next post will be the assembly of the actual frame.