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# Fun with Simulation

June 20, 2017 By: Eric Stamper

I thought I’d have a little fun using simulation and see if I could reproduce the behavior of a few animations I recently saw online. This blog shows the different finite element analyses I ran and the accompanying videos that I found online. They compare quite well! This comparison also emphasizes that FEA can be very accurate and it can also capture all the real life physics shown in these animations.

Intermediate Axis Theorem:

The first animation is of a spinning handle floating in zero gravity on the international space station, compliments of NASA:

It’s a great example of the intermediate axis theorem and moments of inertia of rotating objects. The theorem states that the rotation of an object around its first and third principal axes is stable, and unstable about its second, or intermediate, axis. The video demonstrates this instability as the handle flips back and forth as it’s rotating. What are the chances that spinning an object similar to this in a FEA simulation would also show this behavior? Turns out, pretty good (as should be expected!). I used my  best guess on the size, material, angular velocity, and initial perturbation, and voila, the solution matched up great! This problem is actually about as easy as it gets in terms of a simulation, since it’s simply an initial angular velocity applied to a rigid body for computational efficiency purposes. It could also be modeled with a couple beam elements to further reduce the model size, but for aesthetics, solid elements were used.

Gyroscope Balance:

I think many can relate to seeing or playing with a gyroscope. If not, here’s a short video:

Once the rotor is spinning sufficiently fast, it can balance in a manner that appears to defy gravity. When it’s tipped and supported on one side, the gyroscopic forces will prevent it from falling over and also cause it to spin around on its support. This happens when a force is placed normal to the spinning axis, but only when spinning. This is the condition that is simulated. In this analysis, the gyroscope starts off in the balanced and spinning condition rather than from rest, for computational efficiency, since we’re not interested in what happens up to this point. The FE model is also created with rigid beams and shells for efficiency supposes. The simulated gyroscope matches up quite well to the video!

Tippe Top Instability:

The idea for this last example came from a presentation I saw at a LS-DYNA conference titled “Tippe Top Simulation by LS-DYNA”.  An example of one of these tops in action can be seen here:

I knew ahead of time from both this presentation and from having one of these tops, that it is possible for the top to invert. However; in the first couple of simulations that I ran, the top didn’t invert. Not because the simulation was incorrect, but simply because it wasn’t supposed to invert based on the geometry I initially came up with. I was getting the correct answer, just to a different problem. After calculating a few geometry parameters and tweaking the geometry so that the top is physically supposed to flip, the simulation mimicked exactly what was expected.

All the analyses that were performed in this blog replicate a common workflow for simulation users, which is: simulate a known solution (from test) and compare with physical results. If all the physics are correctly simulated, the answers should match very well. However, when the solution to the problem is not known ahead of time (using simulation as a predictive tool), investigating what is happening, and why, is vitally important to ensuring you’re simulating the correct problem and what would happen in reality.

I hope you enjoyed these videos. If you have any comments about your own experiences with matching simulation to reality, please share them.