Simulate Compound Bow draw cycle

[bjur]

I'm just getting into Fusion 360 and was mainly looking for an answer to if fusion was a good fit for solving this particular problem.  I'm looking to simulate the full draw cycle of a compound bow (see link below).  I'd like to run a non-linear simulation of the bow string being drawn back using cables over an eccentric cam.  There are mathematical ways to simulate this on paper but I was looking for a full 3d way to run this simulation and be able to make 3d tweaks to the design and see how this affects the forces, deflections, and stresses in the various components.  It's a complicated problem where everything varies over time.  As the bow string is pulled back the tension in the cable causes the eccentric cam to rotate.  This cam is linked to an identical cam on the other limb of the bow via another cable.  As the eccentric cam rotates, the distance from the bow string to the axle of the cam changes.  As the cam rotates the limbs (springs) deflect and the load in the limb increases.  At the end of the draw cycle, the cams rotate to a certain point where the tension in the bow string is approximately 20% of the max tension during the draw cycle.  This allows the archer to hold the string at full draw easier.  In a perfect world, the simulation would be able to predict the stress in the limbs, tension in the cable and even predict the acceleration of the bow string once let go.  I've included a gif of how the cams rotate while drawing the string.

https://gfycat.com/sparseellipticalkoi

[John_Holtz]

Hi @bjur .

That looks like an interesting analysis, but very complex once you start to break it down. I do not see Fusion being able to calculate it.

• Fusion does not have anything that resembles a cable.
• There is some mechanism between the cam and bow, right? Maybe a torsion spring or something that prevents the cam from rotating freely. How would that be accounted for in the analysis? Is the relationship linear (like a torsion spring) or nonlinear?
• The cam is on some type of shaft/bushing so that it can rotate. Even if the cam were free to rotate, Fusion does not have an efficient method to simulate that in a stress analysis.
• The cable and bow have an initial stress due to the preload in the cable. Including that in an analysis is another hurdle to figure out.

What I could see you doing in Fusion is modeling the bow itself without the cam and cables. Based on the individual loads F1, F2, and M3, you can calculate the stress and displacement. The response due to any combination of load a*F1+b*F2+c*M3 may be close to the algebraic sum of the three separate results. (In other words, you are determining the force versus displacement response of the bow itself.) From knowing that, you can do some complex hand calculations (or spreadsheet or MathCAD) to determine the draw of the cable with the cam. It's all nonlinear and highly inter-related.

[bjur]

Here's a better video of the draw cycle of the bow.  https://www.youtube.com/watch?v=vYrK4tPzxGY

There's no moment generated at the cams as they are free to spin.  The only moment generated is internal to the limbs as a cantilevered beam.  The cables route between each of the cams to make sure they spin together.  The end result is that by using the mechanical advantage of the pulley system, the limbs are deflected / loaded with a substantial force as a spring.  The non-linear portion of the analysis is that as the limbs deflect, the location of the axle that supports the cams moves, which changes the angle of the string as it's drawn back.  I was hoping that there was a way to set up a cable (or the equivalent) with contact boundary conditions through the cams that could model this mechanism.  There are mathematical ways to model this but it's tedious and I was hoping that fusion could simulate the entire mechanism through its FEA simulation functions.  Any recommendations for software if Fusion isn't the right tool?

[John_Holtz · Accepted solution]

Hi @bjur 

Thanks for the additional video. I also found this website that has simple diagrams with some concepts: How Compound Bow Works.

I think the combination of cable (however modeled), contact, and rotation of the cams will be too large for what Nastran can handle. That rules out Fusion and Inventor Nastran. I am not aware of any other Autodesk products that could handle all of those in one model.