How to Top-Op 😁

 

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Above is a brake pedal mock-up I created (bare with me, I know the initial design isn't pretty but it is to showcase how topology optimization can drastically change and improve a design).

• For starters, Topology Optimization optimizes the material used for a part and can optimize specifically for stiffness-to-weight ratio, minimal mass, etc.

• This is especially useful on parts that are long/larger and inherently have a lot of material, which can lead to small high-stress concentrations and the rest of the material being redundant and unneeded

• All in all, if you are really looking to not just meet design requirements for your part, but truly create an optimized and efficient part, Topology Optimization can be a great help

• Disclaimer: This brake pedal is not necessarily a truly great brake pedal design (aka there is no hole to mount to the bearing bar) but to just show you how top-ops work, this should do fine

Now I am going to run through a simple Topology Optimization setup, what my thought process is, and how to interpret the results.

Firstly, topology optimization utilizes FEA (Finite Element Analysis) to take in stress, strain, factor of safety, etc. etc. to understand how the part reacts to the specified load and situation.

For the FEA, you'll need to set up your material, supports, and loads. For the topology optimization, you'll also need to set your optimization goals.

• The material is self-explanatory. Just ensure that if you are using let's say 6061 aluminum, are you using 6061-0, 6061-t4, or 6061-t6 aluminum? These just signify the different types of processing the metal is put through, which are important to maintaining accurate numerical properties and therefore simulation data

• In terms of loads, this can be as simple (or complicated depending on what the part/situation is) as drawing an FBD and replicating all the forces acting on the part. Also, remember to check your units when simulating, as 1000 N is very different from 1000 kN

• Supports are majorly important, as stated earlier. The topology optimization itself is predicated on the FEA results, so any over or under-constraining will worsen your results, especially when you are literally optimizing a part based on faulty results

Consider this wall-mounted hook/bracket design. The bracket will be screwed into the wall via the top hole, with half the bracket resting on the wall, and the other hanging with the force applied.

Look at these different support setups for a wall-mounted bracket and try and get an understanding of how they would affect your simulations and therefore your results.

• With an under-constrained setup, only the top screw hole is fixed, meaning that your simulation would have too little restriction and results where the model displaces and translates far higher than it would actually be in use. This is because the side that rests on the wall is allowed to bend essentially into where the wall would be. Therefore, this setup results in a poor and inaccurate simulation

• Just to give a definition of under-constrained, this means that there are insufficient motion/deformation restrictions and that the number of constraints is fewer than the DOF (degrees of freedom). Degrees of Freedom just refer to the different variables that make up the possible motions of a system (so think of each translation in the X, Y, and Z to be each a single DOF, each moment on each axis being a single DOF each, etc. etc.)   

• With an over-constrained setup, you'd have the entire back of the bracket essentially bonded to the wall. This is unrealistic because you are basically assuming the part is stuck to the wall no matter the load, which will not happen in a real situation. Therefore, you get simulation results that poorly represent what will actually happen, showing too little deformation for the situation

• Again, just to give a definition, you have too many motion/deformation restrictions and the number of constraints is higher than the DOF if you have an over-constrained setup

• In a well-constrained setup, you'd have constraints to mimic both the screw going into the wall and a proper translation constraint to keep the part from bending back into the wall. This gives you a realistic situation, simulation, equilibrium, and results

Now let me show you all this through the situation of the brake pedal.

For this rather elementary part and situation, all I am assuming is that the pedal is bolted only at the bottom (realistically we would have a balance bar mounting point)

Additionally, we are simulating in this case that the brake is already pushed down and that the driver is now attempting to push the brake pedal past its limit. This is basically a safety check to ensure that in a tense situation, due to adrenaline or whatever other extenuating circumstance, the brake pedal will not break (lol) in a situation where it cannot move anymore past its limit.

• If you were simulating a case where the brake was at its starting position, you would utilize a hinge support, which would restrict the circular edge of the hole in all 6 DOF except for rotation around its own axis. Basically the brake pedal can only move like it would in real life, rotating around the bolt.

In terms of external loads, we simply have a 311 N force applied normally to the pedal contact area (this number represents the force of an average person pushing the brakes, about 70 lbf → 311 N) as well as the gravitational force acting at the center of gravity (as the pedal is being actively pulled down since the top part is essentially floating in the air).

• Disclaimer: In an actually utilized part, I would use a higher load case (preferably 2000 N because that is FSAE regulation) in order to already add a factor of safety to our part and ensure that any extenuating circumstance is accounted for. For this simulation, I chose the smaller number to A) get this example to run quicker and B) showcase how drastic the results of Topology Optimization can be. TL;DR The 311 N is a good benchmark number for everyday use and no crazy circumstance, increase this number to account for those

Once you have your material, load cases, and supports, you can now mesh your part. 

• Now I am still a novice at meshing, I will link a guide here, created by now LHR Combustion Body Lead Ryan Gretta who has some great notes on the different types of meshing and how to optimize a mesh

• What I can tell you is that, generally the finer the mesh, the better/more accurate a simulation’s results are, however, there is a point where refining a mesh leads to minimal sim data change and only increases runtime, called mesh convergence theory. All in all, try and refine your mesh to a reasonable number to be accurate and still run efficiently

• Also, given the shape of your object, you may want to customize the mesh yourself (more so an Ansys thing than a SolidWorks thing), where you might have a sweepable mesh (essentially a consistent, equal line of mesh nodes) across a uniform area, and then more specific shapes and sizes in curved areas or holes

Now with the part setup down, you can select your Topology Optimization goals.

• Generally, you are going to want to A) maximize your weight-to-stiffness ratio, B) minimize as much mass as possible or C) minimize the maximum displacement of the part

• For this part, we want to lose some of the part's mass, but we care more about its stiffness, as we do not want it breaking under load. Hence, we would choose the goal of the best possible weight-to-stiffness ratio while shooting for a mass reduction of 75% (I say “shooting for” as this will only be reached if allowable by the weight-to-stiffness ratio parameter)

  • Additionally, I set another goal which has to do with maintaining a F.O.S. of at least 1.5 for the entire part, to ensure we can take the predicted load case and even more in the case of an extreme circumstance

Lastly, we can run our topology study and await our results.

What we see here is a mass plot that showcases the necessary material layout for the part given the parameters we set, being:

• The best weight-to-stiffness ratio possible while

  • Cutting around 75% mass

  • & Maintaining 1.5 F.O.S around the entire part

To extrapolate this data and update our part to mimic/copy what the topology study determined as needed, we can do this a couple of different ways:

1. We can simply cut the part we already have and loosely copy the results

2. Or we could export a smoothed mesh and trace around the topology optimization to get a more true-to-simulation result

I ended up using the latter, but either will work, as long as you never cut more material than the topology results did as if we take away more material, we could jeopardize the structural integrity of the already optimized part and fail our goals/load cases.

This is what the smoothed mesh will look like and you can simply trace, extrude, and copy the part as needed.

This is now how the part looks after I took the smoothed mesh, traced out the part, and cleaned it up. Once you have redone the part, you are essentially finished! I would recommend statically simulating the part to ensure it still meets any required regulations (i.e. not yielding a specific amount, meeting a certain F.O.S., not hitting a certain stress value, etc.) but otherwise, you’re part is now optimized!

In terms of this specific brake pedal design (though the starter brake pedal was a little overbuilt intentionally), the mass values dropped from 2.56 lbs to .464 lbs, which resulted in a mass reduction of over 82%, while still being able to take the same loads! Again, was the mass reduction and topology optimization in all reality necessary for the part to pass simulations? No. However, we made the part lighter, cut down on the material needed for the part, and made sure that all the material was being put to use and not wasted! Not to mention, if you consider the different types of manufacturing processes, topology optimization can help cut down on production cost and time as well, which makes it such a versatile skill to be able to do and employ. All in all, if time and resources permit it, look into the benefits of topology optimization and understand how it can make your parts more efficient, lighter, and purposeful.