Luke Woodard, TPM Application Engineer
In this post, I’ll set up and run FEA analysis on the initial frame design. To start, I’ll be using all uni-directional tubes, and using the smallest diameter of the tubes I have in my library. But first, a quick background in carbon fiber.
A Crash (pun intended) Course in Carbon Fiber
Before we jump into simulating carbon fiber, I figured I should give a bit of background. When it comes to lighter and stronger, carbon and fiber are the magic words. But is it as easy as simply using carbon fiber? Not exactly.
Understanding and building parts from carbon fiber is as complex as you want to make it. At the most basic level, anyone can buy carbon fiber sheets and resin off of ebay, throw the resin on the carbon fiber, let it dry, and have some form of a carbon fiber part. At the most advanced level, you can get your PhD focusing on composites and go work for NASA. This blog will be somewhere in between, erroring on the side of simplicity.
Orthotropic-This means a material has different properties in different directions. This is the case with carbon fiber-it is much stronger in the fiber direction.
Ply-A single layer of carbon fiber. Generally, a part will have multiple plies with each ply having fibers in different directions. Bike frames will generally have between 5 and 30 plies depending on the area of the frame.
Lay-up-This refers to how the plies are stacked (how many, what fiber direction of each, etc...).
Resin-what ‘holds’ the carbon fiber together. Any carbon fiber part is cured with resin. Generally, the percent by volume will be in the 60% fiber/40% resin range.
Uni-directional-all fibers within a ply or lay-up are going the same direction. This generally will make the part very strong in one direction, but weaker in the others.
Modulus- Refers to how ‘stiff’ a carbon fiber is. Often you will hear ‘Intermediate Modulus’ and ‘High Modulus’. High Modulus generally means stiffer, but this is a bit arbitrary, and stiffer is not always better.
Strengths-Ductile materials have a yield strength and failure strength. Carbon fiber is different in that it is brittle and doesn’t really have a yield point, just a failure or fracture point. This is why carbon fiber parts tend to fail suddenly.
Carbon Fiber Parts
Just because something is made out of carbon fiber doesn’t necessarily mean it’s lighter and stiffer compared to metal counterparts. Designed and built correctly, more than likely, yes, a carbon fiber part made of quality carbon fiber/resin will outperform a metal counterpart. Get it wrong though, and carbon fiber can be both heavier and flexier.
The keys to making a good carbon fiber part are:
1) Shape. The actual shape of the part is just as important as if it was a metal part.Think cross sectional area, moment of inertia and bending calculations.
2) Lay-up design. Carbon fiber is more “engineerable” than metals as there are more options. In a bicycle tube, you might have 15 different layers, all with potentially different fiber directions. Compare that with steel or aluminum where you’ll ‘simply’ have a wall thickness and butted geometry.
3) Manufacturing techniques-No matter how good it is on paper, if you can’t make it, it doesn’t matter. Things like air bubbles, excess resin and uneven resin mixing can significantly decrease performance.
SolidWorks and Composites
Off to Simulation! A quick note-for this first round-all the tubes are unidirectional and have the smallest outside diameters of the uni-directional tubes saved in my configurations. This seemed like a good place to start.
Within a static study within SolidWorks Simulation Premium, you can define shells as a composite, defining the number of plies, lay-up orientations for each ply and even have each ply be a separate material, amongst other things. If you import a solid body, you have to use the “Shell Manager” to define either the outside, middle or bottom surface. Don’t see the option for a composite shell? Don’t worry, that gets defined in the next step.
I defined all of the tubes as separate shells, allowing me to vary lay-ups of each tube independently. Once the tubes were all defined, I was able to edit them by expanding the shell features, right clicking on the shell I wanted to edit, and selecting “Edit Definition”. In the Shell Definition Manager, we can define the shell as a composite.
Here, we can also define the number of plies, the orientation of the ply, and most importantly, the material. I had to add a material, Toray T700 (one of the most commonly used fibers in the bike industry), into my materials property. This can be done directly from the Shell Definition Manager by clicking the “Select Material” button and then adding a material to your material properties. It is very important to choose “Linear Elastic Orthotropic” from the Model Type Drop down. This lets you define properties in the x, y, and z axis independently of each other, and is really the point of using composites in this case. In the case of composites, defining properties takes a bit of research and math, but we won’t dive into the details here.
Use the “Select Material” icon to open up the Material Manager
Enter the material properties.
From here, I set up my fixtures. While the only time a bicycle is “static” is when it’s sitting in your garage, we’re going to use the static state here to simplify things. That being said, if you freeze a bike in motion, the most ‘fixed’ contact point is going to be the rubber of the tire on the ground. I’m only interested in modeling the frame (for the moment), so I’m not going to worry about the tires, wheels, fork, etc… The most direct connection to the frame from the tires on the ground is going to be the rear dropouts and bottom of the headtube. I made both of those locations fixed geometry.
Concerning contacts-each tube is “Bonded”, meaning that in the simulation, the tubes will stay connected to each other at the joint. This is assuming the joint is going to be significantly stronger than the tube itself.
Loads and Mesh
Time to start doing some math and get nerdy! I decided to do two basic load conditions:
- ”Cruising”: 350 watts at a cadence of 90, seated with a weight distribution of 70% on the saddle, 30% on the handlebars.
I then set up the pedals so the right leg would be at the most powerful location of the cycle, 30 degrees below horizontal. With this in mind, I split the 218.45 N 90/10% between each leg. Both of these forces were added as remote forces with the distance from the center of the bottom bracket being defined by crank and pedal geometry (140mm from frame center if you were wondering).
Finally, I added three remote masses, one just behind the seat-tube at 56kg, and two more corresponding to where my hands would be on the handlebars at 12kg each, totaling 80kg (or hopeful race weight…)
Visually, the applied forces are purple arrows, the masses purple dots and the big red arrow gravity.
- “Accelerating”: 1000 watts at a cadence of 60, standing up. (Weight applied to the pedals instead of the saddle through the seat tube)
Again, this translates to:
I used the same pedal position/distribution as the cruising condition.
Without being on the saddle, I modeled the weight that was going through the seat tube in the previous scenario as now going through the pedals.
Finally, I added a remote force (200 N) through the right side of the handlebars to simulate “bracing” under a high-power output (think one legged deadlifts).
After several (as in lots and lots…) trials, I settled on a blended curvature-based mesh with a max element length of 10mm and a minimum element length of 3.33mm. This would translate into “all the way fine” on the mesh density slider.
Running the Simulations-Getting the Pretty Colors
All that was left was hitting run and watching the status bar in anticipation. And then doing it over and over again to get end up with the parameters above. The results are summed up in the table below. At this point, I’m really interested in displacement of the bottom bracket.
Max stress within entire lay-up
(Von Misses, MPa)
Displacement (URES, mm)
The first thing I notice is the large deflection at the top of the seat tube in the cruising condition. I think SolidWorks is telling me to lose some weight…At any rate, I’m not particularly concerned about it and am actually encouraged by it. Deflection through the seat tube, as long as stresses aren’t approaching failure stresses, can be a good thing as it generally translates to a more comfortable ride.
After that, the frame is warping like I’d expect it to, a good sign. There are some stress concentrations, particularly at the joints. At this point, I’m not particularly worried, as much more design work is going to be done in the joint areas. I also have some larger than ideal mesh sizes at the joints, amplifying stress concentrations.
What does this tell me about the design? Not much, as this is just round one. But this sets the stage to run this same study for combinations of different tubes to find the optimal tubeset. But that will have to wait until next time.
Until then, here’s to flying higher with lighter parts made out of carbon fiber.