comparison of 26.0 and 31.8 mm bars w/ COMSOL

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youngs_modulus
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by youngs_modulus

Wingnut, I'm glad you found this interesting despite all the jargon. Let me know if I can clear anything up for you.

The upshot is that 31.8mm bars are a little stiffer than 26.0mm bars. I'd be perfectly happy with 26.0mm bars, but it's hard to find modern handlebars and stems in anything but 31.8mm. A stiffer bike feels better but isn't appreciably more efficient, despite how it feels.

I think Dan's work here is helpful in correlating "it feels stiffer" to actual displacement numbers. Neither FEA nor stiffness testing rigs are commonly available to everyday cyclists. Bicycle component companies use both, but naturally don't publish their results. This is a way for non-engineers to peek behind the product-development curtain, and I think that's a great thing.

Epic-o
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by Epic-o

youngs_modulus wrote:(1) FEA dorks about 15 years older than myself used to engage in holy wars about whether to use many linear elements or fewer quadratic elements. But Moore's Law pretty much rendered the argument moot; most people now use quadratic elements (10-node tets or 20-node hexes)...


Any further comments on this? For the same number of degrees of freedom, the computational cost of linear and quadratic elements should be similar so I don't understand how Moore's law plays a role on this. In any case, linear elements would result in a more diagonally-dominant structure of the [K] matrix that is beneficial for the solution of the LSE.
Last edited by Epic-o on Wed Oct 05, 2016 6:16 pm, edited 1 time in total.

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djconnel
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by djconnel

Quadratic elements have more vertices, so if the number of elements is the same, there's more vertices. If the number of vertices is the same, there's fewer elements, but even so the number of parameters is increased (not just displacements but also displacement gradients).

A classic problem in my experience where quadratic elements help is in beam bending when the beam has a high aspect ratio. Or equivalently, silicon wafer bending when a stressed film has been deposited on the surface (described simply by Stoney's Equation). In this case you're looking for a second order effect, and when the number of linear elements increases, the second derivative can be lost in numerical noise, and convergence can suffer. With second order elements a realistic result can be produced in many fewer points, since the effect is second order and the equations are second order.

So yeah -- now that I think about it, this being a being problem, second order elements would probably help. It's something I should play with. Comsol is GUI driven and such results tend to be buried in submenus which have reasonable defaults.

The geometry generator is primitive, however, especially lacking a license to the design module, and so tapering and producing eccentric pieces is cumbersome. Just hollowing out the thing to uniform wall thickness was time consuming. But I would like to investigate the effect of eccentric tops: that should substantially increase the vertical compliance for the same mass. Ideally I would use spline surfaces for that which I need to figure out how to use.

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djconnel
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by djconnel

I added aerodynamic tops to the model, with variable eccentricity, where the cross-sectional area remains constant while the eccentricity is varied from 1 (at the clamp) to 2 (at the top) and back to 1 (entering the drops), with 1.5 cm transitions. The thickness of the bar remains 1.3 mm although this is somewhat modified by the eccentricity.

Here's the bar:

Image

I apply force to the drops while the stem at the steerer tube is clamped:

Image

The color contours show Mises stress, an indication of tendency to failure, so this design has a weakness at the taper near the clamp.

At 100 N force on each bar there's 3.00 mm deflection. With the same 31.8 mm clamp it was 2.08 mm deflection with a round top. The increase in deflection from the 2:1 isoareal eccentric top is thus 46%.

The bar mass dropped to 225 grams, 2 grams lower than when the bar was round. Usually aero bars are made heavier to offset stiffness loss. So this comparison is for bars of similar mass (within 1%, resulting in a 46% compliance increase).

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djconnel
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by djconnel

I fixed one issue, was that I was using the same aspect ratio for the outer and inner surfaces of the eccentric top, which resulted in non-uniform wall thickness. The inner surface should actually be more eccentric. But it's easy to calculate by how much.

With approximately uniform 1.3 mm wall thickness the result is, surprisingly, the same to the precision I posted above, however.

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F45
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by F45

RussellS wrote:So you didn't actually test any real bars with real forces to measure real deflections? You just made up an imaginary model and made up imaginary results based on how you guessed it should respond?


Umm yeah, actually a model is a good way to test this because it eliminates a fair bit of uncertainty. In the real world, that would be reduced by using many samples. Expensive.

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djconnel
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by djconnel

Just to update this, and perhaps not of much interest, I improved the parametric representation of the bars, to shift the transition from eccentric to circular cross-section from the tops to the forward bend at the end of the drops. I also slightly increased the length of the transition region near the stem clamp to reduce the stress there. The bar looks a lot better now, but the results were essentially unchanged.

Image


maxxevv
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by maxxevv

Ooh... this brings back a lot of memories.

Last time I did a full scale FEA was for back in '99 ! And it was done using Cosmos Works, a sub-module in Solidworks 98.
ANSYS was the de-facto then, but it was cumbersome comparatively.

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