Bionics is the science that applies systems and methods found in nature to engineering and technology.
Trees, for example, can show us how to design optimized mechanical components by reducing notch stresses. Let's take a look at the base of a tree:
As you can see, the shape of the base is not a quarter-circle. It can be approximated using the Method of Tensile Triangles, developed by Claus Mattheck and his co-workers from Karlsruhe Institute of Technology in Germany.
The procedure to draw the tensile triangles is quite simple. The first triangle starts at the bottom with a 45ยบ angle. This creates a new notch on top of the triangle, which can be bridged symmetrically with a second triangle. This second triangle has to start from the middle of the hypotenuse of the first triangle. The third triangle is drawn in the same way. Three tensile triangles are usually enough. The corners have to be rounded, except the lower one.
As you can see in the picture below, the method is quite accurate:
This is a biological solution to the serious problem of reduction of notch stresses. However, engineers still utilize quarter-circle transitions in order to do the same.
In the following pictures we can see the two options. On the left, the engineering solution: the quarter-circle transition. On the right, nature's solution: tensile triangles. Which one is the best?
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| Quarter-circle transition |
In the following pictures we can see the two options. On the left, the engineering solution: the quarter-circle transition. On the right, nature's solution: tensile triangles. Which one is the best?
Using the Finite Element Method to calculate the stresses, we can figure it out.
The quarter-circle transition shows red spots, which indicate high stressed areas. On the contrary, the transition using tensile triangles is less stressed (maximum von Mises stresses are about 20% lower than using quarter-circles).
This means that by imitating the optimized shape from the base of trees we could reduce 20% the maximum stresses in a notch, making our mechanical components not only stronger but also more durable.
We still have a lot to learn from nature!
So please treat it with care!
Now, look at the price to manufacture the two parts (especially if machining is involved) and weigh cost vs benefit. For a few very specialized parts, complete optimization is required, but for most parts, the costs to produce the optimized part outweigh the benefits.
ReplyDeleteYes, you're right! Not every component has to be optimized. But think for example in casted components like engine cylinder blocks. They are full of round transitions that could be easily optimized. For the same manufacturing cost! And that's only an example.
DeleteThe point is, if nature is optimized, why not do the same?
The base of trees is not the only case where we find the geometry that can be approximated using tensile triangles. You will find the same geometry in bones, rocks, leaves... Look at your own hands! The geometry of the flesh between your fingers is optimized.
Not every component needs to be optimized. But knowing how to do this super-simple optimization could be very useful when you find a component which definitely should be optimized.